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CHAPTER 18 INTERNATIONAL CAPITAL BUDGETING
ANSWERS & SOLUTIONS TO END-OF-CHAPTER QUESTIONS AND PROBLEMS
QUESTIONS
1. Why is capital budgeting analysis so important to the firm?
Answer: The fundamental goal of the financial manager is to maximize shareholder wealth.
2. What is the intuition behind the NPV capital budgeting framework?
Answer: The NPV framework is a discounted cash flow technique. The methodology compares
3. Discuss what is meant by the incremental cash flows of a capital project.
Answer: Incremental cash flows are denoted by the change in total firm cash inflows and cash
4. Discuss the nature of the equation sequence, Equation 18.2a to 18.2f.
Answer: The equation sequence is a presentation of incremental annual cash flows associated
with a capital expenditure. Equation 18.2a presents the most detailed expression for calculating
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of McGraw-Hill Education.
actually available for shareholders. Equation 18.2c cancels out the after-tax interest term in
18.2a, yielding a simpler formula. Equation 18.2d shows that the first term in 18.2c is generally
called after-tax net operating income. Equation 18.2e yields yet a computationally simpler
formula by combining the depreciation terms of 18.2c. Equation 18.2f shows that the first term
in 18.2e is generally referred to as after-tax operating cash flow.
5. What makes the APV capital budgeting framework useful for analyzing foreign capital
expenditures?
Answer: The APV framework is a value-additivity technique. Because international projects
6. Relate the concept of lost sales to the definition of incremental cash flow.
Answer: When a new capital project is undertaken it may compete with an existing project(s),
7. What problems can enter into the capital budgeting analysis if project debt is evaluated
instead of the borrowing capacity created by the project?
Answer: If project debt is greater (less) than the borrowing capacity created by the capital
8. What is the nature of a concessionary loan and how is it handled in the APV model?
Answer: A concessionary loan is a loan offered by a governmental body at below the normal
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of McGraw-Hill Education.
similarly converted concessionary loan payments discounted at the MNC’s normal domestic
borrowing rate. The loan payments will yield a present value less than the face amount of the
concessionary loan when they are discounted at the higher normal rate. This difference
represents a subsidy the host country is willing to extend to the MNC if the investment is made.
The benefit to the MNC of the concessionary loan is handled in the APV model via a separate
term.
9. What is the intuition of discounting the various cash flows in the APV model at specific
discount rates?
Answer: The APV model is a value-additivity technique where total value is determined by the
10. In the Modigliani-Miller equation, why is the market value of the levered firm greater than
the market value of an equivalent unlevered firm?
Answer: The levered firm has a greater market value because less money is taken from the
11. Discuss the difference between performing the capital budgeting analysis from the parent
firm’s perspective as opposed to the subsidiary’s perspective.
Answer: The goal of the financial manager of the parent firm is to maximize its shareholders’
wealth. A capital project of a subsidiary of the parent may have a positive NPV (or APV) from
Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent
of McGraw-Hill Education.
the parent and the parent’s stockholders.
12. Define the concept of a real option. Discuss some of the various real options a firm can be
confronted with when investing in real projects.
Answer: A positive APV project is accepted under the assumption that all future operating
decisions will be optimal. The firm’s management does not know at the inception date of a
13. Discuss the circumstances under which the capital expenditure of a foreign subsidiary
might have a positive NPV in local currency terms but be unprofitable from the parent firm’s
perspective.
Answer: The project NPV might be negative from the parent firm’s perspective when it is
positive in local currency terms if all foreign cash flows cannot be legally repatriated to the
PROBLEMS
1. The Alpha Company plans to establish a subsidiary in Hungary to manufacture and sell
fashion wristwatches. Alpha has total assets of $70 million, of which $45 million is equity
financed. The remainder is financed with debt. Alpha considered its current capital structure
optimal. The construction cost of the Hungarian facility in forints is estimated at
HUF2,400,000,000, of which HUF1,800,000,and 000 is to be financed at a below-market
borrowing rate arranged by the Hungarian government. Alpha wonders what amount of debt it
should use in calculating the tax shields on interest payments in its capital budgeting analysis.
Can you offer assistance?
Solution: The Alpha Company has an optimal debt ratio of .357 (= $25 million debt/$70 million
2. The current spot exchange rate is HUF250/$1.00. Long-run inflation in Hungary is estimated
at 10 percent annually and 3 percent in the United States. If PPP is expected to hold between
the two countries, what spot exchange should one forecast five years into the future?
