CHAPTER 8
ANSWERS
8-1
This point is demonstrated in Table 8-1 and Figures 8-2 and 8-3 in the textbook. The marginal cost
of capital is a weighted average of debt, preferred stock, and equity.
8-2
This statement is not valid, because the cost of retained earnings is equal to the cost of common
equity without considering flotation costs. If the firm cannot earn at least this rate of return on
investments funded with retained earnings, then earnings should be distributed as dividends. For a
particular firm, the cost of retained earnings is greater than the after-tax cost of debt and the cost of
preferred stock. The only higher cost of capital component is new common equity, because
flotation costs are involved.
8-3
kdT
a.
The corporate tax rate is lowered.
+
0
+
b.
The Federal Reserve tightens credit.
+
+
+
c.
The firm significantly increases the proportion
of debt it uses.
+
+
+
The dividend payout ratio (% of earnings paid
as dividends) is increased.
0
0
0
The firm doubles the amount of capital it raises
during the year.
0 or +
0 or +
0 or
d.
e.
f.
The firm expands into riskier new areas.
+
+
+
g.
The firm merges with another firm whose earnings
are countercyclical both to those of the first firm and
to the stock market.
-
-
-
The stock market falls drastically, and the value of
the firm’s stock falls along with the rest.
0
+
+
i.
Investors become more risk averse.
+
+
+
j.
The firm is an electric utility with a large investment in
+
+
+
h.
in nuclear plants. Several states propose a ban on
nuclear power generation.
8-4
Probable Effect on
ks
WACC
Assuming that all projects are equally risky, the capital budget should be evaluated at the cost of
capital where the MCC and IOS schedules intersect. Thus, in this case, average-risk projects should
be evaluated at a 10 percent cost of capital. The cost of capital used to evaluate high-risk projects
should be adjusted upward from 10 percent, whereas for low-risk projects, a downward cost of
capital adjustment should be made.
_____________________________________________________________
142
SOLUTIONS
8-1
D̂1
$2.14
g 
 0.07  0.093  0.07  0.163  16.3%
P0
$23
a.
ks 
b.
ks = kRF + (kM - kRF)βs
= 9% + (13% - 9%)1.6 = 9% + (4%)1.6 = 9% + 6.4% = 15.4%.
8-2
c.
ks = Bond rate + Risk premium = 12% + 4% = 16%.
d.
The bond-yield-plus-risk-premium approach and the CAPM method both resulted in lower
cost of equity values than the DCF method. Because financial analysts tend to give the most
weight to the DCF method, Talukdar Technologies’ cost of equity should be estimated to be
about 16.3 percent. If the estimates from each method are averaged, however, ks = 15.9%.
a.
Solving directly, $6.50 = $4.42(1+g)5
g = ($6.50/$4.42)1/5 - 1 = 0.0802% ≈ 8%.
Alternatively, with a financial calculator, input N = 5, PV = -4.42, FV = 6.50, and then solve
for I = 8.02% ≈ 8%.
8-3
b.
D̂1 = D0(1 + g) = $2.60(1.08) = $2.81.
c.
ks = D̂1 /P0 + g = $2.81/$36.00 + 0.08 = 15.8%.
a.
Retained earnings = ($30 million)(1 - Payout) = ($30 million)(0.60) = $18 million.
b.
Break point =
c.
Break point from using debt:
Retained earnings
$18,000,000
=
= $45 million
Equity as a percent of capital
0.40
11% break point = $12 million/Debt percentage = $12 million/0.6 = $20 million.
12% break point = ($12 million + $12 million)/0.6 = $40 million.
8-4
a.
ks =
0.09 =
D̂1 + g
P0
$3.60
$60.00
+g
0.09 = 0.06 + g
g = 3%
143
b.
Current EPS
Less: Dividends per share
Retained earnings per share
Rate of return
Increase in EPS
Current EPS
Next year’s EPS
$5.40
3.60
$1.80
x 0.09
$0.162
5.40
$5.562
Alternatively, EPS1 = EPS0(1 + g) = $5.40(1.03) = $5.562.
8-5
a.
Common equity needed: 0.50($135,000,000) = $67,500,000.
b.
Expected internally generated equity (retained earnings) is $13.5 million. External equity
needed is as follows:
New equity needed
Retained earnings
External equity needed
c.
$67,500,000
13,500,000
$54,000,000
Cost of equity:
ks = Cost of retained earnings
= Dividend yield + Growth rate = 12% = 4% + 8% = 12%.
= D̂1 /P0 + g = $2.40/$60 + 0.08 = 0.04 + 0.12 = 12.0%.
ke = Cost of new equity
= D̂1 /NP + g = $2.40/$54.00 + 0.08 = 0.044 + 0.08 = 0.124 = 12.4%.
d.
BPRE 

