Excerpt

## I. Index

Abstract (English)

Abstract (Italiano)

I. Index

II. List of Tables

III. List of Figures

IV. List of Abbreviations

1. Introduction

1.1 Problem Definition

1.2 Objective and Organization of the Thesis

2. Discounted Cash Flow Method

2.1 Growth Pattern

2.2 Cash Flow Projection

2.3 Discount Rate

3. Beta Factor

3.1 Level of Beta Factor and its Economic Significance

3.2 Estimation of Beta Factor from Historical Returns

3.2.1 Regression Analysis

3.2.2 Practical Problems

3.2.3 Adjusted Beta

3.3 Alternative Methods of Estimation Beta Factor

3.3.1 Accounting Beta

3.3.2 Bottom-up Beta

3.3.3 Time-varying Beta

4. Terminal Value

4.1 Perpetuity Growth Method

4.1.1 Gordon Growth Model

4.1.2 Key Value Driver Formula

4.2 Exit Multiple Method

4.2.1 Equity Price Multiples

4.2.2 Enterprise Value Multiples

4.3 Comparison of Terminal Value Methods

5. Case Study: Microsoft Corporation

5.1 Company Overview

5.2 Database

5.3 Valuation of Microsoft Corporation

5.3.1 Discount Rate

5.3.2 Cash Flow Projection

5.3.3 Terminal Value

5.3.4 Intrinsic Value

5.4 Sensitivity Analysis and Critical Review

6. Conclusion and Outlook

Bibliography

Appendix

## Abstract (English)

Company valuation is requisite to identify the deviation of the intrinsic value of an asset from its market price. The Discounted Cash Flow method is a frequently used method to determine intrinsic value. It determines the intrinsic value based on the discounted future cash flow of the asset and works in two stages. The first stage refers to an explicit forecast of the cash flow followed by the second stage which captures the cash flow beyond the forecast period with a terminal value. The cash flow is usually discounted at the Weighted Average Cost of Capital which consists of the cost of debt and cost of equity. The latter is mainly determined by the systematic risk, measured with a beta factor.

The aim of the present thesis is to analyze beta factor and terminal value as the key input factors of the Discounted Cash Flow model. A comprehensive overview of the different estimation methods of beta factor and terminal value will be provided and critically reviewed. To illustrate the valuation procedure and to analyze the impact of both parameters on the intrinsic value, a case study of Microsoft Corporation is conducted.

The findings of the literature and the case study demonstrate that the main challenge of the Discounted Cash Flow model is the determination of terminal value and beta factor since both parameters can be estimated with different methods that lead to different results. Moreover, the case study provides evidence that the intrinsic value is sensitive to the input factors of terminal value and to the discount rate which is primarily determined by the beta factor.

The results indicate that analysts who apply the Discounted Cash Flow model should be aware that this model is mainly based on assumptions and therefore can lead to different results. The dependence of intrinsic value on the terminal value and the beta factor stresses the importance of a critical examination of these both parameters and requires a need for further investigation.

## Abstract (Italiano)

La valutazione della società è necessaria per identificare la deviazione del valore intrinseco di un'attività dal suo prezzo di mercato. Il flusso di cassa attualizzato è un metodo frequentemente utilizzato per determinare il valore intrinseco. Determina il valore intrinseco in base al flusso di cassa futuro attualizzato dell'attività e opera in due fasi. La prima fase si riferisce a una previsione esplicita del flusso di cassa seguita dalla seconda fase che cattura il flusso di cassa oltre il periodo di previsione da un valore terminale. Il flusso di cassa è generalmente scontato al costo medio ponderato del capitale che consiste in costo del debito e costo del patrimonio netto. Quest'ultimo è principalmente determinato dal rischio sistematico, espresso come fattore beta.

Lo scopo della presente tesi è di analizzare il fattore beta e il valore terminale come fattori chiave di input del modello DCF. Una panoramica completa dei diversi metodi di stima del fattore beta e del valore terminale sarà fornita e rivista criticamente. Al fine di illustrare la procedura di valutazione e analizzare l'impatto del fattore beta e del valore terminale sul valore intrinseco, viene condotto un case study della Microsoft Corporation.

I risultati ottenuti dalla letteratura e del case study dimostrano che la sfida principale del modello DCF è la determinazione del valore terminale e del fattore beta poiché entrambi i parametri possono essere stimati con metodi diversi che portano a risultati diversi. Inoltre, il case study fornisce prove del fatto che il valore intrinseco è sensibile agli input del valore terminale e al tasso di sconto che è principalmente determinato dal fattore beta.

I risultati indicano che gli analisti che applicano il modello di flusso di cassa attualizzato dovrebbero essere consapevoli del fatto che questo modello si basa principalmente su ipotesi e quindi può portare a risultati diversi. La dipendenza del valore intrinseco, dal valore terminale e dal fattore beta, sottolinea l'importanza di un esame critico di questi due parametri e richiede la necessità di ulteriori indagini.

## II. List of Tables

Table 1: Calculation of the Capital Structure in the High Growth Period

Table 2: Calculation of Cost of Debt in the High Growth Period

Table 3: Calculation of Weighted Equity Risk Premium

Table 4: Results of Historical Market Beta Calculation and Comparison with Service Beta

Table 5: Comparison of Microsoft with the Peer Group

Table 6: Calculation of Bottom-up Beta based on a Peer Group and an Industry Beta

Table 7: Calculation of Cost of Equity in the High Growth Period

Table 8: Calculation of WACC in the High Growth Period

Table 9: Calculation of Cost of Equity in the Terminal Period

Table 10: Calculation of WACC in the Terminal Period

Table 11: Summary of Cash Flow Projection

Table 12: Nominal GDP Growth Calculation

Table 13: Calculation of Terminal Value with Gordon Growth Model

Table 14: EV/EBITDA Multiples of the Peer Group (2015-2019)

