Vysoká škola ekonomická v Praze
Diplomová práce
2007 Antonín Dvořák
Vysoká škola ekonomická v Praze Fakulta podnikohospodářská
Hlavní specializace: Podniková ekonomika a management
Název diplomové práce:
Principles and Pitfalls of Terminal Value in DCF
Vypracoval: Antonín Dvořák
Vedoucí diplomové práce: prof. Ing. Eva Kislingerová, CSc.
P r o h l á š e n í
Prohlašuji, že diplomovou práci na téma
„Principles and Pitfalls of Terminal Value in DCF“
jsem vypracoval samostatně.
Použitou literaturu a podkladové materiály uvádím v přiloženém seznamu literatury.
D e c l a r a t i o n
I hereby declare that I wrote this thesis
“Principles and Pitfalls of Terminal Value in DCF“
solely by myself.
The used literature and other sources are stated in the attached reference list.
V Praze dne 24. srpna 2007 Podpis
P o d ě k o v á n í
Na tomto místě bych rád poděkoval vedoucí mé diplomové práce prof. Ing. Evě Kislingerové, CSc. za její vedení. Můj dík za mnoho hodnotných diskusí patří také mým pracovním kolegům, zejména pak PhDr. Tomáši Merknerovi.
A c k n o w l e d g e m e n t s
Here, I would like to express my thanks to the tutor of my thesis prof. Ing. Eva Kislingerová, CSc. for her counseling. My thanks for many rewarding discussions go also to my work colleagues, in particular to PhDr. Tomáš Merkner.
Contents
1 Preface ... 4
2 Objectives and Tasks... 5
2.1 Hypothesis... 5
2.2 Steps... 5
3 Introduction... 7
4 Regulation of Business Valuation... 8
5 Business Value Concepts... 11
6 Business Valuation Methods ... 12
6.1 Balance Sheet Approach... 12
6.2 Market Approach... 13
6.3 Income Approach ... 14
7 Discounted Cash Flow Valuation ... 17
7.1 Cash Flow ... 17
7.2 Discount Rate... 18
7.3 Explicit Forecast Horizon ... 23
8 The Importance of Terminal Value for the Enterprise Value... 24
9 Techniques of Terminal Value Calculation... 26
9.1 No Terminal Value ... 26
9.2 Perpetuity Model ... 27
9.3 Gordon Growth Model ... 27
9.4 Value Driver Formula... 28
9.5 Jennergren’s Formula ... 29
9.6 Derived Formula... 32
9.7 Multiple-based Terminal Value Assessment ... 34
9.8 Liquidation Value... 34
9.9 Replacement Cost... 35
9.10 Terminal Value Equal to Current Enterprise Value ... 35
10 Parameters of Terminal Value ... 36
10.1 Discount Rate for the Terminal Value... 36
10.2 Growth ... 40
10.3 Free Cash Flow in Terminal Value ... 43
11 Terminal Value Guidelines in Valuation Standards... 51
11.1 International Valuation Standards ... 51
11.2 European Valuation Standards... 52
11.3 Other Guidelines for Terminal Value Assessment... 53
12 Recommendations for Terminal Value Assessment ... 54
13 Business Valuations Reviews ... 57
13.1 Česká gumárenská společnost a.s... 58
13.2 Česká pojišťovna a.s... 60
13.3 Farmet a.s... 61
13.4 Holcim (Česko) a.s... 64
13.5 Juta a.s... 65
13.6 MD logistika, a.s. ... 67
13.7 Rubena a.s. ... 69
13.8 Saint-Gobain Vertex, a.s. ... 71
13.9 Wienerberger cihlářský průmysl, a.s... 72
13.10 ZZN Havlíčkův Brod a.s... 75
13.11 Živnostenská banka, a.s. ... 76
13.12 Summary of the Key Findings... 77
14 Conclusion ... 83
15 List of Abbreviations... 85
16 References... 87
Appendices (on CD)
Appendix I Valuation report of Česká gumárenská, a.s.
Appendix II Valuation report of Česká pojišťovna a.s.
Appendix III Valuation report of Farmet a.s.
Appendix IV Valuation report of Holcim (Česko) a.s.
Appendix V Valuation report of Juta a.s.
Appendix VI Valuation report of MD logistika, a.s.
Appendix VII Valuation report of Rubena a.s.
Appendix VIII Valuation report of Saint-Gobain Vertex a.s.
Appendix IX Valuation report of Wienerberger cihlářský průmysl, a.s.
Appendix X Valuation report of ZZN Havlíčkův Brod Appendix XI Valuation report of Živnostenská banka, a.s.
Tables
Table 1: Relations of Capital Expenditures to Depreciation for Different Nominal Terminal
Growth Rate (g) and Average PPE Lifetime (n)... 32
Table 2: Historical Equity Market Risk Premiums... 36
Table 3: Weighted Average Historical EMRP ... 37
Table 4: Country Risk Premium Based on Country Rating... 38
Table 5: Sensitivity of the Terminal Value to the Terminal Growth... 41
Table 6: Estimating the FCFF for Terminal Value 1/2... 44
Table 7: Estimating the FCFF for Terminal Value 2/2... 45
Table 8: Terminal Value Sensitivity to RONIC at Different Levels of Terminal Growth ... 49
Table 9: Comparison of Change in Sales and Working Capital... 63
Table 10: Adjusted WACC for Juta a.s... 66
Table 11: Terminal RONIC Derivation ... 67
Table 12: European Chemical Fibers Producers Provided by Prof. Damodaran ... 71
Table 13: Debt Leverage in the Clay Building Products Manufacture Industry... 74
Table 14: Reasoning of the Assumed Terminal Growth Rates ... 79
Table 15: Terminal Ratio of CapEx to Depreciation ... 80
Figures
Figure 1: Basic Valuation Approaches Overview ... 12Figure 2: How Different Valuation Models Focus on Different Cash Flow Measures ... 15
Figure 3: Terminal Value as a Percentage of Total Value (Eight-Year Forecast Period) ... 24
Figure 4: Weights for the Weighted Average EMRP (q = 0.985)... 37
Figure 5: Estimate of the EMRP for a Mature Equity Market ... 38
Figure 6: ROIC–WACC Spread based on the Life Cycle Theory... 49
Figure 7: Proportion of DCF Value Allocated to the Explicit Forecast Period and to the Terminal Period... 78
Figure 8: Formulas for Terminal Value calculation ... 78
Figure 9: Nominal Growth Gate Assumed for Terminal Period ... 79
Figure 10: Comparison of RONIC and WACC Implicitly Assumed for the Terminal Period 80 Figure 11: Variance of the Original DCF Value from the DCF Value after Adjustments to the Terminal Value... 81
1 Preface
Property valuation is a discipline with a wide range of application. It is an interesting topic bringing together many other disciplines. Especially valuation of a business – to a certain extent an abstract organism – may be amazing challenge. I started to engage in business valuation professionally eleven months ago. Since then, I have been enjoying it.