e.
Estimated retained earnings
Common equity/Tot al capital 
$13,500,000
 $27,000,000 of total funds
0.5
(1) Cost below break:
Component
Debt
Retained earnings
Weight
0.50
0.50
After-tax
Weighted
x
Cost
=
Cost
6.0%*
3.0%
12.0%
6.0
WACC1 below break = 9.0%
*kdT = 10%(1 - T) = 10%(0.60) = 6%.
(2) Cost above break:
Component
Debt
New equity
Weight
0.50
0.50
144
After-tax
Weighted
x
Cost
=
Cost
6.0%
3.0%
12.4%
6.2
WACC2 above break = 9.2%
f.
The IOS curve must cut the MCC at $135 million. The slope of the IOS is not material for
this question.
8-6
a.
After-tax cost of new debt: kd(1 - T) = 9%(1 - 0.4) = 5.4%.
Cost of common equity from retained earnings:
Calculate g as follows:
$7.80 = $3.90(1+g)9
g = ($7.80/$3.90)1/9 - 1 = 0.08005% = 8.0%
Alternatively, with a financial calculator, input N = 9, PV = -3.90, FV = 7.80, and then solve
for I = 8.01% = 8%.
Expected EPS2005 = $7.80(1.08) = $8.42
D̂1 = 0.55($8.42) = $4.63
ks 
b.
D̂1
$4.63
g 
 0.08  0.071  0.08  0.151  15.1%
P0
$65
WACC1 calculation:
Component
Debt = [0.09(1 - T)]
Common equity (RE)
c.
Weight
0.40
0.60
x
After-tax
Cost
5.4%
15.1%
=
Weighted
Cost
2.16%
9.06%
11.22%
In order for the capital structure to remain optimal, retained earnings must comprise 60
145
percent of total new financing before external equity is sold.
Retained earnings for 2005:
RE = (Expected EPS2005)(Number of shares)(0.45)
= ($8.42)(7.8 million shares)(0.45) = $29,554,200
Retained earnings break point = $29,554,200/0.6 = $49,257,000.
d.
Cost of new equity:
From Part a, D̂1 = $4.63 and g = 8%. The cost of new equity is as follows:
ks =
D̂1 + g = $4.63 + 0.08 = 0.079  0.08  0.159  15.9%
NP
$58.50
WACC2 calculation:
Component
Debt = [0.09(1 - T)]
New common equity
8-7
a.
x
Weight
0.40
0.60
After-tax
Weighted
Cost
=
Cost
5.4%
2.16%
15.9%
9.54
WACC = 11.70%
There are three breaks in the MCC schedule. These breaks occur as follows:
Break #1 (New debt):
Break #2 (R.E.):
Break #3 (New debt):
$500,000/0.45 = $1,111,111
[$2,500,000(0.4)]/0.55 = $1,818,182
$900,000/0.45 = $2,000,000
Break #1 is caused by exhausting the 9 percent debt, Break #2 is caused by using up retained
earnings in financing needs, and Break #3 is caused by exhausting the 11 percent debt.
b.
(1) Cost below first break: Total funds of $1 to $1,111,111
Component
Debt = [0.09(1 - T)]
Retained earnings*
Weight
0.45
0.55
x
After-tax
Weighted
Cost
=
Cost
5.4%
2.43%
15.5%
8.53
MCC1 = 10.96% ≈ 11.0%
(2) Cost between first and second breaks: Total funds of $1,111,112 to $1,818,182
Component
Debt = [0.11(1 - T)]
Retained earnings*
Weight
0.45
0.55
146
x
After-tax
Weighted
Cost
=
Cost
6.6%
2.97%
15.5%
8.53
MCC1 = 11.50% = 11.5%
(3) Cost between second and third breaks: Total funds of $1,818,183 to $2,000,000
Component
Debt = [0.11(1 - T)]
Retained earnings*
Weight
0.45
0.55
x
After-tax
Weighted
Cost
=
Cost
6.6%
2.97%
16.67%
9.17
MCC1 = 12.14% = 12.1%
(4) Cost above third break: Total funds greater than $2,000,000
Component
Debt = [0.13(1 - T)]
Retained earnings*
Weight
0.45
0.55
x
After-tax
Weighted
Cost
=
Cost
7.8%
3.51%
16.67%
9.17
MCC1 = 11.68% = 12.7%
*Cost of retained earnings:
ks =
D̂1 + g = $2.20(1.05) + 0.05 = 15.5%
$22
P0
**Cost of external equity:
ke =
c.
D̂1 + g = $2.20(1.05) + 0.05 = 16.67%
$22(0.9)
P0 (1 - F)
1  1 8 
(1 IRR )