3. The Beta Corporation has an optimal debt ratio of 40 percent. Its cost of equity capital is 12
percent and its before-tax borrowing rate is 8 percent. Given a marginal tax rate of 35 percent,
calculate (a) the weighted-average cost of capital, and (b) the cost of equity for an equivalent
all-equity financed firm.
4. Zeda, Inc., a U.S. MNC, is considering making a fixed direct investment in Denmark. The
Danish government has offered Zeda a concessionary loan of DKK15,000,000 at a rate of 4
percent per annum. The normal borrowing rate is 6 percent in dollars and 5.5 percent in Danish
krone. The loan schedule calls for the principal to be repaid in three equal annual installments.
What is the present value of the benefit of the concessionary loan? The current spot rate is
DKK5.60/$1.00 and the expected inflation rate is 3% in the U.S. and 2.5% in Denmark.
Solution:
Year
(t)
St
(a)
Principal
Payment
(b)
DKK
It
(c)
DKK
StLPt
(b + c)/(a)
StLPt/(1 + id)t
1
5.57
5,000,000
600,000
1,005,386
948,477
2
5.55
5,000,000
400,000
972,973
865,943
3
5.52
5,000,000
200,000
942,029
790,946
15,000,000
2,605,366
The dollar value of the concessionary loan is $2,678,574 = DKK15,000,000 ÷ 5.60. The dollar
present value of the concessionary loan payments is $2,605,366. Therefore, the present value
of the benefit of the concessionary loan is $73,208 = $2,678,574 – 2,605,366.
5. Delta Company, a U.S. MNC, is contemplating making a foreign capital expenditure in South
Africa. The initial cost of the project is ZAR10,000. The annual cash flows over the five year
economic life of the project in ZAR are estimated to be 3,000, 4,000, 5,000, 6000, and 7,000.
The parent firm’s cost of capital in dollars is 9.5 percent. Long-run inflation is forecasted to be 3
percent per annum in the U.S. and 7 percent in South Africa. The current spot foreign
exchange rate is ZAR/USD = 3.75. Determine the NPV for the project in USD by:
a. Calculating the NPV in ZAR using the ZAR equivalent cost of capital according to the Fisher
Effect and then converting to USD at the current spot rate.
b. Converting all cash flows from ZAR to USD at Purchasing Power Parity forecasted exchange
rates and then calculating the NPV at the dollar cost of capital.
Solution: The PPP forecasted ZAR/USD exchange rates are:
The two dollar NPVs are identical as they always will be under the assumption that both PPP
and the Fisher Effect hold. Note, that both parity conditions incorporate relative differences in
inflation.
c. What is the NPV in dollars if the actual pattern of ZAR/USD exchange rates is: S(0) = 3.75,
S(1) = 5.7, S(2) = 6.7, S(3) = 7.2, S(4) = 7.7, and S(5) = 8.2?
Solution:
The NPV is negative because actual exchange rates did not evolve as forecasted by PPP.
Consequently, actual NPV and forecasted NPV may be different.
6. Suppose that in the illustrated mini case in the chapter the APV for Centralia had been -
$60,000. How large would the after-tax terminal value of the project need to be before the APV
would be positive and Centralia would accept the project?
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of McGraw-Hill Education.
calculated as follows. Set
STTVT/(1+Kud)T = $60,000. This implies
TVT = ($60,000/ST)(1+Kud)T
= ($60,000/.7261)(1.11)8
= €190,431.
7. With regards to the Centralia illustrated mini case in the chapter, how would the APV change
if:
a. The forecast of
d and/or
f are incorrect?
Answer: A larger or smaller
d will not have any effect because a change will affect the
b. Deprecation cash flows are discounted at Kud instead of id?
c. The host country did not provide the concessionary loan?
MINI CASE: DORCHESTER, LTD.
Dorchester Ltd., is an old-line confectioner specializing in high-quality chocolates. Through
its facilities in the United Kingdom, Dorchester manufactures candies that it sells throughout
Western Europe and North America (United States and Canada). With its current
manufacturing facilities, Dorchester has been unable to supply the U.S. market with more than
225,000 pounds of candy per year. This supply has allowed its sales affiliate, located in Boston,
to be able to penetrate the U.S. market no farther west than St. Louis and only as far south as
Atlanta. Dorchester believes that a separate manufacturing facility located in the United States
would allow it to supply the entire U.S. market and Canada (which presently accounts for 65,000
pounds per year). Dorchester currently estimates initial demand in the North American market
at 390,000 pounds, with growth at a 5 percent annual rate. A separate manufacturing facility
would, obviously, free up the amount currently shipped to the United States and Canada. But
Dorchester believes that this is only a short-run problem. They believe the economic
development taking place in Eastern Europe will allow it to sell there the full amount presently
shipped to North America within a period of five years.
