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MOD4PRACTICEPROBLEMS.pdf
Chapters 11 and 13 Practice Problems and Solutions
11-1 Cost of Debt Oberon, Inc. has a $20 million (face value) 10-year bond issue selling for 97 percent of par that pays an annual coupon of 8.25 percent. What would be Oberon’s before-tax component cost of debt?
Solving equation 11-5 for iD:
Yields iD = 0.087115, or 8.71%
11-7 Cost of Preferred Stock ILK has preferred stock selling for 97 percent of par that pays an 8 percent annual coupon. What would be ILK’s component cost of preferred stock?
Using equation 11-4:
11-2 Weight of Debt FarCry Industries, a maker of telecommunications equipment, has two million shares of common stock outstanding, one million shares of preferred stock outstanding, and 10,000 bonds. If the common shares are selling for $27 per share, the preferred shares are selling for $14.50 per share, and the bonds are selling for 98 percent of par, what weight should you use for debt in the computation of FarCry’s WACC?
Using the computation for debt weight given in example 11-5:
11-3 WACC Suppose that TapDance, Inc.’s capital structure features 65 percent equity, 35 percent debt, and that its before-tax cost of debt is 8 percent, while its cost of equity is
( )
( )
10
10
1 1
1 $1, 000 Solve $970 $82.50 for
1
D
D
D D
i i
i i
−
+ = + +
1
0
$8
$97
0.0825, or 8.25%
P
D i
P =
=
=
10, 000 .98 $1, 000
2m $27 1m $14.50 10, 000 .98 $1, 000
$9.8m
$78.3m
0.1252, or 12.52%
D
E P D
=
+ + + +
=
=
13 percent. If the appropriate weighted average tax rate is 21 percent, what will be TapDance’s WACC?
Using equation 11-1:
(1 )
.65 13% 0 0% .35 8% (1 .21)
10.66%
E P D C
E P D WACC i i i T
E P D E P D E P D = + + −
+ + + + + +
= + + −
=
11-4 WACC TAFKAP Industries has three million shares of stock outstanding selling at $17 per share and an issue of $20 million in 7.5 percent, annual coupon bonds with a maturity of 15 years, selling at 106 percent of par. If TAFKAP’s weighted average tax rate is 21 percent and its cost of equity is 14.5 percent, what is TAFKAP’s WACC?
First, solve equation 11-5 for iD:
Then, using equation 11-1:
(1 )
3 $17 $20 1.06 14.5% 6.8476% (1 .21)
3 $17 $20 1.06 3 $17 $20 1.06
.7064 14.5% .2936 6.8476% (1 .21)
11.83%
E D C
E D WACC i i T
E P D E P D
m m
m m m m
= + − + + + +
= + −
+ +
= + −
=
11-5 Flotation Cost Suppose that Brown-Murphies’ common shares sell for $19.50 per share, that the firm is expected to set their next annual dividend at $0.57 per share, and that all future dividends are expected to grow by 4 percent per year, indefinitely. If Brown- Murphies faces a flotation cost of 13 percent on new equity issues, what will be the flotation-adjusted cost of equity?
( )
( )
( )
( )
15
15
1 1
1 FV Solve PV PMT for
1
1 1
1 $1, 000 Solve $1,060 $75 for
1
6.8476%
N
D
DN
D D
D
D
D D
D
i i
i i
i i
i i
i
−
+ = + +
−
+ = + +
=
Using equation 11-8:
11-6 Divisional WACCs Suppose your firm has decided to use a divisional WACC approach to analyze projects. The firm currently has four divisions, A through D, with average betas for each division of 0.6, 1.0, 1.3, and 1.6, respectively. If all current and future projects will be financed with half debt and half equity, and if the current cost of equity (based on an average firm beta of 1.0 and a current risk-free rate of 7 percent) is 13 percent and the after-tax yield on the company’s bonds is 8 percent, what will the WACCs be for each division?
Using equation 11-2, we can solve for the expected rate of return on the market:
Reusing equation 11-2, we can solve for the divisional costs of equity using the average divisional betas:
Finally, we can solve for the divisional WACCs using equation 11-1:
( )
1
0
$0.57 0.04
$19.50 0.13 $19.50
0.0736, or 7.36%
E
D i g
P F = +
−
= + −
=
( )
( )
( )
( )
13% 7% 1.0 7%
6% 7%
13%
E f E M f
M
M
M
i i E i i
E i
E i
E i
= + −
= + −
= −
=
( )
( )
( )
( )
For Division A: 7% 0.6 13% 7% 10.6%
For Division B: 7% 1.0 13% 7% 13.0%
For Division C: 7% 1.3 13% 7% 14.8%
For Division D:
E f E M f
E f E M f
E f E M f
E f E M f
i i E i i
i i E i i
i i E i i
i i E i i
= + − = + − =
= + − = + − =
= + − = + − =
= + − 7% 1.6 13% 7% 16.6%= + − =
( )
( )
( )
For Division A: WACC 1 0.5 10.6% 0.5 8% 9.3%
For Division B: WACC 1 0.5 13.0% 0.5 8% 10.5%
For Division C: WACC 1 0.5 14.8% 0.5 8% 11.4%
For
E D C
E D C
E D C
E D i i T
E P D E P D
E D i i T
E P D E P D
E D i i T
E P D E P D
= + − = + = + + + +
= + − = + = + + + +
= + − = + = + + + +
( ) Division D: WACC 1 0.5 16.6% 0.5 8% 12.3%E D C E D
i i T E P D E P D
= + − = + = + + + +
13-3 NPV with Non-normal Cash Flows Compute the NPV statistic for Project U and
recommend whether the firm should accept or reject the project with the cash flows
shown as follows if the appropriate cost of capital is ten percent.