From the first time when I learned about the discounted cash flow valuation some seven years ago, I have been fascinated by its element called terminal value. This small object located at the end of the DCF calculation usually comprises the most of the business value. Its importance also implies a considerable potential risk of incorrect enterprise value estimation.
During the last eleven month, I realized that the terminal value assessment is not that straightforward as it might seem at first sight; on the contrary, it might be a very tricky task.
“Most DCF models fail to meet the standards of economic soundness and transparency.”
(Mauboussin, 2006, p. 2) One of the key reasons is inappropriate terminal value assessment.
By now, I have got some evidence of errors in terminal value estimations too. This fact as well as discussions with two of my colleagues – PhDr. Tomáš Merkner, and Ing. Lukáš Vašák – have motivated me to deal with the topic of terminal value assessment in my thesis.
2 Objectives and Tasks
DCF models are the most frequently used tools for business valuation. The terminal value usually represents the core of the value estimated through the DCF models. Potential small insufficiencies in the way of its assessment may have a fatal impact on the business value estimate.
2.1 Hypothesis
- It is possible to define the best practice for the terminal value assessment.
- Practical terminal value assessments often diverge from the best practice substantially, which has a material impact on the resulting business value estimate.
2.2 Steps
The following overview summarizes the suggested steps that are necessary to be passed in the course of the thesis elaboration.
- Definition of the best practice for terminal value assessment;
- Study of literature;
- Study of papers, studies, and conference papers;
- Study of relevant internet sources;
- Analysis of legal acts and valuation standards;
- Discussions with the tutor;
- Discussions with other teachers and experts in the field of property valuation;
- My own considerations and analyses;
- Formulation of the best practice for terminal value assessment.
- Examination of real business valuations with respect to compliance with the best practice for terminal value assessment;
- Business valuations gathering;
- Techniques of terminal value assessment analysis;
- Identification of substantial departures from the best practice;
- Quantification of impact on the value estimate (The quantification makes sense only in cases where the departure is evident and the suggested adjustment towards the best practice can be precisely defined.);
- Conclusions on compliance with the best practice.
3 Introduction
Valuation is not an exact science. Inevitably, it comprises a subjective element. “Value is not a fact, but an estimate of the likely price to be paid for goods and services at a given time in accordance with a particular definition of value.”(IVSC, 2005, p. 26)
Especially to estimate the future benefits of holding an asset is a real challenge in the current turbulent business environment where nobody knows what will happen tomorrow much less in twenty years.
The midstream macroeconomic outlooks for the coming years, for example, are generally positive. “However, under the surface, the imbalances keep building. As the USA leverage itself with abandon, a whole series of risks arise for them and for other countries. Households tend to be more and more leveraged and banks are still taking more and more risks. It’s hard to imagine global leverage growing much longer without consequence.” (Rubino, 2007, p. 49)
However difficult and challenging the task is, still there exist methodologies and basic valuation concepts allowing us to precise the established methodologies with the aim to provide reliable, transparent and unbiased estimates of property value.
4 Regulation of Business Valuation
The practice of business valuation is subject to regulation under numerous legal acts, international and national valuation standards.
In the Czech Republic, the legal acts include the following:
- Act no. 513/1991, Commercial Code (Obchodní zákoník);
- Act no. 151/1997, Property Valuation Act (Zákon o oceňování majetku);
- Act no. 36/1967, Experts and Translators Act (Zákon o znalcích a tlumočnících);
- Regulation no. 540/2002, Regulatory statute implementing the Property Valuation Act Moreover, the valuations for the purpose of so called squeeze-outs (subject to regulation under the Commercial Code) have to fulfill criteria stated by the Securities Committee (Komise pro cenné papíry) which has been integrated into the Czech National Bank recently.
The document regulating the subject is labeled ZNAL (Znalecké posudky pro účely povinných nabídek převzetí a veřejných návrhů smluv o koupi účastnických cenných papírů).
The international valuation standards include:
- International Valuation Standards (issued by IVSC);
- European Valuation Standards (issued by TEGoVA).
Other standards related to business valuation include for example the following:
- Business Valuation Standards (issued by ASA);
- Uniform Standards of Professional Appraisal Practice (issued by The Appraisal Foundation);
- RICS Appraisal and Valuation Standards (issued by RICS);
- German IDW standards (issued by IDW)
- IDW Standard no. 1 (IDW Standard: Grundsätze zu Durchführung von Unternehmensbewertungen) seems to be most related to the Czech environment (Mařík, 2004);
- Canadian Uniform Standards of Professional Appraisal Practice (issued by AIC);
- Russian Society of Appraisers’ Valuation Standards (issued by RSA).
