Chapter 18 International Capital Budgeting
1. Before you pose these next seven questions to your students, give consideration to their
finance backgrounds. At my school (University of Missouri at Columbia) capital budgeting
questions in this level of detail would be "fair game" because the students have had plenty of
capital budgeting before in a prior finance course. Just glancing at equations 18-1 through 18-2f
is not preparation for these seven questions. There are plenty of easier questions in this test
bank.
Tiger Towers, Inc. is considering an expansion of their existing business, student apartments. The
new project will be built on some vacant land that the firm has just contracted to buy. The land
cost $1,000,000 and the payment is due today. Construction of a 20-unit office building will cost
pretax $3 million; this expense will be depreciated straight-line over 30 years to zero salvage
value; the value of the land and building in year 30 will be $18,000,000. The $3,000,000
construction cost is to be paid today. The project will not change the risk level of the firm. The
firm will lease 20 offices suites at $20,000 per suite per year; payment is due at the start of the
year; occupancy will begin in one year. Variable cost is $3,500 per suite. Fixed costs, excluding
depreciation, are $75,000 per year. The project will require a $10,000 investment in net working
capital.

2. What is the unlevered after-tax incremental cash flow for year 0?
A. -$3,660,000
B. -$5,100,000
C. -$4,000,000
D. -$4,010,000
E. None of the above
-$4,010,000 = - [$1,000,000 + $3,000,000 + 10,000]
3. What is the unlevered after-tax incremental cash flow for year 2?
A. -$4,610
B. $102,300
C. $202,300
D. $255,000
E. None of the above

4. What is the unlevered after-tax incremental cash flow for year 30?
A. $12,432,300
B. $12,225,390
C. $12,332,300
D. $12,485,000
E. None of the above
$12,432,300 = $202,300 + return of NWC + building/land
202,300 + $10,000 + $18,000,000 - 0.34  ($18,000,000 - $1,000,000)
Notice that the answer to question 5 is a function of the student's answer to question 4:
Correct response to Q5
= response to Q4 + $10,000 + $18,000,000 - 0.34  ($18,000,000 - $1,000,000)
You may wish to award partial credit based on the following rubric:
12,432,300 if Q4 = c)
12,225,390 if Q4 = a)
12,332,300 if Q4 = b)
$12,485,000 if Q4 = d)

Awarding partial credit on a multiple choice test isn't hard. Import their responses into Excel. Use
"if" statements. The advantage of path-dependent grading is that you can get the same level of
discrimination in grading on a multiple choice test as on an essay test.
5. For the next 3 questions, assume that the firm will partially finance the project with a
$3,000,000 interest-only 30-year loan at 10.0 percent APR with annual payments.
What is the levered after-tax incremental cash flow for year 0?
A. -$1,010,000
B. -$1,000,000
C. -$660,000
D. -$2,100,000

E. None of the above
LCF0 = $3,000,000 - response to Q3
= -$1,010,000
You may wish to award partial credit on this question according to the following rubric
-$1,010,000 is correct if Q3= 4)
-$1,000,000 is correct if Q3 = 3)
-$660,000 is correct if Q3 = 1)
-$2,100,000 is correct if Q3 = 2)


6. For the next 3 questions, assume that the firm will partially finance the project with a
$3,000,000 interest-only 30-year loan at 10.0 percent APR with annual payments.
What is the levered after-tax incremental cash flow for year 1?
A. $4,300
B. -$202,610
C. -$95,700
D. $57,000
E. None of the above
Your response to Q4 - $300,000  0.66

Note: you may wish to award partial credit according to:
$4,300 is correct if Q4 = 3)
-$202,610 is correct if Q4 = 1)
-$95,700 is correct if Q4 = 2)
$57,000 is correct if Q4 = 4)
7. For the next 3 questions, assume that the firm will partially finance the project with a
$3,000,000 interest-only 30-year loan at 10.0 percent APR with annual payments.
What is the levered after-tax incremental cash flow for year 30?
A. $9,027,390
B. $9,234,300

