Chapter 10 The Cost of Capital 317rather than paying them out as dividends. Put another way, since investors are
thought to have an opportunity to earn 13.7 % if earnings are paid out as dividends,
the opportunity cost of equity from retained earnings is 13.7%.
10-5d Averaging the Alternative Estimates
In our examples, Allied’s estimated cost of equity was 13.0% by the CAPM, 14.0%
by the bond-yield-plus-risk premium method, and 13.7% by the DCF method.
Which method should the! rm use? If management is highly con! dent of one
method, it would probably use that method’s estimate. Otherwise, it might use an
average of the three methods, which for Allied is 13.6%:
Average! (13.0% " 13.7% " 14.0%)/3! 13.6%
One could, of course, give different weights to the different methods and thus cal-
culate a weighted average.
As consultants, we have estimated companies’ costs of capital on numerous
occasions. We generally use all three methods and average them, but we rely
most heavily on the method that seems best under the circumstances. Judgment
is important and comes into play here, as is true for most of! nance. Also, we
recognize that our! nal estimate will almost certainly be incorrect to some ex-
tent.^17 Therefore, we always provide a range and state that in our judgment, the
cost of equity is within that range. For Allied, we used a range of 13% to 14%; the
company then used 13.5% as the cost of retained earnings when it calculated its
WACC:
Final estimate of rs used to calculate the WACC: 13.5%.
(^17) Investment bankers are generally regarded as experts on concepts such as the cost of capital, and they are paid
big salaries for their analysis. But those investment bankers aren’t always too accurate. To illustrate, the stock price
of the $ fth-largest investment bank, Bear Stearns, closed on Friday, March 14, 2008, at $30. Its employees owned
33% of the stock. On Sunday, in a special meeting, its board of directors agreed to sell the company to JP Morgan
for $2 per share. Even investment bankers don’t always get it right, so don’t expect too much precision unless
you are given a set of numbers and told to do some relatively simple calculations. As of this writing, JP Morgan
has since increased its o! er for Bear Stearns to $10 per share.
SEL
F^ TEST Why must a cost be assigned to retained earnings?
What three approaches are used to estimate the cost of common equity?
Which approach is most commonly used in practice?
Identify some potential problems with the CAPM.
Which of the two components of the DCF formula, the dividend yield or the
growth rate, do you think is more di$ cult to estimate? Why?
What’s the logic behind the bond-yield-plus-risk-premium approach?
Suppose you are an analyst with the following data: rRF! 5.5%, rM " rRF!
6%, b! 0.8, D 1! $1.00, P 0! $25.00, g! 6%, and rd!! rm’s bond yield!
6.5%. What is this! rm’s cost of equity using the CAPM, DCF, and bond-yield-
plus-risk-premium approaches? Use the midrange of the judgmental risk
premium for the bond-yield-plus-risk-premium approach. (CAPM! 10.3%;
DCF! 10%; Bond yield " RP! 10.5%)