The most significant valuation standards are the International Valuation Standards. Their principal objectives are as following:
- “To facilitate cross border transactions and contribute to the viability of international property markets;
- To serve as a professional benchmark, or beacon, for Valuers around the world; and - To provide Standards of valuation and financial reporting that meet the needs of
emerging and newly industrialized countries.”(IVSC, 2005, p.7)
The content of the IVS is very general and does not include any detail valuation methodology description. Rather, the IVS provide definitions and descriptions of general valuation concepts and principles, ethical requirements, general guidance notes, etc.
The national valuation standards often refer to the IVS and provide further details on valuation procedures and methods.
There do not exist similar national standards in the Czech Republic nowadays; however, the process of preparing the Czech valuation standards is ongoing.
The Czech Chamber of Appraisers (Česká komora odhadců majetku) together with The Institute of Property Valuation – UEP (Institut oceňování majetku – VŠE) are working on preparation of the Czech valuation standards. (ČKOM, 2007)
Participation on preparation of the Czech valuation standards is also one of several objectives within the research project named “Development of Financial and Accounting Theory and its Application in Practice from Interdisciplinary Point of View” that is currently being carried out at the University of Economics, Prague.
The objectives of the research project related to the field of valuation include the following:
- “Compare Czech legislation with international valuation standards;
- Prepare a proposal of complete systems of models and recommended procedures for business valuation and subsequent draft of national valuation standards;
- Develop models of business valuation and valuation of business assets;
- Assess errors in appraisals on regular basis.”(VŠE, 2007)
In the area of financial reporting, there is a clear tendency towards the fair value and market value concepts. Consequently, the financial accounting standards (e.g. IAS/IFRS) place higher attention and also special requirements on the area of property and business valuation.
The theory and the best practice define a framework for valuating businesses as well. There are many researchers and practitioners contributing systematically to the topic. The most well- known authors include:
- McKinsey’s teams led by Copeland T., Koller T., Murin J., and by Koller T., Goedhart M., Wessels D.;
- Damodaran, A.
In the Czech Republic, these include:
- Kislingerová, E.;
- Mařík, M.
5 Business Value Concepts
There are two basic business value concepts:
- Market value; and - Non-market value.
In most cases the market value concept is supposed to be applied. The International Valuation Standards (IVSC, 2005, p. 82) define the market value in the following way:
“Market Value is the estimated amount for which a property should exchange on the date of valuation between a willing buyer and a willing seller in an arm’s-length transaction after proper marketing wherein the parties had each acted knowledgeably, prudently and without compulsion.”
The IVS (IVSC, 2005) define the following non-market value concepts:
- Value in Use;
- Investment Value, or Worth;
- Going Concern Value;
- Insurable Value;
- Assessed, Rateable, or Taxable Value;
- Salvage Value;
- Liquidation or Forced Sale Value;
- Special Value;
- Mortgage Lending Value.
There exist some other value concepts as well. The so called Objectified Value is an example.
6 Business Valuation Methods
There exists a wide range of different valuation approaches and methods. The Figure 1 provides an overview of the basic approaches. There exist many combinations of the methods as well.
Figure 1: Basic Valuation Approaches Overview
Source: based on Kislingerová (2001)
Three largest valuation approaches are balance sheet approach, income approach, and market approach.
6.1 Balance Sheet Approach
The most traditional approach is the balance sheet approach. The value is estimated based on the analysis of the assets which the company possesses. The methods, especially the book
Valuation approaches
Direct
approach Market
approach
Income approach Contingency
claims approach Balance sheet
approach
Discounted cash flow approach Residual
income approach
Replacement value Book value
Liquidation value
EVA Adjusted
asset value
FCFF FCFE DDM
Capitalized net income Net income
approach First-hand
approach Relative
approach
IPOs approach Comparable transactions approach
Public comparables
approach Company’s
market cap.
Multiples AEG
Real options
value method, may be relatively straightforward and objective. The approach is often used in making lending decisions and in liquidation or distressed-company analysis. Its primary shortcoming is that it ignores the value of intangibles and assets in use. (Lee, 2003)
In most cases, however, a business should not be seen as a collection of assets. Rather it should be viewed as a living organism with its specific characteristics and abilities. That is much more than a poor set of bones and tissues. When looking at a balance sheet, one can not see any synergies which are definitely present in a healthy enterprise. Another question is a value of assets that is represented in a balance sheet. The financial statements are subject to accounting standards. Prudence is one of basic accounting concepts and is in conflict with a true and fair view of assets. It leads to intentionally biased financial statements.
Moreover, a value of a business comprises not only assets that it already owns but also assets it expects to invest in the future. The later are called growth assets. Typically, these are not to be found in a balance sheet. It is thus necessary to evaluate not only existing investments but also expected future investments and their profitability. (Damodaran, 2006)
6.2 Market Approach
A fundamentally different approach to business valuation is represented by the market comparison methods. A theoretical background of the approach rests on the law of one price.
It says that the same assets should be exchanged for the same prices. In this approach, similar assets to the valuated asset and their corresponding prices need to be identified.
The simplest technique is to assess the value of equity based on the company’s market capitalization. Obviously, the company’s shares must be publicly traded. A problem of this technique is that the quoted share price and the calculated market capitalization may overvalue or undervalue the equity significantly. Especially if the traded amounts are small and the liquidity is low. The assessment of the equity value is then based on the price of marginal portion of equity.
More often used approach is to compare the valuated company with prices of other similar companies. These may be publicly traded comparable companies listed on an exchange, comparable businesses being traded in an acquisition, or companies after an initial public offering.
Similar ratios between an enterprise (or equity) value and some business characteristics are assumed to hold for similar companies. These ratios are called multiples. The business
characteristics may be of financial as well as of non-financial origin. The most typical financial multiples include: EV/EBIT, EV/EBITDA, EV/Sales, EV/BV (here the BV represents the book value of capital employed), P/E, and P/BV (here the BV represents the book value of shareholders’ capital). Examples of the non-financial multiples may be:
EV/number of passengers per year, EV/number of seats, EV/number of employees etc.
