<?page no="0"?> ISBN 978-3-381-13531-8 This textbook provides readers with an interesting overview of the field of corporate valuation in a quick and easy way. For the second edition, the authors have added a new 9 th chapter devoted to valuations and the use of argumentation values in negotiation situations. The book includes a number of self-test questions with answers. The contents: Introduction / Discounted Cash Flow Valuation (DCF Valuation) / Comparable Companies Analysis / Precedent Transactions Analysis / Further Valuation Methods / From Enterprise Value to Equity Value / The Tension between Principals, Evaluators, Objectives and Leeway in Corporate Valuations / Value and Price - a Tangent on Valuation Theory / Argumentation Values in Negotiations / Self-Test Questions - Proposal for Solutions. Prof. Dr. Ralf Hafner has been Professor of International Business with a focus on Finance & Accounting at the HTW Berlin since 2013. Prior to that, he worked for 25 years as an M&A consultant in leading positions at various consulting firms and investment banks. Prof. Dr. Veit Wohlgemuth is Professor of Business Administration with a focus on Corporate Finance. He has been teaching at the HTW Berlin since 2014 in various programs that offer specialized classes for corporate valuations. Hafner / Wohlgemuth Corporate Valuation 2 nd Ed. Ralf Hafner / Veit Wohlgemuth Corporate Valuation 2 nd Edition <?page no="1"?> Corporate Valuation <?page no="2"?> Prof. Dr. Ralf Hafner has been Professor of International Business with a focus on Finance & Accounting at the HTW Berlin since 2013. Prior to that, he worked for 25 years as an M&A consultant in leading positions at various consulting firms and investment banks. Prof. Dr. Veit Wohlgemuth is Professor of Business Administration with a focus on Corporate Finance. He has been teaching at the HTW Berlin since 2014 in various programs that offer specialized classes for corporate valuations. <?page no="3"?> Ralf Hafner / Veit Wohlgemuth Corporate Valuation 2 nd Edition <?page no="4"?> Umschlagmotiv: © SHansche · iStockphoto Bibliografische Information der Deutschen Nationalbibliothek Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http: / / dnb.dnb.de abrufbar. 2 nd edition 2025 1 st edition 2017 https: / / doi.org/ 10.24053/ 9783381135325 © UVK Verlag 2025 - Ein Unternehmen der Narr Francke Attempto Verlag GmbH + Co. KG Dischingerweg 5 · D-72070 Tübingen Das Werk einschließlich aller seiner Teile ist urheberrechtlich geschützt. Jede Verwertung außerhalb der engen Grenzen des Urheberrechtsgesetzes ist ohne Zustimmung des Verlags unzulässig und strafbar. Das gilt insbesondere für Vervielfältigungen, Übersetzungen, Mikroverfilmungen und die Einspeicherung und Verarbeitung in elektronischen Systemen. Alle Informationen in diesem Buch wurden mit großer Sorgfalt erstellt. Fehler können dennoch nicht völlig ausgeschlossen werden. Weder Verlag noch Autor: innen oder Herausgeber: innen übernehmen deshalb eine Gewährleistung für die Korrektheit des Inhaltes und haften nicht für fehlerhafte Angaben und deren Folgen. Diese Publikation enthält gegebenenfalls Links zu externen Inhalten Dritter, auf die weder Verlag noch Autor: innen oder Herausgeber: innen Einfluss haben. Für die Inhalte der verlinkten Seiten sind stets die jeweiligen Anbieter oder Betreibenden der Seiten verantwortlich. Internet: www.narr.de eMail: info@narr.de Druck: Elanders Waiblingen GmbH ISBN 978-3-381-13531-8 (Print) ISBN 978-3-381-13532-5 (ePDF) ISBN 978-3-381-13533-2 (ePub) <?page no="5"?> 1 To be precise, the name of the class as per our curriculum is “Contemporary Financial and Accounting Issues“, but what I teach is Corporate Valuation. 2 This book is based on my German publication “Unternehmensbewertung” in Schmeisser/ Eckstein/ Hafner/ Hannemann/ Stengel, Wertorientiertes Finanzmanagement, 2015, 81-158. Preface to the Second Edition We are very pleased that, since its publication in 2017, this little booklet has become standard in our courses on corporate valuation at the HTW Berlin and is also used outside our university. After eight years, we are now presenting the second edition. In addition to some textual revisions, there are two major changes. As you can see from the title page, there is a second author. Veit Wohlgemuth has been a professor at the HTW since 2014 and has worked closely with Ralf Hafner from the beginning. He knows the book very well, having used it regularly in his own courses on corporate valuation. By the time you read this, Ralf Hafner will have retired. Veit Wohlgemuth (25 years younger) will continue the work and will take the main responsibility for future editions. We have also added a new 9th chapter, which is devoted to valuations and the use of argumentation values in negotiation situations. The goal of the book remains the same. It is not a compendium, but rather what we go through with our students in one semester at the HTW in our corporate valuation classes. Nothing more. Short and to the point. If you are not a student or a teacher at the HTW and are interested in the lecture notes and other teaching materials, please contact us (veit.wohlgemuth@htw-berlin.de or ralf.hafner@htw-berlin.de). Berlin, March 2025, Ralf Hafner and Veit Wohlgemuth Preface to the First Edition I wrote this book for my students at HTW Berlin, where I teach valuation in our master’s degree program in international business (MIB) 1 . There are excellent books available on valuation. Most of them are quite comprehensive and come with a lot of pages (400, even 800 plus). My personal experience is that students tend to be somewhat reluctant to make use of these textbooks on top of some hundred pages of lecture notes. I wanted to write something more “handy” to address this. Consequently, this book is far from being a compendium on valuation 2 . It is what I cover in my <?page no="6"?> 6 Preface to the First Edition class 3 and it should go along with my lecture notes 4 and the work assignments for the students. Since the background of an author usually influences her or his view on and the way she or he teaches valuation, here is mine so that you know where I come from. I had my first encounters with valuation in my last semesters as a student. In 1985, I became a research assistant of Prof. Dr. Günter Sieben at the University of Cologne in Germany. He certainly belongs to the pioneers and innovators of this discipline in Germany and made significant contributions to the so-called functional valuation theory. 5 So my first interest in valuation was academic and consequently I wrote my PhD thesis on a topic in the field of corporate valuation. 6 Luckily, I also had the opportunity to assist my former teacher in his valuation practice. The first valuation “in real life” I worked on (still as a young research assistant) was for one of the two parties in a divorce, where the value of the company formed the basis for the equal distribution of the surplus earned during the marriage. I learned that valuation practice has its own set of rules 7 and that valuations outside the academic world usually serve as a tool to realize the interests of the parties involved in a transaction. 8 After my time as a research assistant and the finalization of my PhD thesis I worked for over 20 years as an M&A (Mergers & Acquisitions) adviser before I returned to the University in 2012. These years certainly had the biggest impact on my view of what valuations are about and what they are not about. M&A advisers usually don’t focus on true values or fair values. 9 If life is not fair, why should valuations be? The focus is on a realistic estimate of a price that will be achievable in a transaction, given I gratefully acknowledge the permission of my publisher, UVK Verlagsgesellschaft, to reuse the contents in English language. Apologies to my readers in advance for any lexis, grammar and other inaccuracies - I’m not a native English speaker. 3 Prerequisite for the class is good knowledge of the basic principles of Corporate Finance. 4 In case you would like to receive the lecture notes, please send me an E-mail (ralf.hafner @htw-berlin.de) or download them from my publisher’s website here: https: / / files.narr. digital/ 9783381135318/ slides.zip. I’m happy to share but have not found the time yet to set up an own website where they can be downloaded. 5 The main message of the functional valuation theory is that the value of a company is determined by the purpose of the valuation. We will look at this in more detail in chapter 8. 6 It was an attempt to apply the toolset developed by Keeney and Raiffa for decisions with multiple objectives to corporate valuation theory. 7 I still remember the hockey stick projection the adviser of the counterparty made for this mature old-fashioned business without any input from the company’s management. 8 To be fair, this applied to both valuations in the case described, i.e. ours as well. 9 Although these terms are often used by investment bankers and corporate finance advisers, what they do (should do) is to determine a potential range for the purchase price. <?page no="7"?> Preface to the First Edition 7 the status and the projections of the company for sale, the likely interest in the company as well as the expected distribution of the negotiation power. Valuations are used to get the negotiations or bidding processes started. Therefore, a valuation to me is a medium of communication between the buyer and the seller, like a language. And that is what this book (and my valuation class at HTW) is about, to make you acquainted with this language. I would like to thank my faculty and the management of HTW Berlin for granting me a research semester in the winter term 2016/ 17. This made it much easier for me to finalize this book. And many thanks to Ambar, Farel, Frida and Felix, my wonderful family, who had to bear the social costs of this project. Berlin, March 2017 Ralf Hafner <?page no="9"?> How to Use this Book People don’t learn how to play football (soccer) by sitting in front of a TV watching FIFA World Cup games of their favorite team with their friends. They need to go out with them, take a ball along and play! The same applies to valuation. Please don’t just read books, listen to lectures or watch others performing valuations. Pick a company and value it! What we ask our students to do  Team up in groups of 3 to 6 students.  Choose an industry (e.g. apparel, social media, beer, pharma, etc.). Avoid banks and insurances if you do this for the first time in your life.  Each group member picks a company within this industry. The company should be quoted on a stock exchange. This ensures the availability of sufficient data for the valuation. Make sure you like your company - you will spend an entire semester to analyze and value it.  Develop the balance sheets shown in chapter 2.1 for your company.  Perform a company analysis using the structure introduced in chapter 2.2.1. Be brief, work with bullet points, tables and charts. Use a Bloomberg terminal to collect the necessary data. If possible, do field research (if your industry is e.g. apparel, luxury or sporting goods, go downtown and visit the shops, touch the products, compare them - you will learn at least as much as from desk research).  Perform a DCF valuation for your company as described in chapters 2.2.2 till 2.2.5. Determine a range for the enterprise value.  Perform a Comparable Companies Analysis as described in chapter 3, and a Precedent Transactions Analysis as described in chapter 4. Focus on EBITDA and sales multiples.  Determine a range for the equity value of your company using the information given in chapter 6.  We strongly recommend meeting regularly with your team - you will benefit from the ideas of your group members. And it will be much more fun, too. <?page no="10"?> 10 How to Use this book Textbooks on valuation The following list of four books is our personal selection. All four are excellent and very comprehensive.  Damodaran, Investment Valuation: Tools and Techniques for Determining the Value of Any Asset, 3 rd edition, 2012  Holthausen/ Zmijewski, Corporate Valuation: Theory, Evidence & Practice, 2 nd edition, 2020  Koller/ Goedhart/ Wessels, Valuation: Measuring and Managing the Value of Companies, 7 th edition, 2020  Rosenbaum/ Pearl, Investment Banking, Valuation, Leveraged Buyouts, and Mergers & Acquisitions, 3 rd edition, 2022. The valuation templates that come with the book will give you a good flavor as to what is standard in valuation practice. Web  www.damodaran.com. Everything you need to know on corporate finance and valuation. Contains lots of data, spreadsheets, webcasts. Best website of a professor we know.  http: / / macabacus.com/ learn. A good place to visit if you’re looking for Excel templates on valuation.  https: / / www.bloomberg.com/ markets/ stocks http: / / www.morningstar.com https: / / www.google.com/ finance https: / / finance.yahoo.com https: / / www.moodys.com https: / / www.standardandpoors.com/ en_US/ web/ guest/ home https: / / fred.stlouisfed.org https: / / www.destatis.de/ Europa/ EN/ Homepage.html A selection of websites we visit when we are away from our Bloomberg lab at HTW. Lecture notes for download https: / / files.narr.digital/ 9783381135318/ slides.zip <?page no="11"?> 1 Contents Prefaces .....................................................................................................................5 How to Use this Book ............................................................................................9 1 Introduction .................................................................................... 13 2 Discounted Cash Flow Valuation (DCF Valuation) ........... 18 2.1 DCF Valuation Models......................................................................20 2.2 Enterprise DCF Valuation ................................................................24 2.2.1 Company Analysis ............................................................................26 2.2.2 Projection of Future Free Cash Flows ...........................................31 2.2.3 Estimation of Weighted Average Cost of Capital (WACC)......36 2.2.4 Calculation of Terminal Value ........................................................44 2.2.5 Computation of Present Values, Derivation of a Range of Enterprise Values, Sensitivity, Scenario and/ or Simulation Analysis ...............................................................................................48 3 Comparable Companies Analysis .......................................... 51 3.1 Standard Multiples.............................................................................53 3.2 Finding Comparable Companies ....................................................59 3.3 Preparation of Figures ......................................................................60 3.4 Derivation of a Value Range ...........................................................61 4 Precedent Transactions Analysis ........................................... 63 5 Further Valuation Methods....................................................... 69 5.1 LBO Valuation ....................................................................................69 5.2 Option-Based Valuation ...................................................................73 5.3 Asset-Based Valuation ......................................................................75 5.4 APV Valuation ....................................................................................76 5.5 Equity DCF Valuation .......................................................................80 6 From Enterprise Value to Equity Value ............................... 83 6.1 Cash and Cash Equivalents .............................................................83 6.2 Holdings in Other Companies, Non-Controlling Interests and Other Assets Valued Separately .............................................85 <?page no="12"?> 12 Contents 6.3 Pension Obligations, Accrued Liabilities and Provisions ........ 89 6.4 Off-Balance-Sheet Financing .......................................................... 92 6.5 Stock Options, Option Bonds and Convertible Bonds.............. 93 7 The Tension between Principals, Evaluators, Objectives and Leeway in Corporate Valuations .............97 7.1 Principals and their Objectives ...................................................... 98 7.2 Evaluators and their Objectives ...................................................100 7.3 Leeway in Valuations .....................................................................102 7.3.1 Leeway in DCF Valuations ............................................................103 7.3.2 Leeway in Multiple-Based Valuations ........................................107 8 Value and Price ‒ a Tangent on Valuation Theory........ 109 8.1 Prices and Values of Companies ..................................................109 8.2 Intrinsic (Objective, Objectified, Fundamental) and Subjective Company Values ..........................................................111 8.3 Functional Valuation Theory........................................................113 9 Argumentation Values in Negotiations............................. 119 9.1 Determinants of the Argumentation Value...............................119 9.2 The Art of Negotiation...................................................................120 9.3 Argumentation Value Determination.........................................123 Self-Test Questions ‒ Proposal for Solutions ..................................... 125 Index......................................................................................................................129 <?page no="13"?> 1 Introduction Learning Objectives  Get an overview on the different occasions for corporate valuations.  Understand valuation as a complex, interdisciplinary, and comprehensive exercise that requires the application of the entire spectrum of management theory and practice. Corporate Valuation is one of the most relevant subjects for management practice in business administration education. There are numerous occasions for the valuation of enterprises. The occasions listed below are not exhaustive. Exhibit 1: Occasions for Corporate Valuations Acquisition and Disposal of Companies (Mergers & Acquisitions; M&A) In every M&A process, valuation plays a vital role. A potential seller should always investigate  the price range that can realistically be expected from purchase price offers,  how to back the own asking price with a valuation,  and, most importantly, what the minimum proceeds from the sale must be so that the seller does not end up in a worse position compared to omitting the sale and keeping the company. <?page no="14"?> 14 1 Introduction  Conversely, potential buyers will value a target company before submitting a bid. They will analyze  how to back their offer price with a valuation,  how to justify an acquisition with a valuation towards shareholders and supervisory boards,  how much other bidders would be willing to put on the table for the target company,  and, most importantly, what the maximum price is that they could pay so that they do not end up in a worse position compared to not realizing the acquisition and following alternative projects instead. The same applies to mergers, MBOs (management buyouts), MBIs (management buy-ins), transactions between shareholders, IPOs (initial public offerings) and other partial sales of enterprises. Value-Based Management The mantra of modern corporate finance theory and practice is to align management decisions and actions with the value of the company. Decisions that enhance the value are good decisions and should be realized. Strategic decisions, capital budgeting decisions, financing decisions and company value are interrelated and depend on each other. Investment Management Private and institutional investors including their advisers, especially financial analysts, perform valuations to support their investment recommendations and portfolio management decisions. Legal Requirements Many legislations provide for regulations which require valuations at specified special occasions. One example is the so-called squeeze-out, a compulsory sale of the minority shareholders’ shares to the majority shareholder of a publicly traded company. The conclusion of certain agreements, mergers, spin-offs, split-ups will also lead to corporate valuations being required by law in many jurisdictions. Contractual and Other Regulations Corporate valuations may also occur in conjunction with the distribution of estate among heirs, the entry or the exit of partners in a partnership, the distribution of the surplus earned during a marriage in a divorce or in other family law matters. <?page no="15"?> Introduction 15 Financial Reporting and Tax Matters Valuations are also necessary when performing so-called purchase price allocations for the preparation of annual group accounts (allocation of the purchase price paid for a company to the various assets and liabilities including goodwill). The same applies to the necessary goodwill impairment testing in the subsequent years. Valuation occasions may also arise from tax laws. Valuations of enterprises are ambitious, extensive and fascinating projects. They require the application of the entire spectrum of management theory and practice. Take any existing company as an example, Boeing or Siemens, TikTok or the mom-and-pop flower store just around the corner. What is necessary to be able to derive a value for these businesses? Exhibit 2: Determinants of Value  The review of a company’s status is usually based on its financial statements. Hence, a profound knowledge of financial accounting and management accounting is required, so to say the ability to “read” financial statements.  The projection of the future development of a company necessitates an analysis of the entire value chain: research and development, design, sourcing/ production, marketing, distribution, customer service and administration/ information technology should be examined regarding competitive advantages, disadvantages and their sustainability. <?page no="16"?> 16 1 Introduction  In addition, forecasts on procurement and sales markets should be performed. Products or services of the company to be valued should be compared with those of its competitors and peers. Strategy and strategic management can be brought to the table here. Ideally coupled with the ability to transform the results of this analysis into hard figures, a budget of sales, margins, necessary investments in fixed assets and working capital and other balance sheet ratios. How will the profit and loss statement, the balance sheet, the cash flow statement look like in the next five years?  Finally, it should be explored how to factor in the uncertainty associated with any forecast. What is risk, what is opportunity in valuations, how can we measure them and how do we account for them in our analysis? This is one of the most ambitious endeavors in theory and in practice. There will be airplanes in five years, but what will Boeing’s market position be compared to their competitors? Are conglomerates like Tata or Samsung sustainable? How promising is TikTok’s business model? Will we buy our flowers on the web in five years and if so, what impact will this have on the mom-and-pop flower store just around the corner? Difficult questions? Yes, but the more ambitious the valuation, the more necessary it usually is. We will probably still drink Coke in 20 years from now. But will TikTok still be around then? If you don’t feel comfortable with so many insecurities, you might be better advised to turn to other, more simply structured problems. Risks, uncertainties, subjective judgements on future developments that naturally come along with a high probability of being in error on them, are part of corporate valuation. Valuation is not a precise science. Despite the usage of quantitative models, the values derived are neither objective nor exact and above all not timeless. Valuations determine ranges for the values. And these ranges are subject to change. Every day. The magnitude of the available literature on valuation also illustrates the depth of the topic. The list of the standard textbooks in English and in German alone is quite extensive, not even mentioning the numerous scientific papers, PhDs and post-doctoral theses on the topic. Rosenbaum/ Pearl’s book Investment Banking can still be considered “handy” at over 500 plus pages. Damodaran’s Investment Valuation and Koller/ Goedhart/ Wessel’s Valuation easily surpass this with nearly 1,000 pages, and Peemöller’s German Practice Handbook on Valuation comes in at nearly 2,000 pages. Some of the standard German textbooks on valuation are also quite lengthy: Matschke/ Brösel/ Toll is close to 1,000 pages, Drukarczyk/ Schüler over 600. Ballwieser/ Hachmeister, Hering, Spremann/ Ernst and Hommel/ Dehmel are commendable exceptions in terms of length. However, each of the books mentioned has at least a slightly <?page no="17"?> Introduction 17 different focus and approach to the topic, so that one might as well just add up all the pages to get a comprehensive overview of the state of the German textbook opinion on corporate valuation. The variety of valuation methods is another characteristic of our topic. Also, the long and intensive discussion between academia and valuation practice (at least in Germany) on important aspects of valuation, and the pronouncedly critical and partly cold and distant position some prominent representatives of German valuation academia have towards international (i.e. Anglo-Saxon) valuation theory and practice. As strong advocates of applied science, we will start our “valuation journey” by looking at those methods that are currently (late 2024) most prevalent in international valuation practice. These methods have developed more and more towards a valuation industry standard. Chapter 2 introduces the discounted cash flow method in the so-called "enterprise variant", which - although this view is not universally accepted - has become the mother of all corporate valuation methods, just like the net present value method for investment decisions. Chapters 3 and 4 describe two methods which are by now usually also part of most valuations, the comparable companies analysis (“trading comps”) and the precedent transactions analysis (“transaction comps”). Chapter 5 elaborates on further valuation methods, chapter 6 deals with the transition from the enterprise value to the equity value of the firm. Chapter 7 analyses the leeway resulting from the inevitably subjective judgements 10 which are necessary in performing a valuation. With this we would like to sharpen your view for the interaction between the value resulting from a valuation exercise and the purpose the principal (the initiator, the person that pays for the valuation) pursues with the valuation. In chapter 8 we look at the topic of value and price or value versus price and try to build a bridge to the perceptions of the functional valuation theory. Chapter 9 deals with valuations in negotiations. 10 These judgements can at best be objectivized, but will never be objective. <?page no="18"?> 2 Discounted Cash Flow Valuation (DCF Valuation) Learning Objectives  Understand discounted cash flow (DCF) valuation as an application of net present value (NPV) analysis.  Recognize the differences between the enterprise and the equity DCF valuation approaches.  Recognize the valuation-specific terms “enterprise value”, “equity value”, “interest-bearing debt”, “cash and cash equivalents” as well as “net debt”, and understand the relationship between them. DCF valuation is nothing else but the application of the net present value approach in capital budgeting on corporate valuation. The project we look at is the company, being characterized by its future free cash flows. As in capital budgeting, we work with cash flows instead of accounting earnings. The future free cash flows in the years t=1, 2, 3, …, n of the company under investigation are discounted back to t=0 using the appropriate discount rate, i.e. the rate that reflects both the risk of the investment as well as its funding costs, for equity and debt. This discount rate is the weighted average cost of capital (WACC) of the company being valued. The value of the company can be derived by adding up the present values of the future free cash flows. Exhibit 1 on the following page summarizes the relationship. Other than in standard capital budgeting analysis, there is no initial investment in t=0 in a DCF valuation. Instead, this amount, the sum of the present values of all future free cash flows is the number we are looking for. Once determined and put into a standard net present value analysis with a minus sign in t=0, a net present value of 0 will be the result for this project (the acquisition of the company being valued). The internal rate of return (IRR) of this project will be equal to the weighted average cost of capital (WACC) of the company. What does this imply? If you as an acquirer of the company can negotiate a price below the sum of the present values of the future free cash flows of the target company, you are about to make a good deal. Why? Because the net present value of your project (the acquisition of the target company) will be positive. If you pay more than the sum of the present values of the future free cash flows, your initial investment in t=0 goes up and will lead to a negative net present value for your project. As per the decision rule in capital budgeting analysis, you should not pursue such a project, i.e. not realize the acquisition. <?page no="19"?> Discounted Cash Flow Valuation (DCF Valuation) 19 Exhibit 3: Discounted Cash Flow Valuation Before we go into further details, please make sure that you have these basic principles of capital budgeting analysis mentally absorbed:  Don’t do bad projects, i.e. projects with a negative net present value!  Whatever value or range of values you will derive in a DCF analysis; from a buyer’s standpoint, this is the maximum you should pay for the company (the minimum you must ask for from the seller’s standpoint). If you pay more (accept to sell for less as a seller), you will invest in a bad project with a negative net present value. Hence, you will destroy shareholder value. This applies vice versa to a potential seller of a company, who would give up the future free cash flows in case of a divestiture. Consequently, these future free cash flows go into his capital budgeting analysis with a minus sign, whereas the purchase price received is a cash inflow in t=0. If this purchase price equals the sum of the present values of the future free cash flows, the net present value of this project (disposal of the company) will also amount to 0. In case the potential seller receives more than the sum of the present values of the future free cash flows, this will turn into a good project (net present value > 0). If the offers received are below the value derived, the net present value will be negative. As per the basic principles of capital budgeting analysis, the potential seller should keep the company and continue the business. This leaves the seller in a better position compared to selling the company. <?page no="20"?> 20 2 Discounted Cash Flow Valuation (DCF Valuation)  If you buy (sell) at the value derived from a DCF analysis, you will not destroy shareholder value, but you will also not create shareholder value. The applause for doing projects with a net present value of zero will be limited.  Do good projects! Buy below (sell above) the value, i.e. the result of your DCF analysis! 2.1 DCF Valuation Models There are two variants, two different models, different approaches to DCF valuation: [1] Most common in practice is the so-called enterprise DCF valuation model (also known as entity or firm valuation). Free cash flows to the firm are discounted at the weighted average cost of capital (WACC) to derive the enterprise value. [2] The equity DCF valuation model determines directly the value of the company’s equity. It considers free cash flows to equity (after financing expenses and after net changes in interest-bearing debt) and discounts them at the cost of equity. If applied properly, both approaches will lead to the same result. Understanding the distinction between enterprise value, equity value, firm value as well as enterprise DCF and equity DCF is vital in corporate valuation. The following explanations are meant to illustrate the interrelationship. We would strongly recommend that you pick a quoted company and develop the balance sheets shown below for your firm. We will start with the normal accounting balance sheet using book values. Every consolidated balance sheet can be broken down as follows: Exhibit 4: Accounting Balance Sheet <?page no="21"?> 2.1 DCF Valuation Models 21 Netting out assets and other liabilities leads to the following simplified version: Exhibit 5: Accounting Balance Sheet (Net) From a purist’s standpoint, cash includes only cash and cash equivalents not necessary for the operations of the company, i.e. excess cash. Since it is difficult to estimate the cash necessary for the operations if you have no access to the management and sometimes even demanding with access to internal data, most valuations work with the assumption that all cash is excess cash. Interest-bearing debt comprises all financing instruments that explicitly demand the payment of interest. Bonds and bank debt are examples for interest-bearing debt. Accounts payable and warranty provisions are not part of interest-bearing debt. They are part of working capital, hence other liabilities in exhibit 4. The equity in exhibits 4 and 5 is the book value of shareholders’ equity in the balance sheet. If we now replace the book values of equity and debt with the market values of equity and debt, we get to the following equation: Exhibit 6: Market Value Balance Sheet <?page no="22"?> 22 2 Discounted Cash Flow Valuation (DCF Valuation) The market value of equity is what we get as a result from a valuation exercise. Since the aim of our analysis here is to explain basic valuation terminology, let’s assume our company is quoted. In that case, we can derive the market value of equity by multiplying the number of shares outstanding by the share price. This typically leads to an increase of the balance sheet total (unless the company is in a turnaround situation). The market value of debt is easy to determine for those financing instruments that are quoted like bonds. For the other instruments, estimates should be made. The most common one is to assume that market values equal book values. This might be unsatisfying from an academic standpoint, but it is fair to state that most differences between book values and market values typically are caused by equity and not by debt. In a next step, let’s replace the accounting balance sheet by a financial balance sheet. 11 This implies that we mentally turn away from looking at the company as a collection of assets and liabilities and instead regard it as a portfolio of projects, hence investments, those already in place and future investments. 12 All these investments generate cash flows in the future, and their value can be determined by discounting these future free cash flows back to t=0. Exhibit 7: Financial Balance Sheet (Firm Value) 11 See for example Damodaran, Applied Corporate Finance, 4 th ed., 2. 12 Brealey/ Myers/ Marcus, Fundamentals of Corporate Finance, 11 th ed., 210, call the future investments growth opportunities. <?page no="23"?