Table 15: Calculation of Terminal Value with Exit Multiple Method

Table 16: Implied Terminal Growth Rate and Implied Exit Multiple

Table 17: Calculation of Enterprise Value, Equity Value and Share Price

Table 18: Sensitivity Analysis: Gordon Growth Model

Table 19: Sensitivity Analysis: Exit Multiple Method

Table 20: Sensitivity Analysis: Comparison of Terminal Value Methods

Table 21: Sensitivity Analysis: WACC and Beta Factor

## III. List of Figures

Figure 1: Two-Stage DCF Valuation with CF=100, TV=250, n=5 and r=0,05

Figure 2: Growth Pattern

Figure 3: Systematic Risk vs. Unsystematic Risk

Figure 4: Security Market Line (SML)

Figure 5: Movements of Stock Returns with Beta Factor Greater and Lower Than One

Figure 6: Simple Linear Regression

Figure 7: CAPM as an Equilibrium Model

Figure 8: Total Revenue, Operating Income and Operating Cash Flow 2015-2019

Figure 9: Microsoft Three-Stage Growth Model

Figure 10: Simple Linear Regression between Return on Microsoft Stocks and Return on NASDAQ Composite

## IV. List of Abbreviations

ACV Adjusted Company Value

AI Artificial Intelligence

BVE Book Value of Equity

c.p. ceteris paribus

Capex Capital expenditures

CAPM Capital Asset Pricing Model

DCF Discounted Cash Flow

DSV Distress Sale Value

EBIT Earnings Before Interest and Taxes

EBITDA Earnings Before Interest, Taxes, Depreciation & Amortization

EV Enterprise Value

FCFE Free Cash Flow to Equity

FCFF Free Cash Flow to Firm

GDP Gross Domestic Product

IC Invested Capital

LTI Long-term inflation

LTRG Long-term real growth

Non-cash ROC NCROE

NOPAT Net Operating Profit After Taxes

NOPLAT Net Operating Profit Less Adjusted Taxes

OLS Ordinary Least Squares

P Price

ROA Return on Assets

ROE Return on Equity

ROC Return on Capital

ROIC Return on Invested Capital

RONIC Return on New Invested Capital

SML Security Market Line

WACC Weighted Average Cost of Capital

## 1. Introduction

“Price is what you pay. Value is what you get” – this frequently quoted statement by Warren Buffett from 2008 demonstrates the need of distinguishing the market price from the intrinsic value of an asset. Markets are not always rational and market price can deviate from intrinsic value, resulting in a bubble. In response to the recent financial crisis beginning in 2007 caused by a bubble^{1}, the importance of valuation has increased. Understanding what drives value and how to measure it is an important step toward a more secure economy.^{2} By determining the intrinsic value of an asset, mispricing of the market prices and therefore under- or overvalued assets can be identified. However, unlike market prices, intrinsic values are not observable and need to be estimated.^{3}

The most common method to estimate the intrinsic value of an asset is the Discounted Cash Flow (DCF) method which is widely applied by practitioners and widely investigated by academics.^{4} The DCF model determines the intrinsic value by discounting its expected future cash flow. Since cash flow cannot be forecasted forever, the model works in two stages. The first stage corresponds to the explicit forecast period while the second stage corresponds to a terminal value which captures the amount of cash flow beyond the forecast period.^{5} Because the DCF model is future-oriented and future is marked by uncertainty, the cash flow needs to be discounted to reflect the risk of the future cash flow and the time value of money.^{6}

### 1.1 Problem Definition

The main challenge of the DCF model is the determination of its input factors, cash flow and discount rate. The model refers to future cash flow and the development of the company needs to be predicted. Because of the prediction, the model primarily relies on assumptions which can lead to inaccuracy and different outcomes depending on the choice of the input factors.^{7} The cash flow is forecasted for several years in the future but there is no uniform rule about the length of the forecast period. However, the length is critical for the terminal value because it determines how much of the intrinsic value will be obtained in the terminal period.^{8} In practice, the terminal value accounts for 53-80% of the overall value what places great importance on this parameter.^{9} Even small changes in the input factors of the terminal value can have a significant impact on the intrinsic value.^{10} The most discussed approaches in the literature on how to obtain the terminal value are the perpetuity growth and the exit multiple method which assumes the company as a going concern. The different assumptions and input factors of both approaches can lead to different results of the terminal value.^{11} In the literature and the practice, there is no consensus about which method is the more appropriate to obtain the terminal value.^{12} Moreover, Pascual and Jiménez emphasize that the input factors of terminal value are dependent on assumptions and that is why the terminal value is exposed to subjective assessment.^{13}

Another critical parameter of the DCF model is the discount rate. Companies typically use the Weighted Average Cost of Capital (WACC) as the discount rate which consists of the cost of debt and cost of equity.^{14} Unlike the cost of debt, the cost of equity is not observable in the market.^{15} The standard model to estimate the cost of equity is the Capital Asset Pricing Model (CAPM). According to CAPM, the cost of equity is primarily depended on its systematic risk, measured with a beta factor.^{16} However, the CAPM does not specify how to estimate the beta factor. In practice, half of the companies refer to a published source for a beta estimate while 30% estimate beta on their own.^{17} The beta factor is mostly estimated from historical returns since it is assumed that historical performance is a reliable estimate for the future.^{18} Indeed there are alternative methods of beta estimation that are mostly used by non-listed companies since non-listed companies cannot estimate the beta factor from historical returns due to lack of historical data. Because of the leeway concerning the choice of an estimation technique, the estimation can lead to different beta factors.^{19} Different beta factors can have a significant impact on the WACC and consequently on the intrinsic value.^{20}

### 1.2 Objective and Organization of the Thesis

In consequence of the importance and challenges of determining terminal value and beta factor in the DCF model, the objective of this thesis is to analyze the different estimation methods of beta factor and terminal value. The different methods will be critically reviewed and compared to each other. To illustrate the procedure of valuation with the DCF model and to identify the impact of beta factor and terminal value on the intrinsic value obtained by this model, a case study of Microsoft Corporation is conducted. The purpose of the case study is to analyze the sensitivity of the intrinsic value to changes in the input factors of the DCF model, in particular the terminal value and beta factor.