A choice of the best multiple depends on industry, economic reasonability, and data availability. The best multiple may be the multiple that is economically reasonable and has the lowest variability across the peer group of comparable companies. (E. Kislingerová, personal communication, November 2006) With the exception of financial institutions, the EV-based multiples are generally preferred to the equity-based multiples.
After having chosen one or more multiples, a question what data should be put into the denominators of the multiples arises. It is possible to include figures from the latest available financial statements, for example. After all, this is the most common approach. However, it is sometimes better to use normalized values of the measures as some of the business characteristics may be highly volatile in time. EBIT and net income are examples of such characteristics.
One of the problems of multiples is that the numerator (e.g. EV) reflects the future; however, the denominator is usually based on current or historical data. A possibility is to use forecasted data. This makes sense especially for the company that is being valuated. Of course, this makes the valuation more subjective.
Another questionable point is the peer group construction. It is sometimes very difficult to set up a peer group of reasonably comparable companies running their business in the same industry sector, in the same region, having similar outlooks, etc. A valuer has to deal with the problem of information shortage. Consequently, an accuracy of the method might be sometimes very limited.
The approach may be very useful, especially as a secondary valuation method.
6.3 Income Approach
The income approach comprises many derivatives of the dividend discount model (DDM).
The approach is based on future cash flow/income forecasts and reflection of time value of money.
The elementary calculation has the following form:
n
i i
i
r DCF CF
1 (1 )
where: r Discount rate
n Remaining lifetime of an enterprise
“Following the stock market crash of 1929, discounted cash flow analysis gained popularity as a valuation method for stocks. Irving Fisher in his 1930 book "The Theory of Interest" and John Burr Williams’s 1938 text 'The Theory of Investment Value’ first formally expressed the DCF method in modern economic terms.”(Wikipedia: The Free Encyclopedia, 2007)
The following graph may help to orientate oneself in the approach.
Figure 2: How Different Valuation Models Focus on Different Cash Flow Measures
Based on Penman. (2001) cited in Lee (2003)
The Figure 2 ilustrates cash flows within and out of a firm. Net operating assets (NOA) are a value-creating engine of a company. They increase with operating revenue (OR) and decrease with operating expenses (OE). The net operating assets are interrelated with so called net financial assets (NFA) through cash flow from operations (C) and cash flow from investments (I). F represents the cash flow between the firm and its creditors. Net dividends or the cash flow to shareholders is labeled d. (Lee, 2003)
The dividend discount model was the original income approach technique. However, a
Customers
Suppliers Share-
holders Debt Issuers Product
and Input Markets
Capital Markets
Wealth Creation Wealth Distribution
NOA NFA
The Firm OR
I C
OE d
F
DCF (FCFF)
RIM DDM
Operating Activities Financing Activities C – I –ΔNFA + NFI = d OI –ΔNOA = C – I
includes C, I, and F), FCFF (Free Cash Flow to the Firm) and to the residual income models (RIM). Having many variations, the basic representative of RIM is the economic value added (EVA) model.
7 Discounted Cash Flow Valuation
“Discounted cash flow calculations have been used in some form since money was first lent at interest in ancient times. As a method of asset valuation it has often been opposed to accounting book value, which is based on the amount paid for the asset.” (Wikipedia: The Free Encyclopedia, 2007)
The DCF valuation is based, as it is obvious from its name, on transferring future cash flows to their present equivalent.
In the thesis, we aim to focus a priori on the most common valuation method – DCF based on free cash flow to the firm. However, most of the problems discussed apply also to other income methods.
7.1 Cash Flow
The free cash flow to the firm (FCFF) is the cash flow that is distributable to the investors after satisfying all the cash flow requirements of the business itself. The calculation of the FCFF is as following:
Operating Profit Before Interests and Taxes (≈ EBIT) – Tax
= NOPAT (NOPLAT)
+ Depreciation and Amortization – Capital Expenditures
– Change in Working Capital
= FCFF
FCFF belong to both owners and creditors. Thus by discounting the FCFF (and after adjustments for non-operating assets), an enterprise value is calculated. To calculate the equity value, debt (defined as interest-bearing liabilities) has to be subtracted.
Of course, the cash flow projection is inevitably subjective. Even if the projection is supported by appropriate research, industrial and economic knowledge, the element of subjectivity remains.
7.2 Discount Rate
Transfer of the future cash flows to their present value is done using a discount rate. The discount rate is such a rate that makes an investor indifferent between having an amount of money now and anticipating an income at a level of the amount increased by the discount rate in future.
A discount rate reflects the expected return on asset based on its riskiness. Cost of capital is the most common measure used as a discount rate. The cost of capital may, however, have two forms: cost of equity and weighted average cost of capital (WACC).
The cost of equity is used as a discount rate when directly valuing equity (e.g. through FCFE, DDM, CNI), the weighted average cost of capital is used when valuing primarily the whole enterprise (e.g. FCFF, EVA).
The weighted average cost of capital has two components: cost of equity and after-tax cost of debt.
) 1 ( t E r
D r D E D
WACC E e d
where: WACC Weighted average cost of capital
E Equity
D Debt (interest bearing liabilities)
re Cost of equity
rd Pre-tax cost of debt
t Tax rate
7.2.1 Cost of Equity
There are several ways of estimating the cost of equity. The most widespread, the most discussed, the most questionable, but also the most frequently used approach is the capital asset pricing model (CAPM).
The CAPM is based on the assumption that the cost of equity is based on two basic components. The first being the risk free interest rate, the second being a risk premium for a systematic risk of the market and the exposure of an asset to this risk.
The CAPM, firstly introduced by W. Sharpe, J. Lintner, and J. Treynor in the mid-1960s, can be expressed through the following relationship:
m f
f r r
r
r
where: r Expected return on an asset rf Risk free interest rate
rm Expected return on the market portfolio
Sensitivity to market movements
The difference between the expected return on an asset and the risk free interest rate represents the expected risk premium of an asset. The difference between the return on the market portfolio and the risk free interest rate is termed the market risk premium. The beta coefficient is a measure of contribution of an individual asset to the risk of a well-diversified portfolio. It is a measure of systematic risk.
