Problem 15, Chapter 11
Contemporary Financial Management
(a) Compute Rolodex’s marginal cost of capital schedule.
Capital structure weights (w’s) are needed for the
weighted average cost of capital calculation:
ka  weke  wpk p  w k
d i
From the balance sheet:
Long-term debt
Preferred Stock
Common Stock at par value
Contributed in excess of par
Retained Earnings
Total Capital
$128
32
20
30
110
$320
w  Long-term debt  128  0.40
d Total Capital 320
w p  Preferred Stock  32  0.10
Total Capital 320
we  CS at par + Contrib. in excess + RE  2030110  0.50
Total Capital
320
Total of weights = 0.40 + 0.10 + 0.50 = 1.00
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Costs of Capital:
 Rolodex can borrow $40 million from its bank at a pretax
cost of 13 percent. After – tax cost of debt up to $40
million of debt:
k  k 1T 
i d
k 13% 1.40   7.8%
i
 Rolodex can borrow $80 million by issuing (selling)
bonds at a net price of $687 per bond. The bonds
would carry a 10 percent coupon rate and mature in 20
years. This takes the total of debt financing to $120
million.




Pnet  I  PVIFAk ,n   M  PVIFk ,n 
k  YTM




d
d 
d 






$687  $100 PVIFAk ,20   $1,000 PVIFk ,20 


d 
d 


k 15%
d
k 15% 1.40   9%
i
 Additional debt (bonds) can be issued (sold) at a 16
percent pretax cost.
k 16%1.40   9.6%
i
2
 Preferred stock can be issued (sold) at a pretax cost of
16.5 percent.
Dividends are not tax deductible. So the pretax cost is the
same as the after-tax cost.
k p 16.5%
 Rolodex expects to generate $140 million in net income
and pay $2 per share in dividends.
Find the amount of retained earnings for the year.
The balance sheet on page 405 shows that 20 million
shares of common stock are outstanding.
Dividends paid = (20 MM shares) ($2 / share) = $40 MM
Retained earnings = $140 MM net income less $40 MM
paid as dividends = $100 MM.
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 The $2 per share dividend (D1) represents a growth of
5.5 percent over the previous year’s dividend. This
growth rate is expected to continue for the foreseeable
future. The firm’s stock currently is trading at $16 per
share.
Cost of the $100 MM of retained earnings:
D
ke  1  g
P
0
ke  $2  0.055  .18 Or 18%
$16
 Rolodex can raise external equity by selling common
stock at a net price of $15 per share.
Cost of the new equity, i.e., new common stock sold after
using the retained earnings for the year:
D
'
ke  1  g
Pnet
ke'  $2  0.055  .188 Or 18.8%
$15
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The weighted average cost of capital (WACC or ka)
must be calculated for the initial range of capital where
retained earnings are used.
ka must be recalculated whenever one of the costs of
capital (ke, kp, or ki) changes.
We also need the ranges of dollars of total capital for
which each recalculated ka applies.
Find these ranges of total capital by finding the break
points in dollars of total capital.
$ Total capital where one component changes cost
multiplied by the percentage of capital from that source
gives the $ of lower cost capital from the source.
The dollars of total capital where one component changes
cost is the unknown. Let X represent this amount.
(X) (percentage from a source) =
$ lower cost capital from that source before the cost
change
X = $ lower cost capital from the source that changes cost
percentage from the source
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In this problem, debt financing changes cost at $40 million
and at $120 million of debt financing.
The associated break points of in dollars of total capital
are found as follows.
X = $40 million = $100 million of total capital
0.40
and
X = $120 million = $300 million
0.40
Preferred stock never has a cost increase so it doesn’t
create any break points.
Common equity financing changes cost when we use all of
the $100 million of retained earnings and then common
stock must be sold.
X = $100 million = $200 million of total capital
0.50
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The results above placed in a table.
Source of
capital
Weight
Range of $
in capital from the
structure source
(millions)
After-tax
cost of
the
source
Break
Points in
total
capital
(millions)
Debt
0.40
$0 - $40
7.8%
$100
Debt
0.40
$40 - $120
9.0%
$300
Debt
0.40
$120 ----
9.6%
None
0.10
$0 ----
16.5%
None
0.50
$0 - $100
18.0%
$200
0.50
$100 ----
18.8%
None
Preferred
stock
Common
Equity
(RE)
Common
Equity
(New CS)
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Find the marginal cost of capital schedule by
recalculating the weighted average cost of capital (ka)
before and after each break point in total capital.
Range $0 $100 MM - $200 MM - > $300 MM
between $100MM $200 MM
$300 MM
BP’s
ke
18.0%
18.0%
18.8%
18.8%
kp
16.5%
16.5%
16.5%
16.5%
ki
7.8%
9.0%
9.0%
9.6%
ka
MCC
sched.
13.77%
14.25%
14.65%
14.89%
Example of the calculation of ka:
Use the column for $0 to $100 million of total capital.
ka  weke  w pk p  w k
d i
ka   .50  18.0%    .10  16.5%    .40   7.8%  13.77%
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(b) Given the following investment opportunity schedule,
determine Rolodex’s optimal capital budget.
The project investment information from page 406 is
placed here in an expanded table with projects ranked
from highest to lowest expected return (IRR).
Project
Required Cumulative Expected
Investment Investment Return
(NINV)
(IRR)
ka for
the $
range
Accept?
A
$140 MM
$140 MM
17.0%
14.25%
Yes,
IRR>ka
B
$130
$270
16.0%
14.65%
Yes
C
$100
$370
15.0%
14.89%
Yes
D
$80
$450
14.2%
14.89%
No,
IRR<ka
E
$24
$474
13.0%
14.89%
No
F
$16
$490
10.9%
14.89%
No
The optimal capital budget consists of
Projects A, B, and C
For a total investment of $370 million.
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