CHAPTER 15 FOREIGN DIRECT INVESTMENT
SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER
QUESTIONS AND PROBLEMS
1. Recently, many foreign firms from both developed and developing countries acquired high-tech U.S.
firms. What might have motivated these firms to acquire U.S. firms?
Answer: Many foreign firms might have been motivated to gain access to technical know-how residing in
U.S. firms and at the same time monopolize its use. Refer to the reverse-internalization hypothesis
discussed in the text.
2. Japanese MNCs, such as Toyota, Toshiba, Matsushita, etc., made extensive investments in the
Southeast Asian countries like Thailand, Malaysia and Indonesia. In your opinion, what forces are driving
Japanese investments in the region?
Answer: Most likely, these Japanese MNCs have invested heavily in Southeast Asia in order to take
advantage of under priced labor services and cheaper land and other factors of production. Refer to the
life-cycle theory of FDI.
5. Explain the internalization theory of FDI. What are the strength and weakness of the theory?
Answer: According to the internalization theory, firms that have intangible assets with a public good
property tend to undertake FDI to take advantage of the assets on a large scale and, at the same time,
prevent misappropriation of returns from the assets that may occur during arm’s length transactions in
foreign countries. The theory can be effective in explaining green field investments, but not in explaining
mergers and acquisitions.
6. Explain Vernon’s product life-cycle theory of FDI. What are the strength and weakness of the theory?
Answer: According to the product life-cycle theory, firms undertake FDI at a particular stage in the life-cycle
of the products that they initially introduced. When a new product is introduced, the firm chooses to keep
production at home, close to customers. But when the product become mature and foreign demands develop,
the firm may be induced to start production in foreign countries, especially in low-cost countries, to serve the
local markets as well as to export the product back to the home country. As can be inferred from the boxed
reading on Singer in the text, the product life-cycle theory can explain historical development of FDI quite
well. In recent years, however, the international system of production has become too complicated to be
explained neatly by the life-cycle theory. For example, new products are often introduced simultaneously in
many countries and production facilities may be located in many countries at the same time.
7. Why do you think the host country tends to resist cross-border acquisitions, rather than green field
Answer: The host country tends to view green field investments as creating new production facilities and
new job opportunities. In contrast, cross-border acquisitions can be viewed as foreign takeover of existing
domestic firms, without creating new job opportunities.
8. How would you incorporate political risk into the capital budgeting process of foreign investment
Answer: One approach is to adjust the cost of capital upward to reflect political risk and discount the
expected future cash flows at a higher rate. Alternatively, one can subtract insurance premium for
political risk from the expected future cash flows and use the usual cost of capital which is applied to
domestic capital budgeting.
9. Explain and compare forward vs. backward internalization.
Answer: Forward internalization occurs when MNCs with intangible assets make FDI in order to utilize
the assets on a larger scale and at the same time internalize any possible externalities generated by the
assets. Backward internalization, on the other hand, occurs when MNCs acquire foreign firms in order to
gain access to the intangible assets residing in the foreign firms and at the same time internalize any
externalities generated by the assets.
10. What can be the reason for the negative synergistic gains for British acquisitions of U.S. firms?
Answer: Negative synergies for British acquisitions of U.S. firms may reflect that British managers
might have been motivated to invest in U.S. firms in order to pursue their own interests, such as building
corporate empire, rather than shareholders’ interests. Negative synergies can be viewed as agency costs.
11. Define country risk. How is it different from political risk?
Answer: Country risk is a broader measure of risk than political risk, as the former encompasses political
risk, credit risk, and other economic performances.
12. What are the advantages and disadvantages of FDI as opposed to a licensing agreement with a
Answer: The main advantage of FDI over licensing agreement with a foreign partner is that it provides
protection against possible interlopers. The main disadvantage of FDI is that it is costly and time
consuming to establish foreign presence in this manner and FDI is probably more vulnerable to political
13. What operational and financial measures can a MNC take in order to minimize the po litical risk
associated with a foreign investment project?