IRR1: $675,000  $155,401
 IRR 


Financial calculator solution: Input N = 8, PV = -675,000, PMT = 155,401, and FV = 0;
compute I = IRR = 16.0%
1  1 3 
(1 IRR )

IRR3: $375,000  $161,524
 IRR 


Financial calculator solution: Input N = 3, PV = -375,000, PMT = 161,524, and FV = 0;
compute I = IRR = 14.0%
147
%
d.
16
Project 1
16%
Project 2
15%
Project 3
14%
14
12
MCC4 = 12.7
MCC3 = 12.1
MCC2 = 11.5
Project 5
11%
MCC1 = 11.0
10
Optimal budget = $1,950
500
1,000
1,500
Project 4
12%
2,000
2,500
3,000
3,500
Capital Expenditure/Financing
($ thousands)
8-8
e.
From the above graph, we conclude that Ezzell's management should undertake Projects 1, 2,
and 3, assuming that these projects are all about “average risk” in relation to the rest of the
firm.
f.
The solution implicitly assumes (1) that all of the projects are equally risky and (2) that these
projects are as risky as the firm’s existing assets. If the accepted projects (1, 2, and 3) were of
above average risk, this would raise the company’s overall risk, hence its cost of capital.
Possibly, taking on these projects would result in a decline in the company’s value.
g.
If the payout ratio were lowered to zero, this would shift the equity break point to the right,
from $1,818,182, to $4,545,455. This shift would have changed the decision—Project 4
would now be acceptable and the capital budget would have increased from $1,950,000
under the original assumptions to $2,512,500. (Note that at $2,000,000 the 11 percent debt
has been exhausted; thus MCC3 = 12.1%; however, the average marginal cost of Project 4 is
11.99%. Because 11.99% < 12.1%, the project is acceptable—although barely.) If the payout
ratio were raised to 100 percent, the equity break point would shift to zero; however, this
shift would not change the original decision. Note, however, that these reconstructions
assume ks and ke are unaffected by the payout ratio. In reality, ks and ke might be affected, so
a change in the payout ratio might actually raise their values, hence increase MCC.
a.
kdT = kd(1 - T) = 13%(1 - 0) = 13.00%.
b.
kdT = 13%(1 - 0.20) = 10.40%.
c.
kdT = 13%(1 - 0.34) = 8.58%.
8-9
kdT = 12%(1 - 0.34) = 7.92%.
8-10
k ps =
$100(0.11)
$11
=
= 11.94%
$97(1  0.05) $92.15
148
8-11
8-12
a.
F = ($36.00 - $32.40)/$36.00 = $3.60/$36.00 = 10.0%
b.
ke = D̂1 /NP + g = $3.18/$32.40 + 6% = 9.8% + 6% = 15.8%
Capital Sources
Long-term debt
Equity
Amount
$1,152
1,728
$2,880
Percent of Capital Structure
40.0
60.0
100.0
WACC = wdkdT + wsks = 0.4[(13%)(1 - 0.4)] + 0.6(16%) = 3.12% + 9.60% = 12.72%.
8-13
The break points are calculated as follows:
BPRE = $3,000,000/0.5 = $6,000,000
BPDebt = $5,000,000/0.5 = $10,000,000