> 2.1 DCF Valuation Models 23 Exhibit 8: Financial Balance Sheet (Enterprise Value) Here we can see the relations of the terms used in valuation. Adding up the market value of equity and debt leads to the so-called firm value. You also get there by adding up enterprise value and cash. The enterprise value is the sum of the present values of all the company’s investments, current and future. For those with a preference for accounting, it can also be interpreted as the market value of all the company’s assets, tangible and intangible, on or off balance sheet. In a final step, we now deduct cash from interest-bearing debt and get “net debt” (net cash in case that cash > interest-bearing debt). This visualizes the differences between the enterprise DCF valuation approach and the equity DCF valuation approach. And it shows that the enterprise value equals the market value of equity plus the market value of net debt (interest-bearing liabilities minus cash). 13 We will focus in this chapter on the enterprise DCF method. Most DCF valuations in practice follow this approach. Equity DCF valuations are common for the valuation of banks and insurance companies, as interestbearing debt has a different character for financial services firms. Chapter 5.5 gives an overview. 13 There is a bit more between enterprise value and equity value than net debt. For purely pedagogical reasons we will leave it as it is for now, but we will come back to this in detail in chapter 6. <?page no="24"?> 24 2 Discounted Cash Flow Valuation (DCF Valuation) 2.2 Enterprise DCF Valuation Learning Objectives  Define and determine the future net free cash flows to the firm.  Understand and determine the weighted average cost of capital (WACC) with the components (risk-free rate, equity or market risk premium, beta, cost of debt, taxes).  Discover what a terminal value is and learn about different methods to detect it. The enterprise DCF method discounts future free cash flows to the firm, i.e. cash flows before financing costs like interest expenses, those cash flows available to both equity and debt providers, at the weighted average cost of capital (WACC). The result of this discounting exercise is the enterprise value of the company. Deducting net debt from the enterprise value leads to the equity value of the company. So, we need the following “ingredients” for an enterprise DCF valuation: [1] Future free cash flows to the firm, and [2] WACC (weighted average cost of capital) of the company being valued. There is one difference in DCF valuations compared to standard capital budgeting models: the forecast period of the future free cash flows. In capital budgeting, we usually work with a finite planning period as we assume a finite life of our projects. In corporate valuation, it is however common to work with an infinite life of the company. The reason for this is purely convenience. Nothing lasts forever, so no company will, but in most cases, it is reasonable to assume at least a long life of the company. 14 And since the formula for a perpetuity is easy to use compared to discounting cash flows until t=75, and the values of perpetuities and annuities converge for long planning periods, the assumption of infinite lives of the companies being valued is a widely accepted “impreciseness” in corporate valuation. A common tool in corporate valuation is to divide the planning period into stages (usually two, sometimes three or more). In stage one (and two of a three-stage model) future free cash flows are derived from a detailed corporate budget set up for the planning horizon. For the last stage (stage 14 There are exceptions, for example joint ventures that are set up right from the start for a specific time frame. <?page no="25"?> 2.2 Enterprise DCF Valuation 25 two in a two-stage model or stage three in a three-stage model), a socalled “terminal value” is being computed. This terminal value represents the value of all cash flows of the last stage, i.e. all future cash flows after the end of the detailed budget or planning period. Exhibit 9: Two-Stage DCF Valuation Model The length of the budget period, the period for which a detailed planning will be performed, usually varies between three and ten years in practice. It depends on several factors:  If the company has a budget period of three years, and a further projection would be disproportionately time consuming or complex (or both), the usage of three years for the detailed planning period is suitable.  For non-cyclical companies the detailed planning period ideally covers the entire period of above-average growth of the company, so that we have a so-called “steady state” at the end of the budget period. Steady state means that the company grows at a constant rate, e.g. the growth rate of the economy, so that its efficiency ratios can be regarded as stable for the future and that the return on capital for new investments equals the industry average. The question here is how long the current competitive advantage (leading to above-average growth) will persist.  For young and high-growth companies it may be advisable to work with a three-stage valuation model. Stage one for strong above-average <?page no="26"?> 26 2 Discounted Cash Flow Valuation (DCF Valuation) growth, stage two for above-average growth, and stage three as steady state with a growth rate in line with the economy’s growth rate.  For cyclical companies, there is no steady state. It is advisable to cover an entire cycle in stage one, the detailed planning period, and work with an average year for the determination of the terminal value.  For established companies that grow at the growth rate of the economy the detailed planning period can be omitted, i.e. only the terminal value (starting in t=1) will be calculated. We will look at the following five steps of the enterprise DCF valuation: Exhibit 10: Five Steps in Enterprise DCF Valuation 2.2.1 Company Analysis The first step in any valuation should be to gain a deep understanding of the company and its products or services in comparison with the competition. The following five questions (five W’s) offer one possible form to structure the analysis. [1] Who is the company? [2] What exactly does the company offer? [3] Where (i.e. on which markets) are the products or services sold? [4] What does the company’s value chain look like? [5] What were the company’s financial results in past years? <?page no="27"?> 2.2 Enterprise DCF Valuation 27 [1] Who is the company? Who are the shareholders, who are the major debt providers, who is on the management board? What is the legal structure, what is the tax structure? Are there any legal constructions that might have an influence on the value (long-term supply contracts)? What is the company’s history? Recommendation for students There are numerous questionnaires available and each consulting firm, investment bank, academic or non-academic teacher or trainer tends to swear on their own form. The five questions above are those that always helped us and that we still use. You can try to answer them for your company, but you can also use a different format that serves the purpose of understanding the object of the valuation. Summarize your findings in a short report. Be brief, work with bullet points, tables, and exhibits. The objective here is to reduce complexity by condensing information rather than to produce lots of pages. [2] What exactly does the company offer? What are the company’s products, its services? What do customers value in the company’s products or services? In what way do the products or services differentiate from the competition? What strategy does the company follow regarding their products or services (cost leadership, differentiation, focus)? Who are the competitors? What do customers value in the competitors’ products or services? What strategy do the competitors follow? What was the contribution to sales and profits of the different products or services over the past years for the company being valued? Is there a trend indication? What causes this trend? Where in the lifecycle are the products or services of the company? Is there a threat of substitute products or services? [3] Where (i.e. on which markets) are the products or services sold? What markets are served exactly? Are these markets regional markets, national markets, European markets, or global markets? How was the market growth in the past years and how is the growth forecast for the coming years? What observations can be made regarding the life cycle of the markets? What drives the markets, what are their constraints? What is the breakdown of market shares? How did this breakdown change in past years? What caused this change? What is the structure of the markets? How intense is the competition? Are the markets regulated? Who <?page no="28"?> 28 2 Discounted Cash Flow Valuation (DCF Valuation) exactly are the customers? What statements can be made about the customer life cycle? Are the markets buyers’ or sellers’ markets? What is the impact of imports and exports on these markets? How severe are the effects of technology changes on the markets? Recommendation for students Please use these questions as guidelines, as examples. They are neither comprehensive nor do they make sense for every company. Don’t try to answer each one. [4] What does the company’s value chain look like? The issue here is to understand how the company manufactures its products or provides its services. To answer this question, it usually helps to mentally go along the entire value chain of the company: research and development, product design, sourcing, production process and infrastructure, marketing, sales, after-sales services, administration and information technology. How exactly is the company organized in each of the functions mentioned? Let’s take sales as an example: Are the products sold through their own sales force, by independent sales agents, by a franchise system? Are they sold to wholesalers, to retailers, or to end customers directly? How is the company’s competition organized regarding sales? Another example, production: What is the depth of the vertical integration? What production infrastructure is available in-house? How does the company deal with production peaks? Are there any unique features in the production process, any competitive advantages or disadvantages and how sustainable are they? [5] What were the company’s financial results in past years? Show me the money! (Rod Tidwell in the movie Jerry Maguire) How much has the company earned in recent years? What was the total investment, the capital employed (fixed assets plus working capital)? What was the company’s return on assets (ROA), its return on capital (ROC)? How did they perform compared to their peers? To analyze these questions, it is recommendable to summarize the income statement and the balance sheet data of the past three to five years (for companies in cyclical businesses more historical data may be required to cover an entire cycle) in a spreadsheet program. In a next step, these data <?page no="29"?> 2.2 Enterprise DCF Valuation 29 are typically organized in a format convenient for the usage in a DCF valuation. The asset side of the balance sheet is usually subdivided into cash, fixed operating assets, net working capital and non-operating assets that are valued separately. The liabilities side is commonly subdivided into equity and interest-bearing debt. The income statement usually shows sales, operating expenses, depreciation, EBIT (earnings before interest and taxes), financial expenses, EBT (earnings before taxes), taxes and net profit. For companies with significant research and development (R&D) activities, a regrouping of the R&D expenses should be taken into consideration. Accounting regulations require that they are shown as operating expenses whereas their true character is closer to capital expenses. The consequence of the regrouping is that the operating expenses are reduced by the amount of R&D expenses with “capital expenses character”, which are then capitalized on the balance sheet and written off over the useful life of the R&D asset. In case competitors from different countries with different accounting regulations are compared, a consistent methodology must be applied to ensure that the comparison does not lead to wrong conclusions. When valuing companies with large off-balance-sheet lease liabilities, these should be capitalized and added to interest-bearing liabilities. From a financial perspective, this is exactly where they belong. The leased assets (or the right to use them) should also be capitalized and the operating result adjusted accordingly (operating result plus depreciation included in the result for operating leases minus depreciation on capitalized leased assets). The procedures of adjusting for R&D and operating leases are described in detail in the standard valuation textbooks. 15 Damodaran provides spreadsheets on his website 16 to perform the necessary calculations, accompanied by webcasts which explain the process. In a next step, past figures are analyzed regarding extraordinary or oneoff items that affected the bottom line. This process is called normalization. Restructuring expenses are one example. But be careful: In case you find such an expense every three years, it might be more appropriate to distribute the costs evenly over the three years instead of eliminating it. Normalizations require highest attention. For small, owner-run companies it should be analyzed whether the compensation paid to the management is reasonable and comparable to 15 Damodaran, Investment Valuation, 3 rd ed., 232-239, Koller/ Goedhart/ Wessels, Valuation, 7 th ed., 443 ff. and 467 ff. Since the introduction of IFRS 16 and ASC 842, the volume of off-balance sheet lease liabilities has decreased significantly, reducing the scope of reclassifications. 16 http: / / pages.stern.nyu.edu/ ~adamodar/ New_Home_Page/ spreadsh.htm, go to the section corporate finance & valuation inputs. <?page no="30"?> 30 2 Discounted Cash Flow Valuation (DCF Valuation) industry averages. In addition, in owner-run companies there often is no clear dividing line between company assets and private assets (left pocket, right pocket). A sole owner can handle it that way, if he reveals all details to the relevant authorities for tax purposes. However, the missing dividing line clearly can lead to a distortion of the true operating result, and the effects should be normalized. If the sole managing owner of a company intends to withdraw from the business after a sale, this will also influence the revenues and the profitability of the company. The effect can go in both directions. In most cases a reduction in profitability will be the result. This reduction can be part of a normalization exercise of historical income statements, and it clearly should be taken into consideration when making projections. Once the normalized and regrouped financial statements of the company under valuation and its competitors are prepared, standard spreadsheet programs will enable the whole spectrum of ratio analysis:  Common-size balance sheets and income statements  ROE, ROC, ROA analysis (DuPont)  Efficiency ratios  Profitability ratios  Leverage ratios  Liquidity ratios. The idea is not to produce meaningless lists of figures, but to gain an understanding for the key performance drivers of the valuation object compared to its competitors. Special attention is typically on top line growth, return on assets and return on capital. Where to retrieve the data necessary for such a company analysis? If you have access, the company itself, the management and the owners should be the first point of contact. If not and the company is quoted, the company website is usually a good place to start. Google Finance and Yahoo Finance are getting better every day, but they clearly don’t have the depth of information (yet? ) that fee-based services like Bloomberg, Eikon (Refinitiv, formerly Thomson Reuters), Morningstar, S&P Capital IQ and FactSet (just to name a few; this list does not imply a ranking! ) offer. Obtaining data for non-quoted companies is usually more difficult. In many countries, financial statements are available online (Bundesanzeiger and Handelsregister in Germany) nowadays and sometimes even free of charge, but usually they are not up to date and very condensed. Market data and ratios (industry averages) can often be found on websites of Federal Statistical Offices, Federal Banks and Cartel Authorities. Company associations, trade fair catalogues and fee-based services like Frost & Sullivan or GfK are also suitable sources. <?page no="31"?> 2.2 Enterprise DCF Valuation 31 2.2.2 Projection of Future Free Cash Flows In the enterprise DCF approach the free cash flow is the free cash flow to the firm. It is defined as follows: EBIT Earnings before interest and taxes Less: Taxes on EBIT (marginal tax rate) EBIAT Earnings before interest after taxes Plus: Depreciation Less: Capital expenditures Investments in fixed assets Less (Plus): Increase (decrease) in working capital Investments in working capital (without cash and short-term interest-bearing debt) Free cash flow (to the firm) Exhibit 11: Free Cash Flow Starting point for the derivation of the free cash flow to the firm is the operating result (EBIT) of the company, which is in a first step reduced by taxes. Taxes are cash outflows leading to a decrease of the free cash flow. The enterprise DCF method determines and discounts the free cash flow available to both equity and debt providers, i.e. cash flows to the firm. Consequently, taxes are calculated on EBIT. The tax shield resulting from the deductibility of the interest expense from the tax base is accounted for in the computation of the weighted average cost of capital (WACC). It is common to use the marginal tax rate (instead of the effective tax rate), i.e. the rate applied on the last dollar of pre-tax earnings. Taking Germany as an example, this would translate into a tax rate of about 30% for stock corporations (trade tax, corporate tax and solidarity surcharge). The effective tax rate of past years will usually differ from the marginal tax rate. This is caused by different accounting rules for the company’s statutory accounts and its tax accounts, by tax loss carryforwards, or different tax rates applied on profits abroad. Using the marginal tax rate for the derivation of future free cash flows implies that the effects just mentioned will not occur. This assumption becomes normally more likely the further in the future the planning periods are. Valuation differences between statutory and tax accounts balance out over time (except for non-deductible expenses), tax loss carry- <?page no="32"?> 32 2 Discounted Cash Flow Valuation (DCF Valuation) forwards don’t last forever and the transfer of profits realized abroad to the domestic territory leads in some jurisdictions to an upward adjustment, diminishing preceding tax savings. If these assumptions do not hold, it might become necessary to perform a detailed tax planning for the budget period and use the resulting tax rates for the derivation of the future free cash flows. However, such a detailed tax planning will be almost impossible without the input from the management of the company. After the deduction of taxes from EBIT we get EBIAT. To get to the free cash flow we must adjust this number by those income and expenditure items that did not lead to cash movements as well as those cash inflows and outflows that did not affect income and expenditures. In a first step, we add back depreciation. Depreciation leads to an increase in expenses, but does not lead to a decrease in cash. Investments in fixed assets must be deducted. They have not been accounted for as an expense when deriving EBIT, but they reduced the free cash flow since they led to a decline in the cash balance. The same applies to investments in working capital. 17 What we get after the last adjustment is the free cash flow to the firm, the cash flow available to both equity and debt providers, before the consideration of interest expenses. The projection of future free cash flow is typically based on the budget and/ or the forecast of the company or the company’s management. This forecast should always be subject to a detailed review regarding plausibility and consistency. The evaluation is ideally grounded on the findings of the company analysis on products/ services, markets, competitive position, the value chain of the company and its peers, the normalized past results as well as balance sheet ratios. The following five steps are recommendable when performing a consistency check. In case no forecast from management is available, they can also serve as a guideline to develop an own projection for the detailed planning period. [1] Projection of revenues [2] Projection of income statements until EBITDA [3] Projection of depreciation and capital expenditures [4] Projection of working capital requirements [5] Growth and reinvestment 17 We will use non-cash working capital throughout the book, as in valuations cash and interest-bearing debt are treated separately. <?page no="33"?> 2.2 Enterprise DCF Valuation 33 [1] Projection of Revenues The top line of the future income statements, i.e. future revenues, certainly has the biggest impact on the value of the company. The projection should take historical growth rates into consideration, but also include further input. For quoted companies, consensus estimates are available. For non-quoted companies, the consensus estimates of comparable quoted companies will give some guidance. Market studies are another source of information. The point here is not to copy them one to one and extrapolate them. It is moreover important to develop a feeling how the growth trend and the growth momentum affect current sales and how they will influence the revenues of the coming years. Common sense is the best tool here. If possible, projections of revenues should be performed both “top down” (based on market growth rates) and “bottom up” (based on existing orders and customers, and new business) and validated against each other. [2] Projection of Income Statements until EBITDA Conceptually there are two possibilities: Either cost of goods sold (COGS) before depreciation and other expenditures are projected separately (if the company uses a nature of expense method for the income statement, COGS will be replaced by e.g. material costs and personnel costs) or EBITDA is projected directly. If the second alternative is chosen, this will reduce the options for the projection of the working capital requirements in step [4] as COGS are not being projected. In both alternatives, the items are typically projected as a percentage of sales, based on what was mentioned under projection of revenues in [1] above: Current and historical cost structures, consensus estimates on the company and comparable companies, market data on cost structures of competitors and expected developments. Significant deviations (in both directions) from industry average should be challenged. In case there is a competitive advantage, it should be analyzed how sustainable the advantage is and when the cost structure will converge to the industry average. [3] Projection of Depreciation and Capital Expenditures Even though depreciation and capital expenditures are highly interconnected, in practice they are quite often projected separately, even at different percentage of sales rates. The basic relation should not be ignored: You can only depreciate what you invested, and if your capital expenditures go up, your depreciation expenses will do so too. The only exception is when the company acquires assets that are not subject to depreciation, e.g. goodwill or real estate. Ideally a valuation can be based on data from <?page no="34"?> 34 2 Discounted Cash Flow Valuation (DCF Valuation) the company’s asset accounting. If in addition the future investments, their useful life and the depreciation method is available, a depreciation schedule can easily be developed for the forecast period. Capital expenditures are normally projected as a percentage of sales. Investments happen in most companies in batches or waves and are not distributed evenly over time. If the projection relies on historical data, the period analyzed should be long enough (five year or even ten year averages). Depreciation expense should be aligned with the investments made in depreciable assets. Alternatively, fixed assets can be projected as a percentage of sales and in a next step depreciation as a percentage of fixed assets. Finally, capital expenditures are determined by simply adding up the increase in fixed assets and the depreciation expense. [4] Projection of Working Capital Requirements Two approaches are common, a simple one and a more detailed one. The results from the two approaches are often negligible in practice. The simple approach forecasts the working capital as a percentage of sales. The percentage can be derived from historical data of the company, its peers or other market data. The detailed approach projects each component of working capital separately. Trade accounts receivable are normally projected based on future revenues, either directly as a percentage of sales or based on days outstanding (365 × Trade receivables/ Sales). For the projection of inventories, COGS or material costs provide the foundation, usually derived from days in inventory (365 × Inventories/ COGS or Material costs) as both measures are based on costs rather than selling prices. The same applies to trade payables as a function of days payable outstanding (365 × Trade payables/ COGS or Material costs). The other components of working capital are typically projected as a percentage of sales. Please don’t forget that only the changes in working capital affect the free cash flow. If the working capital increases, more funds are tied up at the expense of free cash flow. On the other hand, cash is released if working capital requirements decrease. [5] Growth and Reinvestment There will be no growth without reinvestment. Reinvestment as such is the part of the generated earnings that is plowed back into the corporation. We refine the definition of reinvestment as the investment beyond <?page no="35"?> 2.2 Enterprise DCF Valuation 35 the replacement of existing assets 18 , i.e. the investment that indicates that the productive capacity increases, hence 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝐸𝐸𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅 + 𝐼𝐼𝑅𝑅𝐼𝐼𝐸𝐸𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅 𝑊𝑊𝑊𝑊𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅𝑊𝑊 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 − 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 The reinvestment rate describes the part of EBIAT that is reinvested for growth: 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 = 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝐸𝐸𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅 + 𝐼𝐼𝑅𝑅𝐼𝐼𝐸𝐸𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅 𝑊𝑊𝑊𝑊𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅𝑊𝑊 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 − 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 The free cash flow can also be written as: 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 × (1 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅) At any given reinvestment rate and assuming a stable return on capital (ROC), the growth rate in earnings (here EBIT or EBIAT) is: 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸 𝐺𝐺𝐸𝐸𝑊𝑊𝐹𝐹𝑅𝑅ℎ 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 × 𝑅𝑅𝑅𝑅𝐶𝐶 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝑅𝑅𝑅𝑅𝐶𝐶 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 + 𝑁𝑁𝑅𝑅𝑅𝑅 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 (𝐷𝐷𝑊𝑊𝑅𝑅ℎ 𝑅𝑅𝑅𝑅 𝐷𝐷𝑊𝑊𝑊𝑊𝑊𝑊 𝑅𝑅𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅) In case the company’s ROC deviates significantly from the industry average, this suggests a competitive advantage (higher ROC than industry average) or disadvantage (lower ROC than industry average). It should then be analyzed how sustainable this difference will be. The interrelations shown above can be utilized for a consistency check of a cash flow forecast. They can also be used to project future free cash flows directly. In case you assume that the ROC is changing in t+1 compared to the actual ROC t , the EBIT growth rate can be derived as follows: 19 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸 𝐺𝐺𝐸𝐸𝑊𝑊𝐹𝐹𝑅𝑅ℎ 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 × 𝑅𝑅𝑅𝑅𝐶𝐶 𝑡𝑡+1 + 𝑅𝑅𝑅𝑅𝐶𝐶 𝑡𝑡+1 − 𝑅𝑅𝑅𝑅𝐶𝐶 𝑡𝑡 𝑅𝑅𝑅𝑅𝐶𝐶 𝑡𝑡 18 In academia and practice, the term net investment is often applied to describe the same concept. 19 Damodaran, Investment Valuation, 3rd ed., 294. <?page no="36"?> 36 2 Discounted Cash Flow Valuation (DCF Valuation) 2.2.3 Estimation of Weighted Average Cost of Capital (WACC) Just as the net present value method in standard capital budgeting analysis, the DCF approach in corporate valuation also requires a discount rate to make the projected free cash flows of the company that occur at different times in the future comparable, to discount them to t=0. As in standard capital budgeting analysis, the discount rate should reflect the risk of the investment. From a risky investment, we expect a higher return than from a riskless investment. These very basic principles of corporate finance must also be applied to corporate valuations, where the company under investigation is nothing else but a normal project (maybe a large and complex one, but there are no special rules, especially no rules that override the basic principles of capital budgeting analysis). So, if we discount the projected free cash flows of Coca Cola, we will use a different (lower) discount rate than we would for discounting the future free cash flows of Netflix. 20 We measure the risk with the expected standard deviation (spread) of the future free cash flows around their expected return. We like Damodaran’s visualization. 21 Let’s first look at a risk-free investment. There is no spread: Exhibit 9: Return “Spread” of a Risk-Free Investment The probability distribution of an uncertain future free cash flow for a risky investment can be depicted as follows: 20 As of late 2024; this might be different in 2034. 21 Damodaran, Applied Corporate Finance, 4th ed., 54-56. <?page no="37"?> 2.2 Enterprise DCF Valuation 37 Exhibit 10: Probability Distribution for a Risky Investment The enterprise DCF method in the form we predominantly find it in practice implicitly assumes a normal distribution of the actual returns around the expected return. The higher the standard deviation, the higher the risk, the higher the discount rate as the return expectation of the investor will go up. The following exhibit shows a future free cash flow with the same expected return but a higher standard deviation: Exhibit 11: Probability Distribution for a Riskier Investment The investor will demand a higher return from such an investment compared to the previous one shown in exhibit 10. Consequently, the discount rate will be higher, reflecting the increased spread. 22 22 Most of our students come to our valuation classes with a reasonably good knowledge of corporate finance basics, so that we don’t spend any time on explaining the CAPM, <?page no="38"?> 38 2 Discounted Cash Flow Valuation (DCF Valuation) The discount rate used in the enterprise DCF method should be the market-value weighted average cost of capital (WACC) of the target company (i.e. the company we determine the value for), securing that the return expectations of both equity and debt providers are met. 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 = 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 × 𝐸𝐸 𝐸𝐸 + 𝐷𝐷 + 𝐸𝐸𝑜𝑜𝑅𝑅𝑅𝑅𝐸𝐸-𝐸𝐸𝐶𝐶𝐸𝐸 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 × 𝐷𝐷 𝐸𝐸 + 𝐷𝐷 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝐸𝐸 = 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝐶𝐶𝑅𝑅𝐸𝐸 𝐷𝐷 = 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 The weights (E/ (E+D) and D/ (E+D)) should reflect the target capital structure of the company we value. In case explicit information on the target capital structure is not available, valuation practice uses in 9 out of 10 cases the current capital structure (market values, not book values should be applied), if it is within the normal range of the industry and does not deviate significantly from the company’s capital structure of the preceding years. Industry averages can be obtained easily from the sources given in chapter 2.2.1, last paragraph (page 34). In addition, Damodaran provides relevant data for free on his website. 23 Once we have the weights, we need to determine [1] the cost of equity and [2] the after-tax cost of debt to get to the weighted average cost of capital (WACC), our discount rate. [1] Cost of Equity The derivation of the cost of equity is based on the findings of the capital asset pricing model (CAPM). Despite all the critique of the model’s assumptions and its very limited empirical evidence, the CAPM has become very popular and is widely used around the globe. It is easy to apply in practice, clearly recognizes the linkage between risk and expected return and facilitates the communication in valuation practice. Alternative models are much more complex and have not yet been able to establish themselves. The CAPM looks at the risk through the eyes of the so-called “marginal investor”. It assumes, that this investor is fully diversified. If this investor diversifiable and non-diversifiable risk, the marginal investor etc. In case you did not take a corporate finance class before, please work through chapters 3 and 4 of Damodaran’s Applied Corporate Finance, 4 th ed., alternatively chapters 11, 12, and 13 of Brealey/ Myers/ Marcus Fundamentals of Corporate Finance, 11 th ed., or any other good corporate finance textbook. 23 www.damodaran.com, “Data”, “Current Data”, “Capital Structure”. <?page no="39"?> 2.2 Enterprise DCF Valuation 39 for example analyzes TikTok or Tesla, she or he does not evaluate the total risk associated with these two stocks. Relevant is only the risk that arises when adding one or both stocks to her or his diversified portfolio. Put differently, risk that can be diversified away, will not be rewarded by a higher return. The cost of equity can be derived as follows based on the CAPM: 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊-𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 + 𝛽𝛽 × 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊 𝑃𝑃𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅 So, we need three ingredients to get to the cost of equity, the risk-free rate, the market risk premium, and the beta for the company we value. Risk-Free Rate The risk-free rate is the return an investor can expect from investing in an asset where the probability for the expected return equals 100%. Actual return and expected return will not differ, there is no risk in the investment. Government bonds with a first-class credit rating (AAA) fall into this category, although purists might argue that there still is some risk associated even with these bonds. The returns of AAA rated government bonds are available on the web and the relevant information services. For Germany, the Deutsche Bundesbank announces the returns of German government bonds daily. 