The present thesis is divided into five chapters. The second chapter starts with the explanation of the DCF model and its main inputs. It provides the reader with the first sight of how the beta factor and terminal value contribute to the intrinsic value obtained by the DCF model. In the third chapter, the economic significance of the beta factor and the estimation of the beta factor from historical returns are explained. The problems of this estimation technique are identified and alternative estimation techniques are mentioned. The fourth chapter is dedicated to the terminal value. Terminal value can be determined with the perpetuity growth method or with the exit multiple method. The most common perpetuity growth method is the Gordon Growth model which can be extended to reflect mortality risk or financial distress. Another method to value the company as perpetuity is with the Key Value Driver formula which is a modification of the Gordon Growth model. Alternatively, the terminal value can be obtained with an exit multiple, either with an enterprise value multiple or with an equity price multiple. At the end of the chapter, both methods of terminal value calculation are compared to each other. In the fifth chapter, a valuation using the DCF model will be applied to Microsoft Corporation. The results are critically reviewed based on different sensitivity analyses. The thesis concludes in chapter 6 with a summary of the results and a brief outlook for future research and the practice.

## 2. Discounted Cash Flow Method

The Discounted Cash Flow method has existed since the 1970s^{21} and is the most popular present value approach.^{22} Understanding DCF valuation is necessary to apply other valuation approaches as relative valuation or option pricing models in a correct way. The DCF model determines the intrinsic value of an asset by discounting its expected future cash flow.^{23} Intrinsic value measures what an asset is worth and is used to identify the mispricing of the market prices.^{24} The discount rate reflects the risk in the cash flow and the time value of the money. The required rate of return of the investors is decisive for the discount rate. Hence, the intrinsic value depends on three variables: the amount of cash flow generated, risks associated with this cash flow measured by a discount rate, and the time at which the cash flow occurs.^{25}

The DCF valuation differentiates between two approaches: Enterprise valuation and equity valuation. The enterprise valuation refers to the valuation of the entire company by discounting Free Cash Flow to Firm (FCFF) at the Weighted Average Cost of Capital (WACC). Whereas the equity valuation refers to the valuation of the equity value of the company by discounting either Free Cash Flow to Equity (FCFE) or dividends at the cost of equity. Equity valuation will be the more simple valuation approach if the capital structure of the company is relatively stable. Whereas for levered companies with changing capital structure the enterprise valuation is the better approach because WACC is less sensitive to changes in financial leverage than the cost of equity.^{26} The Dividend Discount model is a specialized form of the equity valuation which assumes that the cash flow is paid out as dividends. Although the FCFE and Dividend Discount model are both valuing equity, both models will only generate the same value if either the amount of dividends paid to stockholders is equal FCFE or if FCFE is greater than the dividends but the difference between FCFE and dividends, the excess cash, is invested in zero net present value projects. But if the company pays out dividends less than FCFE available and the excess cash is invested in negative net present value projects or has below-market interest rates, the value of the FCFE model will be higher.^{27} Based on Jensen’s theory, the managers have incentives to rather invest the excess cash in risky projects than to pay it out as dividends in order to increase their power in the company and to use the excess cash for self-interest instead of using it to maximize the value of the company. This is not in the interest of the shareholders and it is known as the agency problem which describes the interest conflict between shareholders and managers of a company.^{28} Furthermore, the management uses cash, which is not paid out as dividends, as cash cushion in case they expect earnings to drop in the future. Those cash cushions allow the managers to remain in control. Another reason why dividends can be less than FCFE is that companies barely change their amount of dividends. Even if FCFE increases, the companies will not immediately increase their dividends because of uncertainty to maintain these dividends.

On the other hand, if the dividends paid to stockholders are greater than FCFE, the company has to issue new stocks to pay these dividends. The company may become over levered and will lose value if it has to borrow money to pay the dividends.^{29}

FCFE model will be the more appropriate model if the company pays significantly higher or lower dividends than FCFE available or if the company does not have dividends, e.g. private companies. The FCFE model is not dependent on the dividend policy and it has a more realistic estimation of the value for equity. The value of dividends does not “reveal anything about how value is created.” This is called the “dividend conundrum.”^{30} Nevertheless, the components which drive FCFE have to be estimated each year which is time-consuming. That is why the Dividend Discount model is useful for companies in sectors in which it is difficult to estimate FCFE or FCFF. Moreover, it creates a floor value for companies that have a higher FCFE than dividends since the Dividend Discount Model yields a conservative estimate of the value of an asset.^{31}

Practically, cash flow can only be forecasted for a finite horizon. That is why the DCF model works in two stages. The first stage, the finite horizon, corresponds to the explicit forecast period which usually covers a period of 5-7 years. This period is also called an extraordinary growth period. The second stage, the infinite horizon, corresponds to the cash flow after the last forecasted period until perpetuity. The cash flow beyond the forecast period is captured by a terminal value.

Hence the value of an asset is the sum of the present value of the forecasted cash flow for n periods and the present value of the terminal value at the end of period n. The-two stage model is illustrated using an example in figure 1.

Abbildung in dieser Leseprobe nicht enthalten

*Figure 1: Two-Stage DCF Valuation with CF=100, TV=250, n=5 and r=0,05* ^{32}

The DCF method does not apply to all companies and has some limitations. This method values the company as a going concern and therefore it is not appropriate for companies that are expected to fail. Furthermore, assets that are not utilized and do not generate cash flow will be not reflected in the value of the DCF model. For companies that are doing restructuring in terms of changing the capital structure or dividend policy, the expected cash flow is difficult to estimate. DCF primarily relies on assumptions of its input factors and it is sensitive to changes in these input factors. That is why an investigation of each input factor is required to ensure that the input factors are appropriate for valuation.^{33}

In the following, the required input factors for the DCF model are explained. First, an assumption needs to be made about how the company will grow in the future. The most common growth patterns are stable growth, two-stage growth, and three-stage growth. After an assumption about the growth pattern is made, the intrinsic value of an asset can be estimated based on three general steps. The first step is to forecast the cash flow for each forecast period. To forecast the cash flow, either each component of the cash flow is estimated individually or the historical cash flow is assumed to grow at a constant growth rate during the forecast period. The second step is to estimate a discount rate to determine the present value of the cash flow. The last step is to determine the terminal value which captures the cash flow beyond the forecast period. Finally, the value of an asset can be estimated as the sum of the present value of the forecasted cash flow and the present value of the terminal value.^{34}

### 2.1 Growth Pattern

The growth of a company is determined by qualitative factors as management’s strategic vision, the strength of marketing, quality of management, or information about competitors and by quantitative factors as reinvestment rate, return on investments or sales to capital ratio. The latter indicates the amount of sales which is generated by investing one dollar of capital. It links the revenue growth with the reinvestment need of a company by estimating how much reinvestment the company has to make to achieve its projected revenue growth. Thus, a lower sales to capital ratio results in higher reinvestment need whereas a higher sales to capital ratio results in lower reinvestment need.^{35} Moreover, the growth of companies is influenced by the sector in which it operates. Whereas the auto components or food products sector has low growth rates because their markets are already matured, the IT services, software, or health-care equipment sector has high growth as a consequence of the remained high demand for these products in the last four decades.^{36} To value a company, an assumption needs to be made about how the company is expected to grow in the future. There are an infinite number of growth possibilities that can be grouped into three common growth patterns: stable growth, two-stage growth, and three-stage growth.

