9.4 Cost of Common Stock

LG 5 9.4 Cost of Common Stock

In more depth

The cost of common stock is the return required on the stock by investors in the marketplace. There are two forms of common stock financing: (1) retained earn-

To read about Subjective ings and (2) new issues of common stock. As a first step in finding each of these Techniques, go to

costs, we must estimate the cost of common stock equity.

www.myfinancelab.com FINDING THE COST OF COMMON STOCK EQUITY

The cost of common stock equity, r s , is the rate at which investors discount the cost of common stock

expected common stock dividends of the firm to determine its share value. Two tech- equity, r s

niques are used to measure the cost of common stock equity. One relies on the con-

The rate at which investors

stant-growth valuation model, the other on the capital asset pricing model (CAPM).

discount the expected dividends of the firm to

Using the Constant-Growth Valuation (Gordon Growth) Model determine its share value.

In Chapter 7 we found the value of a share of stock to be equal to the present constant-growth valuation

value of all future dividends, which in one model were assumed to grow at a con- (Gordon growth) model

stant annual rate over an infinite time horizon. This is the constant-growth valu-

Assumes that the value of a

ation model, also known as the Gordon growth model. The key expression

share of stock equals the

derived for this model was presented as Equation 7.4 and is restated here:

present value of all future dividends (assumed to grow at

(9.4) expected to provide over an

a constant rate) that it is

infinite time horizon.

where P 0 = value of common stock

D 1 = per-share dividend expected at the end of year 1 r s = required return on common stock

PART 4

Risk and the Required Rate of Return

Solving Equation 9.4 for r s results in the following expression for the cost of common stock equity:

= D r 1 s + g (9.5)

Equation 9.5 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 market price of the stock (the “dividend yield”) and adding the expected growth rate (the “cap- ital gains yield”).

Example 9.8 3 Duchess Corporation wishes to determine its cost of common stock equity, r s . The

market price, P 0 , of its common stock is $50 per share. The firm expects to pay a dividend, D 1 , of $4 at the end of the coming year, 2013. The dividends paid on the outstanding stock over the past 6 years (2007 through 2012) were as follows:

Using a financial calculator or electronic spreadsheet, in conjunction with the tech- nique described for finding growth rates in Chapter 5, we can calculate the annual rate at which dividends have grown,

g, from 2007 to 2012. It turns out to be approximately 5% (more precisely, it is 5.05%). Substituting D 1 = $4, P 0 = $50, and g = 5% into Equation 9.5 yields the cost of common stock equity:

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.

Using the Capital Asset Pricing Model (CAPM)

capital asset pricing model Recall from Chapter 8 that the capital asset pricing model (CAPM) describes the (CAPM)

relationship between the required return, r s , and the nondiversifiable risk of the

Describes the relationship

firm as measured by the beta coefficient,

b. The basic CAPM is:

between the required return, r s , and the nondiversifiable risk of

m the firm as measured by the - r s R F 3b * (r R F ) 4 (9.6)

beta coefficient, b.

where R F = risk-free rate of return

CHAPTER 9

The Cost of Capital

Using the CAPM indicates that the cost of common stock equity is the return required by investors as compensation for the firm’s nondiversifiable risk, meas- ured by beta.

Example 9.9 3 Duchess Corporation now wishes to calculate its cost of common stock equity, r s , by using the CAPM. The firm’s investment advisors and its own analysts indicate

b, equals 1.5; and the market return, r m , equals 11%. Substituting these values into Equation 9.6, the company estimates the cost of common stock equity, r s , to be:

that the risk-free rate, R F , equals 7%; the firm’s beta,

31.5 * (11.0% - 7.0%)4 = 7.0% + 6.0% = 13.0% The 13.0% cost of common stock equity represents the required return of

r s = 7.0% +

investors in Duchess Corporation common stock. It is the same as that found by using the constant-growth valuation model.

Comparing 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, P 0 , as a reflection of the expected risk–return preference of investors in the marketplace. The constant-growth valuation and CAPM techniques for finding r s are theoretically equivalent, though in practice estimates from the two methods do not always agree. The two methods can pro- duce different estimates because they require (as inputs) estimates of other quan- tities, such as the expected dividend growth rate or the firm’s beta.

Another difference is that when the constant-growth valuation model is used to find the cost of common stock equity, it can easily be adjusted for flotation costs to find the cost of new common stock; the CAPM does not provide a simple adjust- ment mechanism. The difficulty in adjusting the cost of common stock equity cal- culated by using the CAPM occurs because in its common form the model does not

include the market price, P 0 , a variable needed to make such an adjustment. Although the CAPM has a stronger theoretical foundation, the computational appeal of the traditional constant-growth valuation model justifies its use throughout this text to measure financing costs of common stock. As a practical matter, analysts might want to estimate the cost of equity using both approaches and then take an average of the results to arrive at a final estimate of the cost of equity.

COST OF RETAINED EARNINGS As you know, dividends are paid out of a firm’s earnings. Their payment, made in

cash to common stockholders, reduces the firm’s retained earnings. Suppose a firm needs common stock equity financing of a certain amount. It has two choices relative to retained earnings: It can issue additional common stock in that amount and still pay dividends to stockholders out of retained earnings, or it can

cost of retained earnings, r r increase common stock equity by retaining the earnings (not paying the cash divi-

The same as the cost of an equivalent fully subscribed

dends) in the needed amount. In a strict accounting sense, the retention of earnings

issue of additional common

increases common stock equity in the same way that the sale of additional shares of stock, which is equal to the cost common stock does. Thus the cost of retained earnings, r r , to the firm is the same

PART 4

Risk and the Required Rate of Return

Stockholders find the firm’s retention of earnings acceptable only if they expect that it will earn at least their required return on the reinvested funds.

Viewing retained earnings as a fully subscribed issue of additional common stock, we can set the firm’s cost of retained earnings, r r , equal to the cost of common stock equity as given by Equations 9.5 and 9.6.

It is not necessary to adjust the cost of retained earnings for flotation costs because by retaining earnings the firm “raises” equity capital without incurring these costs.