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19x0 0.01
0.03 0.0003
0.07 0.04 0.01 0.OOO9
19x1 0.03
19x2 0.04 0.10 0.16 0.0256 0.016
0.2
0.14


0.04 0.14 0.26 0.0676 0.0364
0.3
0.18
39x3
 0.39
0.2 0.0977 0.0539
7
R = 0.05
Kf= 0.0975
2 MK  n&fK  0.0539  (4)( 0.0975)(0.05)  0.0344
=
b= 0.59
0.0977  (4)(0.0975)2
ZCnW 0.0597
+ b(rn8  rf)
= rf
rj
= 4% + (0.59)(18% 4%) = 12.26%
Therefore, the 19x4 riskadjusted rate of return that is required for capital budgeting projects
is 16.18 percent.
Chapter 10
Cost of Capital
10.1 COST OF CAPITAL DEFINED
Cost of capital is defined as the rate of return that is necessary to maintain the market value of the
firm (or price of the firmâ€™s stock). Managers must know the cost of capital, often called the minimum
required rate of return in: (1) making capital budgeting decisions; (2) helping to establish the optimal
capital structure; and (3) making decisions such as leasing, bond refunding, and working capital
management. The cost of capital is computed as a weighted average of the various capital components,
which are items on the righthand side of the balance sheet such as debt, preferred stock, common stock,
and retained earnings.
10.2 COMPUTING INDIVIDUAL COSTS OF CAPITAL
Each element of capital has a component cost that is identified by the following:
ki = beforetax cost of debt
kd = ki(l t ) = aftertax cost of debt, where t = tax rate
k, = cost of preferred stock
k, = cost of retained earnings (or internal equity)
k, = cost of external equity, or cost of issuing new common stock
k, = firmâ€™s overall cost of capital, or a weighted average cost of capital
Cost of Debt
The beforetax cost of debt can be found by determining the internal rate of return (or yield to
maturity) on the bond cash flows, which was discussed in detail in Chapter 7. However, the following
shortcut formula may be used for approximating the yield to maturity on a bond:
I+(MV)/n
ki =
(M+ V ) / 2
I = annual interest payments in dollars
where
M = par value, usually $1,OOO per bond
V = value or net proceeds from the sale of a bond
n = term of the bond in years
Since the interest payments are taxdeductible, the cost of debt must be stated on an aftertax basis. The
aftertax cost of debt is:
k d = k (1  t )
i
where t is the tax rate.
EXAMPLE 10.1 Assume that the Carter Company issues a $l,OOO, 8 percent, 20year bond whose net proceeds
are $940.The tax rate is 40 percent. Then, the beforetax cost of debt, k,,is:
+ (M V)/n
I
k,=
(M+ V)/2
 $80 + ($l,OOO  $940)/20 =
 $83
8.56%
($1,0o0 + $940)/2 $970
280
281
CHAP. 101 COST OF CAPITAL
Therefore, the aftertax cost of debt is:
= k,(l  t )
kd
= 8.56%(1  0.4) = 5.14%
Cost of Preferred Stock
The cost of preferred stock, k p ,is found by dividing the annual preferred stock dividend, d p ,by the
net proceeds from the sale of the preferred stock, p , as follows:
Since preferred stock dividends are not a taxdeductible expense, these dividends are paid out after
taxes. Consequently, no tax adjustment is required.
EXAMPLE 10.2 Suppose that the Carter Company has preferred stock that pays a $13 dividend per share and
sells for $100 per share in the market. The flotation (or underwriting) cost is 3 percent, or $3 per share. Then the
cost of preferred stock is:
$I3 13.4%
==
$97
Cost of Equity Capital
The cost of common stock, k,, is generally viewed as the rate of return investors require on a firmâ€™s
common stock. Three techniques for measuring the cost of common stock equity capita1 are available:
(1)the Gordonâ€™s growth model; (2) the capital asset pricing model (CAPM) approach; and (3) the bond
plus approach.
The Gordonâ€™s Growth Model. The Gordonâ€™s model was discussed in detail in Chapter 7. The
model is:
where PO= value of common stock
D 1= dividend to be received in 1year
r = investorâ€™s required rate of return
g = rate of growth (assumed to be constant over time)
Solving the model for r results in the formula for the cost of common stock:
Note that the symbol r is changed to k, to show that it is used for the computation of cost of capital.
EXAMPLE 10.3 Assume that the market price of the Carter Companyâ€™s stock is $40. The dividend to be paid at
the end of the coming year is $4 per share and is expected to grow at a constant annual rate of 6 percent. Then the
cost of this common stock is:
D
1 $4
k, = +g = +6% = 16%
P
O $40
The cost of new common stock, or external equity capital, is higher than the cost of existing common
stock because of the flotation costs involved in selling the new common stock.
282 COST OF CAPITAL [CHAP. 10
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