There may be also adjustments to the basic version of CAPM. German business valuation guidelines IDW S 1, for example, proposed the so called Tax CAPM in October 2005. The model reflects different personal income tax rates on interest and dividends. The after-tax cost of equity is calculated in the following way (Wiese, 2004, cited in Schmitt & Dausend, 2007):
j
m
m
j j
tax
j r s i s r i s s
r 0.5 1 1 0.5
where: rjtax Expected return of company j after income tax rj Expected return of company j before income tax
rm Expected return of the market portfolio before income tax i Risk-free interest rate
δj Expected dividend yield of company j before income tax
δm Expected dividend yield of the market portfolio before income tax βj Beta factor of company j
s Personal tax rate
There are, however, many unrealistic assumptions behind the CAPM (see for example Kislingerová, 2001) making it too far from reality. As the proposed capital asset pricing model has its significant imperfections (see for example Black (1993) and Fama, French (1992), cited in Brealey, Myers, & Allen (2006)), other more or less different approaches have been developed.
One of the alternative approaches to CAPM is the arbitrage pricing theory (APT). The cost of equity is determined by sensitivity of particular stock to several risk factors contributing by different risk premiums. The calculation is as following:
n n f
e
r s p s p s p
r
1 1
2 2 ...
where: re Cost of equity rf Risk-free interest rate
s Sensitivity of a stock to various risk factors
p Risk premiums corresponding to various risk factors
The model may under certain conditions better explain volatility in returns on particular stocks compared to CAPM. A problem, however, is that the model is not standardized and thus allows for a huge portion of subjectivity regarding choice of the risk factors, assessment of their risk premiums, and sensitivity of the stock to the risk factors. “The general consensus is that APT’s complexity, lack of transparency, and reliance on particular US-based data providers makes it unlikely to become a world standard capable of competing with CAPM in the near future.”(Ogier, Rugman & Spicer, 2004)
Fama-French three factor model represents another alternative approach to CAPM. The authors Eugene F. Fama and Kenneth R. French showed that the relationship between beta and average asset return vanished in the period between 1963 and 1990. In response to this finding they proposed the following model (Ibbotson Associates, 2006):
v v s s m m f
e
r RP RP RP
r
where: re Cost of equity rf Risk-free interest rate
βm Market coefficient in the Fama-French regression RPm Equity market risk premium
βs Small-minus-big (SMB) coefficient in the Fama-French regression RPs The expected SMB risk premium, estimated as the difference between
the historical average annual returns on the small-capitalization and large-capitalization portfolios
βv High-minus-low (HML) coefficient in the Fama-French regression; and RPv The expected HML risk premium, estimated as the difference between
the historical average annual returns on the high book-to-market stocks and the low book-to-market stocks
More pragmatic, even more subjective, and practically more common approach (especially among non-professionals and individual valuers without proper information background) is the so called build-up method. The calculation is based on summation of risk-free rate and various more or less controversial premiums. The premiums may include for example: equity risk premium, industry risk premium, liquidity premium, control premium, flexibility premium, information access premium, etc.
Other approaches to cost of equity assessment include DCF model and Stochastic/Option pricing model.
Despite of its imperfections, CAPM remains the core technique of cost of equity assessment, although some adjustments (most commonly the size premium) are often being made.
7.2.2 Cost of Debt
A debt is defined as interest bearing liabilities. (It is actually very difficult to identify the interest bearing liabilities from the balance sheet prepared under the Czech accounting standards.)
Within the interest bearing liabilities, there are often different types of debt with different duration, different seniority, from different creditors, etc. Consequently the cost of the liabilities might be very different too. Short term senior debt, for example, may have a cost at a level slightly higher than the risk-free interest rate. Interest rate on mezzanine debt is on the other hand in average some 12% (Standard & Poor’s, cited in Davenport & Tinkelman, 2006) plus other fees or/and warrants lifting the overall cost to the range of 18 - 22%. (Abbasi, 2004) The arithmetic average should be used to calculate the overall cost of debt.
Any relevant off balance sheet items should be also accounted for.
There are two basic approaches of cost of debt assessment: direct and indirect. The direct approach means using the effective price of the valued company’s debt. Provided the debt has been obtained under market terms that are comparable to the current and future market terms, the cost of debt is usually known to the valuer and may serve for WACC calculation.
Data from the Czech National Bank may also give an idea about the current cost of debt in the Czech Republic. Bank interest rates on CZK-denominated loans by Czech non-financial corporations sorted according to amount and length of rate fixation period are to be found on the CNB’s websites.
Whenever estimating the cost of debt, a yield to maturity should be used. The yield to maturity should be never approximated by a bond’s coupon rate. (Koller, Goethard &
Wessels, 2005)
It is more appropriate, however, to use the indirect approach for the real market valuation.
The indirect approach is based on determination of cost of debt calculating the yield to maturity on corporate bonds for comparable companies. The yield curves for corporate bonds according to their credit rating are published for example by Bloomberg.
When other than market valuation is being prepared, it may be worthy to consider a possible change in cost of debt as a result of a change in gearing.
As an after-tax cost of debt serves as an input to the WACC calculation, the cost of debt should be lowered by the tax rate. A marginal tax rate should be used for this purpose.
7.2.3 Gearing for WACC
Market values of debt and equity should be used rather than book values. Especially the market value of equity might be far from the book value.
There are two basic possibilities of capital structures that may be applied for the calculation:
- Current structure; and - Target structure.
Which of them should be used to determine the cost of capital?
Some recommend the target weights for WACC calculation (e.g. Koller et al., 2005).
However, Mařík (2003), for example, tends to be in favor of the current structure and an iterative approach.