C. $9,134,300
D. $9,287,000
E. None of the above


the right answer is your response to Q5 - $300,000  0.66 - $3,000,000

You should consider awarding partial credit on this according to this rubric:
$9,027,390 is correct if Q5 = 2)
$9,234,300 is correct if Q5 = 1)
$9,134,300 is correct if Q5 = 3)
$9,287,000 is correct if Q5 = 4)
8. Assume that the firm will partially finance the project with a subsidized $3,000,000 interest
only 30-year loan at 8.0 percent APR with annual payments. Note that eight percent is less than
the 10 percent that they normally borrow at. What is the NPV of the loan?
A. $198,469
B. $53,979.83
C. $102,727.55
D. $1,334,851.09
E. None of the above
Using the cash flow menu on a financial calculator:
CF0 = $3,000,000
CF1 = -$158,400 = -$3,000,000  0.08  .66
F01 = 29
CF2 = -$3,158,400
I = 10%
NPV = $1,334,851.09


9. The firm's tax rate is 34%. The firm's pre-tax cost of debt is 8%; the firm's debt-to-equity ratio

is 3; the risk-free rate is 3%; the beta of the firm's common stock is 1.5; the market risk premium
is 9%. What is the firm's cost of equity capital?
A. 33.33%
B. 10.85%
C. 13.12%
D. 16.5%
E. None of the above
requity = 3% + 1.5  9% = 16.5%
10. The firm's tax rate is 34%. The firm's pre-tax cost of debt is 8%; the firm's debt-to-equity
ratio is 3; the risk-free rate is 3%; the beta of the firm's common stock is 1.5; the market risk
premium is 9%. What is the required return on assets?
A. 33.33%
B. 10.85%
C. 13.12%
D. 16.5%
E. None of the above
16.5% = rasset + 3  [ rasset - rdebt]  (1-.34)
rasset = 10.85%
11. For the next two questions consider a project with the following data

The 5-year project requires equipment that costs $100,000. If undertaken, the shareholders will
contribute $20,000 cash and borrow $80,000 at 6% with an interest-only loan with a maturity of
5 years and annual interest payments. The equipment will be depreciated straight-line to zero
over the 5-year life of the project. There will be a pre-tax salvage value of $5,000. There are no
other start-up costs at year 0. During years 1 through 5, the firm will sell 25,000 units of product
at $5; variable costs are $3; there are no fixed costs.
12. What is the NPV of the project using the WACC methodology?
A. $49,613.03
B. $58,028.68
C. $102,727.55

D. 315,666.16
E. None of the above


Using the cash flow menu of a financial calculator: CF0 = -$100,000; C01 = $39,800; F01 = 4;
C02 = $43,100; I = rWACC = 8.74; NPV = $58,028.68


13. What is the NPV of the project using the APV methodology?
A. $49,613.03
B. $198,469
C. $102,727.55
D. $149,580.12
E. None of the above
APV = -Cost + Base-case NPV + NPV depreciation tax shield + NPV interest tax shield =
The project does not cost $100,000 but rather $98,937.49 = -$100,000 + $1,062.51
(100,000 less the present value of after tax salvage value discounted at rasset = 12%)

For the next 3 questions consider a project with the following data

The 5-year project requires equipment that costs $100,000. If undertaken, the shareholders will
contribute $25,000 cash and borrow $75,000 with an interest-only loan with a maturity of 5 years
and annual interest payments. The equipment will be depreciated straight-line to zero over the 5year life of the project. There will be a pre-tax salvage value of $5,000. There are no other startup costs at year 0. During years 1 through 5, the firm will sell 25,000 units of product at $5;
variable costs are $3; there are no fixed costs.