Abbildung in dieser Leseprobe nicht enthalten

*Figure 2: Growth Pattern* ^{37}

The stable growth model assumes that the company directly grows at a stable growth until perpetuity. This model is appropriate if the growth rate is close to or less than the growth rate of the economy in which the company operates.^{38} It works best for companies in the maturity phase, as companies from the energy supply and food retail sectors.^{39} The stable growth Dividend Discount model is known as the Gordon Growth model. It is a frequent method to calculate the terminal value with the perpetuity growth method which will be further explained in chapter 5.^{40}

According to stable growth or Gordon Growth model respectively, the value of an asset today Abbildung in dieser Leseprobe nicht enthaltenis equal to the expected cash flow in next period Abbildung in dieser Leseprobe nicht enthaltendivided by the difference of the discount rate r and stable growth rateAbbildung in dieser Leseprobe nicht enthalten. The expected cash flow in the next period is equal to current cash flow Abbildung in dieser Leseprobe nicht enthaltenwhich grows at a stable growth rate.

Abbildung in dieser Leseprobe nicht enthalten

The assumption of stable growth from now until infinity is not realistic for most companies.^{41} For most of the products, the life-cycle follows an S-curve until maturity. At some point in time, the sales of the products reach the maximum and beyond that point in time the growth of the sales decreases or it takes on the same rate as the economy. Sustaining high growth is only possible when new product markets are consistently entered.^{42} Therefore, most companies drop from high growth to stable growth. These different growth phases which refer to different periods and different growth rates can be modeled by a multi-stage model.^{43} A-multi stage model provides great flexibility for valuing cyclical companies.^{44} It can be distinguished between the two-stage growth model and three-stage growth model.

The two-stage model assumes that the company maintains its high growth rate for a finite period and then drops abruptly to a stable growth rate which reflects the long-term growth of the economy in which the company operates. Therefore mature companies that grow in the initial period close to the long-term growth have a shorter forecast period than high growth companies.^{45} The high growth period is called the competitive advantage period because in this period the return on capital exceeds the cost of capital.^{46} However, since the growth rate in the initial period abruptly drops down, this model is more appropriate for companies with moderate growth in the initial period because it is not realistic that a high growth rate of 40% abruptly declines to stable growth of 6%. The moderate growth can be maintained for a finite period until the sources which are responsible for the growth disappear. For example, a company with patent rights to a profitable product can maintain its higher growth until the patent rights expire and after the expiration the growth rate becomes stable. In most cases, it is assumed that the growth rate in the first period is higher than in the second period. Nevertheless, the model can also be used to model the case that the growth rate in the first period is low or even negative which is replaced by a high constant growth rate in the second period after overcoming the difficulties of the first period.

According to the two-stage growth model, the current value of an asset is the sum of the present value of expected cash flow which grows at the high growth rate Abbildung in dieser Leseprobe nicht enthaltenduring the initial phase of n periods and the present value of the terminal value at the end of period n when the company becomes stable. The expected cash flow and terminal value are discounted at the discount rate of the high growth period Abbildung in dieser Leseprobe nicht enthalten.

Abbildung in dieser Leseprobe nicht enthalten

The last growth pattern refers to the three-stage model. This model assumes that the company maintains its high growth for a finite period, followed by a transition period in which the growth rate declines gradually to a stable growth which lasts forever. It provides great flexibility because it can be applied for companies that expect that not only their growth rate will change but also other dimensions like payout policies, reinvestment rates, return on capital, or risk.^{47} It works best for companies with the expectation of an abnormally high growth rate which they can maintain for an initial period and a declining growth rate in the transition phase which is still above the average of the economy.^{48}

According to the three-stage growth model, the current value of an asset is the sum of present value of expected cash flow which grows at the high growth rate Abbildung in dieser Leseprobe nicht enthaltenduring the initial phase of n1 periods, the present value of expected cash flow during the transition phase between the periods n1 and n2 and the present value of the terminal value at the end of period n2. The discount rates differ between the phases. Abbildung in dieser Leseprobe nicht enthaltenrefers to the discount rate in the high growth phase and Abbildung in dieser Leseprobe nicht enthaltenrefers to the discount rate in the transition phase. The terminal value is discounted at the cumulated discount rate r of high growth and transition period.

Abbildung in dieser Leseprobe nicht enthalten^{49}

### 2.2 Cash Flow Projection

Depending on which valuation approach is used, different cash flow needs to be estimated. The enterprise value approach is based on FCFF and the equity value approach is based on FCFE or dividends.^{50} Whereas FCFE is the cash flow available to pay to shareholders, dividends reflect the cash flow which the shareholders receive.^{51} Unlike FCFE, dividends cannot be negative. The forecast of dividends is based on less assumption since it is calculated based on the dividends from the previous year and the expected growth rate, while FCFE and FCFF have to be estimated based on more financial information. Because dividends are expected to remain stable, the valuation based on dividends is less volatile than the valuation based on FCFE or FCFF which are sensitive to a fluctuation of earnings and reinvestments of a company.