For market valuation as it is defined by the International Valuation Standards the target capital structure based on the optimal long-term capital structure should be used.
“To estimate Market Value, a Valuer must first determine highest and best use, or most probable use.”(IVSC, 2005, p.81)
The highest and best use is defined as:
“The most probable use of a property which is physically possible, appropriately justified, legally permissible, financially feasible, and which results in the highest value of the property being valued.”(IVSC, 2005, p.29)
Only the optimal capital structure is in accordance with the requirement of the highest and best use. It would be irrational to calculate with another capital structure. A consequent problem of the optimal structure determination arises. The starting point to estimate this might be observation of comparable companies and calculation of the average gearing within the industry.
An assumption is usually made that the capital structure may be changed towards the optimal structure immediately. However, it is possible to make continual adjustments of the current capital structure towards the target (optimal) capital structure.
Nevertheless, if the aim is to estimate other than market value, the current capital structure or the target capital structure that is different from the optimal capital structure might be applied.
7.3 Explicit Forecast Horizon
Typically, the projected cash flows are not explicitly forecasted forever. Rather the valuers forecast the cash flows for several coming years and then forecast the so called terminal value (also continuing or residual value). Terminal value represents the value of a business at the end of the first phase (explicit forecast period). However, it implicitly includes cash flows, which are expected to be generated for infinite future (under the going concern assumption).
The length of the explicit forecast period is usually from 3 to 15 years, most often from 4 to 7 years. As far as the minimum length of the explicit forecast period is concerned, Koller et al.
(2005, p. 278) claim that: “The explicit forecast should be long enough that the business will have reached a steady state by the end of the period.” It is useful and sometimes necessary to extend the explicit forecast beyond the moment of stabilization, as proposed in the section10.3.
The explicit forecast period could be alternatively set based on the investment cycle. Another quite reasonable proposition is to set such a length of the explicit forecast period to be able to capture the excess returns on new investment (returns above the cost of capital) with the terminal value component reflecting value after the company exhausts its incremental value- creation opportunities. (Mauboussin, 2006)
8 The Importance of Terminal Value for the Enterprise Value
The terminal value has an important role in the concept of DCF. In fact, the present value of cash flows beyond the horizon of explicit forecasts is usually much higher than the present value of cash flows projected in a business plan.
It is obvious that the proportion depends on factors like length of the first phase (explicit forecast period), applied discount rate, forecasted long term growth rate, etc. For example, the need for substantial investment in case of highly growing firms might have a strong effect on the initial cash flows. These will be lower and the importance of the terminal value will be higher. In an extreme example, the present value of cash flows after explicit forecast period might be higher than the overall enterprise value.
The following chart published by Copeland, Koller & Murrin (1994) shows terminal value as a percentage of total enterprise value for companies in four industries. In these examples, terminal value accounts for 56 percent to 125 percent of total value.
Figure 3: Terminal Value as a Percentage of Total Value (Eight-Year Forecast Period)
44%
19%
0%
56%
81%
100%
(25%) 125%
Tobacco Sporting goods Skin care High tech
Forecast period cash flow Continuing value
The terminal value is sometimes called continuing value, or residual value. Nevertheless, a residual value is not a good name in most cases, namely under the assumption of going concern. The name evokes a feeling that the terminal value is less substantial. However, the opposite is usually true.
“The terminal value estimate truly is the tail that wags the dog when it comes to DCF valuations.” (Lee, 2003, p. 5)
The terminal value comprises often the core of the enterprise value. The enterprise value is highly sensitive to the changes in the terminal value parameters. That’s why a valuer should pay a great attention to these parameters and the assumptions behind them. „Unfortunately, although terminal value may represent more than 50% of the value conclusion, it typically warrants only about 10% of the intellectual and analytical attention.” (Barnes, 1996, p. 25) The assumptions for the terminal value should be based on a comprehensive analysis as the assumptions for the business plan usually are. The valuer should provide a sound argumentation for all of the parameters of the terminal value.
Courteau, Kao & Richardson (2001, p. 656) compare bias and accuracy of two different valuation methods, RIM and DCF, concluding that “the dilemma over which valuation model to use is replaced by the challenge of forecasting post-horizon valuation attributes.”
9 Techniques of Terminal Value Calculation
9.1 No Terminal Value
One possibility is to use no terminal value and to forecast explicitly cash flows and their components for a very long time period (e.g. 150 years). This approach is not used very often and is sometimes considered as a theoretical option only. In many textbooks the technique is not mentioned at all. A marginalization of this technique may be a heritage from the times when there were no tabular editors or when their usage was not as widespread as it is nowadays. (D. Kittlauss, personal communication, April 2007)
The advantages of long term explicit forecasts include transparency. It is evident from the valuation what is really planned for a distant future. It is then possible to evaluate whether it seems to be reasonable or not. This can avoid some fatal mistakes. For example, it may hardly happen that the return on invested capital would grow without limits (as suggested by Koller et al., 2005).
Another advantage is consistency. There is no need for any artificial simplifications in the forecast for the purpose of fitting into a terminal value formula.
Any terminal value formula assumes a steady development of a firm. However, there is nothing like steady state in reality of many companies. When calculating the terminal value, stable capital expenditures are assumed for example. The real capital expenditures can be often described by the investment cycle. For example, a businessman operating a merry-go- round has to invest into a new device every fifteen years. His capital expenditures will be very high in one year but they will be zero during the following fourteen years. It is possible to reflect the lumpy capital expenditures when using the long term explicit forecasts.
The fact that this approach is not used in practice has its more or less rational reasons. It is partially a result of tradition and the above mentioned lack of computer technology in past.
The Microsoft Excel is, however, a fairly common and user friendly tool to take advantage of this approach.
A disadvantage is that it consumes a lot of space when including the “infinite” forecasts into a valuation report. It may also cause certain skepticism. Many would argue that a valuer is not able to forecast accurately what will happen in one hundred or even more years. Of course, that is not possible. But that is what a valuer must try to do and what valuers implicitly do in
any terminal value formula. The only differences are additional simplifying assumptions behind the terminal value formula.