14. What is the NPV of the project using the WACC methodology?
A. $58,028.68
B. $49,613.03
C. $48,300.47

D. $102,727.55
E. None of the above
Using the cash flow menu of a financial calculator: CF0 = -$100,000; C01 = $39,800; F01 = 4;
C02 = $43,100; I = rWACC = 11.20; NPV = $48,300.47

15. When using the APV methodology, what is the NPV of the depreciation tax shield?
A. $32,051.52
B. $25,777.35
C. $22,794.65
D. $97,152.98
E. None of the above
Using a financial calculator's cash flow menu: N = 5; PMT = $6,800 = $20,000  .34 I/YR = rdebt
= 10%; PVdepreciation tax shield = $25,777.35

16. When using the APV methodology, what is the NPV of the interest tax shield?
A. $9,666.51
B. $12,019.32
C. $9,377.31
D. $7,000.73
E. None of the above
using a financial calculator, N = 5; PMT = $2,550 = .10  $75,000  .34; I/YR = rdebt = 10%;
PVinterest tax shield = $9,666.51


17. Today is January 1, 2009. The state of Iowa has offered your firm a subsidized loan. It will be
in the amount of $10,000,000 at an interest rate of 5% and have ANNUAL (amortizing)
payments over 3 years. The first payment is due today and your taxes are due January 1 of each
year on the previous year's income. The yield to maturity on your firm's existing debt is 8%.
What is the APV of this subsidized loan?
Note that I did not round my intermediate steps. If you did, your answer may be off by a bit.

Select the answer closest to yours.
A. -$3,497,224.43
B. $417,201.05
C. $840,797
D. None of the above


First, get your financial calculator into begin mode and 1 payment per year:
PV = 10,000,000
N= 3
I= 5%
PMT = -$3,497,224.43
Amortize the loan

The size and timing of the cash flows of the loan are:

CF0 = $6,502,775.57
CF1 = -$3,386,677.24
CF2 = -$3,440,602.70
I= 8%; NPV = $417,201.05
If you are covering APV in detail, this kind of question is appropriate. Alternative versions of
this are nearby.


18. Today is January 1, 2009. The state of Iowa has offered your firm a subsidized loan. It will be
in the amount of $10,000,000 at an interest rate of 5% and have ANNUAL (amortizing)
payments over 3 years. The first payment is due December 31, 2009 and your taxes are due
January 1 of each year on the previous year's income. The yield to maturity on your firm's
existing debt is 8%. What is the APV of this subsidized loan?
Note that I did not round my intermediate steps. If you did, your answer may be off by a bit.

Select the answer closest to yours.
A. -$3,497,224.43
B. $417,201.05
C. $840,797
D. None of the above
First, enter the loan into a financial calculator and solve for the payment:
PV=10,000,000
N= 3
I= 5%
PMT = 3,672,085
Then amortize the loan:

Now find the APV of the loan as shown in the book:
CF0 = $10,000,000
CF1= -$3,502,085 = -$3,172,085 - .66  $500,000
CF2= -$3,556,011
CF3= -$3,612,632
I= 8%
NPV = $840,797


19. The required return on assets is 18%. The firm can borrow at 12.5%; firm's target debt to
value ratio is 3/5. The corporate tax rate is 34%, and the risk-free rate is 4% and the market risk
premium is 9.2 percent. What is the weighted average cost of capital?
A. 12.15%
B. 13.02%
C. 14.33%
D. 23.45%
E. None of the above
Kl = 23.45% = 18% + 1.5  (18% - 12.5%)  (1 - .34)

weighted average cost of capital = 2/5  23.45% + 3/5  (12.5%)  (1 - .34)
= 14.33%
20. Your firm is in the 34% tax bracket. The yield to maturity on your existing bonds is 8%. The
state of Georgia offers to loan your firm $1,000,000 with a TWO year AMORTIZING loan at a
5% rate of interest and ANNUAL payments due at the END OF THE YEAR.
The interest will be deductible at the time that you pay. What is the APV of this below-market
loan to your firm? I did not round any of my intermediate steps. You might be a little bit off. Pick
the answer closest to yours.
A. $64,157.38
B. $417,201.05
C. $840,797
D. None of the above
First, enter the loan into a financial calculator to find the payment:
PV=1,000,000
N= 2
I= 5%
PMT = 537,804.88
Next amortize the loan to find out how much interest is paid in each period (it's deductible)

Finally, find the APV of the loan as the NPV of the after-tax cash flows at 8%:
CF0 = $1,000,000
CF1= -$520,804.88 = -$487,804 - .66  $50,000
CF2= -$529,097 = -$512,195- .66  $25,609.76
I= 8%
NPV = $64,157.38


21. The firm's tax rate is 34%. The firm's pre-tax cost of debt is 8%; the firm's debt-to-equity
ratio is 3; the risk-free rate is 3%; the beta of the firm's common stock is 1.5; the market risk
premium is 9%.Calculate the weighted average cost of capital.