Answer: First, MNCs should explicitly incorporate political risk in the capital budgeting process and
adjust the project’s NPV accordingly. Second, MNCs can form joint-ventures with local partners or form
a consortium with other MNCs to reduce risk. Third, MNCs can purchase insurance against political risk
from OPIC, Lloyd’s, etc.
14. Study the experience of Enron in India, and discuss what we can learn from it for the management of
Answer: This question can be used as a mini-case or mini-project. Students can utilize various business/financial
publications, such as Wall Street Journal, Financial Times, and Business week, to study the issue.
15. Discuss the different ways political events in a host country may affect local operations of an MNC.
Answer: The answer can be organized based on the three types of political risk: Namely, transfer risk,
operational risk, and control risk. Transfer risk arises from the uncertainty about cross-border flows of
capital, payments, know-how, etc. Operational risk arises from the uncertainty about the host country’s
policies affecting the local operations of MNCs. Control risk arises from the uncertainty about the host
country’s policy regarding ownership and control of local operations of MNCs.
16. What factors would you consider in evaluating the political risk associated with making FDI in a
Answer: Factors to be considered include: (1) the host country’s political and government system; (2) track
record of political parties and their relative strength; (3) the degree of integration into the world system; (4)
the host country’s ethnic and religious stability; (5) regional security; and (6) key economic indicators.
17. Mini Project: Suppose you are hired as a political consultant by Coca-Cola, which is considering
investing in the bottling facilities in four countries: Mexico, Argentina, China, and Russia. Pick a country
out of the four and analyze the political risk associated with investing there. Prepare a final report to
Coca-Cola using a similar format as Exhibit 15.10.
Answer: This is an open-ended question. Students can collect basic economic data for the country of their
choice from such sources as International Financial Statistics, various publications of the World Bank,
Economist, Financial Times, etc.
Both China and Russia are shedding their socialist economic system and are in the process of
establishing market economies. Often, the “rules of the game” are not clearly stipulated for foreign
investors like Coca-Cola. Corruption is a major problem in both countries. In addition, the property rights,
tangible or intangible, and the tax codes are not well established, adding to the risk of doing business in
In contrast, Argentina and Mexico, which used to be inward-looking and highly protectionist countries,
have made significant progress in liberalizing their economies. In the case of Mexico, joining NAFTA
will no doubt accelerate this liberalization process. As we have seen during the 1994-5 peso crisis,
however, gross mismanagement of the economy can negatively affect foreign investors in Mexico. Also,
there is substantial uncertainty about the long-term viability of the current political system in Mexico.
Argentina, on the other hand, appears to be the most safe among the four countries. The country has
successfully made the transition from the protectionist to the open economy and is well positioned to
become a second Chile, a well publicized success story.
Suggest Answers for Mini Case: Enron in India
[See Chapter 15 for the case text.]
Questions for Discussion:
1) Foreign Direct Investment
a) What are the particular challenges faced by foreign companies investing in India?
Suggested Answer: among the most difficult challenges that foreign investors face in India are the lack
of infra-structure like road and port facilities, an inefficient and massive bureaucracy, and restrictions on
international trade and financing.
b) Are there financially more efficient ways to achieve the same objective without undertaking FDI?
Suggested Answer: Joint-venture with a credible local partner who is more familiar with Indian local
situations could have been an alternative mode for entry to the Indian market.
2) Political Risk
a) What were the various elements of political risk faced by Enron in India?
Suggested Answer: Like in many developing countries, there is a general lack of commitment to legal
contracts. In addition, in India, decision making authorities are diffused among different government
offices, causing confusion and uncertainty.
b) What could Enron have done differently to avoid this political risk in order to safeguard its FDI?
Suggested Answer: Enron could have done a more accurate analysis of political risk and considered the
possibility of election victory of the nationalist party. In addition, Enron could have purchased an
insurance policy against this political risk from Overseas Private Investment Corporation or other
insurers. Further, involving a local partner could have dampened the nationalistic sentiment in India.