Now determine the weighted average cost of capital for the intervals $1-$6,000,000, $6,000,001$10,000,000, and greater than $10,000,000:
Interval: $1-$6,000,000:
WACC1 = 0.5[( 8%)(0.6)] + 0.5(12%) = 8.4%
Interval: $6,000,001-$10,000,000:
WACCB = 0.5[( 8%)(0.6)] + 0.5(15%) = 9.9%.
Interval: Greater than $10,000,000:
WACCC = 0.5[(10%)(0.6)] + 0.5(15%) = 10.5%.
Finally, graph the IOS and MCC schedules.
%
11
10.5
MCC
10.2
10
9
IOS
9.9
8.4
Optimal Capital Budget
8
New Capital ($ millions)
5
10
15
149
20
Thus, the optimal capital budget is $10 million.
8-14
Retained earnings are forecast to be $7,500(1 - 0.4) = $4,500. RE breakpoint = $4,500/0.6 =
$7,500. The cost of retained earnings is:
ks =
D0 (1 + g) + g = $0.90(1.05) + 0.05 = 16.0%
$8.59
P0
The cost of new equity is as follows:
ke =
$0.90(1.05)
+ 0.05 = 18.75%
$8.59(1 - 0.20)
Now determine the weighted average costs of capital:
WACC = wdkdT + ws{ks or ke}
WACC1 = 0.4[(14%)(0.6)] + 0.6(16.00%) = 12.96%.
WACC2 = 0.4[(14%)(0.6)] + 0.6(18.75%) = 14.61%.
Finally, graph the MCC and IOS schedules:
%
17
IRRA = 17%
IRRC = 16%
16
IRRD = 15%
15
14.61
MCC
IRRB = 14%
14
13
IOS
Optimal Capital
Budget = 42
12.96
10
20
30
40
50
60
New Capital ($ thousands)
Therefore, the optimal capital budget is $42,000, and projects A, C, and D are accepted.
8-15
The firm’s marginal cost of capital is 14.61 percent. Thus, Project A (high-risk) should be
evaluated at a risk-adjusted cost of capital of 16.61 percent, while Project B (low-risk) should be
evaluated at 12.61 percent. The average-risk projects (C and D) continue to be evaluated at 14.61
percent.
150
Now we have the following situation:
Project
A
B
C
D
Risk-Adjusted
Cost of Capital
16.61%
12.61
14.61
14.61
IRR
17%
14
16
15
Thus, all projects are now acceptable, and hence the optimal capital budget totals $62,000.
8-16
kd = 10%, kdT = kd(1 - T) = 10(0.6) = 6%.
Debt/Assets = 45%; D0 = $2; g = 4%; P0 = $25; NP = $20; T = 40%.
Project A: Cost = $200 million; IRR = 13%.
Project B: Cost = $125 million; IRR = 10%.
Retained earnings = $100 million.
Retained earnings break point = $100/0.55 = $181.82 million.
Cost of retained earnings = ks = $2(1.04)/$25 + 4% = 12.32%.
a.
Cost of new equity = ke = $2(1.04)/$20 + 4% = 14.40%.
b.
WACC1 = 0.45(6%) + 0.55(12.32%) = 9.48%
WACC2 = 0.45(6%) + 0.55(14.40%) = 10.62%
FEC should use a weighted average cost of capital of 10.62% to evaluate its capital
budgeting projects because the retained earnings break point is $181.82 million and Project
A has a cost of $200 million.
8-17
We can use the equation given (Equation 7-3) in Chapter 7 to find the approximate yield to
maturity:
Approximat e YTM 

