The Cost of Capital: Cost of Retained Earnings

The cost of common equity is based on the rate of return thatinvestors require on the company's common stock. New common equityis raised in two ways: (1) by retaining some of the current year'searnings and (2) by issuing new common stock. Equity raised byissuing stock has a(n)

cost, r_e, than equity raised from retained earnings,r_s, due to flotation costs required to sell new commonstock. Some argue that retained earnings should be "free" becausethey represent money that is left over after dividends are paid.While it is true that no direct costs are associated with retainedearnings, this capital still has a cost, a(n)

cost. The firm's after-tax earnings belong to its stockholders,and these earnings serve to compensate them for the use of theircapital. The earnings can either be paid out in the form ofdividends to stockholders who could have invested this money inalternative investments or retained for reinvestment in the firm.Therefore, the firm needs to earn at least as much on any earningsretained as the stockholders could earn on alternative investmentsof comparable risk. If the firm cannot invest retained earnings toearn at least r_s, it should pay those funds to itsstockholders and let them invest directly in stocks or other assetsthat will provide that return. There are three procedures that canbe used to estimate the cost of retained earnings: the CapitalAsset Pricing Model (CAPM), the Bond-Yield-Plus-Risk-Premiumapproach, and the Discounted Cash Flow (DCF) approach.

CAPM

The firm's cost of retained earnings can be estimated using theCAPM equation as follows:

r_s = r_RF + (RP_M)b_i =r_RF + (r_M -r_RF)b_i

The CAPM estimate of r_s is equal to the risk-free rate,r_RF, plus a risk premium that is equal to the riskpremium on an average stock, (r_M - r_RF),scaled up or down to reflect the particular stock's risk asmeasured by its beta coefficient, b_i. This model assumesthat a firm's stockholders are

diversified, but if they are diversified, then the firm's trueinvestment risk would not be measured by and the CAPM estimatewould

the correct value of r_s.

Bond Yield Plus Risk Premium

If reliable inputs for the CAPM are not available as would betrue for a closely held company, analysts often use a subjectiveprocedure to estimate the cost of equity. Empirical studies suggestthat the risk premium on a firm's stock over its own bondsgenerally ranges from 3 to 5 percentage points. The equation isshown as: r_s = Bond yield + Risk premium. Note that thisrisk premium is

the risk premium given in the CAPM. This method doesn't producea precise cost of equity, but does provide a ballpark estimate.

DCF

The DCF approach for estimated the cost of retained earnings,r_s, is given as follows:

Investors expect to receive a dividend yield, , plus a capitalgain, g, for a total expected return. In

, this expected return is also equal to the required return.It's easy to calculate the dividend yield; but because stock pricesfluctuate, the yield varies from day to day, which leads tofluctuations in the DCF cost of equity. Also, it is difficult todetermine the proper growth especially if past growth rates are notexpected to continue in the future. However, we can use growthrates as projected by security analysts, who regularly forecastgrowth rates of earnings and dividends.

Which method should be used to estimate r_s? Ifmanagement has confidence in one method, it would probably use thatmethod's estimate. Otherwise, it might use some weighted average ofthe three methods. Judgment is important and comes into play here,as is true for most decisions in finance.

Quantitative Problem: Barton Industriesestimates its cost of common equity by using three approaches: theCAPM, the bond-yield-plus-risk-premium approach, and the DCF model.Barton expects next year's annual dividend, D₁, to be$1.50 and it expects dividends to grow at a constant rate g = 3.1%.The firm's current common stock price, P₀, is $28.00.The current risk-free rate, r_RF, = 4%; the market riskpremium, RP_M, = 5.3%, and the firm's stock has a currentbeta, b, = 1.2. Assume that the firm's cost of debt, r_d,is 6.11%. The firm uses a 3.3% risk premium when arriving at aballpark estimate of its cost of equity using thebond-yield-plus-risk-premium approach. What is the firm's cost ofequity using each of these three approaches? Round your answers to2 decimal places.

CAPM cost of equity:	%
Bond yield plus risk premium:	%
DCF cost of equity:	%

What is your best estimate of the firm's cost of equity?