Dorchester presently realizes £3.00 per pound on its North American exports. Once the
U.S. manufacturing facility is operating, Dorchester expects that it will be able to initially price its
product at $7.70 per pound. This price would represent an operating profit of $4.40 per pound.
Both sales price and operating costs are expected to keep track with the U.S. price level; U.S.
inflation is forecast at a rate of 3 percent for the next several years. In the U.K., long-run
inflation is expected to be in the 4 to 5 percent range, depending on which economic service
one follows. The current spot exchange rate is $1.50/£1.00. Dorchester explicitly believes in
PPP as the best means to forecast future exchange rates.
The manufacturing facility is expected to cost $7,000,000. Dorchester plans to finance this
amount by a combination of equity capital and debt. The plant will increase Dorchester’s
borrowing capacity by £2,000,000, and it plans to borrow only that amount. The local
community in which Dorchester has decided to build will provide $1,500,000 of debt financing
for a period of seven years at 7.75 percent. The principal is to be repaid in equal installments
over the life of the loan. At this point, Dorchester is uncertain whether to raise the remaining
debt it desires through a domestic bond issue or a Eurodollar bond issue. It believes it can
borrow pounds sterling at 10.75 percent per annum and dollars at 9.5 percent. Dorchester
estimates its all-equity cost of capital to be 15 percent.
The U.S. Internal Revenue Service will allow Dorchester to depreciate the new facility over a
seven-year period. After that time the confectionery equipment, which accounts for the bulk of
the investment, is expected to have substantial market value.
Dorchester does not expect to receive any special tax concessions. Further, because the
corporate tax rates in the two countries are the same--35 percent in the U.K. and in the United
States--transfer pricing strategies are ruled out.
Should Dorchester build the new manufacturing plant in the United States?
Suggested Solution to Dorchester Ltd.
Summary of Key Information
The before-tax nominal contribution margin per unit at t=1 is $4.40(1.03)t-1.
It is assumed that Dorchester will be able to sell one-fifth of the 290,000 pounds of candy it
presently sells to North America in Eastern Europe the first year the new manufacturing facility
is in operation; two-fifths the second year; etc.; and all 290,000 pounds beginning the fifth year.
The contribution margin on lost sales per pound in year t equals £3.00(1.045)t.
Terminal value will initially be assumed to equal zero.
The marginal tax rate,
, is the U.K. (or U.S.) rate of 35%.
Dorchester will borrow $1,500,000 at the concessionary loan rate of 7.75% per annum.
Optimally, Dorchester should borrow the remaining funds it needs, £1,000,000, in pounds
sterling because according to the Fisher equation, the real rate is less for borrowing pounds
sterling than it is for borrowing dollars:
Calculation of the Present Value of the After-Tax Operating Cash Flows
Year
(t)
t
S
Quantity
t
S
x
Quantity
x $4.40
x (1.03)t-1
Quantity
Lost
Sales
Quantity
Lost
Sales
x £3.00
x (1.045)t
tt
SOCF
)
K
+(
)-(
OCF
St
ud
t
t
1
1
(a)
£
(b)
£
(a + b)
£
£
1
.6764
390,000
1,160,702
(232,000)
(727,320)
433,382
244,955
2
.6863
409,500
1,273,673
(174,000)
(570,037)
703,636
345,832
3
.6963
429,975
1,397,548
(116,000)
(397,126)
1,000,422
427,566
4
.7064
451,474
1,533,373
(58,000)
(207,498)
1,325,875
492,748
5
.7167
474,048
1,682,524
0
0
1,682,524
543,733
6
.7271
497,750
1,846,053
0
0
1,846,053
518,765
7
.7377
522,638
2,025,613
0
0
2,025,613
494,977
3,068,576
Calculation of the Present Value of the Depreciation Tax Shields
Year
(t)
t
S
Dt
)
i
+(
D
St
d
t
t
1
$
£
1
.6764
1,000,000
213,761
2
.6863
1,000,000
195,837
3
.6963
1,000,000
179,404
4
.7064
1,000,000
164,340
5
.7167
1,000,000
150,552
6
.7271
1,000,000
137,911
7
.7377
1,000,000