FCFE is the residual cash flow distributable to equity holders after deducting the payments to debt holders (interest payments, principal payments, new debt issues).^{52} This cash flow is available to be paid out as dividends or stock buybacks to the stockholders and therefore there will be no future cash build-up in the company. FCFE is calculated by subtracting capital expenditures (capex) from the net income and adding back depreciation & amortization and other non-cash charges. Then, the change in non-cash working capital is considered, where an increase is deducted and a decrease is added back. Finally, debt repayments, which represent cash outflow, are deducted and new debt issued, which represents cash inflow, is added back.

Abbildung in dieser Leseprobe nicht enthalten

Whereas the FCFE represents the cash flow distributable only to equity holders, FCFF represents the cash flow distributable to all claim holders, the equity and debt holders. It is calculated by subtracting the taxes from Earnings Before Interest and Taxes (EBIT), given the Net Operating Profit after Tax (NOPAT). Depreciation & amortization and other non-cash charges are added back to NOPAT whereas capex is deducted. Lastly, an increase in change in working capital is deducted whereas a decrease is added back.

Abbildung in dieser Leseprobe nicht enthalten^{53}

FCFF represents predebt cash flow and thus the debt does not have to explicitly taken into account. This is advantageous because the estimation of new debt issues and debt repayments like in FCFE can become complicated if the leverage changes over time.^{54} However, FCFF is a less intuitive measure of cash flow than FCFE. Whereas FCFE displays the real cash flow since it considers interest payments and debt repayment as a cash outflow, FCFF accounts for the cash flow as if the company had no debt and associated payments of the debt.^{55}

Once the historical cash flow is calculated, the cash flow for each forecast period needs to be estimated which can be done based on two different approaches. The first approach refers to the forecast of each component of the free cash flow individually. The development of each component is considered separately what makes it a complex method. To forecast FCFF, EBIT is further split into revenue and EBIT margin to separately assess the main impact on the operating business. Analogously, to forecast FCFE, net income is further split into revenue and profit margin. The revenue and both margins can be forecasted based on an analysis of the economic environment, outlook of the company, and historical data. The other components of the free cash flow are correlated to the development of revenue and it is assumed that these components have a constant relationship to revenue in the future. Therefore they can be forecasted as a ratio of revenue.

The more simple approach is to assume that the cash flow of the last past financial year will grow at a constant growth rate during the forecast period and the fundamental factors will remain unchanged. This approach works for companies that have historical cash flows which tended to grow at a constant rate and which expect that the historical relationship between the cash flow and fundamentals will continue.^{56} According to Damodaran (2002), three different approaches to estimate growth can be applied. The first one refers to the historical growth rate which can be determined by taking the average of past growth rates using arithmetic or geometric average or by building regression models or time series models. The historical growth rate will not be a reliable predictor for future growth rates if the company has negative earnings or volatile growth. By taking the average of historical growth, no information can be provided about how the growth changed over time. Moreover, the historical growth rate can vary depending on how many years of the past are included in the calculation and which model is used.

The second approach of estimating growth refers to analysts’ forecasts of growth. The advantage of this approach is that analysts consider additional information besides the historic data like company public and private information, macro-economic information, and competitor information. Nevertheless, the blind trust of the analyst forecast can be dangerous. Forecast error can occur as a consequence of misleading data sources.

The third approach is based on fundamentals that treat growth as an endogenous variable and link it directly to the cash flow. According to Damodaran, it is the more appropriate way to estimate growth since both other approaches treat growth as an exogenous variable.^{57} However, the estimation of growth as an endogenous variable is only the more appropriate way if the exogenous variable allows the company to further grow. The growth of a company is mainly driven by the growth of the market^{58} and the company cannot grow at a higher rate than the overall market. For example, it is not reasonable to assume that the company grows at 6% whereas the overall market only grows at 2%. Thus, the estimation of growth as an endogenous variable is only appropriate if the exogenous variable is considered as well. The fundamental approach estimates growth as a function of how much a company reinvests for future growth and the return on its reinvestment. Reinvestment is essential to grow over a long period. The reinvestment rate and return on investment are differently defined depending on which cash flow is estimated. Firm cash flow is based upon growth in operating income which is a function of reinvestment in capital and Return on Capital (ROC). Equity cash flow is based upon growth in equity income which is a function of reinvestment in equity and Return on Equity (ROE). The growth in equity income can be further differentiated between growth in earnings per share, which is the growth of dividends, and growth in net income, which is the growth of FCFE.

The growth in the Dividend Discount model refers to the growth in earnings per share and is a function of ROE and reinvestment rate expressed as the retention rate. The retention rate is the percent of earnings not paid out as dividends to stockholders and reinvested back into the company. It is the opposite of the payout ratio. By assuming ROE to be constant over time, the expected growth rate can be expressed as:

Abbildung in dieser Leseprobe nicht enthalten

This growth rate is also called the sustainable growth rate. It is the growth rate of dividends or earnings for a given level of ROE which a company can sustain without increasing debt or raising new equity by issuing new shares.^{59} The higher the ROE, the higher the growth rate by holding all other variables constant. The higher (lower) the retention ratio, the higher (lower) growth rate by holding all other variable constant because if more profit is retained for reinvestment, more profit is available to finance the growth of a company.^{60} A high sustainable growth rate indicates that a company reinvests most of its profits instead of distributes it as dividends to its stockholders.^{61}

The growth in the FCFE model refers to the growth in net income which is a function of equity reinvestment rate and Non-cash ROE (NCROE). FCFE model assumes that there is no cash build-up in the company and therefore ROE has to be adjusted to measure the ROE on non-cash investments. The equity reinvestment rate is the percent of net income a company reinvests back into its business in form of net capex and investments in working capital. By assuming ROE to be constant over time, the expected growth rate can be expressed as:

Abbildung in dieser Leseprobe nicht enthalten

For both expected growth rates, earnings per share and net income, it is assumed that ROE or NCROE respectively will be constant over time. If the return changes over time, an additional component will be added to the growth rate which describes the effect of a change in return on the growth rate. This is called the “efficiency generated growth” because the additional growth comes not from improved returns on new investments but from improved returns on existing investments. By improving the return, the growth rate will increase as a consequence.