It seems to be worthy to use this approach to double-check a reasonability of terminal value calculation.
9.2 Perpetuity Model
The perpetuity model expressed by the following formula is the simplest way of terminal value calculation using DCF approach with the going concern assumption.
WACC NOPLAT
TV n1
The calculation may make an impression that a company will not grow (neither in nominal terms). However, usually that is not a case. Usually we expect the company to grow, although without any impact on its value. In other words, the return on incremental investment is assumed to be equal to the cost of capital. The present value of growth opportunities will be zero. This may be a reasonable assumption as the companies often tend to reach zero economic profit in a long run.
9.3 Gordon Growth Model
The Gordon growth model is a version of the dividend growth model in which dividends grow at a constant rate. The basic Gordon formula is as following:
g WACC TV FCFFn
1
The formula is in fact a sum of infinite series. It is a geometric progression with the first term being FCFFn+1/(1+WACC) and the multiplier of (1+g)/(1+WACC). The formula is widely used and very popular for its simplicity. A certain problem might be its limited transparency.
There is no evidence of assumptions behind the FCFF.
Using this technique a valuer should pay a special attention to assessment of the FCFF in the first year after the period of explicit forecast.
9.4 Value Driver Formula
Koller et al. (2005) recommend the following value driver formula for DCF valuation:
g WACC
RONIC NOPLAT g
TV
t
1 1
where: TV Terminal value
NOPLATt+1 Normalized net operating profit less adjusted taxes in the first year after the explicit forecast period
g Expected growth rate in NOPLAT in perpetuity WACC Weighted average cost of capital
RONIC Expected rate of return on net new invested capital
The numerator of the formula represents FCFF in the first year of the terminal period.
Provided all assumptions (either explicitly or implicitly stated) are consistent, the value driver formula and the Gordon growth model provide exactly the same value.
The formula has several advantages compared to the Gordon growth model. It shows more transparently the assumptions behind the terminal value calculation, namely the expected rate of return on net new invested capital. It assures that the new investment (and thus also FCFF) for the terminal value is interrelated with the terminal growth parameter. Higher the growth higher the retention rate (g/RONIC) and thus lower the FCFF.
Using a sample of 45 IPO’s, Berkman, Bradbury & Ferguson (1998) provided an empirical evidence of higher accuracy of terminal value calculations with explicitly consistent assumptions to standard Gordon growth model.
A specific version of the value driver formula is its two-stage variation (Koller et al., 2005):
N B
B N B
A N t
A A
A A t
WACC g
WACC
RONIC g g
NOPLAT WACC
g g
WACC
RONIC NOPLAT g
TV 1
1 1
1 1 1
1 1
1
where: N Number of years in the first stage of the terminal period gA Expected growth rate in the first stage of the terminal period gB Expected growth rate in the second stage of the terminal period RONICA Expected incremental ROIC during the first stage of the terminal
period
RONICB Expected incremental ROIC during the second stage of the terminal period
The formula is suitable for high-growth companies and companies with significant excess returns allowing to capture the abnormal growth and abnormal returns beyond the explicit forecast period horizon.
It would be also possible to formulate a similar multistage terminal value calculation assuming for example a different length of the abnormal growth period and a different length of the period of abnormal return on invested capital.
9.5 Jennergren’s Formula
An alternative formula for terminal value calculation has been introduced by Jennergren (2003).
g WACC
H g n
H SM H gSw
H n SM
H t F H J gSM H t
H n SM z g S
TV
g
1
* 1 ) 1
1 1 (
* 1 )1 1 (
) 1 ) ( 1 ( )
1 1 (
* 1 )1 1 ( ) 1 )(
1 (
The following parameters need to be specified for the calculation:
g nominal growth rate;
1 ) 1 )(
1
(
i m
g
M steady state ratio between nominal gross PPE (property, plant and equipment) and (nominal) sales revenue;
F K M F
m g *
Fg relation between the nominal value of gross PPE at the end of the current year and the acquisition value of the last PPE cohort, which has been purchased at the end of the last year of the explicit forecast period;
g g F g
n g
) 1
) (
1 (
1
if g > 0; Fg = n if g = 0.
Fm relation between the real value of gross PPE at the end of the current year and the acquisition value of the last PPE cohort;
m m F m
n m
) 1
) (
1 (
1
if m > 0; Fm = n if m = 0.
H steady state accumulated depreciation as a fraction of nominal gross PPE;
1 ) 1 (
1 1
n
gn g
H if g > 0;
n H n
2
1
if g = 0.
n g
g ng
g g g
g g
q g
g qg
J g
n q
q n q
2
) 1 ( )
1 ( 2
) 1
( 1 ( 1)(1 )
) 1 (
* 1 )
1 ( 1 )
1 )(
1 (
1
The numerator in the formula represents the free cash flow to the firm in the first year after the explicit forecast period. It can be decomposed into the following segments.
NOPLAT:
H t F H J gSM H t
H n SM z g S
g(1 )
) 1 ( )
1 1 (
* 1 )1 1 ( ) 1 )(
1
(
Depreciation:
H H n
SM
1
* 1 )1 1 (
Change in working capital:
gSw
Capital expenditures:
H g n H
SM 1
* 1 ) 1
1 (
The additional tax reduction from the increase in deferred taxes is explicitly identified within the NOPLAT:
H t F H J gSM
g(1 )
) 1
(
See Jennergren (2003) for more detailed and comprehensive derivation and explanation of the formula and its particular components. The calculation seems to be somewhat complicated but it can be easily transferred into a valuation model in Microsoft Excel.
In total, there are nine input parameters only. They are as following:
m real growth rate;
i expected inflation;
z cash costs as a fraction of sales revenue;
t tax rate;
K capital intensity;
n PPE economic life;
q PPE life for fiscal depreciation; and WACC weighted average cost of capital.