126,340
1,168,146
Calculation of the Present Value of the Concessionary Loan Payments
Year
(t)
t
S
(a)
Principal
Payment
(b)
$
It
(c)
$
tt
SLP
(a) x (b + c)
£
tt
dt
SLP
(1+i)
£
1
.6764
214,286
116,250
223,574
201,873
2
.6863
214,286
99,643
215,449
175,654
3
.6963
214,286
83,036
207,025
152,402
4
.7064
214,286
66,429
198,297
131,808
5
.7167
214,286
49,821
189,286
113,605
6
.7271
214,286
33,214
179,957
97,523
7
.7377
214,286
16,607
170,330
83,346
1,500,000
956,211
)
i
+(
d
1=t
Calculation of the Present Value of the Interest Tax Shields
from the $1,500,000 Concessionary Loan
Year
(t)
t
S
(a)
It
(b)
$
tt
SI
(a x b x
)
£
tt
dt
SI
(1+i)
£
1
.6764
116,250
27,521
24,850
2
.6863
99,643
23,935
19,514
3
.6963
83,036
20,236
14,897
4
.7064
66,429
16,424
10,917
5
.7167
49,821
12,497
7,501
6
.7271
33,214
8,452
4,581
7
.7377
16,607
4,288
2,098
84,357
Calculation of the Present Value of the Interest Tax Shields from the £1,000,000 Bond Issue
Year
(t)
Outstanding
Loan
Balance
Principal
Payment
Interest
Payment
)
i
+(
It
d
t
1
£
£
£
£
1
1,000,000
0
107,500
33,973
2
1,000,000
0
107,500
30,675
3
1,000,000
0
107,500
27,698
4
1,000,000
0
107,500
25,009
5
1,000,000
0
107,500
22,582
6
1,000,000
0
107,500
20,390
7
1,000,000
1,000,000
107,500
18,411
178,738
Without considering the terminal value of the project, the APV of the project is negative:
Dorchester should not go ahead with its plans to build a manufacturing plant in the U.S. unless
the terminal value is likely to be large enough to yield a positive APV. The terminal value of the
Since the terminal value is expected to be substantial, and the initial cost of the project is
$7,000,000, it appears likely that the terminal value will be sufficient to yield a positive APV.
Thus, Dorchester should go ahead with its plans to build a manufacturing plant in the U.S.
MINI-CASE: STRIK-IT-RICH GOLD MINING COMPANY
The Strik-it-Rich Gold Mining Company is contemplating expanding its operations. To do so it
will need to purchase land that its geologists believe is rich in gold. Strik-it-Rich’s management
believes that the expansion will allow it to mine and sell an additional 2,000 troy ounces of gold
per year. The expansion, including the cost of the land, will cost $2,500,000. The current price
of gold bullion is $1,400 per ounce and one-year gold futures are trading at $1,484 =
$1,400(1.06). Extraction costs are $1,050 per ounce. The firm’s cost of capital is 10%. At the
current price of gold, the expansion appears profitable: NPV = ($1,400 – 1,050) x 2,000/.10 -
$2,500,000 = $4,500,000. Strik-it-Rich’s management is, however, concerned with the
possibility that large sales of gold reserves by Russia and the United Kingdom will drive the
price of gold down to $1,100 for the foreseeable future. On the other hand, management
believes there is some possibility that the world will soon return to a gold reserve international
monetary system. In the latter event, the price of gold would increase to at least $1,600 per
ounce. The course of the future price of gold bullion should become clear within a year. Strik-it-
Rich can postpone the expansion for a year by buying a purchase option on the land for
$250,000. What should Strik-it-Rich’s management do?
Suggested Solution to Strik-it-Rich Gold Mining Company
There is considerable risk in expanding operations at the present time, even though the NPV
a relatively small amount to have the opportunity to postpone the decision until additional
information is learned. Obviously, Strik-it-Rich’s management will only invest if the NPV is
positive. The risk-neutral probability of gold increasing to $1,600 per ounce is:
Since this amount is substantially in excess of the $250,000 cost of the purchase option on the
land, Strik-it-Rich’s management should definitely take advantage of the timing option it is
confronted with to wait and see what the price of gold is in one year before it makes a decision
to expand operations.