24 The European Central Bank publishes the returns of government bonds of the member states of the European Union 25 ; attention: not all the member states have a AAA rating. The FRED (Federal Reserve Bank of St. Louis) provides data for the US. 26 The returns of 10-year bonds usually form the basis for the risk-free rates, since investments in or acquisitions of companies are usually long-term investments. German CPAs determine the risk-free rate based on yield curves (Svensson procedure). 27 Market Risk Premium The market risk premium is the premium or the additional return an investor demands for investing in an average risk asset or the so-called market portfolio (a market-value weighted portfolio of all stocks in an economy) compared to an investment in the risk-free asset (AAA government bond). There are historical data available on the market risk premium (also called equity risk premium). 28 24 https: / / www.bundesbank.de/ resource/ blob/ 650674/ a16e42bc52315c45593bc350ed7dd645/ mL/ urwpart-data.pdf. 25 http: / / www.ecb.europa.eu/ stats/ money/ long/ html/ index.en.html. 26 https: / / fred.stlouisfed.org/ series/ DGS10. 27 Available for free at https: / / kleeberg-valuation.de/ aktuell/ basiszinssatz/ . 28 https: / / papers.ssrn.com/ sol3/ papers.cfm? abstract_id=4751941, pages 49-50. <?page no="40"?> 40 2 Discounted Cash Flow Valuation (DCF Valuation) The market risk premium in developed economies has historically ranged between 3% and 8% with an emphasis on the range between 4% and 6%. There have been debates in academia and in practice on the appropriate period (10 years, 20 years, 50 years) for the analysis and whether to use arithmetic or geometric means. In the meantime, both valuation theory and practice tend to switch from the use of historical risk premiums to future-oriented data, so-called implied market risk premiums. Based on the actual price of a stock, the expected dividend of the stock and the expected growth rate of the dividend, the implied expected return of the stock can easily be calculated (dividend yield plus expected dividend growth rate). Applying this on all stocks of the market portfolio, weighted with the respective market values, leads to the implied return of the market portfolio. If we then deduct the return of the risk-free asset, we get to the implied market risk premium. Most of the professional service providers like Bloomberg offer implied risk premiums. Damodaran calculates them for the US at the beginning of each month and publishes them on his website. 29 Based on the US data he calculates equity risk premiums for almost every country on the globe (updated annually). The website www.market-risk-premia.com is also an option to obtain the data. Investment banks and large consulting firms to some extend set the riskfree rate and the market risk premium for their staff to ensure a certain level of consistency in the evaluations performed by their organization. Beta The beta of a stock measures the systematic, the non-diversifiable risk. The beta specifies how sensitive the returns of a stock are to fluctuations of the market. A beta of 1 indicates that the stock moves with the market portfolio, i.e. it has the same risk as the average risky asset. If the market goes up by 1%, the best estimate for the stock is that it will go up by 1% as well. If the beta is > 1, the stock is expected to fluctuate more strongly than the market portfolio, i.e. the stock has a higher risk. If the beta is < 1, the stock is less risky than the average risk asset. How a stock moves with the market portfolio and how it reacts to the fluctuations of the market portfolio is measured by the covariance of the return of the stock and the return of the market portfolio over a defined period. Dividing the covariance by the variance of the market portfolio leads to the beta, a standardized measure for the risk (standardized around 1). If the stock moves stronger than the market, the higher is the risk, the beta, the required return, the cost of equity, the cost of capital and the discount rate. 29 There is a section called „Implied Equity Risk Premium Update” directly on the home page of the website (www.damodaran.com). <?page no="41"?> 2.2 Enterprise DCF Valuation 41 For quoted companies, the calculation of betas can easily be performed with the help of the standard spreadsheet programs by comparing the return of the stock with the return of the market, usually represented by a stock market index. All necessary statistical functions are available. In Excel, please use “Data”, “Data Analysis”, “Regression”, alternatively “Insert” “Charts” “Scatter” and then right-click “Add Trendline” and “Display Equation on chart”, or (more tedious) with the function “LINEST”, alternatively (easier) “SLOPE”. After all, since many cost-free services like Google Finance and Yahoo Finance offer betas for most quoted companies that usually do not deviate significantly from the betas calculated by the fee-based services 30 , the burdensome collection of the data and the own calculation is usually unnecessary. However, these so-called historical “top-down” betas should be taken with a grain of salt. They usually come along with high statistical standard errors, so that a simple extrapolation to the future is problematic. In addition, most companies are not quoted on a stock exchange. The alternative is to work with so-called “bottom-up” betas, where betas of comparable quoted companies are collected and averaged (this reduces the standard error; the more companies are included in the sample, the higher the reduction of the standard error) or industry betas are utilized to calculate the cost of equity. When comparing betas of different companies, it should be considered that the leverage of the firms will influence their betas. This implies that you cannot simply add up the betas of different companies. You must make them comparable first. This is done by unlevering the betas in a first step and relevering the average unlevered beta in a second step. To unlever a beta, the following formula can be applied: 𝛽𝛽 𝑢𝑢 = 𝛽𝛽 𝑙𝑙 1 + (1 − 𝑅𝑅) × 𝐷𝐷𝐸𝐸 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝛽𝛽 𝑢𝑢 = 𝑈𝑈𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝐸𝐸 𝐸𝐸𝑅𝑅𝑅𝑅𝐶𝐶 𝛽𝛽 𝑙𝑙 = 𝐿𝐿𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝐸𝐸 𝐸𝐸𝑅𝑅𝑅𝑅𝐶𝐶 𝑅𝑅 = 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝐸𝐸𝐶𝐶𝐸𝐸 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝐷𝐷 = 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 𝐸𝐸 = 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 30 The differences between the beta values of the services are due to the data used for their calculations, in particular the historical time frame (1 to 5 years is common), the interval of the returns (daily, weekly, monthly, etc.) and the index used to operationalize the market (DAX, S&P 500, MSCI World, etc.). Some services also assume that the beta approaches 1 as the company matures and artificially correct for this (e.g. Blume method). Unfortunately, this information is rarely provided in a transparent manner. <?page no="42"?> 42 2 Discounted Cash Flow Valuation (DCF Valuation) The unlevered betas of the comparable companies are used to calculate an (as appropriate weighted) average. This average unlevered beta must be relevered again in accordance with the target capital structure of the company being valued: 𝛽𝛽 𝑙𝑙 = 𝛽𝛽 𝑢𝑢 × �1 + (1 − 𝑅𝑅) × 𝐷𝐷𝐸𝐸� 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝐷𝐷𝐸𝐸 = 𝐸𝐸𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝐼𝐼𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑅𝑅𝑅𝑅𝐸𝐸𝐸𝐸𝐼𝐼𝑅𝑅𝐸𝐸𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝑅𝑅ℎ𝑅𝑅 𝐼𝐼𝑊𝑊𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅𝐸𝐸 𝑅𝑅𝑊𝑊 𝐷𝐷𝑅𝑅 𝑅𝑅𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅𝐸𝐸 Example Let the risk-free rate be 2.3%, the market risk premium 6%, the average unlevered beta of comparable companies 1.0, the target capital structure 0.25 (i.e. 20% debt, 80% equity) and the marginal tax rate 30%. Let’s calculate the cost of equity. In a first step, the levered beta is determined as follows: 𝛽𝛽 𝑙𝑙 = 1.0 × (1 + (1 − 0.3) × 0.25) = 1.175 The cost of equity is then calculated in a second step: 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊-𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 + 𝛽𝛽 × 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊 𝑃𝑃𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅 = 2.3% + 1.175 × 6% = 9.35% The valuation of small, owner-managed companies where the owners are not widely diversified, will tend to result in overestimating the value due to underestimating the cost of equity, since the beta measures the systematic risk only. As the owners are not diversified, they are not only exposed to the systematic (market) risk, but also to the unsystematic (companyspecific) risk (to the entire risk if all funds are tied up in the company, which is a very common scenario in small owner-managed firms). There is a work-around, called total beta. The total beta is calculated by dividing the beta by the correlation coefficient r. This total beta is a measure for the total risk, i.e. the risk the owners are exposed to at zero diversification. Let’s assume that in the example above the average correlation coefficient r of the comparable firms of the company is 0.5. The r squared then amounts to 0.25. This means that 25% of the fluctuations in the stock price can be explained by fluctuations of the market portfolio (market risk), whereas 75% of the fluctuations are caused by company-specific risk that could be diversified away. The total beta would amount to 1.175/ 0.5 = 2.35, and the cost of equity to 16.4% (2.3% + 2.35 × 6%). If the owners are partially diversified, the r in the formula can be adjusted between 0.5 for zero diversification to 1 for a fully diversified owner. <?page no="43"?> 2.2 Enterprise DCF Valuation 43 There is a discussion on the theoretical foundation of this approach in academia. Since there is no real alternative (except than making an adjustment based on gut feeling), the total beta approach can be found quite frequently in valuation practice as it is intuitively understandable: Less diversification, more risk, higher beta, higher cost of equity. There are further adjustments in valuation practice for small enterprises. An illiquidity discount of 15% to 30% on the derived company value is discussed based on (not truly reliable) empirical data, to reflect the lack of fungibility compared to larger and quoted companies. In addition, size premiums can be found (4% to 5% on top of the cost of equity). It should be carefully investigated that there is no double-counting of risk when applying these adjustments. [2] After-Tax Cost of Debt The cost of debt should correspond to the interest rate the company would have to pay if it had to refinance its entire debt at the time of the valuation. As in standard capital budgeting analysis, usually a long-term interest rate is applied to reflect the long-term character of corporate valuation. As an insider, this interest rate is normally known (from recent discussions with debt providers). As an outsider with no access to management, you must estimate this interest rate for your valuation. This is relatively easy if the company has a quoted bond with a maturity of about 10 years outstanding. Current price, coupon rate and maturity are given and the yield to maturity can easily be calculated. Most services provide it anyhow, so that even the calculation is not necessary. Nevertheless, it is useful as a sanity check. If the company has a credit rating, the cost of debt can be estimated based on the spread banks would normally add to the risk-free rate for loans to companies in this rating class. Fee-based services provide these data. Damodaran has an annually updated list on his website. 31 In case the company has no credit rating, you can try to estimate a synthetic rating based on the interest coverage ratio (EBIT/ Interest Expense) of the company. Use the same link on Damodaran’s website. The yield to maturity of 10-year bonds of comparable companies with a comparable leverage may also serve as a guideline. The federal banks usually also publish actual interest rates for corporate loans, but unfortunately mostly not by rating classes. In valuation practice you will usually try to find 31 http: / / people.stern.nyu.edu/ adamodar/ New_Home_Page/ datafile/ ratings.html. <?page no="44"?> 44 2 Discounted Cash Flow Valuation (DCF Valuation) your way towards the actual long-term cost of debt by testing several or even all the possibilities described above. Interest on debt reduces, in contrast to dividends paid to equity providers, in most jurisdictions the tax base of the company, i.e. leads to lower taxes. Consequently, in determining the cost of debt the after-tax interest expenses are relevant. Special tax regulations should be taken into consideration. In Germany for example, only 75% of the interest expenses are deductible for trade tax purposes 32 . The tax saving for stock corporations on interest is below the marginal tax rate of 30% for these companies and amounts to approximately 26.5%. Example (continued) Let’s continue with our example and assume that the company is a German stock corporation with pre-tax cost of debt of 6%. The aftertax cost of debt will then amount to 4.41% (6% × (1 - 0.265)). At a cost of equity of 9.35% as calculated above and a target capital structure of 80% equity and 20% debt, the weighted average cost of capital (WACC) can be derived as follows: 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 = 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 × 𝐸𝐸 𝐸𝐸+𝐷𝐷 + 𝐸𝐸𝑜𝑜𝑅𝑅𝑅𝑅𝐸𝐸-𝐸𝐸𝐶𝐶𝐸𝐸 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 × 𝐷𝐷 𝐸𝐸+𝐷𝐷 = 9.35% × 0.8 + 4.41% × 0.2 = 8.362% 2.2.4 Calculation of Terminal Value In DCF valuations we discount future free cash flows back to the date of the analysis, and we usually assume an eternal life of the company. As it is not possible to discount future free cash flows until eternity, the forecast is, as shown above in chapter 2.2.1, typically done in two (or more) stages. Stage 1 is the detailed planning period in which future free cash flows will be forecasted for every year. Stage 2 of a two-stage DCF valuation model would then be the period after stage 1 until eternity, i.e. the period without an explicit forecast of future free cash flows for every year. The terminal value in a DCF valuation represents the value of the free cash flows of this last stage. The terminal value typically represents the much larger portion of the value of the company (75% and more is normal) compared to the discounted free cash flows of the detailed planning 32 § 8 No. 1a GewStG (the German “Gewerbesteuergesetz”). <?page no="45"?> 2.2 Enterprise DCF Valuation 45 period. This requires that the determination of the terminal value should be done with extreme diligence. First, the detailed planning period should be chosen in a way that the last year of the budget can be regarded as “representative” for the future development, for the so-called “steady state”. It should not represent the upper or the lower end of a cycle - for cyclical companies an average year should be taken. There are two approaches in valuation practice for the calculation of the terminal value: [1] Perpetuity growth method [2] Exit multiple method [1] Perpetuity Growth Method The terminal value is calculated as follows: 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 𝑡𝑡+1 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 − 𝑊𝑊 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 𝑡𝑡+1 = 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 𝑊𝑊𝑜𝑜 𝑅𝑅ℎ𝑅𝑅 𝑜𝑜𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅 𝐸𝐸𝑅𝑅𝐶𝐶𝐸𝐸 𝐶𝐶𝑜𝑜𝑅𝑅𝑅𝑅𝐸𝐸 𝑅𝑅ℎ𝑅𝑅 𝐸𝐸𝑅𝑅𝑅𝑅𝐶𝐶𝑅𝑅𝐶𝐶𝑅𝑅𝐸𝐸 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊 𝐶𝐶𝑅𝑅𝐸𝐸𝑅𝑅𝑊𝑊𝐸𝐸 = 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 𝑡𝑡 × (1 + 𝑊𝑊) 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 = 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑜𝑜𝑊𝑊𝐸𝐸 𝐶𝐶𝑅𝑅𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝐹𝐹ℎ𝑅𝑅𝐼𝐼ℎ 𝑅𝑅𝐶𝐶𝐸𝐸 𝐷𝐷𝑅𝑅 𝐸𝐸𝑅𝑅𝑜𝑜𝑜𝑜𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑜𝑜𝐸𝐸𝑊𝑊𝑅𝑅 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡 𝑊𝑊 = 𝑃𝑃𝑅𝑅𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝐺𝐺𝐸𝐸𝑊𝑊𝐹𝐹𝑅𝑅ℎ 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 The constant perpetuity growth rate g has the biggest influence on the terminal value. It increases as g approaches the weighted average cost of capital (WACC). However, the growth rate g should not exceed the expected growth rate of the economy 33 , for globally active companies the expected global growth rate. Any value above this would lead at some point in the future to the situation that the company would be larger than the economy. For companies in mature industries the growth rate g can be well below the growth rate of the economy. And in special cases the growth rate g can also be negative, a scenario we expect to see more often in the future since the expected growth rates of many economies approach zero. In most valuations, the discount rate used to calculate the terminal value does not differ from the discount rate used to calculate the net present value of the future free cash flows in the detailed planning period, i.e. WACC t+1 = WACC t . It should however be considered to adjust the beta 33 Damodaran suggests the risk-free rate of an economy as a proxy for its long-term nominal growth rate, see e.g. Damodaran, Investment Valuation, 3 rd ed., 307. <?page no="46"?> 46 2 Discounted Cash Flow Valuation (DCF Valuation) for the last stage, where mature growth (equal or below the growth rate of the economy) is assumed, as it may be different from the high-growth phase in stage 1. The capital structure might also change and therefore the after-tax cost of debt - mature companies with low but stable growth rates tend to have more debt than young, high-growth companies. These are some examples that could lead to different weighted average cost of capital for the calculation of the perpetuity (WACC t+1 ≠ WACC t ). Finally, the reinvestment needs for mature companies with industry average growth rates differ from the reinvestment needs of young, highgrowth companies. Insofar it does make sense to rearrange the formula above in the following way: 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 𝑡𝑡+1 × (1 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑡𝑡+1 ) 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 − 𝑊𝑊 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑡𝑡+1 = 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝐸𝐸𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅 𝑡𝑡+1 + 𝐼𝐼𝑅𝑅𝐼𝐼𝐸𝐸𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅 𝑊𝑊𝑊𝑊𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅𝑊𝑊 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑡𝑡+1 − 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 𝑡𝑡+1 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 𝑡𝑡+1 As shown above in 2.2.2 under [5], the growth rate g can also be written as: 𝑊𝑊 = 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑡𝑡+1 × 𝑅𝑅𝑅𝑅𝐶𝐶 𝑡𝑡+1 Rearranging this term, we get: 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑡𝑡+1 = 𝑊𝑊 𝑅𝑅𝑅𝑅𝐶𝐶 𝑡𝑡+1 Plugging this into the formula above, we can calculate the terminal value also as: 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 𝑡𝑡+1 × (1 − 𝑊𝑊 𝑅𝑅𝑅𝑅𝐶𝐶 𝑡𝑡+1 ) 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 − 𝑊𝑊 What do we learn from this? The expected return on capital in the last stage of the forecast period (ROC t+1 ), the period with constant growth, also goes into the equation of the calculation of the terminal value, either implicitly or explicitly as in the formula above. The question to analyze now is whether the company will be able to achieve excess returns in this phase of moderate growth. Companies with strong brands (e.g. Coca Cola) and sustainable competitive advantages may be able to do so, but <?page no="47"?> 2.2 Enterprise DCF Valuation 47 for some companies the return on capital in the last stage of the planning period (ROC t+1 ) will converge to the weighted average cost of capital of the last stage of the planning period (WACC t+1 ). This means that new investments will just earn their cost of capital. In this case, we can rearrange the formula for the terminal value to: 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 𝑡𝑡+1 × �1 − 𝑊𝑊 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 � 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 − 𝑊𝑊 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 𝑡𝑡+1 × 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 − 𝑊𝑊 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 − 𝑊𝑊 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 𝑡𝑡+1 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 What does this mean? In case new investments earn only their cost of capital, the growth rate g has no influence on the terminal value. Intuitively that does make sense - an increase in value requires that you earn more than your cost of capital. As this is not the case under our assumption (WACC t+1 = ROC t+1 ), we can stop our forecast after the calculation of EBIAT t+1 and we don’t have to calculate the free cash flow. What is below EBIAT does not affect the value under the specific assumptions we made here. [2] Exit Multiple Method The exit multiple method determines the terminal value by multiplying a key economic parameter of the last year of the detailed planning period (normally EBIT or EBITDA, but you also find sales or book value of equity) with a so-called market multiple. This market multiple, e.g. 7 times EBITDA, is derived from multiples of comparable quoted companies or from precedent transactions of comparable companies (we will look at these valuation approaches in chapters 3 and 4 in more detail). Economically this can be interpreted as a resale of the business at the end of the detailed forecast period at an estimated market price. This also explains the term exit multiple method. As in the perpetuity growth method, it is essential that the last year of the detailed planning period can be regarded as representative for the (longer) future. In addition, the multiples derived from comparable companies and/ or transactions should also not contain any cyclical effects. When applying the exit multiple method, it should be clear that the by far largest component of the company’s value, the terminal value, is not <?page no="48"?> 48 2 Discounted Cash Flow Valuation (DCF Valuation) determined by discounting future free cash flows, but by applying market multiples, which is an alternative valuation approach we will look at in the next two chapters. Nevertheless, it is recommendable to apply both approaches when determining the terminal value and to use each one as a plausibility check for the other. In case the terminal value has been calculated by applying the perpetuity growth method, the implied EBITDA multiple can be derived as follows: 𝐼𝐼𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐸𝐸 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 𝑀𝑀𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅 = 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡𝑢𝑢𝑃𝑃𝑡𝑡𝑃𝑃 𝐺𝐺𝑃𝑃𝐺𝐺𝐺𝐺𝑡𝑡ℎ 𝑀𝑀𝑃𝑃𝑡𝑡ℎ𝐺𝐺𝑜𝑜 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 𝑡𝑡 To check the plausibility of an EBITDA multiple applied in an exit multiple method calculation of the terminal value, the implied growth rate g can be calculated as follows: 𝐼𝐼𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐸𝐸 𝐺𝐺𝐸𝐸𝑊𝑊𝐹𝐹𝑅𝑅ℎ 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑊𝑊 = 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝐸𝐸𝐸𝐸𝑃𝑃𝑡𝑡 𝑀𝑀𝑢𝑢𝑙𝑙𝑡𝑡𝑃𝑃𝑃𝑃𝑙𝑙𝑃𝑃 𝑀𝑀𝑃𝑃𝑡𝑡ℎ𝐺𝐺𝑜𝑜 × 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 − 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 𝑡𝑡 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝐸𝐸𝐸𝐸𝑃𝑃𝑡𝑡 𝑀𝑀𝑢𝑢𝑙𝑙𝑡𝑡𝑃𝑃𝑃𝑃𝑙𝑙𝑃𝑃 𝑀𝑀𝑃𝑃𝑡𝑡ℎ𝐺𝐺𝑜𝑜 + 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 𝑡𝑡 2.2.5 Computation of Present Values, Derivation of a Range of Enterprise Values, Sensitivity, Scenario and/ or Simulation Analysis The next step is of a technical nature: The present values of the future free cash flows must be determined, as well as the present value of the terminal value. Summing up these present values will give us the enterprise value for our company. In case of a two-stage model with a detailed planning period of 5 years, the enterprise value can be calculated as follows: 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 1 (1 + 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶) 1 + 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 2 (1 + 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶) 2 + 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 3 (1 + 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶) 3 + 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 4 (1 + 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶) 4 + 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 5 (1 + 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶) 5 + 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 (1 + 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶) 5 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 6 × (1 + 𝑊𝑊) 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑡𝑡𝑢𝑢𝑃𝑃𝑡𝑡𝑃𝑃 − 𝑊𝑊 𝑊𝑊𝐸𝐸 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝑀𝑀𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅 × 𝑃𝑃𝐶𝐶𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸 (𝑅𝑅. 𝑊𝑊. 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 5 ) <?page no="49"?> 2.2 Enterprise DCF Valuation 49 If the terminal value is calculated based on the exit multiple method, a cash inflow at the end of the detailed planning period, in our case here in t=5, is assumed (i.e. a resale of the company in t=5). In the perpetuity growth method, the terminal value represents a perpetuity starting in t=6 and will consequently be discounted with the same discount factor as the free cash flow in t=5. The reason for this is that the present value of a perpetuity starting in t=1 is already factored in the basic perpetuity formula (Perpetual Cash Flow/ Discount Rate). Therefore, a perpetuity starting in t=2 requires discounting the perpetuity for one year, a perpetuity starting in t=3 for two years and so on. In corporate valuations, you occasionally come across a deviation from the standard capital budgeting practice where we assume that all cash flows occur at the end of each period (in case of valuations at the end of each year). Instead it is assumed that all cash flows occur in the middle of each planning period, the so-called “mid-year convention”. When discounting future free cash flows, “to the power of minus 1” will be replaced by “to the power of minus 0.5”, “to the power of minus 2” by “to the power of minus 1.5” and so on. Typically, only the terminal value (when calculated as per the exit multiple method) is assumed to lead to a cash inflow at the end of the detailed planning period, in our case in t=5. Altogether this leads to lower discount factors and higher enterprise values. Honi soit qui mal y pense. 34 What we have so far is the enterprise value of the company. To get from the enterprise value to the equity value in a simplified way, please revert to exhibit 6 in section 2.1: 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 − 𝑁𝑁𝑅𝑅𝑅𝑅 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝑁𝑁𝑅𝑅𝑅𝑅 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 = 𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅-𝐸𝐸𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑊𝑊 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 − 𝐸𝐸𝐸𝐸𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ For a more detailed explanation, please see Chapter 6. Because of the numerous assumptions which we must make in corporate valuation, it is common to derive the enterprise value in the form of a range and not as a single number. Furthermore, sensitivity analysis and scenario analysis are part of the toolset, just as in standard capital budgeting. In a sensitivity analysis, one input parameter is modified while all other parameters are held constant. Applied to corporate valuation this could for example imply an analysis of how the enterprise value would vary if the WACC are modified or the growth rate g or the exit multiple when determining the terminal value, or the growth rate of the sales or EBITDA or EBIT as a percentage of sales. The possibilities are endless and there is 34 Shamed be the person who thinks evil of it. <?page no="50"?> 50 2 Discounted Cash Flow Valuation (DCF Valuation) a risk to be tempted to produce mountains of undigested figures. Less is more, should be the motto here, and the focus should be on the key value drivers. In a scenario analysis, several input parameters are modified at the same time, as different scenarios are developed. The classical triad here are the “base case”, the “best case” and the “worst case” scenarios, in corporate valuations often supplemented by a “management case”. Additionally, multiple scenarios can be developed reflecting variations in macroeconomic factors or reactions of competitors (competing product is or is not launched). Finally, a simulation analysis can be performed. In a simulation, we use probability distributions for the input parameters instead of expected values. This will then result in a probability distribution for the enterprise value. The Monte Carlo simulation is the standard approach and software packages like Crystal Ball, @Risk, ModelRisk, GoldSim allow an easy application. 35 The results of the sensitivity, the scenario and the simulation analysis will then be evaluated and are usually transformed into a range for the enterprise value. Templates for DCF valuations come along with all the three textbooks mentioned in the section “How to Use this Book”. And there are more available for free on the web. Self-Test [1] Can you explain the difference between the enterprise DCF method and the equity DCF method? [2] The equity value of a company amounts to $200 million, the interest-bearing debt is $100 million, and the company has a cash balance of $50 million (all of this can be regarded as excess cash). What is the enterprise value of the company? [3] Can you describe the two common methods to determine the terminal value? 35 There is an add-on in Google Sheets called Risk Solver which is available for free. <?page no="51"?> 3 Comparable Companies Analysis Learning Objectives  Understand the basic idea behind the comparable companies analysis and form your own opinion about this valuation approach.  Learn about and characterize the common multiples in relative valuation practice.  Get a basic idea on how to detect comparable companies. In a comparable companies analysis, the value of the firm is determined based on market prices of similar quoted companies. The basic idea is that in efficient markets, companies with a  comparable potential to generate future free cash flows,  with a similar growth perspective and  a similar risk profile of future free cash flows should also have similar market prices. Since the stock quotes of companies can’t be simply compared due to the different number of shares outstanding, a standardization is necessary to enable comparability. This standardization is achieved by setting the value of the companies in relation to their economic parameters like  sales,  EBITDA,  EBIT,  book value of equity or other industry-specific metrics like  number of subscribers,  output in gallons,  retail space in square feet or  number of miles travelled. The result of such a standardization is a multiple, and therefore this approach is also referred to as the “market multiple method”. <?page no="52"?> 52 3 Comparable Companies Analysis Example The market value of equity of a quoted company can easily be calculated by multiplying the number of shares outstanding with the current share price. Adding the market value of net debt, we get the enterprise value in market value terms. Sales, EBITDA, EBIT and many other input data for the comparable companies analysis is easily available for quoted companies, so that the derivation of market multiples is a straightforward exercise. A company has 25 million shares outstanding trading at $45. Interest-bearing debt amounts to $500 million and excess cash to $125 million. The market value of the equity is then $1,125 million (25 million shares × $45). The enterprise value (market value of equity plus net debt) is $1,500 million ($1,125 million equity value plus $500 million interest-bearing debt minus $125 million excess cash). There are quite some representatives of the decision-oriented management theory who turn up their noses at such an approach, especially when it comes along with a valuation label. The profound aversion to this methodology becomes almost corporeal while reading some of the (especially German) standard textbooks on corporate valuation. The fact however is that the comparable companies analysis enjoys great popularity all over the globe. There is almost no valuation in practice that does not use comparables at least as a plausibility check. Every analyst report, every fairness opinion contains a multiples analysis. And they are even more common at top management level - probably more decisions are based upon multiples than on DCF valuations. The notion of evaluating new matters based on comparable situations and facts is deeply rooted in us. If people buy a piece of land or a new home or rent an apartment, they retrieve information on price or rent per square foot/ yard/ meter from online real estate portals on the web. Of course, every piece of land, every house and every apartment is unique. Nevertheless, the market metrics, here average price or rent per square foot/ yard/ meter serve as an anchor for our valuation. Discounts and premiums are used to account for specific features of the real estate. The same applies to the sale or the purchase of a used car. Here too, every car is different, but based on model, age, mileage and extras, a range of prices for comparable cars can be derived quite easily. <?page no="53"?> 3.1 Standard Multiples 53 The same principle stands behind the comparable companies approach. It is therefore easier to understand and easier to explain than a DCF valuation analysis. Compared to the comprehensive assumptions we must make to forecast and discount future free cash flows, a statement like “the current market rate for companies in this industry is 6 times EBITDA” implicates a tremendous reduction of complexity, leading also to an easier communication. Addressees of corporate valuations are for the most part persons without a major in this area during their studies. And even though (or perhaps exactly for that reason) these persons are usually very successful: Experienced entrepreneurs for example or senior managers of large international conglomerates. The latter are sometimes deeply rooted in the topic, but they might have to report to people that are not and are therefore usually very open for messages that are easy to understand and easy to deliver. In valuation practice, many discussion rounds between adviser/ investment banker and client, but also within the team of advisers center for hours on assumptions of the right top line growth rate, future profitability ratios, the appropriate beta and the derivation of the upper and the lower end of the range for the value, until at some point in the discussion someone comes up with what she or he thinks is the crucial question: “What does this imply in terms of the EBIT/ EBITDA or sales multiple? ” There are two possible options for the evaluator. You can either constantly repeat that each company is different and neglect multiples or you can include a multiples analysis as a standard in your repertory, because people will ask for multiples anyhow and the analysis of the market valuation of comparables will usually lead to additional insights. And finally, as easy as the multiples approach is to implement, as easy is its misuse. This alone is a good reason to get an own idea on which companies are comparable and what all affected the stock prices of the comparable companies. 