CHAPTER 16 INTERNATIONAL CAPITAL STRUCTURE AND THE COST OF CAPITAL
SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER
QUESTIONS AND PROBLEMS
2. Explain why and how a firm’s cost of capital may decrease when the firm’s stock is cross-listed on
foreign stock exchanges.
Answer: If a stock becomes internationally tradable upon overseas listing, the required return on the
stock is likely to go down because the stock will be priced according to the international systematic risk
rather than the local systematic risk. It is well known that for a typical stock, the international systematic
risk is lower than the local systematic risk.
3. Explain the pricing spill-over effect.
Answer: Suppose a firm operating in a segmented capital market (like China, for example) decides to
cross-list its stock in New York or London. Upon cross-border listing, the firm’s stock will be priced
internationally. In addition, the pricing of remaining purely domestic stocks (other Chinese stocks) will be
affected in such a way that these stocks will be priced partially internationally and partially domestically.
The degree of international pricing depends on the correlations between these purely domestic stocks and
internationally traded stocks.
5. Define and discuss indirect world systematic risk .
Answer: The indirect world systematic risk can be defined as the covariance between a nontradable asset
and the world market portfolio that is induced by tradable assets. In the presence of internationally
tradable assets, nontradable assets will be priced partly by the indirect world systematic risk and partly by
the pure domestic systematic risk.
6. Discuss how the cost of capital is determined in segmented vs. integrated capital markets.
Answer: In segmented capital markets, the cost of capital will be determined essentially by the securities’
domestic systematic risks. In integrated capital markets, on the other hand, the cost of capital will be
determined by the securities’ world systematic risk, regardless of nationality.
7. Suppose there exists a nontradable asset with a perfect positive correlation with a portfolio T of
tradable assets. How will the nontradable asset be priced?
Answer: The nontradable asset with a perfect positive correlation with portfolio T (for tradable) will be
priced as if it were tradable by itself. In a word, it will be priced solely according to its world systematic
8. Discuss what factors motivated Novo Industries to seek U.S. listing of its stock. What lessons can be
derived from Novo’s experiences?
Answer: Novo, a rapidly growing company, was domiciled in a small and segmented Danish market.
This restricted the firm’s ability to raise capital at a competitive rate. As discussed in the text, Novo
solved this problem by listing its stock in London and New York stock exchanges. This move enabled
Novo to gain access to large capital sources and lower its cost of capital.
10. Explain the pricing-to-market phenomenon.
Answer: The pricing-to-market (PTM) refers to the phenomenon that the same securities are priced
differently for different investors. A well-known example of PTM is provided by Nestle. Up until 1988
November, foreigners were only allowed to hold Nestle bearer shares; only Swiss residents were allowed
to hold registered shares. As indicated in Exhibit 16.11 in the text, bearer shares were trading for about
twice the price of registered shares.
11. Explain how the premium and discount are determined when assets are priced-to-market. When
would the law of one price prevail in international capital markets even if foreign equity ownership
restrictions are imposed?
Answer: The premium and discount are determined by (i) the severity of restrictions imposed on
foreigners and (ii) foreigners’ ability to mitigate the effect of these restrictions using their own domestic
securities. In a special case where foreigners can exactly replicate the securities under restriction, then
PTM will cease to apply.
Answer problems 1-3 based on the stock market data given by the following table.
Telmex Mexico World SD(%) R (%)
Telmex 1.00 .90 0.60 18 ?
Mexico 1.00 0.75 15 14
World 1.00 10 12
The above table provides the correlations among Telmex, a telephone/communication company located in
Mexico, the Mexico stock market index, and the world market index, together with the standard
deviations (SD) of returns and the expected returns ( R ). The risk-free rate is 5%.
1. Compute the domestic country beta of Telmex as well as its world beta. What do these betas measure?
2. Suppose the Mexican stock market is segmented from the rest of the world. Using the CAPM
paradigm, estimate the equity cost of capital of Telmex.