Two of the input parameters, namely the capital intensity factor K (relation between real gross PPE and sales revenue) and the PPE economic life n, are rather elusive. Jennergren (2003) suggests a usage of data from Statistics Sweden. Based on this data, it is possible to estimate the parameters K and n for particular industries.
The formula should result in the same value as the formula suggested by Copeland et al.
(1994) under consistent assumptions. A particular value added by this calculation is in the FCFF calculation where the tax reduction from depreciation and the additional tax reduction from the increase in deferred taxes is identified. Moreover, the formula assures a consistency between the terminal value assumptions, namely between real growth, inflation, capital expenditures, depreciation, corresponding tax reductions, etc.
In addition to this, Jennergren (2003) provides a further decomposition of the terminal value formula and quantifies the PVGO (present value of growth opportunities) based on the above mentioned input parameters as a summation of the three following parameters:
i) present value of after tax sales revenue minus cash costs, and investment in working capital, from real growth (over an infinite period):
i WACC
iSw t z i S g
WACC
gSw t z g S
)(1 )(1 ) (1 )(1 )(1 ) 1
( ;
ii) present value of capital expenditures for real growth:
g WACC
i m F F
SM
WACC i
m g
n
) 1 ( 1 *
* 1
1 1
1 ;
iii) present value of tax savings from fiscal depreciation of capital expenditures for real growth:
WACC WACC q
t g
WACC
i m F F
SM
WACC i
m q g n
) 1
(
*1
* ) 1 ( 1 *
* 1
1 1
1
9.6 Derived Formula
Based on the calculations in the section 9.5, it is possible to define what should be the ratio between capital expenditures and depreciation in case of a stabilized business:
1 ) 1 ( 1
* 1 )1 1 (
1
* 1 ) 1
1 (
gn H
H H n
SM
H g n
H SM on Depreciati
CapEx
It is clear from the formula, how is the ratio dependent on the nominal growth rate g (which is a function of real growth and inflation), PPE economic life n, and the steady state accumulated depreciation as a fraction of nominal gross PPE, and H (which is again function of g and n).
The following table indicates the relation for different levels of terminal growth and different lengths of average PPE lifetime.
Table 1: Relations of Capital Expenditures to Depreciation for Different Nominal Terminal Growth Rate (g) and Average PPE Lifetime (n)
0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5% 5.0% 5.5% 6.0%
2
1.00 1.01 1.02 1.02 1.03 1.04 1.05 1.05 1.06 1.07 1.08 1.08 1.09 3
1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 4
1.00 1.01 1.03 1.04 1.05 1.06 1.08 1.09 1.10 1.11 1.13 1.14 1.15 5
1.00 1.02 1.03 1.05 1.06 1.08 1.09 1.11 1.12 1.14 1.15 1.17 1.19 6
1.00 1.02 1.04 1.05 1.07 1.09 1.11 1.13 1.14 1.16 1.18 1.20 1.22 7
1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.17 1.19 1.21 1.23 1.25 8
1.00 1.02 1.05 1.07 1.09 1.12 1.14 1.16 1.19 1.21 1.24 1.26 1.29 10 1.00 1.03 1.06 1.08 1.11 1.14 1.17 1.20 1.23 1.26 1.30 1.33 1.36 12 1.00 1.03 1.07 1.10 1.13 1.17 1.21 1.24 1.28 1.32 1.35 1.39 1.43 15 1.00 1.04 1.08 1.12 1.17 1.21 1.26 1.30 1.35 1.40 1.45 1.49 1.54 20 1.00 1.05 1.11 1.16 1.22 1.28 1.34 1.41 1.47 1.54 1.60 1.67 1.74 25 1.00 1.07 1.14 1.21 1.28 1.36 1.44 1.52 1.60 1.69 1.77 1.86 1.96 30 1.00 1.08 1.16 1.25 1.34 1.43 1.53 1.63 1.73 1.84 1.95 2.06 2.18 40 1.00 1.11 1.22 1.34 1.46 1.59 1.73 1.87 2.02 2.17 2.33 2.49 2.66 50 1.00 1.13 1.28 1.43 1.59 1.76 1.94 2.13 2.33 2.53 2.74 2.95 3.17
n \ g
The underlying assumption is that the capital intensity (real gross PPE to sales) is stable, which does not necessarily hold for all industries. In case of power generation, for instance, the ratio has dropped substantially during the last decades. (T. Maršálek, personal communication, March 2007)
The derived ratio may be quite useful for terminal value calculation. Depreciation (and amortization) is relatively stable item within a balance sheet provided a company does not intend to carry out any extraordinary growth or substantial changes in operations. Any such events should not be planned to happen immediately before the end of the explicit forecast period. By the end of this period, a company should have reached a stable stage. The usage of PPE expressed by depreciation should be then also stable and economically adequate. As stated in the IVS (IVSC, 2005, p. 221): “Depreciation may need to be adjusted to an estimate that compares more accurately to depreciation used in similar businesses.” It is thus appropriate and useful for a sound estimate of depreciation to adjust it towards the benchmark values.
Consequently, it is possible to estimate the capital expenditures in the (first year of) terminal value based on the depreciation and amortization estimate and on the above derived relation between capital expenditures and depreciation for stabilized business.
Now, we may express another formula for terminal value calculation:
g WACC
gSw H
gn D D t D EBITDA
TV
1 1 1
All the inputs are relevant to the first year after the explicit forecast horizon. Labeling of the individual parameters is the same as suggested in the previous section.
Using this approach for estimating capital expenditures assures that the capital expenditures (and thus also FCFF) for the terminal value are interrelated with the terminal growth parameter.
The approach appears to be very practical and relatively easy. On the other hand, an inappropriate assessment of depreciation may lead to error in estimate of capital expenditures.
Also the parameter of average PPE lifetime is a bit problematic.