3.1 Standard Multiples P/ E Multiples The price/ earnings multiple is the most common performance evaluation standardization of quoted companies: <?page no="54"?> 54 3 Comparable Companies Analysis 𝑃𝑃 𝐸𝐸 ⁄ = 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑁𝑁𝑅𝑅𝑅𝑅 𝐼𝐼𝑅𝑅𝐼𝐼𝑊𝑊𝑅𝑅𝑅𝑅 = 𝑃𝑃𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅 𝐶𝐶𝑅𝑅𝐸𝐸 𝑆𝑆ℎ𝐶𝐶𝐸𝐸𝑅𝑅 𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 𝐶𝐶𝑅𝑅𝐸𝐸 𝑆𝑆ℎ𝐶𝐶𝐸𝐸𝑅𝑅 P/ E multiples normally play only a minor part in a comparable companies analysis. The reason is that the net income 36 of the companies included in the analysis is affected by different accounting rules and/ or policies, different tax regimes and tax rates as well as different leverages so that the bottom line of the income statements is not a suitable input variable for a comparable companies analysis. Example (continued) Returning to our example above, if the net income of the company is $75 million, the P/ E multiple will amount to 15 (market value of equity of $1,125 million divided by $75 million). In addition to different leverages and accounting policies, the P/ E multiple also reflects different expected growth rates. Companies with a higher expected growth rate will, ceteris paribus, have a higher P/ E ratio. The expected earnings growth rate can be obtained from services like Bloomberg or Value Line. Based on price per share, earnings per share and expected annual growth of earnings per share, the price/ earnings to growth (PEG) ratio can be derived as follows: 𝑃𝑃𝐸𝐸𝐺𝐺 = 𝑃𝑃 𝐸𝐸 ⁄ 𝐸𝐸𝐸𝐸𝐶𝐶𝑅𝑅𝐼𝐼𝑅𝑅𝑅𝑅𝐸𝐸 𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐶𝐶 𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 𝐺𝐺𝐸𝐸𝑊𝑊𝐹𝐹𝑅𝑅ℎ 𝑅𝑅𝑅𝑅 𝑃𝑃𝑅𝑅𝐸𝐸𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅 Example (continued) The expected earnings growth rate of our company is 10%. The PEG ratio amounts to 1.5 (P/ E of 15 divided by 10). The PEG ratio of comparable companies can help us to get a first idea as to whether a quoted company is overor underpriced on the market: 𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝑊𝑊𝑅𝑅 𝑃𝑃𝐸𝐸𝐺𝐺 𝑊𝑊𝑜𝑜 𝐶𝐶𝑊𝑊𝑅𝑅𝐶𝐶𝐶𝐶𝐸𝐸𝐶𝐶𝐷𝐷𝐶𝐶𝑅𝑅 𝐶𝐶𝑊𝑊𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 × 𝐸𝐸𝐸𝐸𝐶𝐶𝑅𝑅𝐼𝐼𝑅𝑅𝑅𝑅𝐸𝐸 𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐶𝐶 𝐺𝐺𝐸𝐸𝑊𝑊𝐹𝐹𝑅𝑅ℎ 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅 𝑃𝑃𝑅𝑅𝐸𝐸𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐶𝐶𝑊𝑊𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅𝐸𝐸 𝐸𝐸𝑅𝑅𝐶𝐶𝐶𝐶𝐸𝐸𝐴𝐴𝑅𝑅𝐸𝐸 = 𝐸𝐸𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑃𝑃 𝐸𝐸 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊 𝑜𝑜𝑊𝑊𝐸𝐸 𝐶𝐶𝑊𝑊𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅𝐸𝐸 𝐸𝐸𝑅𝑅𝐶𝐶𝐶𝐶𝐸𝐸𝐴𝐴𝑅𝑅𝐸𝐸 ⁄ Comparing target P/ E and actual P/ E ratio will give us a first answer. 36 Net income and earnings per share are typically adjusted for extraordinary and non-recurring items. <?page no="55"?> 3.1 Standard Multiples 55 Example (continued) The average PEG ratio of comparable quoted companies amounts to 1.2. Therefore, the target P/ E ratio for our company would be 12 (1.2 times 10). The actual P/ E ratio of 15 indicates that the company may be overvalued at its current share price. In case you feel uncomfortable with the linearity assumed between the P/ E ratios and the expected annual growth rates of the comparable companies, you can get the standard deviations for the consensus forecasts from the services and run a non-linear regression and apply the results on the company you analyze. EBIT and EBITDA Multiples EBIT and EBITDA multiples are typically the core of a comparable companies analysis. Both EBIT and EBITDA appear at first glance to be unaffected by taxes. However, we show at the end of this section that taxes still have an effect. However, it is much smaller than for P/ E ratios, though, so companies from different tax jurisdictions can be compared. Different leverages do not influence them as they are before interest expenses. We find EBITDA multiples more often in valuation practice as the EBITDA is compared to the EBIT also not affected by different depreciation policies and practices. But EBIT multiples remain quite common, especially if detailed information on depreciation are not easily accessible. 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 𝑀𝑀𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅 = 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸 𝑀𝑀𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅 = 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸 Example (continued) Let’s assume our company has an EBITDA of $200 million and an EBIT of $150 million. At an enterprise value of $1,500 million as derived above, this translates into an EBITDA multiple of 7.5 ($1,500 million divided by $200 million) and an EBIT multiple of 10 ($1,500 million divided by $150 million). Multiples can be calculated using data (i.e. EBITDA or EBIT) of the last finalized business year, current data (last twelve month or expected EBIT- <?page no="56"?> 56 3 Comparable Companies Analysis DA or EBIT for the current business year) and projected data (EBITDA and EBIT for the next business year or even for two years ahead). We will examine the EBITDA multiple, which comes along quite simple or even dull, in more detail. In chapter 2.2.4 when analyzing the terminal value, we learnt that: 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 𝑡𝑡+1 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 − 𝑊𝑊 If we now assume that the company we analyze already generates from year 1 onwards free cash flows that grow at a constant rate forever, then t+1 becomes t=1 and the terminal value will equal the enterprise value: 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 1 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 − 𝑊𝑊 We also know from our analysis in chapter 2 that the free cash flow can be rewritten in the following form: 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 − (𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝐸𝐸𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅 + 𝐼𝐼𝑅𝑅𝐼𝐼𝐸𝐸𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅 𝑊𝑊𝑊𝑊𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅𝑊𝑊 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 − 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅) = (𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 − 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅) × (1 − 𝑅𝑅) − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 × (1 − 𝑅𝑅) − 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 × (1 − 𝑅𝑅) − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 = 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝐸𝐸𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅 + 𝐼𝐼𝑅𝑅𝐼𝐼𝐸𝐸𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅 𝑊𝑊𝑊𝑊𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅𝑊𝑊 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 − 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 Inserting this term into our equation for the enterprise value above leads to: 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 × (1 − 𝑅𝑅) − 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 × (1 − 𝑅𝑅) − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 − 𝑊𝑊 If we now divide both sides of the equation by EBITDA, the left side of the equation represents the EBITDA multiple (Enterprise Value/ EBITDA), and the right side of the equation is the enterprise DCF valuation formula for a company with constant growth from the first year, divided by EBITDA: 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 = (1 − 𝑅𝑅) − 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 × (1 − 𝑅𝑅) − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 − 𝑊𝑊 DCF valuation and EBITDA multiple valuation can be transformed into each other. The same exercise can also be performed for EBIT multiples. <?page no="57"?> 3.1 Standard Multiples 57 The simple-looking EBITDA multiple suddenly turns into a quite informative measure. We like the expression of Bretzke, who described this in a slightly different setting as the “hidden intelligence of a rule of thumb”. 37 The denominator of the right side of the equation above shows that the EBITDA multiple will increase the lower the WACC and the higher the growth rate g will become. The numerator reflects that the EBITDA multiple will increase if depreciation and reinvestment decrease. And finally, even though EBITDA is a measure before taxes, a statement regarding the effect of taxes on the EBITDA multiple is possible: The lower the tax rate, the higher the multiple. Sales Multiples Sales multiples are especially used when the company being valued is a company in difficulties or a start-up company, i.e. a company with either unusually low or negative earnings. This is also the main danger in the use of sales multiples: The fact, that every company must generate positive free cash flows at some point in the future to have a positive value is often forgotten in the heat of the moment. In the valuation of mature companies, sales multiples are also routinely determined, since the top line of the profit and loss statement is (in most, not in all cases) the figure with the least impact of innovative interpretations of accounting rules. The sales multiple is defined as: 𝑆𝑆𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅 𝑀𝑀𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅 = 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑆𝑆𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅 In practice, you still find occasionally the relation of equity value to sales instead. The prevailing opinion however is that this procedure is not consistent as it leads to low sales multiples for companies with a high leverage and makes the aggregation of sales multiples of companies with a different leverage difficult, if not impossible. Example (continued) If the sales of our company are $1,200 million, the sales multiple is 1.25 (enterprise value of $1,500 million divided by $1,200 million sales). There is also much more in a sales multiple than people think at a first glance. Let’s convert the sales multiple and a DCF valuation into each 37 Bretzke, Risiken in der Unternehmensbewertung, in: Busse von Colbe/ Coenenberg, Unternehmensakquisition und Unternehmensbewertung, Grundlagen und Fallstudien, 1992, 143 ff. <?page no="58"?> 58 3 Comparable Companies Analysis other. As per the enterprise DCF method, the enterprise value of a company with a free cash flow growing with a constant rate from year 1 onwards can be calculated as follows: 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 − 𝑊𝑊 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 × (1 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅) 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 − 𝑊𝑊 If we divide both sides of the equation by sales, we get the sales multiple on the left side (enterprise value/ sales) and the corresponding enterprise DCF formula divided by EBITDA on the right side of the equation: 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑆𝑆𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 𝑆𝑆𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅 × (1 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅) ⁄ 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 − 𝑊𝑊 = 𝐸𝐸𝑜𝑜𝑅𝑅𝑅𝑅𝐸𝐸-𝐸𝐸𝐶𝐶𝐸𝐸 𝑅𝑅𝐶𝐶𝑅𝑅𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 × (1 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅) 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 − 𝑊𝑊 The sales multiple increases as the weighted average cost of capital (WACC) decreases, the growth rate g increases, the after-tax operating margin increases and the reinvestment rate decreases. Other Multiples You will come across price/ book multiples, where the market value of the equity is divided by the book value of the equity (especially for financial services companies). In addition, there are industry-specific multiples, where usually the enterprise value is set in relation to figures like gallons or hectoliters of a beverage or tons of steel produced, the number of hits on a website or the number of subscribers, just to name a few examples. The multiples can usually also be set in relation to the three components that influence the result of a DCF valuation: risk (WACC), growth (g) and future free cash flows. Example (continued) Let’s assume our company’s book value of equity amounts to $500 million. The price/ book multiple amounts then to 2.25 (market value of equity of $1,125 million divided by book value of equity of $500 million). The company produces 7.5 million hectoliters of a beverage. This translates into a multiple of 200$ per hectoliter (enterprise value of $1,500 divided by 7.5 million hectoliters). <?page no="59"?> 3.2 Finding Comparable Companies 59 3.2 Finding Comparable Companies In many cases, it is obvious which companies are comparable and should be included in a comparable companies analysis. Even though the large car manufacturers differ in their model range and their presence in certain geographical markets, it would be apparent that all of them should be included in a comparable companies analysis for a valuation of Toyota or BMW. But what if we want to do a comparable company analysis for a niche company like Tesla? Or for high-tech specialists in blockchain or electronic price displays at gas stations? Then the question arises whether there are any comparable companies at all. The selection of the comparable companies plays a vital role in this valuation approach. The decision which companies to include should be based on the objective of the analysis, which is to derive market multiples of companies with a comparable potential to generate future free cash flows, a comparable growth potential and a comparable risk. The basis for the selection of comparable companies should be a clear understanding of the company being valued. To get there, the same steps as described in chapter 2.2.1 must be taken. Without a good knowledge of the company’s products, market position and its value chain as well as all companies that potentially come into consideration to be comparable, the analysis will lead nowhere. The seemingly advantage of a lower effort compared to a discounted cash flow analysis (no explicit forecast of future free cash flows necessary) disappears here and can even switch completely. A good comparable companies analysis is just as comprehensive and time-consuming as a discounted cash flow valuation. A thorough understanding of the company being valued and its peers is essential for the explanation of the multiples as well as the differences in the multiples between the companies included in the analysis. Starting point in finding comparables are typically the company’s competitors. Many companies disclose them in their filings. Bloomberg and other services including free services like Google Finance and Yahoo Finance provide comparable companies (which usually cannot be adopted without any changes). Market surveys or even catalogues of trade fairs are another good source for finding comparables. Typically, you start with a long list that is being reduced step by step to a short list containing companies with for example similar products, production methods, similar distribution systems, similar research and de- <?page no="60"?> 60 3 Comparable Companies Analysis velopment activities and similar end customers. Also, company size, profitability, growth potential and risk structure should be comparable. Correlation analyses can help to determine whether companies are comparable. In principal companies from other industries can also be taken into consideration, if they have a similar potential to generate future free cash flows, a similar growth perspective and a similar risk. Typically, these companies are only referred to in case there are not enough comparables within the industry of the company being valued. 3.3 Preparation of Figures As the comparable companies are quoted on a stock exchange, there is usually access to comprehensive company data. The websites of the companies are the first port of call for facts and figures. In addition, the feebased services like Bloomberg, but also free services provide company data. Bases for the derivation of multiples are typically:  figures of the most recent completed business year,  last twelve month (LTM) or trailing twelve month(TTM) figures,  forecast for the current business year  consensus forecasts for the next two business years. In case of deviating business years, the data should be made comparable by a so-called calendarization exercise. Example: If the business year ends on March 31 and we want to make sales or EBITDA comparable to a company where the business year equals the calendar year, we take 3/ 12 of the business year that ended on March 31 in the relevant calendar year and add 9/ 12 of the business year ending on March 31 of next year. If you analyze high-growth companies, this can make a huge difference. Last twelve months (LTM) or trailing twelve months (TTM) figures are derived in a similar way. If we have a third quarter report, we add to the figures for the first three quarters the corresponding data of the last quarter of the preceding business year. The easiest way to do this in practice is to add the figures of the first three quarters to the figures of the last finalized business year (giving you seven quarters) and deduct the figures for the first three quarters of last year (typically provided in the current report on the first three quarters). Extraordinary and non-recurring items should be accounted for (normalization or exclusion). Quoted companies normally provide information on these items in their annual reports in the section where the earnings per <?page no="61"?> 3.4 Derivation of a Value Range 61 share are explained. As in all normalizations, the evaluator should form her or his own judgement as to whether the items presented are truly non-recurring or extraordinary. There is typically a very broad scope for interpretation in this area. To give an example, think about management stock options for young, high-growth companies. Many young quoted companies add back these costs when calculating earnings per share. And this is, to put it politely, debatable. 3.4 Derivation of a Value Range Once we have defined the universe for the comparable companies and prepared the figures, the next step is a technical one, the calculation of the multiples. 38 The final move, the derivation of a value range based on the different multiples, is as in the DCF valuation methods often more art than science. First, we will get a range for every multiple calculated (sales, EBITDA, EBIT etc.). Let’s take the EBITDA multiple as an example. If we analyze ten comparable companies, we will have ten different EBITDA multiples. Let’s assume that the range for the multiples is between 4.2 (lower limit of the range) and 18.7 (upper limit of the range). There is not much we can do with a wide range like this. Therefore, as a next step we would examine whether there are any outliers. Let’s further assume that nine multiplies range between 4.2 and 8.5, implying that the 18.7 is an outlier. We would then eliminate the outlier and narrow the range down to 4.2 till 8.5. In the following step, mean and median are calculated. Let’s assume this leads to results of 6.5 and 6.4 (without the outlier). Now, if the two companies that we believe are most comparable to the company being valued have multiples of 6.25 and 6.75, we would define that as the range for the EBITDA multiple. Hence, we would apply this range on the data of the company being valued (i.e. multiply the company’s EBITDA by 6.25 and 6.75) and get to a range for the enterprise value based on EBITDA multiples of comparable quoted companies. The same procedure would be applied to all other multiples, leading to a range for every multiple considered. These ranges are then transformed into a range for the enterprise value. The standard format chosen for this exercise in practice is the so-called football field format. 38 There are templates available on the web (just google for them). The templates that come along with Rosenbaum/ Pearl, Investment Banking, 3 rd ed., are very comprehensive and give an excellent impression as to what investment banks and consulting firms use. <?page no="62"?> 62 3 Comparable Companies Analysis Exhibit 12: Football Field Format The football field format also works well for the presentation of the results of different valuation approaches (discounted cash flow, comparable companies analysis, precedent transactions, etc.). Self-Test [1] What is the advantage of EBITDA multiples compared to EBIT multiples? [2] How does the profitability of a company get into the sales multiple? <?page no="63"?> 4 Precedent Transactions Analysis Learning Objectives  Recognize the precedent transaction analysis as a variant of the multiple-based valuation approach, based on “done deals” or announced transactions.  Learn about and describe the advantages, disadvantages and characteristics of this approach compared to the comparable companies analysis. As the comparable companies analysis, the precedent transactions analysis is a multiple-based valuation approach. The basic idea is the same: Companies with a similar potential for future free cash flows, a similar growth perspective and a similar risk structure of future free cash flows should be priced comparably in efficient markets. Other than in the comparable companies analysis, the precedent transactions analysis does not use stock market valuation as a reference point. It uses prices paid or offers made in acquisitions of comparable companies. The multiples derived from these prices paid in “real deals”, i.e. the acquisition of the majority or even 100% of comparable companies, take into consideration two items that are not included in the multiples derived from stock prices of comparable companies, as these prices refer to transactions of small shares in the company only:  Control premium  Synergies. The control premium is the amount an acquirer is willing to put on the table on top of the price per share for a quoted company for obtaining the majority in the company and being able to actively influence the potential to generate future free cash flows, growth and risk by actions he can take as a majority or 100% shareholder. The market price of stocks does not reflect this premium - only minorities are traded at stock exchanges. Example If the offer price per share is $50 and the share price amounted to $40 before the offer was launched on the market, the control premium is $10 per share or 25% ($50 divided by $40 minus 1). <?page no="64"?> 64 4 Precedent Transactions Analysis Synergies that could be realized by a strategic investor with the company being valued are also not included in the stock price (unless an actual takeover offer of a strategic acquirer is on the table). They are however included in the prices paid (or offered) in transactions of majorities or 100% of comparable companies and multiples derived from these transactions. As the comparable companies analysis, the precedent transactions analysis belongs today to the standard repertory of corporate valuation. This approach will, ceteris paribus, lead to higher multiples as control premiums and synergies are taken into consideration. Like the comparable companies analysis, in the precedent transactions analysis the selection of the transactions to be included is vital for the calculation of the multiples. Meaningful multiples can only be derived from transactions of companies with a similar potential to generate future free cash flows, a similar growth perspective and a similar risk structure. Without access to fee-based services you will be at your wits’ end quite soon, as it is very tedious to collect all the relevant data on the web (yet, this might change in the next years). Fee-based services 39 provide an easy access to “all you need”, i.e. all publicly available data on all transactions around the globe in all industries. Sector/ industry teams in investment banks and consulting companies usually maintain an own database on transactions in their industry (based on own research and data from feebased services), so that transaction multiples are available at the touch of a button. In absence of such luxury, the available data on a comparable transaction must be prepared in a first step before they can be used in the calculation of multiples. Especially if the target company (the company that was acquired in the comparable transaction) was a private company at the time of the acquisition, the obtainable data will most likely be incomplete. Not all the input data commonly used in a multiples analysis (sales, EBITDA, EBIT, net income, book value) might be available, nor will information on non-recurring and extraordinary items be at hand. In case the target company was quoted at the time of the acquisition, the LTM data for the standard parameters (sales, EBITDA, EBIT, net income, book value) should be determined in a first step. 39 Following is a selection in alphabetical order (this enumeration should not be considered as an assessment; we just mention the databases we use and worked with in the past): Bloomberg, Mergermarket, SDC, Zephyr. <?page no="65"?> Precedent Transactions Analysis 65 Enterprise value and equity value will not be derived based on the number of shares outstanding multiplied by the share price as in the comparable companies analysis. Instead the transaction value, which can typically be taken from the databases, will serve as a basis. However, it is often not clear whether the transaction value published refers to the enterprise value or the equity value, especially for transactions in private companies. An own research of the source data is usually recommendable. Example Company A paid $500 million for 80% of the equity of company B. The equity value of company B at the time of the acquisition then was $625 million ($500 million divided by 80%). If the interest-bearing debt at the time of the acquisition was $200 million and excess cash amounted to $25 million, the enterprise value was $800 million ($625 million equity value plus $200 million interest-bearing debt minus $25 million excess cash). There are more possible sources for mistakes in preparing the data. The following questions should be investigated:  Was the transaction a majority takeover? If not, it can be considered to exclude the data of this transaction from the analysis - a control premium was most likely not paid.  Were 100% of the shares acquired? If not, do the published information on the purchase price or the transaction value relate to 100% of the company or just to the share acquired? Make sure to translate the number to 100% of the shares if necessary.  Were parts of the purchase price paid in shares of the acquiring company? If so, the conversion ratio and the share prices on the day before the announcement of the transaction need to be obtained. We also need the interest-bearing debt and the cash balance at the date of the transaction to be able to derive transaction multiples. The universe of the potential multiples does not differ from those described in chapter 3.1. Example Company C acquired the entire share capital of company D for a total consideration of $200 million in cash plus 2 shares of company C for every 5 shares of company D. The share price of company C on the day before the announcement was $30. Company D had 15 million shares outstanding. <?page no="66"?> 66 4 Precedent Transactions Analysis Company C had to issue 6 million new shares (15 million divided by 5 times 2), corresponding to a value of 180 million (6 million shares multiplied by the share price of $30). Together with the cash consideration of $200 million, the total compensation paid amounted to $380 million for the entire equity. Net debt at the time of the transaction must be added to the equity value of $380 million to get to the enterprise value. Comparing the results of the comparable companies analysis and the precedent transactions analysis will give us an indication on the control premiums paid in the industries analyzed. For some transactions (especially larger ones with quoted targets) the expected synergies are disclosed, so that the transaction multiples can be broken down into a multiple with and a multiple without synergies: 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 𝑀𝑀𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅 (𝐹𝐹𝑅𝑅𝑅𝑅ℎ𝑊𝑊𝐸𝐸𝑅𝑅 𝑆𝑆𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅𝑅𝑅) = 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝐿𝐿𝐸𝐸𝑀𝑀 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 𝑀𝑀𝐸𝐸𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅 (𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝑆𝑆𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅𝑅𝑅) = 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝐿𝐿𝐸𝐸𝑀𝑀 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐷𝐷𝐸𝐸 + 𝐸𝐸𝐸𝐸𝐶𝐶𝑅𝑅𝐼𝐼𝑅𝑅𝑅𝑅𝐸𝐸 𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐶𝐶 𝑆𝑆𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅𝑅𝑅 Example Company E acquired company F at an enterprise value of €800 million. LTM EBITDA of company F was €100 million. The management of company E states that it expects to realize annual synergies because of this transaction in the amount of €25 million. The EBITDA multiple without synergies is 8 (€800 million divided by €100 million), the EBITDA multiple with synergies amounts to 6.4 (€800 million divided by €125 million). The selection of comparable transactions typically starts with analyzing deals in the industry of the company being valued. As in the comparable companies analysis, a deep understanding of the products or services, the competitive position and the value chain of the company being valued as well as the target companies in the comparable transactions is inevitable for the derivation of meaningful and reliable multiples. A precedent transactions analysis is more than a pure collection and compilation of transactions on a spreadsheet with the subsequent calculation of means and medians. Each target company must be analyzed and compared carefully with the company being valued to conclude, whether it is truly comparable regarding the criteria just mentioned as well as size, risk and growth <?page no="67"?> Precedent Transactions Analysis 67 potential. Furthermore, it needs to be analyzed which factors of the company being valued compared to the peer group should enhance and which should reduce value and how this should be reflected in the multiples. In addition, it should be taken into consideration that in a precedent transactions analysis we work with historical data and not with current stock prices as in the comparable companies analysis. It does not make much sense to use multiples based on fire sales in 2021 during the Corona crisis The market conditions at the time of the comparable transactions should ideally be comparable with the market conditions at the time of the valuation. In general, recent transactions in the past two to three years should receive a higher weight than older transactions. However, if there were no comparable transactions in the past years, the older deals will still be analyzed as in most cases at least trends of an industry can be illustrated. Furthermore, attention should be paid to the qualitative factors of the transactions analyzed. Beauty is in the eye of the beholder. A financial sponsor will have a different view on a target company than a strategic investor with the possibility to realize synergies. Even though there have been market conditions when financial buyers could outbid strategic buyers, for example when acquisition financing was extremely cheap and easily available, or when the target company was a good add-on to another portfolio company (in this case the financial sponsor acted as a strategic investor). The way the target company was sold also has an impact on the purchase price achieved and consequently on the multiples derived from that price. Prices paid in a hostile takeover usually exceed those paid in a merger of equals, prices achieved in a global competitive auction process normally exceed those accomplished in a negotiated deal between two parties with almost no competitive tension. Self-Test [1] Why are the multiples derived from a precedent transactions analysis typically higher than those calculated based on publicly quoted comparable companies? [2] You perform research on comparable transactions and come across data from a deal where 5% of the shares in a company were sold. How do you handle this? <?page no="69"?> 5 Further Valuation Methods Learning Objectives  Get an overview of further corporate valuation approaches in valuation practice.  Define and determine the free cash flow to equity and understand the equity DCF valuation approach. In the preceding three chapters, we introduced the enterprise DCF valuation approach, the comparable companies analysis and the preceding transactions analysis. These are the three most common methods for corporate valuations in practice. However, you will occasionally come across further methods. They are partly variants of the three main approaches already discussed and partly independent approaches. The following discussion of  LBO (leveraged buyouts) valuation,  Option-based valuation,  Asset-based valuation,  APV (adjusted present value) valuation, and  Equity DCF valuation is a selection and brief description of further methods of corporate valuation and not meant to be exhaustive. 5.1 LBO Valuation LBO stands for leveraged buyout(s), the largely debt-financed acquisition of companies as usually practiced by private equity investors. Apax, Apollo, Blackstone, Carlyle, CVC, KKR, and TPG Capital belong to the biggest players in this industry. The websites of these companies provide information on their investment focus, portfolio companies and their investment approach. There are numerous other large, medium-sized and small private equity houses. Despite some gradual differences between the players, the business model of private equity can be summarized as follows:  They invest (predominantly) other people’s money. Whose money? Investors in private equity funds are the large institutional investors, i.e. insurance companies, public and private pension funds, fund of funds, <?page no="70"?> 70 5 Further Valuation Methods sovereign wealth funds, high net worth individuals, trusts and private universities (mainly from the US).  The collected contributions of the investors are then typically structured in a fund with a term of 10 years. The management of the private equity fund invests this money by acquiring typically the majority or 100% of target companies. Besides the capital collected from the investors, debt is used in these acquisitions (bank loans, mezzanine debt, sometimes high yield bonds). The debt portion of the total financing package usually amounts to 60% - 70% and normally leads to an increase in the total leverage of the acquired company. Leverage is pushed to the limits of the debt capacity of the target companies in these transactions. That’s why they are called leveraged buyouts.  