3. Suppose now that Telmex has made its shares tradable internationally via cross-listing on NYSE.
Again using the CAPM paradigm, estimate Telmex’s equity cost of capital. Discuss the possible effects of
international pricing of Telmex shares on the share prices and the firm’s investment decisions.
1. The domestic beta, T , and the world beta, T , of Telmex can be computed as follows:
TM T M TM (18)(15)(0 .9) 243
(15) 2 225
TW T W TW (18)(10)(0 .6) 108
(10) 2 100
Both the domestic and world beta turn out to be the same. As the market moves by 1%, Telmex stock
return will move by 1.08%
RT R f ( RM R f ) T
5 (14 5)(1.08) 14.72%
3. RT R f ( RW R f ) T
5 (12 5)(1.08) 12.56%
As the equity cost of capital decreases from 14.72% to 12.56%, Telmex will experience an increase in its
share price. In addition, Telmex will be able to undertake more investment projects profitably.
CHAPTER 17 INTERNATIONAL CAPITAL BUDGETING
SUGGESTED ANSWERS AND SOLUTIONS TO END-OF-CHAPTER
QUESTIONS AND PROBLEMS
1. Why is capital budgeting analysis so important to the firm?
Answer: The fundamental goal of the financial manager is to maximize shareholder wealth. Capital
investments with positive NPV or APV contribute to shareholder wealth. Additionally, capital
investments generally represent large expenditures relative to the value of the entire firm. These
investments determine how efficiently and expensively the firm will produce its product. Consequently,
capital expenditures determine the long-run competitive position of the firm in the product marketplace.
2. What is the intuition behind the NPV capital budgeting framework?
Answer: The NPV framework is a discounted cash flow technique. The methodology compares the
present value of all cash inflows associated with the proposed project versus the present value of all
project outflows. If inflows are enough to cover all operating costs and financing costs, the project adds
wealth to shareholders.
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 outflows
that can be traced directly to the project under analysis.
4. Discuss the nature of the equation sequence in the chapter of going from equation 17.2a to 17.2f.
Answer: The equation sequence is a presentation of incremental annual cash flows associated with a
capital expenditure. Equation 17.2a presents the most detailed expression for calculating these cash
flows; it is composed of three terms. Equation 17.2b shows that these three terms are: i) incremental net
profit associated with the project; ii) incremental depreciation allowance; and, iii) incremental after-tax
interest expense associated with the borrowing capacity created by the project. Note, the incremental “net
profit” is not accounting profit but rather net cash actually available for shareholders. Equation 17.2c
cancels out the after-tax interest term in 17.2a, yielding a simpler formula. Equation 17.2d shows that the
first term in 17.2c is generally called after-tax net operating income. Equation 17.2e yields yet a
computationally simpler formula by combining the depreciation terms of 17.2c. Equation 17.2f shows
that the first term in 17.2e 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 frequently
have cash flows not encountered in domestic projects, the APV technique easily allows the analyst to add
terms to the model that represent the special cash flows.
6. Relate the concept of lost sales to the definition of incremental cash flow.
Answer: When a new capital project is under taken it may compete with an existing project(s), causing
the old project(s) to experience a loss in sales revenue. From an incremental cash flow standpoint, the
new project’s incremental revenue is the total sales revenue associated with the new project minus the lost
sales revenue from the old 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 project, and
tax shields on the actual new debt are used in the analysis, the APV will be overstated (understated)
making the project unjustly appear more (less) attractive than it actually is.
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 market rate
of interest as an enticement for a firm to make a capital investment that will economically benefit the
lender. The benefit to the MNC is the difference between the face value of the concessionary loan
converted into the home currency and the present value of the 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
9. What is the intuition of discounting the various cash flows in the APV model at specific discount
Answer: The APV model is a value-additivity technique where total value is determined by the sum of
the present values of the individual cash inflows and outflows. Each cash flow will not necessarily have
the same amount of risk associated with it. To account for risk differences in the analysis, each cash flow
is discounted at a rate commensurate with the inherent riskiness of the cash flow.
