The Foundation
5.1 Valuation Fundamentals
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• explain and calculate the current yield, yield to maturity, and yield to call of a bond;
• calculate the intrinsic value of preferred stock;
• calculate the intrinsic value of common stock using dividend discount models with different growth rate assumptions;
• discuss when using multiples is appropriate to value a stock;
• describe the major characteristics and features of bonds, preferred stock, and common stock.
These various types of value – book value, market value and intrinsic value – can differ for the same financial asset. For example, in a market in which security prices rapidly reflect all information about securities, called an efficient capital market, the intrinsic value of a security is equal to its market value. In less than perfectly efficient markets, market value and intrinsic value may differ. Although controversy surrounds the degree of market efficiency, most experts agree that the capital markets are not perfectly efficient. Thus, mispricing may occur for financial assets.
In this chapter, we focus on estimating the intrinsic value of three types of financial assets – bonds, preferred stock, and common stock. We do not examine valuation of the overall firm.1 Corporate managers, especially financial managers, need to know how to estimate the intrinsic value of financial assets to determine if the market properly prices these assets. Financial managers also need to estimate the price that their firms are likely to receive when issuing bonds or shares of common or preferred stock. In addition, financial managers need to understand how corporate decisions may affect the value of their firm’s outstanding securities, especially common stock. For example, financial management deci- sions determine the risk/return characteristics of the firm. These decisions cause both cash flows and the required rate of return to change, which in turn cause changes in the firm’s stock price.
Analysts and investors often compare the current market price of a security to the intrin- sic value they estimate from a security valuation formula. If the estimate of intrinsic value exceeds an asset’s market value (price), investors would consider buying the asset. Con- versely, if the market value (price) exceeds the estimated intrinsic value, investors would not consider buying the asset (or would consider selling if they own it). Because the financial rewards from identifying an undervalued or overvalued security can be great, many analysts and investors devote substantial time and resources to developing innovative security valuation models, especially for common stock.
Valuation Approaches
There are three basic approaches to valuing financial assets – discounted cash flow (DCF) valuation, relative valuation, and contingent claim valuation. DCF valuation and relative valuation are the standard approaches to valuation.
With discounted cash flow valuation, the estimated value of a financial asset is the present value of the asset’s expected future cash flows. The discount rate should reflect the riskiness of these cash flows. Thus, DCF valuation serves as a way to estimate the intrinsic value of a security.2 While DCF models are considered to be theoretically correct, they often
1 For a discussion of corporate valuation, see Phillip R. Daves, Michael C. Ehrhardt, and Ronald E. Shrieves, Corporate Valuation: A Guide for Managers and Investors, Thomson/South-Western, 2004.
2 In addition to applying DCF valuation to stocks and bonds, this approach is also applicable to determining the value of the entire firm, which includes the value of common equity plus other claimholders of the firm such as bondholders and preferred stockholders. Using DCF valuation for valuing individual securi- ties and the entire firm involves discounting the expected cash flows. Yet, the relevant cash flows and the appropriate discount rate differ for each. A discussion of firm valuation is outside of our scope.
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provide intrinsic value estimates that differ from prevailing market prices. These differences are likely to result from the difficulty in estimating inputs for the models.
With relative valuation, the value of a financial asset is computed relative to how the market prices similar assets. For example, relative valuation of common stock uses firm- specific multiples such as price-to-earnings, price-to-cash flows, price-to-book value, and price-to-sales ratios. This valuation method provides information on current valuation, but it does not provide guidance on the appropriateness of the current valuations. That is, the approach measures relative value, not intrinsic value. Relative valuation techniques are appropriate to consider when a good set of comparable entities is available and when serious undervaluation or overvaluation does not prevail in the market.