The acquired companies will be sold again, usually between three and seven years after their acquisition (target is typically maximum of five years), depending on the status of the company and the market. Acquirers can be other private equity players, strategic buyers, or the company can be sold in an initial public offering (IPO). At the time of the exit the equity portion is, in a successful deal, much higher compared to the equity portion at the time of the acquisition. This is achieved by using the cash generated during the holding period to pay down debt, by growth, and by other value-enhancing measures, e.g. improving the company’s operations.  The relation between the equity at the time of the exit and the equity invested in the deal at the time of the acquisition is called “cash return” and serves together with the IRR (internal rate of return) of the invested equity as the major key performance indicator in private equity. A large part of the compensation of the private equity fund managers is based on the IRR achieved in realized transactions. The fund management usually receives a fixed compensation of about 1% to 2% of the fund size to cover the fixed costs of the fund (salaries, office rent, travel expenses etc.). The variable compensation usually consists of a share of 20% of the investment profit achieved in a deal exceeding a hurdle rate of usually 8%. This part of the compensation is called “carried interest” and accounts for the much bigger portion of the total compensation of successful fund managers. The investors in the fund receive 100% of the hurdle rate (if achieved in the investment) plus 80% of the returns over and above the hurdle rate (the other 20% go to the management).  In case the investors are satisfied with the fund’s performance, they will consider investing in the next fund of the private equity house as well. Based on the expected return of the investors, the fact that on some investments a loss of the entire equity might occur and under <?page no="71"?> 5.1 LBO Valuation 71 consideration of own return expectations, a minimum expected internal rate of return on the invested equity of 20% to 25% over a five-year time horizon has become the market rate for private equity deals. This means that every potential acquisition will be analyzed by the private equity house as to whether under realistic assumptions it can generate an internal rate of return of (minimum) 20% to 25% on the equity invested over an average holding period of five years. This translates into cash returns of 2.49 (for 20% over five years) to 3.05 (for 25% over five years) - cash return being the relation between equity at the end of the holding period, i.e. at the exit, and equity at the beginning of the holding period, i.e. at the acquisition. Tripling the equity in five years as a rule of thumb. The LBO valuation now is based on this market rate. It is an iterative process to determine the maximum purchase price  at a given (realistic) forecast of the operating results,  taking into consideration the actual debt market conditions with the resulting borrowing options and the subsequent restrictions, and  achieving the minimum internal rate of return of 20% to 25% on the invested equity over a period of five years. To avoid any misunderstandings: Financial sponsors also carry out DCF valuations, comparable companies analyses and precedent transactions analyses. But if they present a new project to their respective investment committees, the managers must demonstrate that they can and how they intend to achieve the minimum target of 20% to 25% for the internal rate of return on the equity to be invested in the deal. Consequently, the LBO valuation should be a mandatory part of the preparation for a transaction if the potential buyers’ universe includes private equity funds. The objective of this exercise is to find out what can reasonably be expected in terms of purchase price offers from financial sponsors. Performing a LBO valuation requires advanced Excel (or alternative spreadsheet programs) modeling skills in case a template is not available. Most investment banks and consulting companies have own standard templates that are then adapted to the company being valued. There are however in the meantime templates available on the web with a reasonably good quality. 40 Rosenbaum/ Pearl provide a very good template that comes with their textbook. 41 Starting point for the model is typically the company’s forecast in the same format as it serves as a basis for a DCF valuation. Reference can be 40 https: / / www.macabacus.com/ excel/ templates/ lbo-model-long. 41 Rosenbaum/ Pearl, Investment Banking, 3 rd ed. <?page no="72"?> 72 5 Further Valuation Methods made to the remarks in chapter 2.2.2. The planning horizon is typically between seven and ten years. In a first step, the income statement is forecasted from sales to EBIT, the operating result. It is kind of an industry standard to perform this for different scenarios, e.g.  a management case based on the company’s budget,  a base case based on the financial sponsor’s analysis,  a downside case as a stress test, and  a banking or sponsor case that serves as a basis for the discussions with the financing banks. Depreciation, capital expenditures and working capital are budgeted as described in chapter 2.2.2 and work together with the results of the forecasts of the income statements as a basis for the derivation of budgeted balance sheets. The line items cash, interest-bearing debt and equity in the budgeted balance sheets are left blank in this step - they will be finalized after the next step in the process. The same applies to the budgeted cash flow statements, where the investments in fixed assets and in working capital can be forecasted in step one, whereas the financing parts (interest and change in interest-bearing debt) are left blank for the time being. In step two, assumptions on the probable purchase price and the financing structure are implemented into the model. Normally an EBITDA multiple customary in the industry of the company being valued is used to determine the purchase price for a first run of the model - this purchase price will be varied later to find out the maximum possible price at which the required internal rate of return on the invested capital can still be earned. In addition, sources and uses of funds must be budgeted. Sources of funds comprise equity and debt (bank loans, mezzanine and high-yield bonds), uses consist of the purchase price for the equity, the existing debt at the company being valued, and fees. The forecast of the debt structure requires deep insights into the present conditions of the corporate debt market. There are some fee-based services 42 , but without the input from financing experts it is difficult if not impossible to come up with robust assumptions on debt to EBITDA multiples acceptable to banks as well as the covenants associated with debt (e.g. minimum interest coverage ratio, i.e. EBIT/ interest expenses) in the current market environment. 43 Once the (preliminary) financing structure 44 is available, the blank spaces in the income statements (interest and taxes), cash flow statements 42 S&P Capital IQ LCD is one example. 43 For a detailed discussion of the LBO models please revert to chapters 4 and 5 of Rosenbaum/ Pearl, Investment Banking, 3 rd ed. 44 The financing structure will usually also be varied in an LBO valuation. <?page no="73"?> 5.2 Option-Based Valuation 73 (interest and change in interest-bearing debt and cash) and balance sheets (cash, interest-bearing debt and equity) can be completed and linked to each other. The last input necessary before running an analysis of the returns on the invested equity is an assumption on the purchase price that can be achieved when the company being valued is resold in five years. Special attention is given to the relation between the entry multiple (the purchase price paid for the company today as a multiple of EBITDA or EBIT) and the exit multiple (the projected EBITDA or EBIT multiple in five years when the company is sold) - the exit multiple should not be larger than the entry multiple (unless you have a very convincing story). Step three is an iteration, i.e. running the model with different input variables to come up with a defendable and bankable scenario. This scenario should be based on reasonable assumptions on the operating result of the company as well as the financing structure, and it should back up the 20% to 25% internal rate of return on the equity to be invested in the transaction. Sensitivity analysis varying entry multiple, exit multiple and time of exit (three, four, five years from now) are common and lead then to a range of values rather than a point estimate. 5.2 Option-Based Valuation The option-based valuation approach is rooted in a critique on the net present value method in capital budgeting. Simply calculating the net present value of a project is too static as it does not consider options that might come up during the life of the project. Consequently, the full potential of a project will not be reflected in its net present value, leading to an undervaluation. Let’s demonstrate this with an example. A company owns a patent for the fabrication of artificial meat. The net present value of all future free cash flows (t=1, 2, …, n) discounted back to today shall be €150 million, the necessary investment now (i.e. in t=0) shall be €200 million. The net present value of this project is negative (minus €50 million), the project should not be realized. This is what we all learn in our first corporate finance class. On the other hand, we would probably all agree that this patent still might have a value, despite the negative net present value if the investment is realized today. The reason for this is that we can wait with the investment until the demand for artificial meat has increased significantly, leading to higher future free cash flows. This is called the option to delay. Besides the option to delay there are other options discussed in the literature. The option to abandon in case the actual free cash flows are below <?page no="74"?> 74 5 Further Valuation Methods the budgeted free cash flows is one example. The option to expand is another one - the staged set-up of manufacturing facilities or entering further attractive markets under the condition that a first investment (with a negative net present value) is done today. These so-called “real options” increase the value of the projects, and the question now is how to account for them. In option-based valuations, the toolset developed for the valuation of financial options, i.e. call and put options on traded stocks, is applied to the valuation of the real options. A financial option constitutes the right (not the obligation) to either buy (call option) or sell (put option) a pre-agreed number of shares at a preagreed price during a pre-agreed period. Based on  current market price of the stock,  volatility of the stock’s returns,  expected dividends on the stock,  strike price, i.e. the price at which the option can be exercised,  life of the option, and  risk-free rate a value for the financial option can be derived. The standard models (binomial and Black-Scholes) determine the value of the financial option by creating a so-called “replicating portfolio” consisting of the stock and the risk-free asset (either an investment yielding the risk-free rate or borrowing at the risk-free rate) that has the same properties as the option, i.e. the same cash flows. The value of this portfolio is equal to the value of the option. The question now is whether this methodology can also be applied to the patent for the fabrication of artificial meat. We have all we need to determine the value for an option: Current market price of €150 million, strike price of €200 million, life equals the patent protection period, the risk-free rate is available and volatility and dividends can be estimated. So far this looks good, but we would be skating on thin ice with this value. Stocks are traded on stock exchanges; artificial meat is not. A replication of the option by the underlying asset and borrowing or lending at the risk-free rate assumes that the underlying asset is traded. A financial option constitutes the exclusive right to sell or buy a stock. But what does the patent constitute? Exclusivity on artificial meat? No, only exclusivity regarding a certain fabrication technology. And there will be competitors with alternative technologies that will enable them to have access to the market for artificial meat as well. The comparability to financial options is not given in our example, and there is no justification to apply the toolset developed for financial options here. The decision tree method could be an option to include real options in the capital budgeting decision. <?page no="75"?> 5.3 Asset-Based Valuation 75 Since the acquisition of companies is also an investment, there have been attempts in literature and practice to apply the real option valuation approach to corporate valuation as well. As of today, option-based valuation methods have not been established often in valuation practice compared to the standard valuation approaches. However, at the heyday of the dotcom boom there were some attempts to justify the supposedly “strategic” prices by real option valuations and it cannot be excluded that in times of high valuations this approach will appear more often. Before seriously considering using an option-based valuation approach in practice, the following points should be analyzed:  Does the acquisition (or the sale) of the company being valued entail an option with the typical asymmetrical pay-off structure at all?  What exactly constitutes the option? What is the underlying asset (a commodity, a drug, a technology)?  Does the option have a term?  Does the option guarantee exclusive access to the underlying asset?  Is the underlying asset traded at an exchange? If these conditions are met, it does make sense to consider option-based valuation methods. We would guess that in 99 out of 100 occasions this will not be the case. If there is practical relevance at all, then for companies with exclusive access to unutilized resources like oil, gas or precious metals. Templates for valuation can be found on the web. 45 5.3 Asset-Based Valuation In asset-based valuations, the value of the firm is not determined as an overall value based on future free cash flows or by applying multiples derived from comparable quoted companies or comparable transactions. The value is determined by valuing all assets the company owns individually as opposed to the overall valuation approaches we looked at so far. Deducting all liabilities will give us the equity value. There are different variants of asset-based valuations:  Book value, where appropriate with adjustments  Liquidation value  Replacement value 45 For example, on Damodaran’s website: http: / / pages.stern.nyu.edu/ ~adamodar/ New_Home_Page/ spreadsh.htm, the files equity.xls, natres.xls, project.xls. <?page no="76"?> 76 5 Further Valuation Methods Book values play a role in external accounting (derivation of goodwill, fair value etc.). You will also find them in regulations on the compensation of departing partners in a partnership or withdrawing shareholders in corporations. In case a company is being liquidated by the sale of all assets or being restructured by the sale of certain assets, attention should be paid to the fact that not all assets and liabilities may be captured in the company’s (pre-liquidation) balance sheet. Brand names are one example, redundancy payments arising from the liquidation decision are another one. The (pre-liquidation) balance sheets might be incomplete with the necessity to adjust them. Occasionally asset-based valuations (usually in the form of replacement values) can be found in practice in the context of purchase price negotiations regarding difficult to value companies with high losses. In these cases, it should be borne in mind that no reasonable buyer would replace exactly all the assets that in their current configuration generate the losses. At best the buyer would replace only parts of them. 5.4 APV Valuation The APV (adjusted present value) valuation is a variant of the enterprise DCF valuation method. The enterprise value is derived in steps. The normal first step is the calculation of the enterprise value under the assumption that the company is entirely debt-free. The future free cash flows are determined as described in chapter 2.2.2 in the enterprise DCF method. Instead of discounting the future free cash flows back to t=0 by applying the weighted average cost of capital (WACC) as in the enterprise DCF method, the APV method uses the hypothetical cost of capital the company would have in case it had no interest-bearing debt at all as the discount rate. In the special case of cash flows growing at a constant rate in perpetuity, the “unlevered” hypothetical enterprise value at zero interest-bearing debt is: 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑢𝑢 = 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝐹𝐹𝐶𝐶𝑊𝑊𝐹𝐹 1 𝐶𝐶𝐶𝐶 𝑢𝑢 − 𝑊𝑊 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑢𝑢 = 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 (𝐸𝐸𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝐸𝐸 𝐼𝐼𝑊𝑊𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅𝐸𝐸) 𝐶𝐶𝐶𝐶 𝑢𝑢 = 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 (𝐸𝐸𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝐸𝐸 𝐼𝐼𝑊𝑊𝑅𝑅𝐶𝐶𝐶𝐶𝑅𝑅𝐸𝐸) The (weighted average) cost of capital of the unlevered company (CC u ) are equivalent to the company’s cost of equity, since the weight for the cost of debt is zero. In calculating the cost of equity, both the risk-free <?page no="77"?> 5.4 APV Valuation 77 rate and the market or equity risk premium are given and not influenced by the leverage of the company. It’s only the beta that changes when the leverage is being altered. The higher the leverage, the higher the beta. To estimate the beta and the hypothetical cost of equity at zero interest-bearing debt, we will use the relations illustrated in chapter 2.2.3 between the levered and the unlevered beta: 𝛽𝛽 𝑢𝑢 = 𝛽𝛽 𝑐𝑐𝑢𝑢𝑃𝑃𝑃𝑃𝑃𝑃𝑐𝑐𝑡𝑡 1 + (1 − 𝑅𝑅) × 𝐷𝐷 𝐸𝐸 ⁄ 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝛽𝛽 𝑢𝑢 = 𝐸𝐸𝑅𝑅𝑅𝑅𝐶𝐶 𝑜𝑜𝑊𝑊𝐸𝐸 𝑅𝑅ℎ𝑅𝑅 𝐸𝐸𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝐸𝐸 𝑜𝑜𝑅𝑅𝐸𝐸𝑅𝑅 𝛽𝛽 𝑐𝑐𝑢𝑢𝑃𝑃𝑃𝑃𝑃𝑃𝑐𝑐𝑡𝑡 = 𝐶𝐶𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝐸𝐸𝑅𝑅𝑅𝑅𝐶𝐶 𝐶𝐶𝑅𝑅 𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊 𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝑊𝑊𝑅𝑅 𝑅𝑅 = 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝐸𝐸𝐶𝐶𝐸𝐸 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝐷𝐷 = 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 𝐸𝐸 = 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 Example You estimated the free cash flow of a company being valued at €100 annually with a growth rate of 0.5% in perpetuity. The risk-free rate is 1%, the equity risk premium 6%, the tax rate 25%, and the company’s current beta at a D/ E ratio of 0.5 is 1.2. The first step here would be to calculate the beta for the unlevered company. This leads to a value of 0.87 (1.2 divided by (1 plus 0.75 times 0.5)). The company’s cost of equity at zero interest-bearing debt amount to 6.24% (1% plus 0.87 times 6%). Discounting the €100 growing at 0.5% at a discount rate of 5.74% (the company’s hypothetical cost of equity at zero interest-bearing debt of 6.24% minus the growth rate of 0.5%) leads to a hypothetical enterprise value of the unlevered company of €1,743.26. The underlying idea behind the adjusted present value approach is to break up the enterprise value of the company into two parts. Part one is the value of the company’s operating activities; this is the first step just described. The second part is the value resulting from leverage, i.e. using debt in addition to equity to fund the company. This is the second step in the adjusted present value approach, and this second step should comprise the following elements:  The derivation of the so-called “tax shield”, the net present value of future tax savings resulting from the issuance of debt.  The calculation of the net present value of future bankruptcy costs resulting from the issuance of debt. <?page no="78"?> 78 5 Further Valuation Methods  Other effects caused by the choice of leverage, e.g. subsidies, hedges or issue costs. In most cases (both in practice and in literature) however only the tax advantage is taken into consideration in step two. This procedure is highly questionable. Especially when the leverage is high, the expected insolvency costs will not be a “quantité négligeable”, i.e. they cannot simply be ignored. The tax savings result from the deductibility of interest expenses from the tax base. Remember from your corporate finance class that this is the main advantage the use of debt has over the use of equity - the cost of debt reduces the tax base. Dividends paid to shareholders do not receive such a privileged treatment. This is the case in most tax authorities. There are special regulations all over the globe that should be accounted for appropriately when performing a valuation. As mentioned in chapter 2.2.3, in Germany for example only 75% of the interest expenses can be deducted from the tax base of the trade tax. In Brazil, to give another example, there is besides dividends an instrument called interest payments on net equity 46 which is tax deductible (and so reduces the tax advantage of debt over equity). To calculate the tax savings, we need the tax rate (in Germany about 26.5% for stock corporations, adjusted for the special regulation mentioned above), the pre-tax cost of debt (the interest rate agreed upon with the debt providers) and the amount of interest-bearing debt. The annual tax savings are discounted typically at the cost of debt (risk equivalence assumed; there are other approaches discussed in literature). In the special case of constant annual tax savings in perpetuity we get: 𝑃𝑃𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐶𝐶𝐸𝐸 𝑆𝑆𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 = 𝐸𝐸𝐶𝐶𝐸𝐸 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 × 𝑃𝑃𝐸𝐸𝑅𝑅-𝐸𝐸𝐶𝐶𝐸𝐸 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 × 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 𝑃𝑃𝐸𝐸𝑅𝑅-𝐸𝐸𝐶𝐶𝐸𝐸 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 = 𝐸𝐸𝐶𝐶𝐸𝐸 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 × 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 = 𝑅𝑅 × 𝐷𝐷 Example (continued) Let’s assume the company described has €950 interest-bearing debt and the tax rate of 25% would also be appropriate here. If we assume constant debt levels and annual tax savings in perpetuity, the value of the tax shield will amount to €237.5 (25% of €950, i.e. tax rate times interest-bearing debt). 46 Juros sobre o capital próprio. <?page no="79"?> 5.4 APV Valuation 79 Much trickier is the calculation of the expected bankruptcy cost resulting from the leverage. As mentioned, in most APV valuations this step is simply skipped. Damodaran gives examples in which he refers to Altman’s Z-score (probability of bankruptcy) and rough estimates for the direct and indirect cost of bankruptcy (as a percentage of the enterprise value). 47 Finally, special features like government subsidies should be brought into the equation. The enterprise value of a levered company using the adjusted present value approach is then: 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑢𝑢 + 𝑃𝑃𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐶𝐶𝐸𝐸 𝑆𝑆𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅 − 𝑃𝑃𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐶𝐶𝑅𝑅𝐼𝐼𝑅𝑅𝑅𝑅𝐸𝐸 𝐸𝐸𝐶𝐶𝑅𝑅𝑊𝑊𝐸𝐸𝐸𝐸𝐶𝐶𝑅𝑅𝐼𝐼𝐸𝐸 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅𝑅𝑅 ± 𝑅𝑅𝑅𝑅ℎ𝑅𝑅𝐸𝐸 𝐸𝐸𝑜𝑜𝑜𝑜𝑅𝑅𝐼𝐼𝑅𝑅𝑅𝑅 Example (continued) We estimate the direct and indirect cost of bankruptcy at 30% of the enterprise value. This would be an amount of €594.23 (30% of the sum of the unlevered enterprise value of €1,743.26 and the value of the tax shield of €237.5). At an estimate of 15% for the probability of bankruptcy, this will lead to expected bankruptcy cost of €89.13. The enterprise value amounts to €1,891.63: €1,743.26 enterprise value of the unlevered company plus €237.5 value of the tax shield minus €89.13 value of the expected bankruptcy costs. The APV approach does have its charm. It shows the sources of the enterprise value. Especially if you can forecast the interest-bearing debt in absolute terms (for example in LBO financing structures), the APV method shows its strength. A simple Excel table with total borrowings at the end of each period, interest rate, resulting interest expenses, tax rate and resulting tax savings, present value and sum of all present values is quickly set up. As shown in chapter 2.2.3, the enterprise DCF method works with the market value based relation of debt and equity and not with absolute amounts. Fluctuating annual total borrowing can be handled via annually fluctuating weighted average cost of capital (WACC), but this is not as user-friendly as in the adjusted present value (APV) approach. A great future was once predicted for the adjusted present value (APV) method. There were even expectations that the APV approach would replace the discounted cash flow approach one day in practice. This did not and probably will not happen. The pragmatic concept of determining the weighted average cost of capital (WACC) has prevailed so far, despite the imprecisions associated with it, especially when interest-bearing debt ratios are not stable. 47 See for example Damodaran, Investment Valuation, 3 rd ed., 398-422. <?page no="80"?> 80 5 Further Valuation Methods 5.5 Equity DCF Valuation Every country on the globe has its own history when it comes to corporate valuation. In Germany, the “Ertragswertverfahren” (earnings value method is the best translation we can come up to) was the prevailing methodology for corporate valuations, until in the early nineties the Anglo-Saxon enterprise DCF approach became more and more popular. In its original form, the term “earnings” had a wide scope and comprised all contributions to an objective that would provide utility to a valuation subject, i.e. the owners of the business or a potential buyer. Valuation practice however focused almost exclusively on financial surpluses and discounted them back to the valuation point. Hence, the earnings valuation method is like the DCF approach a net present value calculus. The financial surpluses relevant for the earnings valuation method as applied in practice are those surpluses that the shareholders are entitled to. Insofar there is, despite some arguments on this in literature, identity between the German earnings valuation method and the equity DCF approach. The amount the shareholders are entitled to is the free cash flow to equity (FCFE) that is derived as follows: Net income Plus: Depreciation Less: Capital expenditures Investments in fixed assets Less (Plus): Increase (decrease) in working capital Investments in working capital (without cash and short-term interest-bearing debt) Plus: New debt issues Loans, bonds and other interestbearing debt Less: Repayments of debt Loans, bonds and other interestbearing debt Free cash flow to equity (FCFE) Exhibit 13: Free Cash Flow to Equity The equity DCF method (like the German earnings value method) requires just as the enterprise DCF method a comprehensive company analysis as described in chapter 2.2.1, and based on this analysis an integrated planning of income statements, balance sheets and cash flow statements. The procedures outlined in chapter 2.2.2 must be supplemented <?page no="81"?> 5.5 Equity DCF Valuation 81 with a forecast of the interest-bearing debt and the interest expenses of the company being valued. The next step then is to discount the future free cash flows to equity back to t=0 at a risk-equivalent discount rate, the company’s cost of equity. As described in chapter 2.2.3, we start with the risk-free rate and add a premium. This premium is the market or equity risk premium multiplied with the company’s beta. The German earnings value method has adopted this procedure in the meantime. Originally the evaluators took, for good or for bad, much more degrees of freedom in determining the risk premium. Some had lists of criteria (e.g. attractiveness of the product program, degree of dependence on customers, expected development of the industry, dependence on key personnel etc.) and performed difficult to decrypt calculations that led to the risk premium. Others referred to risk premiums used in law-suits. By now, most valuations utilize the CAPM, i.e. make judgements on the riskfree rate, the market or equity risk premium and the company’s beta (or total beta). The equity value of the company (equivalent to the German earning value) is calculated as follows: 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = � 𝐹𝐹𝐶𝐶𝐹𝐹𝐸𝐸 𝑡𝑡 (1 + 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸) 𝑡𝑡 𝑐𝑐 𝑡𝑡=1 + 𝐹𝐹𝐶𝐶𝐹𝐹𝐸𝐸 𝑐𝑐 × (1 + 𝑊𝑊) (𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑃𝑃 − 𝑊𝑊) Cost of equity p are the cost of equity for the perpetuity that may differ from the cost of equity for the detailed planning period, where appropriate. The enterprise value then is: 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 + 𝑁𝑁𝑅𝑅𝑅𝑅 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 = 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 + 𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅-𝐸𝐸𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑊𝑊 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 − 𝐸𝐸𝐸𝐸𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ Instead of using the perpetuity approach to value the cash flows that occur after the detailed planning period as in the formula above, you can also apply an exit multiple approach as in the enterprise DCF method (see chapter 2.2.4). This was (and still is, where applied) however uncommon in the German Ertragswertverfahren. The equity DCF approach is by far less common in valuation practice compared to the enterprise DCF variant. It is however the default method for valuations of banks, insurance companies and other financial services operations. The enterprise DCF method would lead to difficulties here. “Operating result before interest” makes no sense for companies in these industries. Interest income and interest expenses are part of the operating result in the financial services sector. In addition, interest-bearing debt and cash belong to the operations of the business and have a different <?page no="82"?> 82 5 Further Valuation Methods character compared to manufacturing companies, where debt is one form of funding besides equity. Self-Test [1] Can you explain the differences between the adjusted present value method and the enterprise discounted cash flow method? [2] How does the equity discounted cash flow approach differ from the German earnings value approach? <?page no="83"?> 6 From Enterprise Value to Equity Value Learning Objectives  There is more between enterprise value and equity value than net debt. How to handle items that are not or not clearly equity, interest-bearing debt, working capital or part of the operating assets?  In addition to the on-balance-sheet items there are off-balancesheet issues that need to be accounted for when deriving the equity value from the enterprise value. 6.1 Cash and Cash Equivalents Each company needs a certain level of cash to keep its operations running. McDonalds and H&M (still) can’t get along without cash, and even companies that are only active in the B2B area and settle their payments cashless typically also maintain a small level of cash and cash equivalents. Adapting the macroeconomic terminology of the Keynesian theory of demand for money, this would be the transactions motive for holding cash. Since it is almost impossible to perfectly match cash inflows and outflows, and to provide for contingencies, most companies add a margin of safety to these levels - the precautionary motive for holding cash. Where exactly this level of cash is, depends on the company’s business and differs from industry to industry and by geography. These two parts of a company’s liquidity should be treated as working capital. In valuations where we have access to the management, we can analyze the cash position over a representative period to determine this cash level. If we have no internal information, we need to estimate it. In practice, in nine out of ten cases in the absence of better intelligence a value of zero is assessed, i.e. the entire balance of cash and cash equivalents is classified as non-operational. And this is, considering the increased use of cashless settlements, in most industries and most countries not a problem (though not in all). The part of the cash and cash equivalents exceeding the transactions and precautionary levels - the cash held for speculative motives pursuant to Keynes (which we call “excess cash”) - represents an additional value to the company’s shareholders. This part should be shown and valued separately. When performing the valuation with the enterprise DCF approach, this is done “automatically”. Basis for the derivation of the future free cash flows is the company’s EBIT, i.e. the earnings before interest <?page no="84"?> 84 6 From Enterprise Value to Equity Value (income and expenses) and taxes. Consequently, future interest income generated by the excess cash will not be part of the future free cash flows. The enterprise value is a value before excess cash. Enterprise value plus cash add up to the value available to both debt and equity providers, called “firm value” (see the exhibits in chapter 2.1). Please note that there is no DIN standard for valuation terminology. In this book, we use the term enterprise value in a sense that it is the value before excess cash, but some textbooks and practitioners use a different definition where enterprise value is the total of the value of the operations including excess cash. However, the clear majority uses the term “firm value” for this measure. Example A company projects an EBIT of $200 for t=1 and expects that the EBIT will grow at 0.5% annually in perpetuity. The company has no debt but holds a cash balance of $500. The WACC equal the cost of equity in this case and amount to 7.5% (risk-free rate of 1.5%, equity or market risk premium of 6%, beta of 1). The tax rate is 50%. EBIT after taxes is then $100. $100 divided by WACC minus the growth rate (7.5% minus 1%) will give us the enterprise value of $1,538.46. Adding the cash of $500 leads us to an equity value of $2,038.46. Albeit the equity DCF method starts at the net income in the derivation of the future free cash flows to equity. The consequence is that the interest income generated by the excess cash will become part of the future free cash flows to equity. The problem is that this future interest income will be discounted at the cost of equity if no adjustment is made. Cash and excess cash are normally invested in bank deposits, short-term money market papers and other short-term and liquid financial assets. Those are typically investments with little or even no risk (There are exceptions! ). Discounting the proceeds from these next to risk-free assets at the cost of equity, a measure that includes a premium for risk, is not consistent. Example (continued) Let’s assume the company projects to earn a return of 1.5% on the excess cash of $500, i.e. $7.5 annually. The EBT amounts to $207.5 then (EBIT plus interest income). The net income at a tax rate of 50% is $103.75. If we would discount this net income at the company’s cost of equity minus the growth rate, i.e. at 6.5%, we would get an equity value of only $1,596.15. This is $442.31 below the equity value determined using the enterprise DCF approach. <?page no="85"?