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 firm by the
government in taxes due to tax-deductible interest payments. Thus, there is more cash left for investor
groups than when the firm is financed with all-equity funds.
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 project what future
decisions it will be confronted with because all information concerning the project has not yet been
learned. Consequently, the firm’s management has alternative paths, or options, that it can take as new
information is discovered. The application of options pricing theory to the evaluation of investment
options in real projects is known as real options.
The firm is confronted with many possible real options over the life of a capital asset. For
example, the firm may have a timing option as when to make the investment; it may have a growth option
to increase the scale of the investment; it may have a suspension option to temporarily cease production;
and, it may have an abandonment option to quit the investment early.
1. The Alpha Company plans to establish a subsidiary in Greece 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 Greek facility in drachmas is estimated at Dr2,400,000,000, of which Dr1,800,000,000 is to be
financed at a below-market borrowing rate arranged by the Greek 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 $25 million debt/$70 million assets = .357 or
35.7%. The project debt ratio is Dr1,800/Dr2,400 = .75 or 75%. Alpha will overstate the tax shield on
interest payments if it uses the 75% figure because the proposed project will only increase borrowing
capacity by Dr856,800,000 (=Dr2,400,000,000 x .357).
2. The current spot exchange rate is Dr240/$1.00. Long-run inflation in Greece is estimated at 8 percent
annually and 4.5 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?
Solution: Dr240(1 + .08)5 /(1 + .045)5 = Dr283/$1.00.
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.
(a) K = (1 - .40).12 + (.40).08(1 - .35)
= .0928 or 9.28%
(b) A weighted-average cost of capital of 9.28% for a levered firm implies:
K =.0928 = Ku (1-(.35)(.40)). Solving for Ku yields .1079 or 10.79%.
4. Suppose in the illustrated mini case in the chapter that 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?
Solution: Centralia should not go ahead with its plans to build a manufacturing plant in the Spain unless
the terminal value is likely to be large enough to yield a positive APV. The terminal value of the project
must be $299,010 in order for the APV to equal zero. This is calculated as follows. Set
S TTVT/(1+Kud )T = $60,000. This implies
TVT = ($60,000/S T)(1+Kud )T
5. 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 numerator and
denominator of each APV term in an offsetting manner. A larger (smaller) f , however, will decrease
(increase) the project APV because the foreign currency received will buy less (more) parent country
currency upon repatriation.
b. Deprecation cash flows are discounted at Kud instead of id?
Answer: The APV would be less favorable because Kud is a larger discount rate than id .
c. The host country did not provide the concessionary loan?
Answer: The APV would be less favorable because the project would have to cover a higher finance
charge, i.e., there would be no benefit received from below market financing.
MINI CASE ONE: 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 only to borrow that amount. The local community in which Dorchester has
decided to build will provide $1,500,000 of debt financing for a period of seven years at 7.75 percent.
The principal is to be repaid in equal installments over the life of the loan. At this point, Dorchester is
uncertain whether to raise the remaining debt it desires through a domestic bond issue or a Eurodollar
bond issue. It believes it can borrow pounds sterling at 10.75 percent per annum and dollars at 9.5
percent. Dorchester estimates its all-equity cost of capital to be 15 percent.
The U.S. Internal Revenue Service will allow Dorchester to depreciate the new facility over a seven
year period. After that time the confectionery equipment, which accounts for the bulk of the investment,
is expected to have substantial market value.
Dorchester does not expect to receive any special tax concessions. Further, because the corporate tax
rates in the two countries are the same--35 percent in the U.K. and in the U.S.--transfer pricing strategies
are ruled out.
Should Dorchester build the new manufacturing plant in the United States?
Suggested Solution to Dorchester Ltd.
Summary of Key Information
The current exchange rate in European terms is S o (£/$) = 1/1.50 = .6667.
The initial cost of the project in British pounds is S o Co = £0.6667($7,000,000) =
The U.K. inflation rate is estimated at 4.5% per annum, or the mid-point of the 4%-5% range. The U.S.
inflation rate is forecast at 3% per annum. Under the simplifying assumption that PPP holds S t =
.6667(1.045)t /(1.03)t .