A. 33.33%
B. 8.09%
C. 9.02%
D. 16.5%
E. None of the above

NOTE TO FACULTY: the next six questions are similar to the six that follow them, but have
different answers as the debt-equity ratio changes from 2 to 3. This can discourage cheating,
especially if you only give credit to students who have the right answers on the right test!
Consider a project of the Cornell Haul Moving Company, the timing and size of the incremental
after-tax cash flows (for an all-equity firm) are shown below in millions:

The firm's tax rate is 34%; the firm's bonds trade with a yield to maturity of 8%; the current and
target debt-equity ratio is 2; if the firm were financed entirely with equity, the required return
would be 10%

22. Using the APV method, what is the value of the debt side effects?
A. $239,072,652.70
B. $66,891,713.66
C. $59,459,301.03
D. $660,000,000
E. None of the above
CF0 = 660,000,000; CF1 = -34,848,000 = .08  $660,000,000  (1 - .34); F01 = 3 CF2 = $694,848,000 = -$660,000,000 - .08  $660,000,000  .66; Use I = 8%


NOTE TO FACULTY: the next six questions are similar to the last six, but have different
answers as the debt-equity ratio changed from 2 to 3. This can discourage cheating, especially if
you only give credit to students who have the right answers on the right test!
Consider a project of the Cornell Haul Moving Company, the timing and size of the incremental
after-tax cash flows (for an all-equity firm) are shown below in millions:


The firm's tax rate is 34%; the firm's bonds trade with a yield to maturity of 8%; the current and
target debt-equity ratio is 3; if the firm were financed entirely with equity, the required return
would be 10%
23. Using the weighted average cost of capital methodology, what is the NPV? I didn't round my
intermediate steps. If you do, you're not going to get the right answer.
A. -$1,406,301.25
B. $12,494,643.75
C. $36,580,767.55
D. $108,994.618.20
E. $59,459,301.03
The weighted average cost of capital is
requity = 10% + 3  (10% - 8%)  (1 - .34) = 13.96%
rWACC = 13.96%  .25 + 8%  .75  .66 = 7.45%

NOTE TO FACULTY: the next six questions are similar to the last six, but have different
answers as the debt-equity ratio changed from 2 to 3. This can discourage cheating, especially if
you only give credit to students who have the right answers on the right test!
Consider a project of the Cornell Haul Moving Company, the timing and size of the incremental
after-tax cash flows (for an all-equity firm) are shown below in millions:

The firm's tax rate is 34%; the firm's bonds trade with a yield to maturity of 8%; the current and
target debt-equity ratio is 3; if the firm were financed entirely with equity, the required return
would be 10%
For the next 5 questions, the firm will partially finance the project with an 8% interest-only 4year loan.


24. What is the levered after-tax incremental cash flow for year 2?
A. $185,796,000
B. $215,152,000

C. $267,952,000
D. $284,848,000
E. None of the above
LCF2 = $190,152,000
= $225,000,000 - .08  $742,500,000  (1 - .34)
25. What is the levered after-tax incremental cash flow for year 4?
A. -$281,704,000
B. $465,152,000
C. -$194,848,000
D. $460,796,000
E. None of the above
LCF5 = -$281,704,000
= $500,000,000 - $742,500,000 - .08  $742,500,000  (1 - .34)
26. Using the flow to equity methodology, what is the value of the equity claim?
A. -$1,540,000
B. $446,570,866.00
C. $36,580,767.55
D. $470,953,393.70
E. $30,716,236.13
Discount the levered cash flows at requity = 13.96%
LCF 0 = -247,500,000; LCF 1 = 85,796,000;
CF2 = 185,796,000; CF3 = 335,796,000;
CF4 = -281,704,000
27. Using the APV method, what is the value of this project to an all-equity firm?
A. -$46,502,288.10
B. $12,494,643.75
C. $36,580,767.55
D. -$67,163,445.12
E. $59,459,301.03
Discount the unlevered cash flows at rasset = 10%