> 6.2 Holdings in Other Companies, Non-Controlling Interests and ... 85 If this is done for simplification purposes when - as in many cases - the excess cash amounts to a very small percentage of the total assets and the enterprise value, this is not a problem. However, when companies like Apple hold several billions of dollars in cash, the procedure must be adjusted:  Either the proceeds from the excess cash should be discounted at a riskequivalent rate - if the beta of the assets the cash is invested in is zero at the risk-free rate, or  the future free cash flows to equity are cleaned up for interest income and the excess cash is valued separately. Example (continued) In our example a simplification argument cannot be made as the excess cash makes up almost 25% of the equity value. If we discount the $7.5 annual interest income at the risk-free rate of 1.5% (the $7.5 and the 1.5% are both pre-tax, discounting $3.75 at 0.75% will lead to the same result) instead of 6.5%, we will get a value of $500 for the cash, equivalent to the face value today. Adding the result of discounting the $100 net income without interest income at 6.5% ($1,538.46) leads us to the same equity value as calculated using the enterprise DCF method ($2,038.46). Alternatively, we can take the face value of the cash ($500) and add the $1,538.46 from discounting the net income cleaned up for interest of $100 at 6.5% (WACC minus growth rate). Basis for the valuation of excess cash is its market value. Adjustments may become necessary if the cash is held abroad and will be taxed when repatriated. This phenomenon is called “trapped cash” and almost regularly occurs when valuing US firms. When determining the value of a business, it is important to examine on a case-by-case basis whether a short-term repatriation of funds, with the associated taxation, is actually intended or whether the liquid funds can be used for overseas investment. 6.2 Holdings in Other Companies, Non-Controlling Interests and Other Assets Valued Separately Generally, holdings in other companies should be valued separately. This should also be applied on majority holdings, i.e. when the other company is part of the consolidated accounts. The consolidated company might have a completely different risk structure compared to the parent company, leading to possible mistakes in a consolidated valuation. However, in valuation practice not all information necessary might always be avail- <?page no="86"?> 86 6 From Enterprise Value to Equity Value able, or the process might be regarded as too time-consuming, if the number of companies included in the consolidated accounts is very large. Hence it is, despite the issues raised above, common business practice to base the valuation on the consolidated statements. In case the parent company holds a majority, but less than 100% in a company included in the consolidated accounts, accounting rules require a 100% consolidation and the recognition of a position called “non-controlling interest” (sometimes referred to as minority interest) in the company’s income statement and balance sheet. These positions account for the part of the profits and shareholders’ equity which economically “belong” to third parties. They should be interpreted as shares in the income and the equity of subsidiaries, not in the parent company or the group. In case the calculation of the enterprise value is done in accordance with common business practice based on the consolidated accounts and not based on a separate valuation of all companies of the group, this must be reflected when deriving the equity value from the enterprise value. Instead of: Enterprise value = Equity Value Plus: Cash Plus: Interest-bearing debt We get: Enterprise value = Equity value Plus: Cash Plus: Interest-bearing debt Plus: Non-controlling interests And: Equity value = Enterprise value Plus: Cash Less: Interest-bearing debt Less: Non-controlling interests When valuing non-controlling interests, please keep in mind that the values given in the financial statements are book values that should be replaced by the respective shares in the real values of the subsidiaries included in the consolidated accounts. This is easy when the subsidiaries are quoted on an exchange, as the actual share price can serve as an indicator for the derivation of the real value. In case of an absence of a stock quote, a DCF analysis should be performed. If the necessary information to run a DCF analysis is not available, the value of the subsidiary can be estimated based on a multiples approach (comparable companies analysis <?page no="87"?> 6.2 Holdings in Other Companies, Non-Controlling Interests and ... 87 and/ or precedent transactions analysis). And if this information cannot be obtained, the book value can serve as a last resort. In cases where the value of the non-controlling interests is low compared to the enterprise value, we can live with this imprecision. Example You calculated an enterprise value of €1,200 for a company based on its group figures. For simplicity, let’s assume the company has no cash and no interest-bearing debt. The company owns only 80% in one of its several subsidiaries. In the group balance sheet, a value of €20 for non-controlling interest is recognized. If we use this book value, we would get to an equity value for the company of €1,180 (€1,200 minus €20). You perform some research on the subsidiary. It is not quoted, and a forecast allowing a DCF valuation is not available. You discover however that companies comparable to the subsidiary are traded at 8 times EBIT, and that the subsidiary in question has reported an EBIT of €25 and net debt of €50. This would lead to an equity value of the subsidiary of €150 (8 times €25 equals €200 minus €50). 20% of the equity value would then be €30, and the equity value for the company being valued will amount to €1,170 instead of the €1,180 derived based on the book value for the non-controlling interest. Minority holdings should also be valued separately. If the company is quoted, the value can be calculated based on the most recent stock quote. If it is not quoted, a DCF analysis should be performed where possible. Complementary or alternatively, a valuation based on multiples should be conducted. To avoid double-counting, the proceeds from the minority holdings (income from equity affiliates) should be excluded when estimating the future free cash flows to the firm or to equity. There are manufacturing companies that operate their own financial services companies to finance the sale of their products. Car manufacturers are one example. Because of the totally different business structure (manufacturing of cars and financial services), a separate valuation is highly recommendable. Most car manufacturers provide the necessary information in their consolidated accounts. Apart from holdings in other companies, there are further assets that must be valued separately. Assets up for sale and the so called non-operating assets (assets that can be sold without influencing the operating cash flow) belong to these items. Unused property in an attractive downtown location would be an example for a non-operating asset of a manufacturing company. This asset would be valued separately with the <?page no="88"?> 88 6 From Enterprise Value to Equity Value expected proceeds from the sale. In case the sale can be realized in a couple of years only, the proceeds must be discounted. Tax effects resulting from the sale must be taken into consideration, i.e. reduce the value. This also applies to debt associated with non-operational assets. Proceeds from non-operational assets must be excluded from the calculation of future free cash flows to the firm or to equity to avoid double counting. Example A company owns real estate that is non-operational. The book value is $100 and the real estate can be sold for $200. The tax rate is 30%. There is interest-bearing debt on the real estate of $80, leading to interest-expenses of $4. The income from renting out the real estate is $10. Annual depreciation amounts to $5. For the calculation of the future free cash flows to the firm, the rental income and the depreciation must be excluded. For the calculation of the future free cash flows to equity, rental income, depreciation and the interest expense must be excluded. The gross proceeds from selling the real estate is $200, leading to a tax burden of $30 (30% on the capital gain of $100, the difference between the realized market value of $200 and the book value of $100) and net proceeds of $170. After repaying the debt, a value of $90 for the non-operating asset remains. In case the real estate can only be sold in two years from now, a separate NPV should be calculated with all cash inflows and outflows generated by the real estate, including rental income, taxes and proceeds from the sale. These future cash flows must be discounted at a risk-equivalent rate. Here we would go for the after-tax cost of debt as a reasonable approximation. We now get: Enterprise value = Equity value Plus: Cash Plus: Interest-bearing debt Plus: Non-operating assets Plus: Non-controlling interests And: Equity value = Enterprise value Plus: Cash Plus: Non-operating assets Less: Interest-bearing debt Less: Non-controlling interests <?page no="89"?> 6.3 Pension Obligations, Accrued Liabilities and Provisions 89 6.3 Pension Obligations, Accrued Liabilities and Provisions Future obligations resulting from pension promises to employees can account for a large portion of a company’s balance sheet total. Relevant for corporate valuations are primarily the so-called “defined benefit” pension promises made to the employees of the company being valued. These promises can be funded by setting up own pension plan assets or by a pension plan reinsurance. The following cases can occur:  The value of the pension plan assets exceeds the value of the future obligations from the pension promises. The pension scheme is overfunded.  The value of the pension plan assets is equivalent to the value of the future obligations from the pension promises. The pension scheme is fully funded.  The value of the pension plan assets is below the value of the future obligations from the pension promises. The pension scheme is underfunded.  There are no pension plan assets at all. The future obligations from the pension promises are unfunded. In most countries, it has become good business practice to set up a separate fund of pension plan assets to cover the obligations from pension promises made towards employees. Thus, you will usually come across overfunded, fully funded or underfunded pension plans. There are exceptions. In Germany for example no separate plan assets were set aside for pension promises for a long time. This was caused by the absence of legal requirements to fund pension schemes (as opposed to the US) and the (naive) assumption that the proceeds from this form of internal financing would be sufficient to make up for the liquidity necessary when the payments become due. Only in the last decades the companies slowly started to set up separate pension plan assets to fund the obligations. Nowadays, about 80% of the pension obligations of the German DAX companies are funded. 48 The average funding percentage of all pension promises in Germany is significantly below this mark, so that unfunded pension plans will be a topic in almost every valuation of a German company. To determine the magnitude of the underfunding, an actuarial expert opinion is necessary. Most annual reports of the DAX companies inform about the assumptions used in the actuarial appraisal, i.e. mortality tables, discount rates, expected growth rates for salaries and pensions, and expected return of the plan assets (where available). To a limited extent, sensitivity analyses on the impact of changes of key input parameters on the actuarial value are also provided. 48 You may argue that this is only another way of stating that 20% of the obligations are still unfunded. <?page no="90"?> 90 6 From Enterprise Value to Equity Value If the company being valued is not quoted, access to management is necessary to gain reliable information on the actuarial value of the pension obligations. The book values can only serve as very broad reference due to transitional German accounting regulations. If we have an overfunded pension scheme, it seems reasonable to add this surplus to the enterprise value. However, it should be investigated whether it is at all legally possible to get access to these assets. In addition, possible tax consequences must be considered. In some fiscal jurisdictions (e.g. US) high tax rates will be applied on withdrawals of assets from a pension plan. As an alternative, the overfunding (if significant) can be taken into consideration when forecasting the future retirement expenses (chapter 2.2.1 when you project the future income statements down to EBIT). The underfunded (or fully unfunded) amount is from an economic perspective the actuarial present value of the future cash outflows resulting from the pension promises (net of any proceeds from the plan assets). This amount must be deducted from the enterprise value when calculating the equity value - it is not available to the company’s shareholders. 49 We get the following relation between enterprise value and equity value now (it’s a journey from enterprise value to equity value, and we’re not there yet, so the equation will change as we proceed): = Equity value Enterprise value Plus: Interest-bearing debt Plus: Cash Plus: Non-controlling interests Plus: Non-operating assets Plus: Unfunded pension obligations And: Equity value = Enterprise value Plus: Cash Plus: Non-operating assets Less: Interest-bearing debt Less: Less: Non-controlling interests Unfunded pension obligations When calculating the future free cash flows to the firm, make sure that you do not double-count: Only the expected service costs should go into the projections, not the interest costs and other positions like actuarial gains and losses or expected returns of the plan assets, if the equity value 49 This calculation should be done on an after-tax basis. But be careful: Whenever the elimination of the underfunding does not save you taxes, pre-tax will equal after-tax. <?page no="91"?> 6.3 Pension Obligations, Accrued Liabilities and Provisions 91 is calculated based on the equation above. There is a debate in literature and in practice as to whether the unfunded amount of the pension obligations should be treated as a third component besides equity and interest-bearing debt with its own (after-tax) cost when calculating the weighted average cost of capital. Apart from pension obligations, there are other positions on the liabilities side of the balance sheet that are neither clearly interest-bearing debt nor part of the working capital. Provisions for one-time restructurings or risks resulting from large lawsuits are examples. Deutsche Bank’s provisions for (very likely) future fines, Bayer’s Glyphosat lawsuits and Volkswagen’s “Dieselgate”-caused future cash outflows come to our mind. For items like these, after-tax net present values, where appropriate calculated with probabilities of occurrence, should be estimated. These amounts should be treated as “debt-like” and deducted from the enterprise value to arrive at the equity value. Deferred taxes should be analyzed as to whether they are caused by operating assets, non-operating assets, non-deductible expenses or other events, and if at all and when they will lead to a cash outflow. 50 Tax loss carryforwards and tax credits are assets that should be valued separately (non-operating assets) and added to the enterprise value (net present value of future taxes saved). Our equation now looks like this: = Equity value Enterprise value Plus: Interest-bearing debt Plus: Cash Plus: Non-controlling interests Plus: Non-operating assets Plus: Plus: Unfunded pension obligations Other debt-like items For the equity value, we get: Equity value = Enterprise value Plus: Cash Plus: Non-operating assets Less: Interest-bearing debt Less: Less: Less: Non-controlling interests Unfunded pension obligations Other debt-like items 50 In many valuations, this will be immaterial. If not, please revert to chapter 20 of Koller/ Goedhart/ Wessels, Valuation, 7 th ed., 413 ff. <?page no="92"?> 92 6 From Enterprise Value to Equity Value 6.4 Off-Balance-Sheet Financing With the implementation of IFRS 16, lease liabilities are (finally) recognized on the balance sheet. For companies that do not publish their financial statements in accordance with IFRS 16,  the net present value of the lease obligation must be estimated and recognized as debt on the adjusted balance sheet,  the value of the right to use the asset must be estimated and recognized as an asset on the adjusted balance sheet,  the lease payments that reduced the operating income must be replaced by the depreciation of the asset, leading to a higher operating income. The information necessary to perform the steps mentioned can be found in the notes to the financial statements. There is an easy to use Excel tool on Damodaran’s website for the calculations. 51 If the relation between equity and interest-bearing debt is not correct, the calculation of the weighted average cost of capital (WACC) will lead to incorrect results as well. The estimated net present value of the future operating lease obligations increases the amount of interest-bearing debt and will be deducted from the enterprise value when calculating the equity value. Example A company reports €200 operating lease expenses for the last business year and for the next five years. From t=6 onwards, the operating lease expenses will be zero. EBIT of the last business year was €1,000, interest-bearing debt (without operating leases) €4,000 with an interest expense of €120, i.e. 3%. If we discount the future operating lease expenses at the pre-tax cost of debt (3%), we get a value of €915.94. We must adjust the interestbearing debt from €4,000 to €4,915.94. We will use the €915.94 also as the value for the right to use the assets. Depreciating this amount over five years leads to additional depreciation expense of €183.19 annually. This amount replaces the €200 operating lease expenses, leading to an EBIT of €1,016.81. The same applies to similar off-balance-sheet financing forms, e.g. factoring. The accounts receivable sold to the factoring company should be 51 Go to: http: / / people.stern.nyu.edu/ adamodar/ New_Home_Page/ spreadsh.htm, file oplease.xls; see also the webcast explaining the details of how to use the spreadsheet. <?page no="93"?> 6.5 Stock Options, Option Bonds and Convertible Bonds 93 added back to the working capital, and interest-bearing debt should be increased by the same amount. The factoring fee can be interpreted as an interest expense. Together with the off-balance-sheet financing, the equations now look like this: = Equity value Enterprise value Plus: Interest-bearing debt (on-balance-sheet and off-balance-sheet) Plus: Cash Plus: Non-controlling interests Plus: Non-operating assets Plus: Plus: Unfunded pension obligations Other debt-like items And: Equity value = Enterprise value Plus: Cash Plus: Non-operating assets Less: Interest-bearing debt (on-balance-sheet and off-balance-sheet) Less: Less: Less: Non-controlling interests Unfunded pension obligations Other debt-like items 6.5 Stock Options, Option Bonds and Convertible Bonds Managers of quoted companies often receive stock options as part of their compensation package. These options give the managers the right to buy a certain amount of the company’s shares at a pre-set price within a certain period. Granting such options does not affect the enterprise value as future free cash flows, discount rates and terminal values will not change. But it does affect the equity value since the managers will potentially show up and make a claim when the enterprise value is allocated to interest-bearing debt, non-controlling interests, unfunded pension obligations, other debt-like items, and finally, the value of the equity. <?page no="94"?> 94 6 From Enterprise Value to Equity Value Example Let’s assume the management is entitled to buy shares of the company at a price of $20. First, the managers will exercise this option only if the market price of the shares is above the strike price of $20. Otherwise they would realize a loss. If the market price goes up to $25 and the managers exercise the options, they realize a gain of $5 per share. The company can issue new shares if the managers exercise their options. This will result in a dilution of the existing shareholder’s stake in the equity as the company will only receive $20 for each share that is worth $25 on the market. The company could alternatively buy the shares on the market for $25. As it will only receive $20 from the managers, the cash flow to equity diminishes and leads to a reduction in the equity value. There are several methods customary in practice to account for this effect. Still widespread as it is easy to use, is the so-called treasury stock method. The treasury stock method only considers options that are “in the money”, i.e. where the market price is over and above the strike price (in our example above this would be the case as the market price is $25 and the strike price is $20). Options that are “out of the money” are not considered. In a first step, it is assumed that all “in the money” options are exercised immediately. In a second step, the proceeds that the company receives from the managers is used to buy back shares of the company at the market price. This will result in an increased number of shares outstanding, called fully diluted shares outstanding. Example (continued) Let the number of options granted to the managers be 100. If they exercise their options as assumed in the treasury stock method, this leads to a cash inflow of $2,000 for the company (100 options times $20 strike price per option) and 100 additional shares. The company uses the $2,000 to buy back shares. The market price for the shares is $25 each, so that it can buy back 80 shares ($2,000 divided by $25). The entire operation will result in 20 additional shares (100 issued to the managers minus 80 bought back with the proceeds received from them for the shares). If the company has 10,000 shares outstanding, the number of fully diluted shares outstanding is 10,020 (10,000 plus 20). <?page no="95"?> 6.5 Stock Options, Option Bonds and Convertible Bonds 95 If we now put the shares outstanding, the fully diluted shares outstanding and the equity value in relation to each other, we can derive the value of the options as follows: 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝑊𝑊𝑜𝑜 𝑅𝑅ℎ𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅𝑅𝑅 (𝐸𝐸𝐸𝐸𝑅𝑅𝐶𝐶𝑅𝑅𝐸𝐸𝐸𝐸𝐸𝐸 𝑆𝑆𝑅𝑅𝑊𝑊𝐼𝐼𝑊𝑊 𝑀𝑀𝑅𝑅𝑅𝑅ℎ𝑊𝑊𝐸𝐸) = 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 − 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 𝐹𝐹𝐸𝐸𝐶𝐶𝐶𝐶𝐸𝐸 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑆𝑆ℎ𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅 𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑊𝑊 × 𝑆𝑆ℎ𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅 𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑊𝑊 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝐹𝐹𝐸𝐸𝐶𝐶𝐶𝐶𝐸𝐸 𝐷𝐷𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑆𝑆ℎ𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅 𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑊𝑊 = 𝑆𝑆ℎ𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅 𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑊𝑊 + 𝐼𝐼𝑅𝑅 𝐸𝐸ℎ𝑅𝑅 𝑀𝑀𝑊𝑊𝑅𝑅𝑅𝑅𝐸𝐸 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅𝑅𝑅 − 𝑆𝑆𝑅𝑅𝐸𝐸𝑅𝑅𝑊𝑊𝑅𝑅 𝑃𝑃𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅 × 𝐼𝐼𝑅𝑅 𝐸𝐸ℎ𝑅𝑅 𝑀𝑀𝑊𝑊𝑅𝑅𝑅𝑅𝐸𝐸 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅𝑊𝑊𝑅𝑅𝑅𝑅 𝐶𝐶𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑃𝑃𝐸𝐸𝑅𝑅𝐼𝐼𝑅𝑅 𝐶𝐶𝑅𝑅𝐸𝐸 𝑆𝑆ℎ𝐶𝐶𝐸𝐸𝑅𝑅 Example (continued) Let’s assume the equity value for the company is $250,000. Hence, we get for the value of the options $499 (or $4.99 per option): $250,000 minus $250,000/ 10,020 × 10,000 equals $250,000 minus $249,501. Alternatively, the standard option price models (Black Scholes or Cox, Ross, Rubinstein’s binominal model) can be used to determine the value of the options. The annual reports of the quoted companies that grant stock options to their managers typically show the results of the calculations in the notes. There are several tools available on the web 52 that can be utilized to perform own calculations. The advantage of these models compared to the treasury stock method is that they take the life of the option into consideration and don’t assume an immediate exercise if the option is “in the money”. Apart from management stock options, option bonds and convertible bonds can also lead to a decrease of the equity value since they also lead to a dilution if they are exercised. Other than management stock options, option bonds and convertible bonds are typically traded on an exchange. The current market price of the bond gives a good approximation of its value if the market value of the equity does not significantly deviate from the equity value determined by a valuation. The standard option price models can also be used to come up with a value. Another alternative is to assume that all “in the money” option bonds and convertible bonds are exercised (if-converted method) and adjust debt and equity accordingly. 52 Just google for Black Scholes calculator or Cox Ross Rubinstein calculator. <?page no="96"?> 96 6 From Enterprise Value to Equity Value The relation between enterprise value and equity value now is as follows: = Equity value Enterprise value Plus: Interest-bearing debt (on-balance-sheet and off-balance-sheet) Plus: Cash Plus: Non-controlling interests Plus: Non-operating assets Plus: Plus: Plus: Unfunded pension obligations Other debt-like items Options And: Equity value = Enterprise value Plus: Cash Plus: Non-operating assets Less: Interest-bearing debt (on-balance-sheet and off-balance-sheet) Less: Less: Less: Less: Non-controlling interests Unfunded pension obligations Other debt-like items Options Please be aware that there may be additional items to be considered in a specific valuation on the way from enterprise value to equity value. The equations are not meant to be exhaustive. The main and typically most relevant issues should have been addressed though. Self-Test [1] What is the fundamental difference between the treasury stock method and the option price models in determining the value of management stock options? [2] Please explain the different treatments of excess cash in the enterprise DCF method and the equity DCF method. <?page no="97"?> 7 The Tension between Principals, Evaluators, Objectives and Leeway in Corporate Valuations Lies, damned lies, statistics, and corporate valuations. (Author unknown) Learning Objectives  Corporate valuations are not performed for their own sake in business practice. You should try to develop a sense for the objectives that the principals as well as the parties and persons conducting the valuations are pursuing with the appraisals.  Try to develop a feeling for where the leeway is in corporate valuations and how it can be utilized in a targeted manner. Let’s summarize some of the main characteristics of corporate valuations:  They are future-oriented.  The company being valued is typically set up for an indefinite time horizon. Consequently, the life of the project is not limited to a fixed number of years as in standard capital budgeting projects.  There is uncertainty about the future developments.  Notwithstanding some form of a common business practice and in some countries (like in Germany) even standards for corporate valuations 53 , different approaches of and opinions on many individual issues exist in both valuation practice and in academia.  The individuals and organizations conducting the valuations (in the sense that they determine the value) are rarely identical with the principals placing the orders for the valuations and being responsible for the actions taken or omitted based on the results of the valuations. There are exceptions, e.g. private equity, Warren Buffet, Carl Icahn and comparable professional investors, although some of them might draw on external valuations complementing their own analyses.  There is a market for corporate valuations with supply and demand as in every other market. And in many countries, the competition 53 IdW S1 „Principles for the Performance of Business Valuations“, issued by the Association of the German CPAs. <?page no="98"?> 98 7 The Tension in Corporate Valuations between the suppliers, i.e. the organizations and individuals trying to sell their valuation expertise, is intense. These factors lead to an interesting area of tension. A careful reflection on this usually pays off and is just as important as a good knowledge of the different methods of corporate valuation described in the preceding chapters. Try to find answers to the following questions:  Who is the principal? Who placed the order for the valuation?  What is her or his objective? What does she or he need the valuation for?  Who conducted the valuation?  How much did she or he or the organization receive for the valuation and in in which form (fixed, hourly-based, contingent, other)? The answers to these questions will give you generally a good idea where the result of the valuation will be. There is no reason for too much reverence for illustrious names, titles, complex equations, comprehensive Excel files and perfectly styled exhibits. Especially when analyzing expert or fairness opinions and/ or terms like “objective”, “objectified”, “theorybased”, “intrinsic” and “generally accepted standards” come into play. 7.1 Principals and their Objectives Top managers like CEOs, CFOs and heads of divisions “order” valuations. If this is done for a potential acquisition of another company, the objectives of the principals can be diverse.  One objective could be to find out whether the acquisition will create value, i.e. increase the shareholders’ value of the own (acquiring) company. This is also in the interest of the shareholders. The question is whether the project “acquisition of target company …” has a positive net present value, or if there are better investment alternatives with a higher net present value and a better utilization of the company’s funds. This is where the focus of most of the available literature (from both academia and practitioners) is.  “Power” undoubtedly plays the largest role in almost every acquisition, although only few of the individuals involved will probably admit this. An acquisition just as one that did not happen usually strengthens the position of certain members of the management team and weakens the position of others, since it leads to a change in the relation of the areas of responsibilities. Even though it is called “management team”, reality often shows that this is a contradiction in terms, an oxymoron. Power can also be related to a stronger market position, access to a new technology, a new distribution channel or a <?page no="99"?> 7.1 Principals and their Objectives 99 new geographical market. Sometimes, the decision to acquire or to prevent the acquisition has already been made by the principal before ordering the valuation. The result will then only serve as a basis to realize the interests of the principal. And if market prices on the valuation object are available, we often see the procedure described by Damodaran as “value first - valuation to follow”. The outcome of the valuation that still must be prepared is being delivered together with the order, e.g. “could you please check whether this is attractive for us at a price of …” 54 .  Safeguarding is another very common objective of principals. There are more acquisitions that fail (fail in the sense that the expectations are not met) than those that work out well. If worse comes to worst, a valuation, ideally an expert opinion performed by a prime address, considering the purchase price paid to be market conform, appropriate, fair, or similar, is nice to have in the safe. It might not save the principal from getting fired, but it will reduce the fear of claims for indemnification.  Finally, it might be necessary to perform a valuation for negotiations. Especially in negotiated sales, where the seller talks to one or very few potential buyers, valuations are a common tool to communicate expectations on the price. But also in auctions, bidders are expected to substantiate their offers with valuations, revealing the assumptions that led to the purchase price offer. The deliberations above can also be applied to divestment decisions of entire companies or divisions. In addition, the preparation of fairness opinions comes into play here, an instrument to convince the own shareholders that an offer, a negotiated sales price is “fair”. Bottom line, the valuation’s only objective here is to serve as an instrument for the realization of the interests of the principals, typically the management of the target company. This is also the case in valuations conducted within the context of impairment tests. Besides the top management, shareholders (with and without a role in management) can also be principals of valuations. The objectives of the valuations can comprise an analysis of the economic advantageousness or the determination of a minimum sales price for a divestment to be favorable. In many situations, especially in small owner-managed companies, the decision to sell has already been made before a valuation has been conducted. Instead of “value first - valuation to follow” we have “decision first - valuation to follow”, which is just as awkward. In these cases, the principals typically have high sympathy for those advisers that 54 See for example Damodaran, Investment Valuation, 3 rd ed., 2. <?page no="100"?> 100 7 The Tension in Corporate Valuations will indicate a high value to their companies. The same applies to situations where a sale is not seriously considered, and the valuation serves informational purposes or the strengthening of the self-consciousness of the principal. Analysts in investment banks perform valuations of quoted companies. Their interest is to generate further business based on an excellent research. Courts and parties involved in court disputes act as principals of valuations. The latter’s intention clearly is to realize own interests. The items mentioned above are only an extract of all possible combinations of principals and their intentions. What we want to achieve with this enumeration is that you develop a sense for the objectives principals might have when they ask for valuations in practice. The calculation of a true, fair, intrinsic, objective, objectified or market-standard value (we will discuss in chapter 8 whether these values exist at all) is very seldom - even though empirical surveys may come to different results (Whom do you ask? ). Valuations serve in most cases as tools. They are instruments to realize the interests of parties, here the principals of the valuations. 