Abbildung in dieser Leseprobe nicht enthalten

The growth in the FCFF model refers to the growth in operating income which is a function of reinvestment rate and ROC. The reinvestment rate is the percent of after-tax operating income reinvested back into the business as net capex and non-cash working capital. This measure can change over time as long as a company is doing investments in projects. By assuming ROC to be constant over time, the expected growth rate can be expressed as:

Abbildung in dieser Leseprobe nicht enthalten

Similar to ROE, ROC can change over time and the effect of the change can be expressed by an additional component which is added to the growth rate as follows:

Abbildung in dieser Leseprobe nicht enthalten

As a general rule, growth in operating income is expected to be lower than the growth in net income. If a company uses debt for investments in their projects which generate earnings higher than the after-tax cost of debt, ROE will exceed ROC. The relationship between ROE and ROC is expressed as follows:

Abbildung in dieser Leseprobe nicht enthalten^{62}

### 2.3 Discount Rate

For companies accepting risk is necessary to achieve success. Nevertheless, the company’s stakeholders want to be compensated for the risk they were facing. This risk can be translated into the cost of capital at which future cash flow will be discounted. The cost of capital is the cost that a company incurs as a result of using equity or raising debt for investment. It indicates the required return which is needed on investment to make this investment worthwhile.^{63} The estimation of an appropriate discount rate is important for the valuation process since the discount rate affects the intrinsic value of an asset. If the estimated discount rate is lower than the true rate, the asset will be overvalued. An estimated discount rate higher than the true rate will lead to an undervaluation of the asset.^{64} When determining the enterprise value, FCFF needs to be discounted by a discount rate that represents the risk all investors, equity and debt holders are facing. This is called the Weighted Average Cost of capital (WACC). To determine the equity value, FCFE or dividends need to be discounted at cost of equity which is one component of the WACC.^{65}

WACC is the weighted average of the cost of equity Abbildung in dieser Leseprobe nicht enthaltenand cost of debtAbbildung in dieser Leseprobe nicht enthalten. It is the after-tax cost of capital since the cost of debt is reduced by tax shield benefits with Abbildung in dieser Leseprobe nicht enthaltenas the corporate tax rate. The weighting parameters are expressed with D as the total debt of the company and E as total equity of the company.^{66}

Abbildung in dieser Leseprobe nicht enthalten^{67}

The capital structure, which defines the amount of debt and equity of the company, should be based on market values. If the capital structure is not disclosed or the company is privately held, an estimation of the capital structure needs to be made. Either a reference to the capital structure of comparable companies that are in the same industry is made or an iteration procedure to estimate the capital structure based on market values is used.^{68}

The cost of debt Abbildung in dieser Leseprobe nicht enthaltenis the required rate of return by debt holders.^{69} It is the interest rate which the company has to pay for its debts. The simplest way to estimate pre-tax cost of debt is to refer to the current Yield of Maturity of the currently traded long term bonds of the company on the capital market.^{70} Alternatively, the pre-tax cost of debt can be calculated as the sum of the risk-free rate Abbildung in dieser Leseprobe nicht enthaltenand the credit default spread Abbildung in dieser Leseprobe nicht enthalten.

Abbildung in dieser Leseprobe nicht enthalten^{71}

The credit default spread is equivalent to the risk premium on the debt. The most common way is to measure it by bond rating and the associated default spreads. The most known rating agencies are Standard & Poor’s and Moody’s.

The risk-free rate is the expected return of a security that an investor can receive without incurring default risk, reinvestment risk, or uncertainty about the rate.^{72} To estimate the risk-free rate analysts usually refer to long-term government securities as “the 10-year rate on Treasury bonds or bills”.^{73}

Since the interest payments are tax-deductible, the cost of debt is reduced by the taxes. Therefore the cost of debt needs to be multiplied by (1-tax rate) which is related to the value of tax shield.^{74} The effective tax rate of a company is calculated as the amount of taxes divided by the taxable income. In contrast to the effective tax rate, the marginal tax rate reflects the tax which is incurred on an additional dollar of income. It means that increasing income will be taxed at a higher rate. Therefore in the terminal period, the marginal tax rate should be applied.^{75}

The cost of equity Abbildung in dieser Leseprobe nicht enthaltenis the required rate of return by equity holders.^{76} It is usually estimated using CAPM. The CAPM was introduced in the early 1960s by William Sharpe (1964), Jack Treynor (1962), John Lintner (1965) and Jan Mossin (1966) independently^{77} and is built on the modern portfolio theory by Markowitz in 1959. Modern portfolio theory assumes that by holding a diversified portfolio of assets, the risk of the portfolio can be reduced. Investors are risk-averse and investment decisions are based solely on the criteria of expected return and volatility. They choose a portfolio that “minimize the variance of portfolio return, given expected return” and “maximize expected return, given variance”. This approach is called the “mean-variance model”.^{78} According to the CAPM, the expected rate of return, which defines the cost of equity, can be broken down into a risk-free and risk-related portion. The risk-free portion is expressed as the risk-free interest rate whereas the risk-related portion is expressed as the systematic risk Abbildung in dieser Leseprobe nicht enthaltenmultiplied by the equity risk premium.

Abbildung in dieser Leseprobe nicht enthalten^{79}

Investors will only hold a portfolio with risky assets instead of investing in a riskless asset if they expect to be compensated for this risk.^{80} This is reflected by the equity risk premium which is a measure of the return that investors demand over the risk-free rate to get compensated for the investment in a risky asset. It is calculated as the difference between the expected return on the market portfolio and the risk-free rate. Risk premium can be either estimated as an implied risk premium or as an average of the historical risk premium. Since most companies operate globally, it is important to add a country risk premium to the historical risk premium which reflects the additional return for higher risk in a foreign country.^{81} The equity risk premium is multiplied by the beta coefficient which represents the risk parameter in CAPM and measures the systematic risk.^{82} The expected rate of return and the systematic risk are positively correlated. The higher (lower) the systematic risk of the investment, the higher (lower) the risk premium and consequently the higher (lower) expected return of an asset. Investors only get a risk premium for the systematic risk because this risk cannot be diversified. The unsystematic risk can be eliminated by diversification and is therefore not considered in the risk premium.^{83} Diversification is a strategy to combine a variety of assets within a portfolio to spread the risk across different assets and to reduce the overall risk of the portfolio.^{84}