28. Using the APV method, what is the value of the debt side effects?
A. $239,072,652.70
B. $66,891,713.66
C. $59,459,301.03
D. $660,000,000
E. None of the above
CF0 = 742,500,000; CF1 = -39,204,000 = .08  $742,500,000  (1 - .34); F01 = 3
CF2 = -$781,704,000 = - $742,500,000- .08  $742,500,000  .66
Use I = 8%
29. Your firm's existing bonds trade with a yield to maturity of eight percent. The state of
Missouri has offered to loan your firm $10,000,000 at zero percent for five years. Repayment
will be of the form of $2,000,000 per year for five years the first payment is due in one year.
What is the value of this offer?
A. $4,729,622.75
B. $2,014,579.93
C. $0
D. $196,929.88
E. None of the above
Using a financial calculator: N = 5; I/Y = 8% PMT = -$2,000,000 solve for PV = $7,985,420.07
The state is giving you $10,000,000 for a promise that's worth only $7,985,420.07. The value of
that is $2,014,579.93
30. What proportion of the firm is financed by debt for a firm that expects a 15% return on
equity, a 12% return on assets, and a 10% return on debt? The tax rate is 25%.
A. 20%
B. 1/3
C. 60%
D. 2/3
E. 80%



From Modigliani-Miller Proposition II (perhaps not displayed to its best advantage in footnote 2,
but surely something students know coming into the course) we can find the debt-equity ratio.

With a debt equity ratio, it's easy to find debt to value:

31. The required return on equity for a levered firm is 10.60%. The debt to equity ratio is ½ the
tax rate is 40%, the pre-tax cost of debt is 8%. Find the cost of capital if this firm were financed
entirely with equity.
A. 10%
B. 12%
C. 8.67%
D. None of the above
From Modigliani and Miller proposition 2 the required return on equity for a levered firm is Kl =
Ku + (1- )(Ku - i)(Debt/Equity)

Instructors note: some students will select b) the WACC. Students who have had corporate
finance should know M&M proposition 2. Good questions for graduate courses.


32. The required return on equity for an all-equity firm is 10.0%. They are considering a change
in capital structure to a debt-to-equity ratio of ½ the tax rate is 40%, the pre-tax cost of debt is
8%. Find the new cost of capital if this firm changes capital structure.
A. 14.93%
B. 8.67%
C. 7.40%
D. None of the above
From Modigliani and Miller proposition 2 that the required return on equity for a levered firm is
Kl = Ku + (1- )(Ku - i)(Debt/Equity)


Instructors note: Students who have had corporate finance should know M&M proposition 2. A
common mistake will be a); a grievous mistake confusing D/E and D/V would be c). Good
questions for graduate courses.\
33. The required return on equity for an all-equity firm is 10.0%. They currently have a beta of
one and the risk-free rate is 5% and the market risk premium is 5%. They are considering a
change in capital structure to a debt-to-equity ratio of ½ the tax rate is 40%, the pre-tax cost of
debt is 8%. Find the beta if this firm changes capital structure.
A. 1.12
B. 1
C. 7.4%
D. None of the above
From Modigliani and Miller proposition 2: Kl = Ku + (1- )(Ku - i)(Debt/Equity)

Instructors note: Students who have had corporate finance should know M&M proposition 2 and
the difference between an asset beta and an equity beta. Good questions for graduate courses.


34. What is the expected return on equity for a tax-free firm with a 15% expected return on
assets that pays 12% on its debt, which totals 25% of assets?
A. 24%
B. 15.60%
C. 16%
D. 20%
E. 15.75%
Start with debt-to-value ratio of 25%, find debt-to-equity ratio, then use
Kl = Ku + (1- )(Ku - i)(Debt/Equity)

35. What is the expected return on equity for firm in the 40% tax bracket with a 15% expected
return on assets that pays 12% on its debt, which totals 25% of assets?

