**Unformatted text preview: **umed
to grow at a constant rate) that it
is expected to provide over an
infinite time horizon. Finding the Cost of Common Stock Equity
The cost of common stock equity, ks, is the rate at which investors discount the
expected dividends of the firm to determine its share value. Two techniques are
used to measure the cost of common stock equity.5 One relies on the constantgrowth valuation model, the other on the capital asset pricing model (CAPM). Using the Constant-Growth Valuation (Gordon) Model
In Chapter 7 we found the value of a share of stock to be equal to the present value
of all future dividends, which in one model were assumed to grow at a constant
annual rate over an infinite time horizon. This is the constant-growth valuation 4. For simplicity, the preferred stock in this example is assumed to be sold for its par value. In practice, particularly
for subsequent issues of already outstanding preferred stock, it is typically sold at a price that differs from its par
value.
5. Other, more subjective techniques are available for estimating the cost of common stock equity. One popular
technique is the bond yield plus a premium; it estimates the cost of common stock equity by adding a premium, typically between 3% and 5%, to the firm’s current cost of long-term debt. Another, even more subjective technique
uses the firm’s expected return on equity (ROE) as a measure of its cost of common stock equity. Here we focus only
on the more theoretically based techniques. 478 PART 4 Long-Term Financial Decisions model, also known as the Gordon model. The key expression derived for this
model was presented as Equation 7.5 and is restated here:
D1
ks g P0 (11.4) where
P0
D1
ks
g value of common stock
per-share dividend expected at the end of year 1
required return on common stock
constant rate of growth in dividends Solving Equation 11.4 for ks results in the following expression for the cost
of common stock equity:
ks D1
P0 g (11.5) Equation 11.5 indicates that the cost of common stock equity can be found by
dividing the dividend expected at the end of year 1 by the current price of the
stock and adding the expected growth rate. Because common stock dividends are
paid from after-tax income, no tax adjustment is required.
EXAMPLE Duchess Corporation wishes to determine its cost of common stock equity, ks.
The market price, P0, of its common stock is $50 per share. The firm expects to
pay a dividend, D1, of $4 at the end of the coming year, 2004. The dividends paid
on the outstanding stock over the past 6 years (1998–2003) were as follows:
Year Dividend 2003 $3.80 2002 3.62 2001 3.47 2000 3.33 1999 3.12 1998 2.97 Using the table for the present value interest factors, PVIF (Table A–2), or a
financial calculator in conjunction with the technique described for finding
growth rates in Chapter 4, we can calculate the annual growth rate of dividends,
g. It turns out to be approximately 5% (more precisely, it is 5.05%). Substituting
D1 $4, P0 $50, and g 5% into Equation 11.5 yields the cost of common
stock equity:
ks $4
$50 0.05 0.08 0.05 0.130, or 13.0% The 13.0% cost of common stock equity represents the return required by existing shareholders on their investment. If the actual return is less than that, shareholders are likely to begin selling their stock. CHAPTER 11 The Cost of Capital 479 Using the Capital Asset Pricing Model (CAPM)
capital asset pricing model
(CAPM)
Describes the relationship
between the required return, ks,
and the nondiversifiable risk of
the firm as measured by the beta
coefficient, b. Recall from Chapter 5 that the capital asset pricing model (CAPM) describes the
relationship between the required return, ks, and the nondiversifiable risk of the
firm as measured by the beta coefficient, b. The basic CAPM is
ks RF [b (km RF)] (11.6) where
RF
km risk-free rate of return
market return; return on the market portfolio of assets Using CAPM indicates that the cost of common stock equity is the return
required by investors as compensation for the firm’s nondiversifiable risk, measured by beta.
EXAMPLE Duchess Corporation now wishes to calculate its cost of common stock equity,
ks, by using the capital asset pricing model. The firm’s investment advisers and
its own analyses indicate that the risk-free rate, RF, equals 7%; the firm’s beta,
b, equals 1.5; and the market return, km, equals 11%. Substituting these values
into Equation 11.6, the company estimates the cost of common stock equity, ks,
to be
ks 7.0% [1.5 (11.0% 7.0%)] 7.0% 6.0% 13.0% The 13.0% cost of common stock equity represents the required return of investors
in Duchess Corporation common stock. It is the same as that found by using the
constant-growth valuation model. Comparing the Constant-Growth and CAPM Techniques
The CAPM technique differs from the constant-growth valuation model in that it
directly considers the firm’s risk, as reflected by beta, in determining the required
return or cost of common stock equity. The constant-growth model does not look
at risk; it uses the market price, P0, as a reflection of the expec...

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