Abbildung in dieser Leseprobe nicht enthalten

*Figure 3: Systematic Risk vs. Unsystematic Risk* ^{85}

The CAPM can be represented by the Security Market Line (SML). SML displays the expected rate of return of each security as a linear function of its systematic risk, measured in a beta factor. Beta is on the horizontal axis and the expected rate of return is on the vertical axis.^{86} Beta shows the linear relationship between the expected rate of return on an asset and the expected rate of return on a market portfolio. It measures the degree to which the rate of return on asset changes in percentage points when the return on the market portfolio changes by one percentage point.^{87}

SML is determined by two risk-return points. The first point refers to the expected rate of return on a risk-free asset. Because of borrowing and lending money at an identical risk-free rate, a risk-free asset does not have any variability in the return which results in a beta of 0. The expected rate of return on as risk-free asset is the risk-free rate itself which represents the intercept of SML. The second point of the SML refers to a market portfolio with a beta of 1. Mathematically, the beta factor corresponds to the covariance between the return on asset i and return on market portfolio divided by the variance of the return on the market portfolio.^{88} Since “the covariance of the market portfolio with itself is its variance”, the market portfolio has a beta factor of exactly one.^{89} If an asset has the same beta as the market portfolio, the expected rate on the return of the asset is equal to the expected rate of return on the market portfolioAbbildung in dieser Leseprobe nicht enthalten. By connecting the two risk-return points, the SML can be determined. The slope of SML is expressed as the difference between Abbildung in dieser Leseprobe nicht enthaltenandAbbildung in dieser Leseprobe nicht enthalten.^{90}

In equilibrium, all assets will be plotted on the SML.^{91} Assets that are above the SML are undervalued because, for its given amount of risk, they yield a higher expected rate of return. Assets that are below the SML are overvalued because for its given amount risk, the yield a lower expected rate of return^{92}

Abbildung in dieser Leseprobe nicht enthalten

*Figure 4: Security Market Line (SML)* ^{93}

## 3. Beta Factor

As a key input factor of CAPM, the beta factor has a significant impact on the cost of equity which is a component of the WACC. The cost of equity is primarily depended on its systematic risk because an increase of systematic risk increases the cost of equity. Cost of equity and WACC respectively are used for discounting the forecasted cash flow and terminal value back to the present.^{94} Since the intrinsic value is sensitive to changes in the discount rate and the beta factor has a significant influence on the discount rate, the beta factor is a crucial parameter in the DCF method and needs to be analyzed.^{95}

In the following chapter, the economic significance of the beta factor is demonstrated and the different levels of beta factor and their interpretations are explained. Afterward, the estimation of the beta factor from historical returns is explained which is the most common estimation technique and the problems of this estimation technique are clarified. Therefore, alternative methods of estimation the beta factor are mentioned.

### 3.1 Level of Beta Factor and its Economic Significance

The beta factor is a measure of the systematic risk which indicates how sensitively the return of an investment security (i.e. stock) reacts to changes in the market. It records the change in the return of a security caused by changes in the return on the market portfolio. That means that it indicates the statistical relationship between the fluctuation in the return of a security and the fluctuation in the return of the market. Thus, the beta factor measures the risk of a security relative to the market portfolio.^{96} The systematic risk results from the market and it is caused by factors that affect all securities equally.^{97} Those market factors are for example economic changes, macroeconomic indicators, or natural disasters. In contrast to unsystematic risk, the systematic risk cannot be eliminated by diversification.^{98} The unsystematic risk relates to the risk of certain security that occurs regardless of the market. This includes events such as unexpectedly loss or gain or high bankruptcy risks which can be eliminated by diversification.^{99}

The beta factor is useful in understanding how volatile a security is compared to the market and if it moves in the same direction as the market. As already mentioned, the beta factor of the market portfolio is exactly one.^{100} If the beta factor of the asset is greater than one, the asset will have greater systematic risk than the market portfolio.^{101} This is called an aggressive asset since it is more volatile than the overall market.^{102} For example, a beta factor of 1.5 implies that the price of a security will increase by 1.5% if the market increases by 1%. Vice versa if the market decreases by 1%, the price of the security will decrease by 1.5%. The asset has a greater systematic risk than the market because the price goes further up and down than the market. On the other hand, a higher systematic risk leads to a higher return. The return of an asset is not affected by its variance but by the covariance of the return on the asset with the return on the market portfolio. On average the asset has a return which is equal to 1.5 times that of the return of the market portfolio. If the return of the market is 8%, an asset with a beta of 1.5 will have a return of 12%.^{103} If the beta factor of the asset is below one, the asset will have less systematic risk than the market portfolio and consequently lower return.^{104} It is called a defensive asset since it is less volatile than the overall market.^{105}

If the beta factor is equal 1, the systematic risk of the asset equals the one of the market portfolio which means that the expected return on asset matches the expected return on market portfolio. On average the asset fluctuates to the same extent relative to the market. No additional risk will be added to the portfolio if an asset with a beta factor of 1 is added to the portfolio.

If the beta factor is equal 0, the asset has no systematic risk. It is a risk-free asset that does not react to any changes in the market portfolio.^{106}

Abbildung in dieser Leseprobe nicht enthalten

*Figure 5: Movements of Stock Returns with Beta Factor Greater and Lower Than One * ^{107}

The beta factor can have both positive and negative values. Positive values indicate a change of the return in the same direction with the market as described above. Negative values indicate an opposite return trend related to the market. If the market tends to increase, the return on the asset will tend to decrease and vice versa. A negative beta implies a negative risk premium and consequently, the expected return is below the risk-free rate. At first glance, it seems unreasonable to invest in an asset with a negative risk premium. However, the behavior of the corresponding security in the opposite direction to the market represents a kind of hedging against general market fluctuations. Moreover, the investor accepts a negative risk premium because the addition of securities with a negative beta factor to a portfolio leads to a reduction of the overall risk.^{108} Theoretically, a negative beta factor is possible, but in practice it is unrealistic and it is not often observed. Examples of companies with a negative beta factor are oil companies or gold mines whose stocks perform better when the market declines. Gold does not fluctuate in the same direction as the market and it acts as a hedge against higher inflation.^{109}

**[...]**

^{1} Shefrin, Statman (2013), p.103

^{2} Koller, Goedhart, Wessels (2010), pp.3f.