7.2 Evaluators and their Objectives The individuals conducting the valuations can be staff members of the top management, special departments within the organization or external advisers. Certified public accountants perform valuations, investment banks, M&A advisers and other management consultants do so too. In some cases, these valuations or parts thereof become public, for example in squeeze-outs. The majority of the valuations will not be made available to the public, though. Courts appoint external advisers to conduct valuations in certain situations. In the bread and butter valuation business however, the top management or the owner of the company places the order for the valuation and acts as the principal. Consequently, there is a strong dependence between the principal and the evaluator. One side pays, and the other side must deliver. Stick and carrot mechanism can be found. “If you deliver what I expect, I will reward you. But only then.” If the principal then on top adds a price tag, there is a high probability of an anchoring effect on the side of the evaluator. 55 Existing 55 The anchoring and adjustment heuristics were first described by Tversky/ Kahnemann, Judgement under Uncertainty: Heuristics and Biases, Science, Vol. 185, Iss. 4157, 1974, 1124-1131, here 1128 ff. See also the experiments of Kaustia/ Alho/ Puttonen, How Much Does Expertise Reduce Behavioral Biases? The Case of Anchoring Effects in Stock Return Estimates, Financial Management, Autumn 2008, 391-411. Both sources are available on the web (just google for them). <?page no="101"?> 7.2 Evaluators and their Objectives 101 market prices can also serve as anchors, as self-fulfilling prophecies. If the result of the valuation deviates from the anchor, the supposed cause for the deviation will be sought and the valuation will be adjusted until the result is reasonably close to the anchor. This is done even though the person who set the anchor possibly has no better information than the person who conducts the valuation. Market rumors or alleged offers of competitors for the same company can also serve as anchors in valuations (I heard they put in a bid of …). Research analysts value quoted companies to identify overand undervalued stocks to issue buy and sell recommendations. Needless to mention that the colleagues in the same bank doing other business with the companies being valued don’t like to see sell recommendations. Since there still are far more buy than sell recommendations from research analysts, this can also be interpreted as an indicator for the existence of a reward and sanction mechanism. Having a look at the compensation structure usually also helps to “read” the results of valuations. Apart from fairness opinions, valuations or the compensation earned with valuations only play a minor role in investment banks. Valuations are by-products, means to an end, the end being a done deal. If an owner invites several investment banks and M&A advisers for a pitch presentation regarding the potential sale of her or his business, each of the invitees will perform a comprehensive valuation based on the information provided. As mentioned before, it is human nature that the potential sellers have more sympathy for those advisers that come up with higher values for their businesses than for those who address the main difficulties in the sell-side process. “If we find a buyer for this business at all, you should light up a candle in every church between our offices and your home” might be an honest statement, but it will not help in winning the mandate. This leads to a similar phenomenon as we can see it in the award of public contracts: The party that did the biggest miscalculation (in a sell-side M&A pitch the highest, in public contracts the lowest result) gets the contract. It should be no surprise that in Germany no large construction site that was tendered publicly is finished within the initial time frame and budget - all trades were awarded to the cheapest suppliers. 56 Additionally, it should also be no surprise that so many M&A sell-sides fail in the first attempt. This failure is very often the necessary storm that clears the air and brings down the purchase price expectations (that were pushed up by the pitch presentations) to a realistic level. 56 A famous example is the BER , the airport in Berlin, with all its delays. The airport opened in October 2020 , originally the opening was planned for 2010! . <?page no="102"?> 102 7 The Tension in Corporate Valuations In M&A buy-side mandates the largest part, sometimes 100% of the adviser’s compensation is contingent on the closing of a transaction. This implies that you should not expect very timid valuations here from the M&A adviser. Other advisers who charge their compensation for the valuations based on hours or as a fixed fee are also not rewarded for delivering “good”, “true”, “fair” or whatever results - this is taken as given and for granted. They get rewarded by their organizations for selling lots of hours and lots of valuations. Repeat business and recommendations are the success drivers here. The following assumptions are probably helpful when analyzing valuations:  Principals of valuations utilize the appraisals predominantly to realize their own interests.  The persons and organizations conducting the valuations typically benefit if the results of the valuations are in line with the expectations of the principals.  The evaluators know their compensation schemes and act accordingly. 7.3 Leeway in Valuations Below you will find, without any claim to completeness, an extract from the toolkit of how to vary the result of corporate valuations. 57 The evaluator will make the usage of the tools dependent on the addressee and the objective of the valuation. In a squeeze-out valuation the leeway is more limited than in a purchase price negotiation between two parties where each side can walk away from the deal. But even in squeeze-outs there is a wide scope in the approaches used in practice. There is a study that summarizes the different methods, discount rates, calculation methods for betas, size of the peer group in the comparable companies analysis, etc. used in German squeeze-outs between 2010 and 2023 (usually updated every year). This study is only available in German. 58 57 See also Setiadarma, Building Bridges to Successful Deals: The Art of Valuation and Negotiation, pages 18 ff., available here: https: / / opus4.kobv.de/ opus4-htw/ frontdoor/ index/ index/ docId/ 1919, and Damodaran’s “template of ‘tricks’”, accessible on the web (we can’t find it in any of his books), e.g. here (see pages 5 ff.): http: / / people.stern.nyu.edu/ adamodar/ pdfiles/ country/ ValuationBermudaTriangle.pdf. 58 https: / / www.i-advise.de/ wp-content/ uploads/ 2024/ 04/ Studie-Bewertungspraxis- 2023.pdf. <?page no="103"?> 7.3 Leeway in Valuations 103 7.3.1 Leeway in DCF Valuations Let’s look again at the formula for the enterprise value in a two-stage enterprise discounted cash flow model: 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = � 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝑜𝑜𝐶𝐶𝑊𝑊𝐹𝐹 𝑐𝑐 (1 − 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶) 𝑐𝑐 𝑡𝑡 𝑐𝑐=1 + 𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝐶𝐶𝐶𝐶𝑅𝑅ℎ 𝑜𝑜𝐶𝐶𝑊𝑊𝐹𝐹 𝑡𝑡 × (1 + 𝑊𝑊) 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 − 𝑊𝑊 (1 + 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶) 𝑡𝑡 Top down and from left to the right we can identify the following starting points to influence the result of the valuation: [1] Free cash flow in detailed planning period [2] WACC [2] Terminal value. And we will look at: [3] Further leeway. [1] Free Cash Flow in Detailed Planning Period Again, we start with a look at the calculation scheme: EBIT Earnings before interest and taxes Less: Taxes on EBIT (marginal tax rate) EBIAT Earnings before interest after taxes Plus: Depreciation Less: Capital expenditures Investments in fixed assets Less (Plus): Increase (decrease) in working capital Investments in working capital (without cash and short-term interest-bearing debt) Free cash flow Exhibit 14: Free Cash Flow The derivation of the free cash flow starts with the operating result of the firm, the earnings before interest and taxes (EBIT). The EBIT is a result of the company’s sales and its operating margin. The projection of future <?page no="104"?> 104 7 The Tension in Corporate Valuations sales has a big, if not the biggest influence on the value of the company. Assumptions on growth rates of the top line should therefore always receive high attention. This applies to both the magnitude and the sustainability of growth. The length of the detailed planning period, i.e. the length of the high-growth phase, can also influence the result. The evaluator can find arguments for several scenarios. And this happens in practice. Most confidential information memoranda on companies for sale contain a “hockey stick” in the top line of the budget. In estimating the future EBIT margin there is also room for bias. Starting point is typically the average normalized margin of the past three to five years. But leeway exists in normalizations, in both directions. And in adjusting or not adjusting the margin to the industry average. The people involved in conducting the valuation can find arguments for almost any position. Taxes are the next line item. And you can have splendid arguments for using the average current tax rate or the marginal tax rate and if and when to move from the average to the marginal tax rate. And there is scope in forecasting future capital expenditures. The same applies to working capital: Defining what working capital comprises, usage of industry or company-specific data, treatment of all or only part of the cash as excess cash, just to name a few. Furthermore, the triangle between earnings growth rate, reinvestment and return on capital also leaves room for manipulating the outcome of the valuation. See point 5 in chapter 2.2.2 and chapter 2.2.4. In the long run the implied return on capital should converge to the industry average and the weighted average cost of capital. But since a reconciliation is often not performed, a disparity might not become apparent. Best case and worst case scenarios for projections of future free cash flows can be relabeled and utilized for the realization of the principals’ or evaluators’ objectives. [2] WACC Let’s recall what all goes into the weighted average cost of capital (WACC): 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 = (𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊-𝐹𝐹𝐸𝐸𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 + 𝐸𝐸𝑅𝑅𝑅𝑅𝐶𝐶 × 𝑀𝑀𝐶𝐶𝐸𝐸𝑊𝑊𝑅𝑅𝑅𝑅 𝑅𝑅𝑅𝑅𝑅𝑅𝑊𝑊 𝑃𝑃𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅) × 𝐸𝐸 𝐸𝐸 + 𝐷𝐷 + 𝐸𝐸𝑜𝑜𝑅𝑅𝑅𝑅𝐸𝐸-𝐸𝐸𝐶𝐶𝐸𝐸 𝐶𝐶𝑊𝑊𝑅𝑅𝑅𝑅 𝑊𝑊𝑜𝑜 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 × 𝐷𝐷 𝐸𝐸 + 𝐷𝐷 In valuation practice you will find current interest rates as well as average interest rates of the past years, 10 year rates, 30 year rates or rates derived from yield curves that all can serve as a basis for the determination of the risk-free rate. So even for a measure as the risk-free rate that looks <?page no="105"?> 7.3 Leeway in Valuations 105 relatively straight-forward to project, there is leeway, leading to differences in the results of the valuation. Beta: You will find “bottom-up” betas as well as “top-down” betas in valuations. In bottom-up betas there are degrees of freedom as to which companies and which industries are considered comparable, especially if the company being valued is active in more than one segment. In top-down betas the time horizon for the regression (one, two, five years), the interval (monthly, weekly, daily) as well as the index the stock’s returns are regressed against will have an influence on the result. You should unlever and relever betas, but this step is often skipped. Betas from services sometimes contain adjustments, which can be adopted or not. Bloomberg for example calculates an “adjusted” beta as two thirds times the historical beta (“raw” beta) plus one third times one. 59 For small owner-run companies where the shareholders are not fully diversified you can use the total beta concept or an alternative or you can use the same beta as for companies where the marginal shareholder is fully diversified. You can adjust for size and fungibility or you can omit this step - you will find all variants in valuation practice. And arguments for and against each variant. The market or equity risk premium can be estimated based on historical data or as an implied premium. If historical data are utilized, different time periods (10, 20, 50 years or longer) will lead to different results as will different methods to calculate the average (arithmetic or geometric mean). For companies with activities in several geographies with a different risk profile, this fact can be considered by adjustments or it can be omitted. Even for the pre-tax cost of debt and the appropriate tax rate to get to the after-tax cost of debt there is ample scope. Maturity, spread, synchronization of spread and intended leverage, marginal or current average tax rate, considering pension promises or not, all this can be argued for and against in calculating the WACC. In determining the weights between the cost of equity and the cost of debt there is also leeway. Very often you will find weights based on book values instead of market-value based weights. What can also be found quite often in valuation practice is an increase in debt without adjusting the cost of debt and equity, i.e. “forgetting” that an increase in leverage leads to increased cost of debt and equity and increased weighted average cost of capital (WACC). 59 This is called the Blume adjustment. The idea is to reflect that in the long run, all companies will converge to the average risk. But why two-thirds to one-third and not threequarters to one-quarter or some other ratio? That is where the leeway is. <?page no="106"?> 106 7 The Tension in Corporate Valuations [3] Terminal Value As mentioned above, the terminal value typically accounts for the largest part of the enterprise value of the company in a discounted cash value valuation. Creativity of the evaluator pays off best here. In determining the terminal value, we first have the option to choose between the perpetuity growth method (as in the equation above) and the exit multiple method (see chapter 2.2.4). In the perpetuity growth method, we can rearrange the equation for the terminal value, as described above in chapter 2.2.4, as follows: 𝐸𝐸𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐶𝐶𝐶𝐶 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐸𝐸𝐸𝐸𝐼𝐼𝐸𝐸𝐸𝐸 𝑡𝑡+1 × (1 − 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑅𝑅𝐶𝐶𝑅𝑅𝑅𝑅 𝑡𝑡+1 ) 𝑊𝑊𝐸𝐸𝐶𝐶𝐶𝐶 𝑡𝑡+1 − 𝑊𝑊 EBIAT t+1 can be split up into EBIT t+1 and taxes on EBIT t+1 . Manipulations are possible here too, especially for cyclical companies: Boom year, slump year, average year as basis for EBIT t+1 , marginal tax rate or average current tax rate. Reinvestment rate, growth, return on capital and WACC give further leeway. If the intention is to show a high value, evaluators will pick a growth rate above the risk-free rate (i.e. assume a stronger growth for the company than the growth of the economy 60 ) combined with a low reinvestment rate (depreciation equal capital expenditures, increase in working capital ignored), high return on equity and low WACC (“in the long run all companies are mature companies with a lower WACC than high-growth companies”). Applying the exit multiple methods opens the leeway described in the next chapter (7.3.2) to adjust the valuation (choice of multiple, choice of comparable companies, choice of period for the application of the multiple(s), i.e. LTM or forecast). [4] Further Leeway There is further leeway when calculating the equity value based on the enterprise value. In chapter 6.5 we introduced the following equation: Equity value = Enterprise value Plus: Cash Plus: Non-operating assets Less: Interest-bearing debt (on-balancesheet and off-balance-sheet) Less: Less: Less: Less: Non-controlling interests Unfunded pension obligations Other debt-like items Options 60 If you accept the long-term risk-free rate as a good proxy for the long-term nominal growth rate of an economy; see e.g. Damodaran, Investment Valuation, 3 rd ed., 307. <?page no="107"?> 7.3 Leeway in Valuations 107 There is scope to move the equity value in either direction in each of the reconciliation positions mentioned:  Magnitude and evaluation of excess cash  Expected time of disposal of non-operating assets  Estimation of present value of future lease obligations  Estimation of the value of non-controlling interests  Estimation of future increases in salaries, pensions and other parameters in the calculation of the actuarial present value of pension liabilities  Estimations of the magnitude and the probability of a one-time litigation risk  Calculation of the value of management options (treasury stock method; Black Scholes; Cox, Ross, Rubinstein’s binominal model). Even if the effect of one single item looks negligible - it’s the total amount of all together that makes the difference. 7.3.2 Leeway in Multiple-Based Valuations The first variable the evaluator has in a multiple-based valuation is the multiple itself. There is no DIN norm stipulating whether to use EBITDA or EBIT for example. If the objective is to come up with a high value, evaluators will find arguments for the utilization of those multiples (sales, enterprise value per user, book value - everything is possible) that lead to these high results. As a recipient of a multiples analysis it is recommendable to perform an own comprehensive analysis to understand the intentions of the other party and counter them in an intelligent way. The next variable is the choice of the companies included in or excluded from the multiples analysis. On the one hand, the evaluator will not get away with everything. For example, in a multiples analysis for Daimler it would be difficult to argue not to include BMW. But on the other hand, arguments can be found for and against a limitation of the universe of comparable companies to a certain geography versus going international, whether to include companies in related sectors, how far the search for companies with similar production methods, similar distribution channels, similar research and development activities or similar end customers should be conducted - enough room to influence the result of the analysis. There is further leeway in calculating the averages from the values of the companies included in the analysis. How should outliers be handled? What is the criterion to classify a value as an outlier? Shall we take an arithmetic mean, a geometric mean, a harmonic mean, or should we rely on the median? This is a wonderful playground for creative minds! <?page no="108"?> 108 7 The Tension in Corporate Valuations The preparation of the data (see chapter 3.3) of the companies included in the sample should also be scrutinized. How was the market value of equity calculated? Share price multiplied with the number of shares outstanding or with the number of fully diluted shares outstanding? If number of shares outstanding, has an appropriate adjustment been made for outstanding options? Were extraordinary and one-time effects at the comparable companies properly accounted for when deriving the multiples? Was the reconciliation from the equity value to the enterprise value done correctly? Remember from chapter 6.5 the definition of the enterprise value: Enterprise value = Equity value Plus: Interest-bearing debt (on-balancesheet and off-balance-sheet) Plus: Non-controlling interests Plus: Unfunded pension obligations Plus: Plus: Less: Less: Other debt-like items Options (unless equity value was calculated based on fully diluted shares outstanding) Cash Non-operating assets Leeway exists in every single item in the equation. See point 4 in chapter 7.3.1. In most valuations in practice you will find a reconciliation based on book values only from equity value to enterprise value, and very often only net debt is added to the equity value. Finally, the period chosen to calculate the multiples will lead to different values. LTM (last twelve month), TTM (trailing twelve month) (LTM = TTM), last finalized business year, current business year, next business year - multiples can be calculated for all these periods (provided the base data are available). And arguments for and against each measure will also be found. Self-Test [1] You suspect that the other side “tuned” the valuation to come up with a high value for the company. What would you look for first? [2] You intend to dispose of a subsidiary of your group and invited five investment banks/ M&A advisers to a pitch presentation. Do you expect “conservative” or “ambitious” valuations? <?page no="109"?> 8 Value and Price ‒ a Tangent on Valuation Theory Learning Objectives  Recognize the difference between the value and the price of a company.  Form an own opinion about the existence of “intrinsic”, “objective” or “objectified” values for companies.  Understand the basics of the so-called functional corporate valuation theory and the derivation of decision values. 8.1 Prices and Values of Companies Price is what you pay; value is what you get. (Benjamin Graham as quoted in Warren Buffet’s 2008 letter to the shareholders of Berkshire Hathaway) 61 There is a difference between price and value. The citation above illustrates this. The price paid for a company or a share in the company is a result of a transaction between a seller and a buyer. It can be objectively determined. Stock quotes are prices as is the one dollar that René Benko, the Austrian investor, paid for the shares (the entire equity) of Karstadt, the old-established German retail chain. But what are company values? What did we really cover in the first seven chapters of this book? Was it corporate valuation? Or was it the estimation of a potential range for the purchase price? The answer is obvious for the multiples-based “valuations” in chapters 3 and 4 and the LBO “valuation” approach introduced in chapter 5.1. Utilizing stock quotes of comparable companies, prices paid in comparable transactions and expected purchase price offers from financial sponsors leads to a derivation of an expected range for the purchase price of the company being analyzed. It is labelled everywhere in practice and even in parts of the literature as “valuation”, but it is a “pricing” of the company. And this finding is not meant to be pejorative. It’s a clarification. 61 http: / / www.berkshirehathaway.com/ letters/ 2008ltr.pdf, 5. <?page no="110"?> 110 8 Value and Price ‒ a Tangent on Valuation Theory The case is different for the discounted cash flow approaches including the adjusted present value and the German earnings value methods. These valuation approaches are based (not exclusively, but substantially) on figures derived from the company being valued - the future free cash flows (to the firm or to equity). They determine the value of the company, that can conform with the price of the company, but doesn’t have to. DCF methods are therefore in principle suitable methods for the calculation of company values. It would be too simple though to classify all DCF methods as “valuations” and all multiples-based methods as “pricings”. There are numerous DCF valuations performed solely for the estimation of a potential purchase price range. If you are aware of how the counterparty calculates, it is very reasonable to prepare accordingly for the negotiations. In case you know that the counterparty will conduct a DCF analysis, your own DCF calculation does not necessarily serve the derivation of a value. The objective might well be to estimate the purchase price offer or purchase price expectation of the other party. There are DCF valuations in most of the analyst reports on quoted companies. And the results of these valuations usually don’t differ substantially from the “value” range derived from multiples-based “valuation” approaches. This tendency to align the results of different valuation approaches also exists in other segments of valuation practice. The DCF “valuation” in these cases is very often nothing else but a tokenism to support the price range derived from the multiples analyses. 62 If the value of the company exceeds the price, the buyer makes a good deal, and the seller a bad one. 63 If the price exceeds the value (for the entire company or a share in it), the seller should be happy with the transaction and the buyer unhappy. These statements are based on the assumption that the value is the same for both the buyer and the seller. The subjectivity of value is discussed later. Buying stocks below their (so-called fundamental) value is the basis of value investing, an investment strategy established by Benjamin Graham. Warren Buffet and John Templeton belong to his most popular disciples and successful practitioners of his theories. But value investing is not the only way to make money with buying and selling companies or shares in companies. Prices for stocks or for entire companies are formed and set on markets. If you understand and can project how supply and demand will develop, i.e. recognize correctly what 62 Damodaran pointedly labels this as “quasi DCF” in several of his blog posts. 63 That is correct if we assume that the value is the same for the buyer and the seller. We will come back to this topic later in this chapter. <?page no="111"?> 8.2 Intrinsic ansd Subjective Company Values 111  The value of a company and the price of a company are two different pairs of shoes.  Many valuations in practice are in fact estimates of a potential price range for the company.  Of the different valuation methods introduced in this book, the DCF methods are best suited for real valuations.  Value investing, i.e. the acquisition of companies or stocks below their true value or the sale above their true value, is only one possibility to earn (and lose) money with the acquisition and disposal of companies and shares in companies. 8.2 Intrinsic (Objective, Objectified, Fundamental) and Subjective Company Values There are numerous publications on whether values in economics and business sciences have an objective or a subjective character. Adam Smith, even Karl Marx dealt with this topic, the protagonists of the marginalism school, and many more. In the German academic literature on corporate valuation an intensive discussion took place on whether company values can be objective or at least objectified, or if because of the definition of “valuation” as an allocation of a certain amount of money to a valuation object by someone (the valuation subject), company values must inevitably be of a subjective nature. Part of this discussion in the fifties and sixties of the last century was caused by a dispute on whether the net asset value (as a supposedly objective measure) or the earnings value (as a supposedly subjective measure) should govern corporate valuations and the calculation of company values. “drives” the prices, you can make a lot of money as a trader, a speculator, without having to deal too much with values and valuations. It does not bother the trader whether Tesla or Alibaba are overvalued. The only important thing is whether the price will go up or not. The dotcom boom can serve as an example. Almost every IPO was overpriced, not only in hindsight, but also at the time of the offering people knew that the new shares were overpriced. That did not worry them as due to the large demand prices went up on the first trading day in almost every IPO, leading to first day trading profits. The realization of these profits and the timely withdrawal from the later collapsing market (when prices and values converged again) however was only accomplished by very few traders. Let’s summarize: <?page no="112"?> 112 8 The Tension in Corporate Valuations In the Anglo-American academic literature on corporate valuation such a dispute between proponents of net asset valuations and DCF valuations did not occur (at least we didn’t find any traces). Additionally, a deepening discussion on objective and subjective company values also did not happen. The different ownership structures, capital market oriented in the Anglo-American world and focused on private owners (few and often managing their own companies) and their objectives probably also played their part. Bottom line, there is not much on objective versus subjective values in the Anglo-American academic literature. Subjective elements like synergies for example are not denied. And no one would probably argue about the existence of a maximum price a buyer can pay for the company or a minimum price a seller must ask for in order not to be worse off compared to not buying or not selling, and that this maximum price can differ from buyer to buyer, because different buyers would run the business differently if they own it. At the same time, the existence of an “intrinsic” or a “fundamental” value, a value attached to the company with an objective or objectified character is at least implicitly assumed. In Damodaran’s Investment Valuation book we can find the following definition for the intrinsic value on page 12: “... consider it the value that would be attached to the firm by an unbiased analyst, who not only estimates the expected cash flows for the firm correctly ..., but also attaches the right discount rate to value these cash flows.“ 64 And as a counter to the famous saying, that beauty is in the eye of the beholder, which is often quoted by the proponents of subjective company values, we find right on page 1 of the book the following statement: “There are those who are disingenuous enough to argue that value is in the eye of the beholder, ... That is patently absurd. Perceptions may be all that matter when the asset is a painting or a sculpture, but investors do not (and should not) buy most assets for aesthetic or emotional reasons; financial assets are acquired for the cash flows expected on them.“ 65 In a nutshell, this means that companies and shares in companies are financial assets and that the value of these financial assets is determined by the ability of the companies to generate future free cash flows. This intrinsic value attached to the companies can be derived by an unbiased evaluator who projects the future free cash flows correctly and finds the right discount rate. This opinion is representative not only for the Anglo- American valuation theory, but also for the international and for large parts of the German valuation practice. 64 Damodaran, Investment Valuation, 3 rd ed., 12. 65 Damodaran, Investment Valuation, 3 rd ed., 1. <?page no="113"?> 8.3 Functional Valuation Theory The position of the German valuation theory differs from the opinion just described. The dispute between the proponents of the subjective and the objective school of corporate valuation in Germany was settled in the mid-seventies with the wide acceptance of the so-called functional valuation theory. 66 Functional to be interpreted in the sense of purpose-oriented, asking for the objective of the valuation. As per the functional valuation theory, the value of a company as well as the method to determine this value depends on the purpose of the valuation. There is no such thing as the one and only value or the one and only method to derive it. The functional valuation theory recognizes three main functions (purposes, objectives),  the decision function,  the mediation function, and  the argumentation function, as well as several minor functions (tax assessment, information, contract arrangement, control, motivation), that will not be discussed here. Decision Function The objective of the valuation in the decision function is to support and back-up decisions of acquisitions or disposals of companies (or shares in companies). The value to be determined is called the “decision value”. The decision value plays a vital role in all three main functions of the functional valuation theory. The basic idea is as follows: I can’t provide you with the “true”, “correct”, “objective”, “fundamental” or “intrinsic” value, as no such value exists. But as a potential buyer, I can provide you with a maximum price that you can pay for the company, a limit. If you pay more, you will be off worse compared to not buying the company and realizing your investment alternatives. As a potential seller, the limit is the minimum price that you must receive in order not to be in a worse position compared to not selling the company and continue as the owner. The decision value results from a subject-object-object-relationship. Valuation subject is the buyer (seller) with her or his objectives, whatever they might be. In the calculation of a decision value, beauty unquestionable is in the eye of the beholder. If the buyer (seller) is interested in future 66 For an overview on the functional valuation theory in English language see Matschke/ Brösel, Business Valuation, Functions, Methods, Principles, 2021. 8.3 Functional Valuation Theory 11 3 <?page no="114"?> 114 8 Value and Price ‒ a Tangent on Valuation Theory free cash flows only, there is no difference to the calculation of an intrinsic value. But if the buyer (seller) has multiple objectives and for example derives utility from being an entrepreneur, this must be considered when calculating the decision value. The first “object” in the above-mentioned subject-object-object-relationship is the company being valued. The buyer (seller) must determine the contributions to her or his objectives that she or he can achieve with the company. It’s not the unbiased analyst calculating the free cash flows on an ‘as is where is’ basis. Relevant is what the buyer (seller) would draw from the company. The second “object” stands for the investment alternatives of the buyer (seller), the options she or he would follow if the company is not acquired (sold). Decision Value The calculation of the decision value is performed by a comparison of investments. Starting with a base program, defined as the optimal (utilsmaximizing) allocation of funds to the investment alternatives available if the company is not acquired (sold), it is analyzed which projects of the base program would be eliminated if the company is acquired (not sold), without changing the utils-level of the base program. The price of the eliminated investment alternatives, those replaced by the company, gives us the decision value. Let’s look at a short example: A potential buyer has funds available of $1,000. The company (C) being valued would provide 1,200 units of utils. The following investment alternatives (IA) are available: IA Price in $ Utils Utils/ $ 1 600 750 1.25 2 200 350 1.75 3 300 400 1.33 4 200 300 1.50 All investments are completely divisible. The base program of the potential buyer will be: IA Investment in $ Utils 2 200 350 4 200 300 3 300 400 1 (300) 300 375 1,000 1,425 <?page no="115"?> 8.3 Functional Valuation Theory 115 The potential buyer would realize projects (the investment alternatives) 2, 3 and 4 completely and invest $300 in project 1 if he would not do the acquisition. All funds ($1,000) are invested. Total utils amount to 1,425 units. The next step is to perform the valuation program, where the company and the best investment alternatives (in the sense of utils/ $) are combined in a way that the total level of utils of 1,425 is maintained. This is the result of the valuation program: IA Investment in $ Utils 2 (128.57) 128.57 225 C ? (871.43) 1.200 1,000 1,425 By admitting the company to the valuation program, the investment alternatives 1, 3 and 4 and $71.43 of investment alternative 2 are eliminated from the base program. The resulting valuation program has the same level of total utils of 1,425 as the base program. The decision value, the limit, the maximum price a buyer should pay, is the sum of the prices for all investment alternatives eliminated from the base program. It amounts to $871.43 in our example. 