INT + 
M - Vd 

 N 
 2(V d ) + M 


3


$60  $1,00030$515.16

2 ($515.16) $1, 000
3


$76.16
 0.113  11.3%
$676.77
Note that we use the number of years rather than the number of interest payments in this
computation, because the “approximate YTM” computation does not consider the time value of
money.
Using the calculator, enter these values: N = 60, PV = -515.16, PMT = 30, and FV = 1000, to get I
= 6% = periodic rate. The simple rate is 6%(2) = 12%, and the after-tax component cost of debt is
12%(0.6) = 7.2%.
151
8-18
Debt = 40%, Equity = 60%, NI = $600, Retain = 40%.
P0 = $30, D0 = 2.00, D̂1 = 2.00(1.07) = 2.14, g = 7%, F = 25%.
RE = $600(0.4) = $240.
REBP = RE/Equity ratio = $240/0.6 = $400.
At total capital of $500, retained earnings will have been used up, so equity will come from new
common stock, whose cost will be:
ke =
$2.14
+ 0.07 = 0.095 + 0.070 = 16.5%
$30(1 - 0.25)
8-19
The solution is given in the Instructor’s Manual, Solutions to Integrative Problems.
8-20
Computer-Related Problem
a.
Under this scenario, the MCC schedule has moved down because all of
the WACCs have decreased. Projects 1, 2, and 3 are still
acceptable; however, Project 4 becomes acceptable. The capital
budget is now $2,512,500.
INPUT DATA:
Debt ratio:
65.00%
Earnings:
$2,500,000.00
Dividend payout:
60.00%
Tax rate:
40.00%
Current Stock Price:
$22.00
Previous dividend (D0):
$2.20
Growth rate:
6.00%
Equity flotation cost:
10.00%
Beginning of
New debt cost:
Range
$
0
$500,001
$900,001
Project
Number/rank
1
2
3
4
5
k(d)
10.00%
12.00%
14.00%
Cost
ROR
$675,000
900,000
375,000
562,500
750,000
16.00%
15.00%
14.00%
12.00%
11.00%
152
KEY OUTPUT:
Ret. earnings break
1st debt break
2nd debt break
WACC
WACC
WACC
WACC
before break 1
before break 2
before break 3
after break 3
Accepted
Projects
(non-zero)
1
2
3
4
0
ROR
16%
15%
14%
12%
0%
$2,857,143
$ 769,231
$1,384,615
9.7%
10.5%
11.3%
11.7%
Project
Cost
$ 675,000
900,000
375,000
562,500
0
__________
Capital budget = $2,512,500
MODEL-GENERATED DATA:
Breaks in the MCC schedule:
Use of retained earnings
Use of debt at:
10%
Use of debt at:
12%
$2,857,143
$ 769,231
$1,384,615
Cost of financing below first break:
Component
_________
Weight
______
Debt
Equity
0.65
0.35
After-tax
Cost
_________
Weighted
Cost
________
6.00%
3.90%
16.60%
5.81%
WACC 1 = 9.71%
Cost of financing between first and second breaks:
Component
_________
Weight
______
Debt
Equity
0.65
0.35
After-tax
Cost
_________
Weighted
Cost
________
7.20%
4.68%
16.60%
5.81%
WACC 2 = 10.49%
Cost of financing between second and third breaks:
Component
_________
Weight
______
Debt
Equity
0.65
0.35
After-tax
Cost
_________
Weighted
Cost
________
8.40%
5.46%
16.60%
5.81%
WACC 3 = 11.27%
Cost of financing above third break:
Component
_________
Weight
______
Debt
Equity
0.65
0.35
After-tax
Cost
_________
8.40%
5.46%
17.78%
6.22%
WACC 4 = 11.68%
Capital Cost:
Range of financing
__________________
$
0
769,231
769,232
1,384,615
1,384,616
2,857,143
2,857,144
5,000,000
Capital cost
____________
9.7%
9.7%
10.5%
10.5%
11.3%
11.3%
11.7%
11.7%
153
Weighted
Cost
________
Optimal capital budget:
b.
Project
Number/rank
___________
ROR
___
1
2
3
4
0
16%
15%
14%
12%
0%
Project
Cost
__________
$
675,000
900,000
375,000
562,500
0
$2,512,500