A. 24%
B. 15.60%
C. 16%
D. 20%
E. 15.75%
Start with debt-to-value ratio of 25%, find debt-to-equity ratio, then use
Kl = Ku + (1- )(Ku - i)(Debt/Equity)


36. Assume that XYZ Corporation is a leveraged company with the following information:
Kl = cost of equity capital for XYZ = 13%
i = before-tax borrowing cost = 8%
t = marginal corporate income tax rate = 30%
Calculate the debt-to-total-market-value ratio that would result in XYZ having a weighted
average cost of capital of 9.3%.
A. 35%
B. 40%
C. 45%
D. 50%
Equation 17.1
Let D = debt-to-total-market-value ratio
0.093 = (1 - D/V)  0.13 + D/V  (1 - 0.30)  0.08
0.093 = 0.13 - 0.13D/V + D/V  0.70  0.08
0.13D/V - 0.056 D/V = 0.13 - 0.093
0.074D/V = 0.037
D/V = 0.50 = 50%


37. Today is January 1, 2009. The state of Iowa has offered your firm a subsidized loan. It will be
in the amount of $10,000,000 at an interest rate of 5% and have ANNUAL (amortizing)

payments over 3 years. The first payment is due today and your taxes are due January 1 of each
year on the previous year's income. The yield to maturity on your firm's existing debt is 8%.
What is the APV of this subsidized loan? Note that I did not round my intermediate steps. If you
did, your answer may be off by a bit. Select the answer closest to yours.
A. $406,023.10
B. $840,797
C. $64,157.38
D. $20,659.77
E. None of the other answers are within $100 of my answer
First, get into begin mode
and 1 payment per year:
PV = 10,000,000
N= 3
I= 5%
PMT = -$3,497,224.43
Amortize the loan

The size and timing of the cash flows of the loan are:

CF0 = $6,502,775.57
CF1 = -$3,497,224.43
CF2 = -$3,386,667.24
CF3 = -$56,621.73
I= 8%
NPV = $406,023.10


38. An Italian firm is considering selling its line of coin-operated cappuccino machines in the
U.K. The business risk will be identical to the firm's existing line of business in the euro zone,
the cost of capital in the euro zone is i€ = 10%. The expected inflation rate over the next two

years in the U.K. is 3% per year and 2% per year in the euro zone. The spot exchange rates are
$1.80 = 1.00 and $1.15 = €1.00
The pound sterling denominated cash flows are as follows:

What is the €-denominated NPV of this project? I did not round my intermediate steps, if you
did, select the answer closest to yours.
A. €5,563.23
B. €2,270.79
C. €7,223.14
D. €3,554.29
E. There is not enough information (e.g. U.S. inflation) to do this problem.


the appropriate cost of capital for the firm to use on these -denominated cash flows is

Use that discount rate in the cash flow menu of a financial calculator with CF0 = -100,000; CF1
= 25,000; CF2 = 100,000; NPV = 3,554.2877
Finally translate to pounds at the spot cross rate: Most students will take this approach:

Where the year-1 cash flow is given by

, and the year-two cash flow is

given by
These euro-denominated cash flows have an NPV of exactly €5,563.23. Students who take this
approach have lots of room for grievous rounding errors.


39. The spot exchange rate is 125 = $1. The U.S. discount rate is 10%; inflation over the next
three years is 3% per year in the U.S. and 2% per year in Japan. Calculate the dollar NPV of this

project.

I did not round my intermediate steps, if you did, select the answer closest to yours.
A. $267,181.87
B. $14,176.67
C. $2,536.49
D. $2,137.46
E. None of the above
the easy way to do this is to estimate the yen-denominated required return

The yen-denominate cash flows given above yield an NPV = 267,181.87, which converts to
$2,137.46 at the spot exchange rate.
In the alternative, you could convert the cash flows at the exchange rates expected to prevail over
the next three years

When discounted at 10% this series of dollar-denominated cash flows has NPV = $2,137.46
Students prefer taking this approach, but they do tend to make a great deal of rounding errors.
40. As of today, the spot exchange rate is €1.00 = $1.25 and the rates of inflation expected to
prevail for the next year in the U.S. is 2% and 3% in the euro zone. What is the one-year forward
rate that should prevail?
A. €1.00 = $1.2379
B. €1.00 = $1.2139
C. €1.00 = $0.9903
D. $1.00 = €1.2623