^{3} Pinto, Henry, Robinson, Stowe (2010), pp.2f.

^{4} Petersen, Plenborg (2012), p.216

^{5} Damodaran (2002), pp.16ff.

^{6} Petersen, Plenborg (2012), p. 208

^{7} Svetlova (2012), p. 9f.

^{8} Mauboussin (2006), p.2

^{9} Reis, Augusto (2015), p. 46

^{10} Pascual, Jiménez (2009), p. 10

^{11} Damodaran (2002), pp.425ff.

^{12} Reis, Augusto (2013), p.1622

^{13} Pascual, Jiménez (2009), p.4

^{14} Koller, Goedhart, Wessels (2010), p.113

^{15} Viebig, Poddig (2008), p. 37

^{16} Petersen, Plenborg (2010), p.249

^{17} Damodaran (2002), p.299

^{18} Elton, Gruber, Brown, Goetzmann (2013), pp.138f.

^{19} Damodaran (2002), pp. 255ff.

^{20} Bodmer (2015), p.348

^{21} Reis, Augustuo (2013), p.1624

^{22} Petersen, Plenborg (2012), p.216

^{23} Damodaran (2002), p.16

^{24} Pinto, Henry, Robinson, Stowe (2010), p.2f.

^{25} Petersen, Plenborg (2012), p.212

^{26} Pinto, Henry, Robinson, Stowe (2010), p. 147f.

^{27} Damodaran (2002), pp.18ff.

^{28} Jensen (1986), p.2ff.

^{29} Damodaran (2002), pp.496ff.

^{30} Petersen, Plenborg (2012), p.215

^{31} Damodaran (2006), pp.170ff.

^{32} Damodaran (2002), pp.425ff.

^{33} Damodaran (2002), pp.18ff.

^{34} Kramná (2014), pp.456ff.

^{35} Damodaran (2002), p.416ff.

^{36} Koller, Goedhart, Wessels (2010), pp.82ff.

^{37} Adapted from Damodaran (2002), 515

^{38} Damodaran (2002), p.453

^{39} Mondello (2018), p.216

^{40} Damodaran (2002), p. 451

^{41} Pinto, Henry, Robinson, Stowe (2010), pp. 97ff.

^{42} Koller, Goedhart, Wessels (2010), p.89

^{43} Viebig, Poddig (2008), p.16

^{44} Koller, Goedhart, Wessels (2010), p.89

^{45} Petersen, Plenborg (2012), p. 214

^{46} Viebig, Poddig (2008), p.17

^{47} Damodaran (2002), p.443ff.

^{48} Pinto, Henry, Robinson, Stowe (2010), p. 112

^{49} Damodaran (2002), p.472ff.

^{50} Petersen, Plenborg (2012), pp. 216f.

^{51} Pinto, Henry, Robinson, Stowe (2010), p. 146

^{52} Damodaran (2006), pp.79ff.

^{53} Damodaran (2002), pp.488ff.

^{54} Damodaran (2006), p.210

^{55} Damodaran (2002), p.542

^{56} Pinto, Henry, Robinson, Stowe (2010), pp. 173f.

^{57} Damodaran (2002), pp.374ff.

^{58} Koller, Goedhart, Wessels (2010), p.99

^{59} Damodaran (2002), pp.374ff.

^{60} Pinto, Henry, Robinson, Stowe (2010), pp.128f.

^{61} Petersen, Plenborg (2012), p.131

^{62} Damodaran (2002), pp.401ff

^{63} Petersen, Plenborg (2012), p.245

^{64} Nhleko, Musingwini (2016), p.216

^{65} Koller, Goedhard, Wessels (2010), p. 113

^{66} Viebig, Poddig (2008), p.36

^{67} Koller, Goedhard, Wessels (2010), pp. 113f.

^{68} Petersen, Plenborg (2012), p.246ff.

^{69} Koller, Goedhardt, Wessels (2010), p. 113

^{70} Damodaran (2002), p. 284

^{71} Petersen, Plenborg (2012), p.265

^{72} Damodaran (2002), pp.108ff.

^{73} Viebig, Poddig (2008), p.37

^{74} Koller, Goedhardt, Wessels (2010), p.114

^{75} Damodaran (2002), p.342

^{76} Petersen, Plenborg (2012), p.249

^{77} Perold (2004), p.3

^{78} Fama, French (2004), pp.25f.

^{79} Petersen, Plenborg (2010), pp.249ff.

^{80} Viebig, Poddig (2008), pp.37

^{81} Damodaran (2002), pp.219ff.

^{82} Sahadev, Ward, Muller (2018) p.327

^{83} Viebig, Poddig (2008), p.37

^{84} Francis, Kim (2013), pp.408f.

^{85} Adapted from: Trading Campus (2017)

^{86} Perold (2004), p.17

^{87} Lisicki (2017), p.33

^{88} Fama, French (2004), p.28

^{89} Damodaran (2002), p.97

^{90} Fabozzi, Grant (2001), p.33

^{91} Perold (2004), p.17

^{92} Francis, Kim (2013), p.400

^{93} Adapted from: Perold (2004), p.18

^{94} Petersen, Plenborg (2012), pp.246ff.

^{95} Bodmer (2015), p.348

^{96} Fama, French (2004), p.28

^{97} Lisicki (2017), p.31

^{98} Al-Afeef (2017), p.183

^{99} Lisicki (2017), p.31

^{100} Damodaran (2002), p.97

^{101} Petersen, Plenborg (2012), p.251

^{102} Lisicki (2017), p.33

^{103} Fabozzi, Grant (2001), pp.31ff.

^{104} Petersen, Plenborg (2012), p.251

^{105} Lisicki (2017), p.33

^{106} Petersen, Plenborg (2012), p.251

^{107} Adapted from Petersen, Plenborg (2012), pp.251f.

^{108} Cloninger, Waller, Bendeck, Revere (2002), pp.4f.

^{109} Ziemer (2018), pp.143f.

- Quote paper
- Marie Happe (Author), 2020, Analysis of Terminal Value and Beta Factor in the Discounted Cash Flow Method, Munich, GRIN Verlag, https://www.grin.com/document/951091

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