Project U
Time 0 1 2 3 4 5
Cash Flow -$1,000 $350 $1,480 -$520 $300 -$100
Using equation 13-2:
The project should be accepted.
13-7 Discounted Payback Compute the discounted payback statistic for Project C and
recommend whether the firm should accept or reject the project with the cash flows
shown as follows if the appropriate cost of capital is 8 percent and the maximum
allowable discounted payback is three years.
Project C
Time 0 1 2 3 4 5
Cash Flow -$1,000 $480 $480 $520 $300 $100
Solving equation 13-5 for N, cumulative PV of cash flow will switch from negative and
positive between years 2 and 3:
Year 0 1 2 3 4 5
Cash Flow -$1,000 $480 $480 $520 $300 $100
Cash Flow PV -$1,000
Cum. Cash Flow PV -$1,000 -$555.56 -$144.04 $268.75
Specifically, DPB = 2+$144.04/412.79 = 2.35 and this project should be accepted.
13-11 MIRR Compute the MIRR statistic for Project I and tell whether to accept or reject the
project with the cash flows shown as follows if the appropriate cost of capital is 12
percent.
( ) ( ) ( ) ( ) ( ) 1 2 3 4 5
$350 $1, 480 $520 $300 $100 $1, 000
1.10 1.10 1.10 1.10 1.10
$293.45
NPV − −
= − + + + + +
=
( ) 1
$480
1.08
$444.44=
( ) 2
$480
1.08
$411.52=
( ) 3
$520
1.08
$412.79=
Project I
Time 0 1 2 3 4
Cash Flow -$11,000 $5,330 $4,180 $1,520 $2,000
Cash flows will be moved as shown as follows:
Year 0 1 2 3 4
Cash Flow -$11,000 $5,330 $4,180 $1,520 $2,000
Future
Value (If
Positive)
Sum of FV $16,434.06
Modified
CFs -$11,000 $16,434.06
With this new set of modified cash flows, the MIRR is:
Since our MIRR decision statistic is less than the 12 percent cost of capital, we would
reject the project under the MIRR method.
13-15 Multiple IRRs How many possible IRRs could you find for the following set of cash
flows?
Time 0 1 2 3 4
Cash Flow -$11,000 $3,350 $4,180 $1,520 $2,000
Since there’s only one change in sign, there can only be one IRR.
13-19 IRR Use the IRR decision rule to evaluate this project; should it be accepted or rejected?
The IRR for this project will be the solution to:
( ) 3
$5, 330 1.12
$7, 488.27
=
( ) 2
$4,180 1.12
$5, 243.39
=
( ) 1
$1, 520 1.12
$1, 702.40
= $2, 000
( ) ( ) 0 4
$11, 000 $16, 434.06 0
1 1
10.56%
IRR IRR
IRR
− = +
+ +
=
IRR > than required rate of return this project should be accepted.
13-23 Payback Use the payback decision rule to evaluate this project; should it be accepted or
rejected?
Cumulative cash flow will switch from negative a positive between years 2 and 3:
Year 0 1 2 3 4 5
Cash Flow -$235,000 $65,800 $84,000 $141,000 $122,000 $81,200
Cumulative
Cash Flow
-$235,000 -$169,200 -$85,200 $55,800 $177,800 $259,000
Specifically, so this project should be accepted.
13-27 NPV Use the NPV decision rule to evaluate this project; should it be accepted or
rejected?
Since NPV > 0, the project should be accepted.
13-31 Multiple IRRs Construct an NPV profile and determine EXACTLY how many
nonnegative IRRs you can find for the following set of cash flows:
$85, 200 2 2.60 years
$141, 000 PB = + =
( ) ( ) ( ) ( ) ( ) 1 2 3 4 5
$65, 800 $84, 000 $141, 000 $122, 000 $81, 200 $235, 000
1.11 1.11 1.11 1.11 1.11
$124,106.98
NPV = − + + + + +
=
As the following graph shows, there appears to be only one.