At a tax rate of 20 percent, the MCC curve shifts up, so only
Projects 1, 2, and 3 remain acceptable. If the tax rate falls to 0
percent, only Projects 1 and 2 would be acceptable.
TAX RATE = 20 PERCENT:
INPUT DATA:
Debt ratio:
65.00%
$2,857,143
Earnings:
$2,500,000.00
Dividend payout:
60.00%
$1,384,615
Tax rate:
20.00%
Current Stock Price:
$22.00
Previous dividend (D0):
$2.20
Growth rate:
6.00%
Equity flotation cost:
10.00%
Beginning of
New debt cost:
Range
____________
$
0
$500,001
$900,001
k(d)
______
10.00%
12.00%
14.00%
KEY OUTPUT:
Ret. earnings break
1st debt break
2nd debt break
WACC
WACC
WACC
WACC
$
before break 1
before break 2
before break 3
after break 3
Accepted
Projects
(non-zero)
__________
ROR
___
1
16%
2
15%
3
14%
0
0%
0
0%
Capital budget =
769,231
11.0%
12.1%
13.1%
13.5%
Project
Cost
__________
$
675,000
900,000
375,000
0
0
$1,950,000
TAX RATE = 0 PERCENT:
INPUT DATA:
Debt ratio:
65.00%
$2,857,143
Earnings:
$2,500,000.00
Dividend payout:
60.00%
$1,384,615
Tax rate:
0.00%
Current Stock Price:
$22.00
Previous dividend (D0):
$2.20
Growth rate:
6.00%
Equity flotation cost:
10.00%
KEY OUTPUT:
Ret. earnings break
1st debt break
2nd debt break
WACC
WACC
WACC
WACC
154
before break 1
before break 2
before break 3
after break 3
$
769,231
12.3%
13.6%
14.9%
15.3%
Beginning of
New debt cost:
Range
____________
$
0
$500,001
$900,001
c.
Accepted
Projects
(non-zero)
__________
k(d)
______
10.00%
12.00%
14.00%
ROR
___
1
16%
2
15%
0
0%
0
0%
0
0%
Capital budget =
Project
Cost
__________
$
675,000
900,000
0
0
0
$1,575,000
If earnings are as high as $3.25 million or as low as $1,000,000
Projects 1, 2, 3, and 4 are still acceptable. Project 5 is still
not acceptable in either situation.
EARNINGS = $3.25 million:
INPUT DATA:
KEY OUTPUT:
Debt ratio:
65.00%
Ret. earnings break $3,714,286
Earnings:
$3,250,000.00
1st debt break
$ 769,231
Dividend payout:
60.00%
2nd debt break
$1,384,615
Tax rate:
40.00%
Current Stock Price:
$22.00
WACC before break 1
9.7%
Previous dividend (D0):
$2.20
WACC before break 2
10.5%
Growth rate:
6.00%
WACC before break 3
11.3%
Equity flotation cost:
10.00%
WACC after break 3
11.7%
Beginning of
New debt cost:
Range
____________
k(d)
______
$
0
$500,001
$900,001
10.00%
12.00%
14.00%
Accepted
Projects
(non-zero)
__________
ROR
___
1
16%
2
15%
3
14%
4
12%
0
0%
Capital budget =
Project
Cost
__________
$
675,000
900,000
375,000
562,500
0
$2,512,500
EARNINGS = $1 million:
INPUT DATA:
Debt ratio:
65.00%
$1,142,857
Earnings:
$1,000,000.00
Dividend payout:
60.00%
$1,384,615
Tax rate:
40.00%
Current Stock Price:
$22.00
Previous dividend (D0):
$2.20
Growth rate:
6.00%
Equity flotation cost:
10.00%
155
KEY OUTPUT:
Ret. earnings break
1st debt break
2nd debt break
WACC
WACC
WACC
WACC
before break 1
before break 2
before break 3
after break 3
$
769,231
9.7%
10.5%
10.9%
11.7%
Beginning of
New debt cost:
Range
____________
$
0
$500,001
$900,001
d.
k(d)
______
10.00%
12.00%
14.00%
Accepted
Projects
(non-zero)
__________
ROR
___
1
16%
2
15%
3
14%
4
12%
0
0%
Capital budget =
Project
Cost
__________
$
675,000
900,000
375,000
562,500
0
$2,512,500
No. A change in the payout ratio would certainly affect g, hence
the cost of equity. This point is explained in more detail in
Chapter 9.
156