67 If the buyer pays more than the decision value, the investment in investment alternative 2 would have to be reduced, leading to a lower level of utils of the program. If the buyer pays less than $871.43, and this will be the objective in the negotiations, the investment in investment alternative 2 can be enlarged and therefore the level of utils will increase, i.e. value is created by the acquisition and the buyer is better off with the acquisition than without it and with the realization of the investment alternatives. The described procedure should be known from the cost accounting lectures (product mix decisions). It can be extended to include financing alternatives, investment alternatives that are not divisible and other variants (simultaneous valuation of two or more acquisitions). 68 These models can (if they are not too complex) be solved with Excel and its Solver function. The decision value is a “private” value, a value that should not be disclosed to the other party. It should form the basis for the preparation of a negotiation strategy and serve as the last and final line of retreat. 67 $300 of IA 1 plus $300 of IA3 plus $200 of IA4 plus $71.43 of IA 2 equals $871.43. 68 See for example Matschke/ Brösel, Business Valuation, Functions, Methods, Principles, 2021, Chapter 2, with further citations. <?page no="116"?> 116 8 Value and Price ‒ a Tangent on Valuation Theory If the decision maker, the valuation subject, derives utility only from future free cash flows, and if the return of the investment alternatives can be described reasonably well by a discount rate (e.g. WACC), the DCF methods including the APV and the earnings value can be interpreted as a special case of the investment comparison (base program, valuation program) described above, i.e. they lead to the same result. These assumptions are regularly made in valuation practice for reasons of complexity reduction. Consequently, the investment comparison does not appear in valuation practice (at least we have never seen it in a valuation). Instead of regret, the following two aspects should be considered when performing a DCF analysis: [1] For the decision value (not for the value brought into a negotiation) in the sense of a limit price, i.e. the maximum amount a potential buyer should pay in order not to be off worse compared to not pursuing the acquisition and following alternative investments (analogue: the minimum price a potential seller must receive to not end up in a worse position compared to not selling), it does not matter what an unbiased third person believes what the future free cash flows will be. The only thing that matters is what the buyer (or the seller) will do with the business and how much cash flow the company will make then. [2] Management is all about selecting the best alternative, and there are always alternatives to acquiring or selling a company. Instead of varying the discount rate to the limits in a sensitivity analysis, better ask yourself what is behind the discount rate: the return of your investment alternatives. Decision Value and Valuation Practice If the decision value is so vital in corporate valuation, why do we hardly come across it in valuation practice? Given the fact that more acquisitions fail (in the sense that they do not meet the original expectations) than succeed, it is legitimate to ask whether the decision value receives the attention it deserves. We looked at the principals’ objectives in chapter 7.1. Evaluating whether an acquisition (or a disposal) creates value or not is on the list, but only amongst other topics like power and politics, safeguarding and negotiations. And it seems that most of the demand for external valuation advice is for the determination of market prices. Reward and sanction mechanism (“overpaid” or “sold too cheap”) for top managers are normally also rather tied to market values than to decision values. Finally, just imagine the two parties involved - on the one side the successful top manager or even better the wealthy investor with a long list of successful deals, and on the other side the valuation expert (easily exchangeable by many other experts available and probably already knocking on the door). It is much <?page no="117"?> 8.3 Functional Valuation Theory 117 more likely that the principal will draw on the expert’s knowledge about actual prices paid in the market than enter a discussion on her or his personal preferences and with which events she or he associates utility. Valuation practice has found a work-around for those cases where objectives and investment alternatives of the principal are not available - the intrinsic value, the valuation on an ‘as is where is’ basis. The German CPAs for example did not adopt the functional valuation theory one to one. They omitted the argumentation function and added instead the function of acting as an independent and neutral appraiser, determining a so-called “objectified” value. And the definition for this objectified value is almost identical with the definition given above by Damodaran on the intrinsic value. Bottom line, it’s pure pragmatism, driven by demand. Mediation Function The objective of the valuation in the mediation function is to determine a so-called “arbitration” value. This is a value calculated by an independent and neutral evaluator that must be reasonable to both parties in the sense that it protects their interests. The analyst must know the decision values of both parties (i.e. determine them) to be able to come up with an arbitration value. If the decision value of the buyer is above the decision value of the seller, there is a positive “area of agreement”. This area comprises all values between the two decision values. Exhibit 15: Positive Area of Agreement A transaction at any price between the two decision values protects the interests of both parties insofar as no side would end up in a worse situation compared to the status quo, i.e. without a transaction. How this positive area of agreement should be split between buyer and seller, has been object of intensive research in the German academic literature. 69 The practical relevance of the situation described here, i.e. two parties that can’t agree on a price calling for an independent and neutral evaluator to resolve the issue, is probably limited if the seller can’t be forced to 69 See for example Matschke/ Brösel, Business Valuation, Functions, Methods, Principles, 2021, 218 ff. <?page no="118"?> 118 8 Value and Price ‒ a Tangent on Valuation Theory sell. Typically, both parties would have their own “expert”, who would at best be ostensibly independent. The more likely scenario is that one party would build up negotiation power and strive for a solution that way. From the seller’s viewpoint, the easiest way to achieve this is to secure another firm offer for the company, i.e. generate an additional alternative. The same applies in principle to the buyer - only that the spectrum of the alternatives is different. He can consider acquiring a similar company (in case such a company exists and is available for sale), he can think about a greenfield investment, or follow other opportunities. If the decision value of the seller is above the decision value of the buyer, there is no positive area of agreement. A transaction makes no sense, since at any price at least one party would end up in a worse situation compared to the status quo (no transaction). In a so-called “non-dominated conflict situation”, where no party can enforce a transaction, each side would follow their own path - there would be no transaction. Things become different in a “dominated conflict situation”, i.e. in a situation where one party can enforce a transaction (e.g. squeeze-out of minority shareholders). Here typically requirements from the legislature and/ or the judicature will be made regarding the valuation. These regulations differ from legislation to legislation and are subject to (usually inertial) changes over time. Argumentation Function The objective of the valuation in the argumentation function is to support the negotiation position of one party. The purpose of the argumentation value is to influence the other party and so enhance the probability to finalize a favorable transaction. In chapter 7 we already worked out that most valuations performed in business practice serve the realization of the principal’s interest. We could exaggerate and - at the risk of sounding sarcastic - say that in the light of the functional valuation theory, all valuations performed in practice are argumentation valuations. Many people might turn up their noses at such a statement as they regard valuations as one of the supreme disciplines of management education with the requirement to fulfill rigorous scientific criteria. We’ve come full circle though if we look back at chapter 1 and remember the occasions at which valuations are performed: Apart from a few exceptions where legal regulations exist, most cases are about the unforced transfer of ownership in companies and shares in companies. To reach an agreement on this transfer, communication is necessary between buyer and seller, a common language. And valuations constitute such a language. Self-Test [1] What is the notion of a decision value? [2] Can values of companies be objective? <?page no="119"?> 9 Argumentation Values in Negotiations Learning Objectives  Recognize what it takes to come up with an argumentation value.  Gain an understanding of the most important ways to negotiate.  How to determine an argumentation value. 9.1 Determinants of the Argumentation Value What do you want to achieve in a negotiation to acquire or dispose of a company? As a potential buyer, you want to pay the lowest possible price. As a seller, you want the highest possible price. There is no difference between buying or selling a business and buying or selling a used car. An argumentation value or an argumentation opinion is a valuation that serves to assert your position. For a car, this could be the asking price for the same model with similar mileage and equipment, adjusted for the attractiveness of the car's color, level of usage, etc. There's nothing wrong with doing the same thing when negotiating the acquisition or sale of a business. As mentioned above, valuations serve as a communication tool. Own Decision Value But be careful: don't take the second step before the first! Don't forget the basic rules of corporate finance. An acquisition only makes sense if it creates value. So don't start calculating argumentation values right away, but first determine your own decision value. What is the maximum price you can pay for the company to be sold, with your options and alternatives, without being in a worse position than if your best realistic alternatives were realized? If you calculate an argumentation value without knowing where your decision value is, you are likely to shoot yourself in the foot. If you don't know where your decision value is because you've been focusing on market values and/ or prices, you're missing the most important reference point for calculating an argumentation value. Fix that first! If you're the principal and don't want to disclose that value to your external or internal advisors, fine but make sure you have the value. You should also be aware that your investment bankers have their own agendas. A higher purchase price usually leads to higher fees as a potential buyer, this is a conflict. You can mitigate this to some extent with a fee <?page no="120"?> 120 9 Argumentation Values in Negotiations structure that aligns interests, but the bottom line is that the majority of investment banking fees are contingent fees, i.e. the bankers will always push for a transaction, whether on the buy side or the sell side. Assumed Decision Value of the Other Party The next important point of reference is the estimated decision value, the likely limit of the other party's willingness to make concessions. Before you invest time in calculating an argumentation value, find out if there is a positive area of agreement. What is your counterparty's best realistic alternative? What is your estimate of the highest competitive offer? What are the costs of liquidating the business? Are there similar businesses on the market and what is their expected purchase price? How much would it cost a potential buyer to start from scratch and how long would it take? These are all sample questions designed to assess the best realistic alternative for the other side. The result will be an estimate, but invest the time, it usually pays off. Power plays an important role in negotiations. If you are one of thirtyfive bidders in an auction process, your negotiation power will be smaller compared to being the preferred buyer in a one-to-one negotiated transaction. Power is, among other things, a function of alternatives. Try to find out what alternatives the counterparty has and think about your own alternatives. If you are not happy with them, work on your alternatives before you come to the negotiation table. Your alternatives influence your decision value. 9.2 The Art of Negotiation If you can't spot the sucker in your first half hour at the table, then you are the sucker. (Mike McDermott in the movie Rounders) Now that you have an estimate of the other party's decision value and your own decision value, let's further assume that you are the potential buyer and your decision value is above the seller's decision value, i.e., there is a positive area of agreement. It goes without saying that you would like to have the largest part, ideally the entire positive area of agreement for yourself. But how do you achieve this? Where should the argumentation value be? There are many “schools of negotiation” you can revert to. The Havard Negotiation Project, developed by Harvard Law School, is the best known and most widely taught. 70 The following explanations are based on “The 70 For more information, visit https: / / www.pon.harvard.edu/ about/ . <?page no="121"?> 9.2 The Art of Negotiation 121 Complete Negotiator” by Michael Hartley-Brewer. 71 Try to make use of the anchoring effect described before and place the argumentation value near the estimated decision value of the counterparty. The following exhibit shows this from the viewpoint of a potential buyer: Exhibit 16: Argumentation Value Move first and don’t wait for the counterparty to make the first move, because the anchoring effect might work against you. This is the advice of most negotiation experts. There are numerous psychological studies that essentially support it. 72 And don’t go too far beyond the expected limit of concession willingness as the anchor might not work there. Examples Let's say you're the seller and your decision value is $200. If the buyer moves first and makes an offer of $195, the danger is that all your thoughts will be focused on how to get the buyer to at least $200 (if so, your counterpart has successfully placed the anchor). If your best guess of the buyer's decision value was $250, it would have been better to move first and make an offer of $255. If your estimate was correct and the anchor effect works, the buyer's efforts will be focused on negotiating the price down to a maximum of $250. The anchor would probably not work at $100 or $350, as the other side would probably find it unreasonable. 71 Not publicly available. We are using the 2001 edition, but there are numerous references and practical examples on this company's website, https: / / hartley-brewer.com. 72 See, for example, Galinsky/ Mussweiler, First Offers as Anchors: The Role of Perspective- Taking and Negotiator Focus, Journal of Personality and Social Psychology, 2001, Vol. 81, No. 4, 657-669. <?page no="122"?> 122 9 Argumentation Values in Negotiations To take another more personal example, suppose you and your partner are discussing your next holiday destination. Your partner prefers a beach holiday, while you would like to go hiking in the mountains. If you start the negotiations by suggesting a trekking holiday in Nepal, there is a good chance that you will end up spending your next holiday on a beach that is boring from your point of view. Suggesting a place like Lake Garda in Italy should work better there is a beach (by the lake and not by the sea, but still a beach) and there are mountains. The anchor could work there in such a way that future negotiations would focus on which lake in the Alps would be best, rather than which beaches in France, Italy, Greece or Turkey would be best. When negotiating, it is wise to first analyze whether we are in a cooperative or competitive situation. Are we "baking a cake" or "cutting a cake"? This is usually referred to as  Win-Win or  Win-Lose. Creativity is required in cooperative negotiation situations. For example, if you are negotiating with an entrepreneur to sell his or her life's work, you can try to create value for all parties by removing non-operating assets, entering into a consulting agreement, and retaining the company car and housing rights. Creativity is undoubtedly the most difficult mode of negotiation. Nevertheless, we should use it as often as possible because it stands for maximizing the overall benefit (Win-Win) while maintaining good relations with the counterparty. However, it also requires that the other party is interested in a cooperative solution in the first place. In Win-Lose situations, there are two possible negotiation modes:  Reason or argument, and  Power. Many people tend to think of reason as the ideal approach to negotiation. May the party with the better arguments win. However, many negotiations are decided on the basis of power. Think about how many arguments we had with our parents as kids about why we wanted to turn off the lights later or why we wanted to come home later. And honestly, are we any different to our own children when it comes to how long they can use their smartphones in the evening? The power, or even the perceived power, over the Wi-Fi password or the amount of allowance works wonders and makes long arguments with the other side unnecessary. However, this comes at a cost, as it can have a negative impact on the relationship. <?page no="123"?> 9.3 Argumentation Value Determination 123 73 Readers interested in auction theory are referred to Klemperer, Auctions: Theory and Practice, available online here: https: / / www.nuffield.ox.ac.uk/ users/ klemperer/ Virtual- Book/ VBCrevisedv2.asp The same applies to negotiations to buy or sell a business. If the size of the cake is fixed, i.e., it is just a matter of cutting it, and it is a one-time transaction with no impact on the relationship, and we have most of the power, then we should use it. The same is true if the other party is playing the power card and is not open to arguments. Before entering into negotiations, it is advisable to analyze the distribution of negotiating power and to consider how one's own negotiating position can be strengthened. For a potential seller, each additional serious party interested in the business for sale represents an improvement in his or her position of power. For this very reason, sellers often try to sell companies through an auction process. 73 As an interested buyer, you are then one of many, which means you have little or no negotiating power. As one of many potential buyers in an auction, what can you do to improve this situation? The so-called "last man standing" strategy, where you try to survive round after round of the auction process until you are the winner at the end, is risky because you will not be the only one pursuing this strategy. A possible alternative would be to break the rules by submitting a preemptive bid to gain exclusivity for a period of time and complete the transaction. However, the seller will only accept this if the preemptive bid is attractive to the seller and significantly higher than the expected bids of the other auction participants. This, in turn, carries the risk that you lose sight of your own decision value in the course of the dynamics, i.e. that you submit a bid that is above your concession threshold. You would then be making a bad deal, violating the basic rules of corporate finance, and destroying value. Therefore, it is important for the buyer to consider his or her alternatives prior to the auction process and to work on developing additional alternatives if necessary. The alternatives ultimately determine the decision value and thus the bid. 9.3 Argumentation Value Determination To come up with an argumentation value, use the toolset introduced in chapter 7.3. If you did your “homework” (described in chapters 2, 3, 4 and 6), you should have everything at hand, and it should be fun! Regard it as an intellectual challenge and confrontation, not as a scientific exercise. Chances are high that the counterparty will act similar. <?page no="124"?> 124 9 Argumentation Values in Negotiations As pointed out in chapter 7.3, any valuation method requires judgment. And wherever we use judgment, there is room for leeway. Use this leeway, there is nothing wrong with it. You are not being asked to provide a high quality and independent appraisal. You want the biggest piece of the pie, ideally the whole pie. But use the leeway wisely. For example, if your counterparty is a multinational conglomerate and you know they use a DCF approach with a discount rate of, say, 10% for all their investment proposals, don't argue about the 10%. Instead, focus on future free cash flows. And do not overdo it. Anchors may not work if you stray too far from what is considered best practice. As an example of what is possible and sort of normal in valuation practice, search the web for published valuations by investment banks in connection with public mergers or squeeze-outs. The valuations of the investment banks involved in Tesla's acquisition of Solar City drew bitter (but justified) comments from the "Dean of Valuation" 74 , but the deal went through. The valuation methods to be used for determining argumentation values depend on the individual case. It is difficult to make general statements. 75 Self-Test [1] What should you have before you commence purchase price negotiations on an acquisition? [2] Suppose you are the prospective buyer of a company and you have set a decision value for yourself, i.e. a maximum possible price of 500, based on your investment alternatives. You assume that there is exactly one other seriously interested bidder, but that the business for sale would not suit this bidder as well as it would suit you. You expect this bidder to make a maximum offer of 400. You also estimate the decision value of the seller, a family business, at 420, based on the assumption that non-family managers will run the business in the future. How should you approach the negotiations? 74 Damodaran, Keystone Kop Valuations: Lazard, Evercore and the TSLA/ SCTY Deal, https: / / aswathdamodaran.blogspot.com/ 2016/ 09/ keystone-kop-valuations-lazard-evercore.html 75 Setiadarma made an analysis based on the types of companies, but did not get a clear result. Setiadarma, Building Bridges to Successful Deals: The Art of Valuation and Negotiation, pages 47 ff., https: / / opus4.kobv.de/ opus4-htw/ frontdoor/ index/ index/ docId/ 1919. <?page no="125"?> Self-Test Questions ‒ Proposal for Solutions Chapter 2 [1] Can you explain the difference between the enterprise DCF method and the equity DCF method? 𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 = 𝐸𝐸𝐸𝐸𝐸𝐸𝑅𝑅𝑅𝑅𝐸𝐸 𝑉𝑉𝐶𝐶𝐶𝐶𝐸𝐸𝑅𝑅 + 𝑁𝑁𝑅𝑅𝑅𝑅 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 𝐹𝐹𝑅𝑅𝑅𝑅ℎ 𝑁𝑁𝑅𝑅𝑅𝑅 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 = 𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝐸𝐸𝑅𝑅𝑅𝑅𝑅𝑅-𝐸𝐸𝑅𝑅𝐶𝐶𝐸𝐸𝑅𝑅𝑅𝑅𝑊𝑊 𝐷𝐷𝑅𝑅𝐷𝐷𝑅𝑅 − 𝐶𝐶𝐶𝐶𝑅𝑅ℎ The enterprise DCF method determines the enterprise value by discounting the future free cash flows to the firm (cash flows before debt and cost of debt) at the weighted average cost of capital (WACC). The equity DCF method directly determines the equity value by discounting the future free cash flows to equity (cash flows after changes in interest-bearing debt and cost of debt) at the cost of equity. [2] The equity value of a company amounts to $200 million, the interestbearing debt is $100 million, and the company has a cash balance of $50 million (all of this can be regarded as excess cash). What is the enterprise value of the company? $250 million = $200 million plus ($100 million minus $50 million) [3] Can you describe the two common methods to determine the terminal value? The two methods are the perpetuity growth method and the exit multiple method. The perpetuity growth method assumes that the cash flow of the last year of the detailed planning period grows at a constant rate (the rate can be positive, zero, or negative). The terminal value is the present value of this growing perpetuity. The exit multiple method assumes a sale of the company at the end of the detailed planning period at a market multiple (typically EBITDA or EBIT). Chapter 3 [1] What is the advantage of EBITDA multiples compared to EBIT multiples? Depreciation expenses have no effect on the multiple. Companies with different depreciation policies and amortization cycles can be compared in a more meaningful way. <?page no="126"?> 126 Self-Test Questions ‒ Proposal for Solutions [2] How does the profitability of a company get into the sales multiple? The sales multiple is defined as the enterprise value divided by sales. The denominator, i.e. the enterprise value can be rewritten as free cash flows to the firm divided by WACC minus the growth rate. The free cash flows to the firm again are affected by the company’s profitability (EBIAT times (1 minus the reinvestment rate)). Chapter 4 [1] Why are the multiples derived from a precedent transactions analysis typically higher than those calculated based on publicly quoted comparable companies? Because they typically contain a control premium and/ or a premium for expected synergies. [2] You perform research on comparable transactions and come across data from a deal where 5% of the shares in a company were sold. How do you handle this? Since it’s not a majority takeover, the purchase price paid will probably not contain a premium for control and/ or synergies. The information has a different quality compared to a purchase price paid in a majority takeover. Nevertheless, it can serve as an indicator. Chapter 5 [1] Can you explain the differences between the adjusted present value method and the enterprise discounted cash flow method? The APV (adjusted present value) method is a variant of the enterprise DCF method. In a first step, an enterprise value is derived under the assumption that the company being valued is entirely debt-free. In a second step, the value of the tax shield is determined separately. [2] How does the equity discounted cash flow approach differ from the German earnings value approach? Both methods determine directly the equity value by discounting future free cash flows to equity at the cost of equity. Insofar there is no difference. Historically there used to be a dissimilarity in the derivation of the risk premium in the discount rate. Internationally, a recourse on the capital asset pricing model (CAPM) has been the standard approach for long, whereas in Germany this has gained acceptance later. <?page no="127"?> Self-Test Questions ‒ Proposal for Solutions 127 Chapter 6 [1] What is the fundamental difference between the treasury stock method and the option price models in determining the value of management stock options? The treasury stock method only recognizes options that are in the money and assumes their immediate exercise. The option price models consider the life of the option. [2] Please explain the different treatments of excess cash in the enterprise DCF method and the equity DCF method. The enterprise DCF method is based on the operating result of the company being valued, the EBIT. Therefore, neither interest income nor interest expenses affect the calculation of the enterprise value. Excess cash is valued separately and added to the enterprise value; the result is typically labelled as “firm value”. The equity DCF method typically starts the derivation of the free cash flows to equity at the company’s net income. Net income is a measure after interest expenses (no problem), but also after interest income (there is a potential problem). If the interest income is not properly adjusted, it will be discounted at the cost of equity, i.e. at a non-risk equivalent rate. Chapter 7 [1] You suspect that the other side “tuned” the valuation to come up with a high value for the company. What would you look for first? We would suggest starting with the sales projections, since the top line of the income statement normally has the biggest impact on the value. The growth rate assumed for the calculation of the terminal value would be next on our list. [2] You intend to dispose of a subsidiary of your group and invited five investment banks/ M&A advisers to a pitch presentation. Do you expect “conservative” or “ambitious” valuations? Since all advisers want to win the mandate (let’s assume it’s a reasonably good project), they will all try to convince you that they are the ones that will get the most out of the deal for you. In principle, you can expect the values presented to be at the upper end of a realistic range. Chapter 8 [1] What is the notion of a decision value? A decision value is a limit price. For a potential buyer, it is the maximum price she or he can afford to pay. For a potential seller, it is the minimum <?page no="128"?> 128 Self-Test Questions ‒ Proposal for Solutions price she or he must receive. For both: to not end up in a worse position compared to the next best alternative. Decision-oriented business economics. [2] Can values of companies be objective? The answer to this question depends on which school of thought regarding values you intend to follow. If you see companies as financial assets generating free cash flows that can be projected properly by an unbiased analyst as the company’s weighted average cost of capital, your answer will probably be “yes”. If you interpret valuation as a process of assigning a monetary term by someone (the valuation subject) to the company (the valuation object), your answer will be “no”. Chapter 9 [1] What should you have before you commence purchase price negotiations on an acquisition? You should first know your own decision value, your limit price, your limit of concession willingness. Second you should have an estimate where the limit of your counterparty is. What is their best realistic alternative? If there is a positive area of agreement, you should third have an argumentation value, ideally close to the decision value of the counterparty. Additionally, you should have a valuation backing this argumentation value and be prepared for expected counters of the other party. [2] Suppose you are the prospective buyer of a company and you have set a decision value for yourself, i.e. a maximum possible price of 500, based on your investment alternatives. You assume that there is exactly one other seriously interested bidder, but that the business for sale would not suit this bidder as well as it would suit you. You expect this bidder to make a maximum offer of 400. You also estimate the decision value of the seller, a family business, at 420, based on the assumption that nonfamily managers will run the business in the future. How should you approach the negotiations? We suggest that you do not wait for other parties' bids, and that you move first with an offer of 410. This is above the other bidder's estimated decision value and slightly below the seller's decision value. If the anchor effect is working, there is a good chance of getting a deal at a little above 420, taking most of the pie, i.e., the positive range of agreement (prices between 420 and 500). <?page no="129"?> Index After-tax cost of debt see cost of debt APV (adjusted present value) valuation 76-79 Arbitration value 117-18 Area of agreement 117-18 Argumentation function 118 Argumentation value 118 determinants 119-20 determination 123-24 in negotiations 120-23 Asset-based valuation 75-76 Base program 114 Beta 40-43 Cash and cash equivalents 21, 83-85 Comparable companies analysis 51 Control premium 63 Cost of debt 43-44 Cost of equity 38-43 DCF valuation 18 Debt 21-23 Decision function 113-14 Decision value 113-17 Earnings value method see equity DCF valuation EBIT multiple 55-57 EBITDA multiple 55-57 Enterprise DCF valuation 20, 23, 24 Enterprise value 23 Equity 21-23 Equity DCF valuation 20, 80-82 Equity risk premium see market risk premium Exit multiple method 47-48 Firm value 23 Football field format 61 Free cash flow 18, 31-35 Functional valuation theory 113 Holdings 85-86 Interest-bearing debt see debt Intrinsic value 111-12 LBO valuation 69-73 Leeway in valuations 102-8 Market risk premium 39-40 Mediation function 117-18 Minority interest see noncontrolling interest Noncontrolling interest 86-87 Non-operating assets 87-88 Normalization 29 Objective (objectified) value 111-12 Objectives of valuations 98-102 Occasions for corporate valuations 13 Off-balance-sheet financing 92- 93 Option-based valuation 73-75 P/ E multiple 53-54 <?page no="130"?> 130 Index PEG (price/ earnings to growth) ratio 54-55 Pensions 89-91 Perpetuity growth method 45- 47 Prices and values of companies 109-11 Real options see option-based valuation Reinvestment 34-35 Risk-free rate 39 Sales multiple 57-58 Stock options 93-95 Subjective value 111-12 Synergy 64 Terminal value 25, 44-48 Treasury stock method 94-95 Two-stage DCF valuation model 25 Valuation program 115 Weighted average cost of capital (WACC) 36-44 <?page no="131"?> ISBN 978-3-381-13531-8 This textbook provides readers with an interesting overview of the field of corporate valuation in a quick and easy way. For the second edition, the authors have added a new 9 th chapter devoted to valuations and the use of argumentation values in negotiation situations. The book includes a number of self-test questions with answers. The contents: Introduction / Discounted Cash Flow Valuation (DCF Valuation) / Comparable Companies Analysis / Precedent Transactions Analysis / Further Valuation Methods / From Enterprise Value to Equity Value / The Tension between Principals, Evaluators, Objectives and Leeway in Corporate Valuations / Value and Price - a Tangent on Valuation Theory / Argumentation Values in Negotiations / Self-Test Questions - Proposal for Solutions. Prof. Dr. Ralf Hafner has been Professor of International Business with a focus on Finance & Accounting at the HTW Berlin since 2013. Prior to that, he worked for 25 years as an M&A consultant in leading positions at various consulting firms and investment banks. Prof. Dr. Veit Wohlgemuth is Professor of Business Administration with a focus on Corporate Finance. He has been teaching at the HTW Berlin since 2014 in various programs that offer specialized classes for corporate valuations. Hafner / Wohlgemuth Corporate Valuation 2 nd Ed. Ralf Hafner / Veit Wohlgemuth Corporate Valuation 2 nd Edition