Excerpt

## Table of Content

**1. Introduction**

1.1 Reasons for firm valuation

1.2 Firm valuation methods

**2. Weighted Average Cost of Capital (WACC)**

2.1 The Cost of Equity Capital: Major considerations and its calculation using CAPM

2.1.1 Estimating the Risk-Free Rate

2.1.2 The Concept of Beta

2.1.3 Estimating the Market Risk Premium

2.2 Alternatives to CAPM

2.3 Cost of Debt and the Weighted Average Cost of Capital (WACC)

**3. The Free Cash Flow Approach**

3.1 Firm Value determination using the FCF/DCF Approach

3.2 AFN calculation - a byproduct of Pro Forma Financial Statements

3.3 Scenario Analysis with Monte Carlo Simulation

**4. Conclusion**

**5. References**

**Appendix A**

## 1. Introduction

This paper will deal with the procedure and implementations of firm/stock valuation using FCF approach and WACC – the weighted average cost of capital. On the road, the different approaches and methods of firm valuation, the various inputs of WACC^{[1]} and the final procedure finding the fair market value of the firm using Pro Forma Financial Statements^{[2]}, will be discussed. In this valuation method the two main parts contributing to the final value of the firm are Free Cash Flows (FCF) and the weighted average cost of capital. It is then used the time value of money concept along with some educated guesses about the long term sales growth rate and the long term WACC to apply common capital budgeting rules of project evaluation. Besides that, the paper will shortly discuss the influence of capital structure on a firm’s value. It will come out that there is a difference in value whether the company is leveraged and uses debt or not. When it comes to the different inputs of the WACC, a main focus will be on the required rate of return for shareholders. Finding the ‘right’ beta and an appropriate estimate for the market risk premium are the main issues of that part. Therefore, the CAPM model and its specific determinants will be analyzed. Thereafter, the nature of pro forma financial statements and the different parts of them will be defined. It will be described how the ‘free cash flows’ are determined and how that leads to the actual valuation procedure. Finally, the paper will focus on the terminal value as probably the most important and affecting part of the calculated firm value and its nature as a perpetuity in an investing perspective. The conclusion will finally deal with a critical assessment of the firm valuation process with the FCF method.

### 1.1 Reasons for firm valuation

Both management and exterior investors may have vital interests in knowing the true value of a firm. Management has a primary objective of maximizing shareholder value at least as featured by Anglo-American markets.^{[3]} It is in itself remunerated and evaluated according to the firm value by taking the firm’s stock price as the benchmark for top managers’ salaries. In a same way investors might be interested in the fair ‘intrinsic’ firm value for investment purposes. It might be important for capital investors to know the real value of their investments, i.e. whether it is higher or lower as the actual market value. If it is lower, then arbitrage may be possible and a risk less profit may be earned from that transaction. The financial asset could be sold or not be bought and thus creating an instant profit for the investor. If it is higher the appropriate opposite of buying or holding might be recommended. In both cases calculating the intrinsic stock price and the real value of the firm is an important part to support investment or managerial decisions. Besides that, calculating a firm’s value might make sense in enterprise transaction situations like mergers and acquisitions of enterprise equity to find the marginal price of the corporate entity.^{[4]} Whenever a corporate entity is object of ownership change, both the buyer and the seller are interested in determining the marginal price, the highest price the seller can request and the lowest price the buyer is able to ask for.

### 1.2 Firm valuation methods

In practice and the academic literature there are several ways and methods applied to value a company or the shares of a company’s stock. The first method is commonly and widely used in practice. The fairly simple Price-Earnings (P/E) -Approach uses current or the latest available annual Earnings per Share (EPS) of a given company, the payout ratio and relative Price/Earnings (P/E) -multiples to come up with an estimate of the intrinsic value per share^{[5]}, , which is, multiplied by the number of shares outstanding, the estimated firm value. This approach is often used by managers especially for stock evaluations. In this approach, the key difficulty is to come up with a ‘correct’ estimate of the P/E ratio. The P/E ratio is a function of several variables, including: 1) the projected annual growth rate of the company’s earnings, 2) the general state of the market, 3) the amount of debt in the company’s capital structure, 4) the current and projected rate of inflation and, 5) the level of the company’s dividends. Principally, there is a positive relationship between the projected earnings growth rate, an optimistic market outlook, high dividend payouts on the one hand and the P/E-multiple on the other hand. But there is a negative relationship between the current and projected rate of inflation, the amount of debt used by the company and the P/E-multiple. A useful starting point to estimate the P/E ratio is the average market multiple, which is a simple average P/E ratio of all stocks in a given market index. The average market multiple indicates the general state of the market. It gives an idea of how ‘aggressively’ the market is pricing stocks. Other things being equal, the higher the average P/E ratio the more optimistic the market.^{[6]}

The second method is the Dividend Valuation Model (DVM) that uses annual dividends and the concept of the required rate of return (CAPM Approach),

rs = rRF + beta × (rMkt - rRF)

Dependent on whether zero growth, constant growth or variable growth of the company’s future dividends, different formulas are applied. In case of zero growth it is assumed that the company pays a fixed stream of dividends. In other words, future dividends are expected to stay constant. Under such condition, the value of a zero-growth stock is the capitalized value of its future annual dividends.^{[7]} To find the capitalized value, the total amount of future annual dividends must be divided by the required rate of return, the capitalization rate. The calculated firm value can thus be seen as a financial perpetuity. In the contrary, the constant growth case assumes a growing stream of dividends. This version of the DVM assumes that dividends grow over time at a specific rate. In fact, they are expected to grow forever (to infinity) at a constant rate of growth (g). Accordingly, a firm’s value (or share of stock if dealing with dividends per share) can be found by the Gordon growth formula as follows:

Gordon’s Growth Formula: P0 = D0 (1+g)/ (rs - g),

Where P0 is the firm’s price at t=0, g is the constant growth rate and rs the required rate of return. One endogenous problem of the constant growth model is that is does not allow for changes in expected growth rates. To overcome this problem, another form of DVM might be used, which allows for growth rates varying over time. The also called supernormal growth model derives the firm’s value from future dividends and the estimated future price of the stock and assumes that the growth rate of the dividends are higher than the required rate of return for the first couple of years.^{[8]} That is why the supernormal growth model consists of two parts, an annuity and perpetuity. The first part represents the supernormal growth (rs<g) period and is calculated as an annuity by taking the present value of future dividends of the initial variable growth period. The second part is calculated by taking the present value of a perpetuity, the price of the stock/firm at the end of the variable growth period, which is based on a constant growth to infinity. The sum of these two parts is the value of the firm at t=0 (or the value of a share of stock if dividends per share are used for the calculations). The DVM relies on three pieces of information: future dividends, future growth of the dividends, and a required rate of return. The most difficult and challenging part to find is the appropriate growth rate. It is also the most significant due to the sensitivity of the DVM to the rate of growth been used. Nevertheless, an appropriate estimate of the future growth rate is possible to find by looking at a company’s dividends of the past e.g. 10 to 5 years and running a regression with this data.^{[9]} The output of that regression is the annualized average growth rate of the past that is used for an estimate of the future growth rate. However, most companies and financial managers use another simplified way to find it. The growth rate (g) is defined as the product of the latest firm’s Return on Equity (ROE) and its retention rate, which is 1 – the dividend payout ratio.^{[10]} However, the actual growth rate might be a little bit higher as the equation above because it ignores financial leverage, which in itself will magnify growth. But at least it can serve as a starting point to figure out the real growth rate.

There are some alternatives to DVM that do not use dividends as a major formula input, mainly because of the need of having a valuation model for firms that do not pay any dividends at all. One is the Dividend-and-Earnings (D&E) -Approach that uses P/E-multiples and forecasted EPS instead of a perpetuity of constant dividend growth to come up with a future price at the end of the investment period (at the date of sale) that can be then discounted to the present. The P/E Approach discussed earlier is also a frequently applied alternative to the DVM. All of these methods have in common that the value of the firm is a function of the amount and timing of future cash flows and the level of risk that must be taken on to generate a return, sometimes in a present-value context, sometimes not. There is also a more sophisticated and complex method of firm valuation called the Free Cash Flow (FCF) Approach, which will be discussed later in this paper.

## 2. Weighted Average Cost of Capital (WACC)

Before the discussion will be held on creating and using the pro formas, this paper will focus on the key input figure of the valuation process, the WACC. The WACC is the cost of both equity and debt capital and thus represents the total financing cost a company must face to finance its operations. It includes and compensates all risk factors, from business over market to financial default risk by also taking the level of leverage (the level with which a company is debt financed) into account. The WACC serves as the discount rate in the valuation model to discount the estimated future ‘free cash flows’ to the present and to find an appropriate estimate of the firm value. The components of the WACC are the cost of equity, the cost of debt, the weight of equity relative to the total amount of the financing capital, the weight of debt and the effective tax rate. It is: WACC = wdkd(1-Tc)+wsks. First of all, it will be focused on the single most important component of the WACC which is as well the most difficult to estimate correctly, the cost of equity or also called the required rate of return on equity.

### 2.1 The Cost of Equity Capital: Major considerations and its calculation using CAPM

The Cost of Equity Capital, or also called the Cost of Common Stock rs is the rate of return that the company must earn to satisfy their stockholders that is equivalent to the rate of return that stockholders can expect to earn on equivalent- risk investments. To calculate the cost of equity, typically three methods are used: (1) the Capital Asset Pricing Model (CAPM), (2) the discounted cash flow (DCF) method, and (3) the bond-yield-plus-risk-premium approach. These methods are not mutually exclusive and they are all subject to error when used in practice. Therefore, when faced with the task of estimating a company’s cost of equity, generally all three methods are used to choose the most appropriate result. In this paper, the focus will be on the CAPM approach, although the other two approaches will be briefly discussed. CAPM uses the Security Market Line (SML), a linear equation that is composed of the risk-free rate, the market risk premium and beta. It is:

rs = rRF + (RPm) x bi.

To estimate the cost of common stock using CAPM, all of the components must be estimated appropriately.

**[...]**

^{[1]} Components and elements such as beta, cost of equity and the cost of debt

^{[2]} Intrinsic Value (Warren Buffett, Brigham, 2005, Financial Management)

^{[3]} In comparison to the European and Japanese model of Corporate Wealth Maximization (Mofett, 2006)

^{[4]} Compare Ballwieser, W, 2004, Unternehmensbewertung

^{[5]} Price per share = EPS*Payout Ratio*P/E-Multiple

^{[6]} Compare Gitman and Joehnk, 2004, Fundamentals of Investing, 9th ed.

^{[7]} Gitman and Joehnk, 2004, Fundamentals of Investments, 9th ed.

^{[8]} So that the denominator would be (rs-g) < 0 which would lead to an unsolvable mathematical construction

^{[9]} Finding the beta/slope of the regression of logn dividend data which is the annualized average growth rate of the dividends (Brigham and Ehrhardt, 2005, Financial Management, 11th edition)

^{[10]} g = ROE*(1-div payout ratio), Gitman and Joehnk, 2004, Fundamentals of Investing (p.350)

- Quote paper
- Ralph Johann (Author), 2005, The free cash flow approach, Munich, GRIN Verlag, https://www.grin.com/document/114406

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