In some situations, option-pricing models may give more realistic estimates of value than those obtained using DCF valuation or relative valuation models. With contingent claim valuation, an asset with the characteristics of an option is valued using an option-pricing model. Some cases in which managers and analysts may view equity in a firm as an option include equity in a deeply troubled firm, natural resource firms, and firms deriving much of their value from product patents. In this chapter, we focus mainly on DCF valuation, but briefly discuss relative valuation.3
Practical Financial Tip 5.1
Corporate managers must understand the valuation process to maximize value or shareholder wealth. Financial decisions may influence the firm’s risk-return character- istics, which in turn are reflected in the price of its common stock.
Discounted Cash Flow Valuation
The valuation of any financial asset is a function of the:
1 amount of the expected cash flows (returns) generated by the asset over its life;
2 timing of the cash flows;4 and
3 riskiness associated with these cash flows as measured by the required rate of return.
The value of a financial asset is directly related to the amount of expected cash flows, but inversely related to the amount of risk. In addition, the timing of cash flows affects the value of a financial asset. For example, a dollar in cash flow expected in 5 years is worth less than the same dollar in cash flow expected in 2 years, due to the time value of money. The basic DCF valuation model combines these variables into Equation 5.1, which shows that intrinsic
3 For further discussion of option pricing approaches to equity valuation, see Aswath Damodaran, Damodaran on Valuation, John Wiley & Sons, Inc., 1994; and Aswath Damodaran, Investment Valuation, John Wiley &
Sons, 1996.
4 Cash flows can occur at any time during a year, but we will assume that they occur at the end of the year unless otherwise noted. This assumption is customary and simplifies the calculations.
value is the sum of an asset’s discounted cash flows over the life of the security. With certain modifications and customization, this model serves as the basis for valuing bonds, preferred stock, and common stock.
V CF
k
t t t
n 0
1 1
=
∑
( )+=
(5.1) where Vo is the intrinsic value of an asset at time zero; CFt is the expected future cash flow at the end of year t; k is the appropriate required rate of return (discount rate); n is the remaining term to maturity; and t is the time period.
One assumption of the basic DCF valuation model is that returns in the form of cash flows consist of a point estimate or single value at a particular time, rather than a probability distribution of values. Another assumption is that the investor’s required rate of return (k) reflects the risks associated with these cash flows.
Applying the basic DCF model involves a three-step valuation process:
1 Estimate the future cash flows expected over the life of the asset.
2 Determine the appropriate required rate of return on the asset.
3 Calculate the present value of the estimated cash flows using the required rate of return as the discount rate.
Practical Financial Tip 5.2
The results of DCF valuation are only as accurate as the estimates of the amount and timing of the expected future cash flows and the required rate of return. Because these variables are uncertain in many cases, the intrinsic value is only an estimate of the security’s value. Users of DCF valuation should treat the results of these models with caution.
Estimating future cash flows
The nature of the cash flows differs among various financial assets. For bonds, the cash flows represent the coupon interest payments and the recovery of the principal (or par value) at maturity or retirement. For preferred stock, the cash flows are dividends. Because most bonds and preferred stock provide stable cash flows at regular intervals, the cash flows resulting from these investments are relatively easy to forecast. In the case of floating-rate securities, the coupons on bonds and the dividends on preferred stock may vary period by period, depending on conditions in the market. Estimating such cash flows requires forecast- ing interest rates, which is a topic that extends beyond the scope of this book.
For common stock, the cash flows can be dividends or free cash flow to equity. The more straightforward measure of cash flow is dividends, which are cash payments to stock- holders. Free cash flow to equity (FCFE) is the residual cash flow remaining after meeting interest and principal payments and providing for capital expenditures to maintain existing assets and acquire new assets for future growth. Various techniques are available to forecast these different types of cash flows.
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Practical Financial Tip 5.3
Using dividends instead of free cash flow to equity (FCFE) usually provides a more conservative estimate of the value of common stock because most firms pay a lower amount of dividends than they are capable of paying. Using FCFE generally provides a more realistic value of equity because FCFE is the amount that a firm can pay in dividends. In practice, FCFE may be greater or smaller than the dividend. From a practical perspective, estimating FCFE is more difficult when leverage changes over time because FCFE is net of debt issues or payments.