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.
Straight line depreciation over the seven year economic life of the project is assumed: Dt = $1,000,000 =
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:
5.98% or .0598 = (1.1075)/(1.045) - 1.0 versus
6.31% or .0631 = (1.095)/(1.03) - 1.0.
Kud = 15%.
Calculation of the Present Value of the After-Tax Operating Cash Flows
S t OCF t ( 1 - )
Year Quantity Quantity Quantity Quantity
(t) St S t OCF t
x $4.40 Lost Lost Sales ( 1 + K ud )t
x (1.03)t-1 Sales x £ 3.00
(a) (b) (a + b)
£ £ £ £
1 .6764 390,000 1,160,702 (232,000) (696,000) 464,702 262,658
2 .6863 409,500 1,273,673 (174,000) (545,490) 728,183 357,897
3 .6963 429,975 1,397,548 (116,000) (380,025) 1,017,523 434,875
4 .7064 451,474 1,533,373 (58,000) (198,563) 1,334,810 496,068
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
Calculation of the Present Value of the Depreciation Tax Shields
Year St Dt
S t Dt
( 1 + i d )t
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
Calculation of the Present Value of the Concessionary Loan Payments
Year St Principal It S t LPt
(t) Payment S t LPt
(1+i d )
(a) (b) (c) (a) x (b + c)
$ $ £
1 .6764 214,286 116,250 330,536 201,873
2 .6863 214,286 99,643 313,929 175,654
3 .6963 214,286 83,036 297,321 152,402
4 .7064 214,286 66,429 280,714 131,808
5 .7167 214,286 49,821 264,107 113,605
6 .7271 214,286 33,214 247,500 97,523
7 .7377 214,286 16,607 230,893 83,346
Calculation of the Present Value of the Benefit from the Concessionary Loan
S t LP t =£0.6667 x $1,500,000 - £956,211 = £43,839
S o CL o - t
t =1 ( 1 + i d )
Calculation of the Present Value of the Interest Tax Shields
from the $1,500,000 Concessionary Loan
Year St It St I t St I t
(b) (1+i d )
(a) (a x b x )
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
Calculation of the Present Value of the Interest Tax Shields
from the £1,000,000 Bond Issue
Year Outstanding Principal Interest It
(t) Loan Payment Payment
Balance ( 1 + i d )t
£ £ £ £
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
Without considering the terminal value of the project, the APV of the project is negative:
APV = £3,108,972 + 1,168,146 + 43,839 + 84,357 + 178,738 - 4,666,900 =
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 proje ct
must be $298,736 in order for the APV to equal zero. This is calculated as follows. Set
S TTVT/(1+Kud )T = £82,848. This implies
TVT = (£82,848/S T)(1+Kud )T
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 2000 troy ounces of gold per year. The expansion,
including the cost of the land, will cost $500,000. The current price of gold bullion is $275 per ounce and
one-year gold futures are trading at $291.50 = $250(1.06). Extraction costs are $225 per ounce. The
firm’s cost of capital is 10%. At the current price of gold, the expansion appears profitable: NPV =
($275 – 225) x 2000/.10 - $500,000 = $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 $240 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 $310 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 $25,000. 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 based on the
current price of gold is a positive $500,000. If the price of gold falls to $240 per ounce, the NPV = ($240
– 225) x 2000/.10 - $500,000 = -$200,000. On-the-other-hand, if the price of gold increases to $310, the
NPV is a very attractive NPV= ($310 – 225) x 2000/.10 - $500,000 = $1,200,000. The purchase option
for $25,000 on the land is 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 $310 per ounce is:
q = (F0 - S 0 ·d)/S 0 (u – d) = (291.50 – 240)/(310 – 240) = .7357.
Thus, the value of the timing option to postpone the decision one year is:
C = .7357($1,200,000)/(1.06) = $832,868.
Since this amount is substantially in excess of the $25,000 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.