Introduction to Finance

T
), where 
T
is the fi rm’s marginal tax rate.
4
Thus the after-tax cost 
of debt, 
k
d
, is the following:
k
d
= YTM (1 – 
T
) (18-1)
Suppose Eastnorth Manufacturing has a 40 percent marginal tax rate and it can issue debt 
with a 10 percent yield to maturity. Its after-tax cost of debt will be 10 percent (1 – 0.40) = 
6 percent.
4
In reality, this is an approximation. We know from Chapter 10 that the YTM refl ects interest paid and the diff erence 
between market price and par value. Only the interest is tax deductible to the fi rm. For coupon-paying bond issues, 
the coupon rate many times is set so the bonds’ market or off ering price is close to par. In these cases, equation 18-1 
is a close approximation to the cost of debt.

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572
C H A PT E R 1 8 Capital Structure and The Cost of Capital
Cost of Preferred Stock 
Chapter 9 explained how to model preferred stock as a perpetuity. The investor pays a price, 
P
, for a share of preferred stock and, in return, expects to receive 
D
p
of dividends every year, 
forever. Valuing the stock as perpetuity, the maximum price an investor will pay for a share is 
D
p
∕
r
p
, where 
r
p
represents the rate of return required by investors in the fi rm’s preferred stock. 
Rearranging the valuation equation to solve for 
r
p
yields the following equation:
r
p
 = D
p
∕
P
When issuing preferred stock, the fi rm will not receive the full price, 
P
, per share; instead, 
there will be a fl otation cost of 
F
p
per share.
5
Thus, the cost to the fi rm of preferred stock 
fi nancing, 
k
p
, is the following result:
k
p
= 
D
p
∕(
P
– 
F
p
) (18-2)
Suppose a fi rm wants to issue preferred stock that pays an annual dividend of $5 a share. 
The price of the stock is $55, and the cost of fl oating a new issue will be $3 a share. The 
cost of preferred stock to this fi rm is will be 
k
p
= 
D
p
∕(
P
– 
F
p
) = $5∕($55 – $3) = 0.0962, or 
9.62 percent.
Cost of Common Equity
Unlike debt and preferred stock, cash fl ows from common equity are not fi xed or known 
beforehand, and their risk is harder to evaluate. In addition, fi rms have two sources of common 
equity, retained earnings and new stock issues, which are two costs of common equity. It may 
be clear that an explicit cost (dividends) is associated with issuing new common equity, but 
although the fi rm pays no extra dividends to use retained earnings, they are not a free source of 
fi nancing. We must consider the opportunity cost of using funds the shareholders could have 
received as dividends.
Retained earnings are the portion of net income the fi rm does not distribute as dividends. 
As owners of the fi rm, common shareholders have a claim on all of its net income, but they 
receive only the amount the fi rm’s board declares as dividends.
From the shareholders’ perspective, the opportunity cost of retained earnings is the return 
the shareholders could earn by investing the funds in assets whose risk is similar to that of 
the fi rm. Suppose, for example, that shareholders expect a 15 percent return on their invest-
ment in a fi rm’s common stock. If the fi rm could not invest its retained earnings to achieve a 
risk-adjusted 15 percent expected return, shareholders would be better off receiving all of its 
net income as dividends. That way, they can re-invest the funds in similar-risk assets that can 
provide a 15 percent expected return.
To maximize shareholder wealth, management must recognize that retained earnings have 
a cost. That cost, 
k
re
, is the return that shareholders expect from their investment in the fi rm. 
We will review two methods of estimating the cost of retained earnings. One method uses the 
security market line (SML); the other uses the assumption of constant dividend growth.