One popular method of deriving these estimates is the top-down approach. This approach to the valuation process involves three steps.5
1 Economic analysis. The analyst begins by making a forecast of the economic environment in which the company will operate. The forecast involves identifying general economic influences such as fiscal policy and monetary policy.
2 Industry analysis. Based on this economic forecast, the analyst projects the outlook of each industry in which the company will operate.
3 Company analysis. The analyst forecasts the individual company’s future prospects and earnings capability. This analysis provides the basis for estimating the expected dividends to stockholders or the FCFE.
Estimating the required rate of return
The required rate of return, also known as the discount rate, reflects the riskiness of the estimated cash flows. Riskier cash flows carry a higher discount rate than less risky cash flows.
Unlike the cash flows for bonds and preferred stock, which are contractually stated, the cash flows for common stock may exhibit substantial uncertainty. Thus, the required rate of return on a firm’s common stock should be higher than on its bonds or preferred stock.
The required rate of return consists of three major components:
• Real risk-free rate of interest (RRFR) is a default free rate in which investors know the expected returns with certainty.
• Expected inflation rate premium (INF) is an adjustment to the real risk-free rate to compensate investors for expected inflation. The nominal risk-free rate (NRFR) is the combination of the real risk-free rate and the expected inflation rate premium.
• Risk premium (RP) is the “extra return” that investors demand for the uncertainty associated with the investment. The risk premium reflects the additional return de- manded for internal and external risk factors. Internal risk factors are diversifiable and include factors that are unique to a particular firm such as financial risk and liquidity risk.
External risk factors, known as market risk factors, are macroeconomic in nature and are nondiversifiable.
5 For a detailed discussion of the top-down valuation process, see Frank K. Reilly and Keith C. Brown, Investment Analysis and Portfolio Management, 6th edn, Dryden Press, 2000.
In order to reflect risk, one approach is to combine all internal and external risk factors into a single risk premium. Equations 5.2 and 5.2a show that the required rate of return (k) is a function of the real risk-free rate of interest, an inflation premium, and a risk premium.
k = [ (1 + RRFR)(1 + INF )(1 + RP ) ] − 1 (5.2) Equation 5.2a is the approximation formula for the required rate of return.
kapproximation≅ RRFR + INF + RP (5.2a)
Note that the NRFR equals (1 + RRFR)(1 + INF) − 1 or is approximated by RRFR + INF.
Later in the chapter, we show how to apply these components to estimate the required rate of return for a bond, preferred stock, and common stock.
Example 5.1 Estimating the Required Rate of Return
An analyst estimates that the real risk-free rate of return for a financial asset is 4 per- cent, the inflation premium is 3 percent, and the risk premium is 5 percent. What is the nominal required rate of return for this asset?
Solution: Using Equation 5.2, the nominal required rate of return is:
k = [ (1.04)(1.03)(1.05) ] − 1 = 1.125 − 1 = 0.125 or 12.5%
Using Equation 5.2a, the approximation formula for the nominal required rate of return is:
kapproximation = 0.04 + 0.03 + 0.05 = 0.12 or 12.0%
In this example, the approximation formula understates the nominal required rate of return by 0.5 percentage points or 50 basis points. A basis point is one hundredth of 1 percent or 0.01 percent. There are 100 basis points in each 1 percentage point.
Concept Check 5.1 1 What is valuation?
2 What are five types of value? How do they differ?
3 Under what circumstances can the market value and intrinsic value of a financial asset differ?
4 Why should a financial manager understand the valuation process?
5 How does discounted cash flow (DCF) valuation differ from relative valuation?
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6 What is the basic DCF valuation model and its three key inputs?
7 What are the three steps in the DCF valuation process?
8 How do the cash flows differ between bonds and common stock?
9 What are the three major components of the required rate of return?