International FInancial Management 2nd Edition Solution Manual

©2012 Pearson Education, Inc.

Chapter 1

Globalization and the Multinational

Corporation QUESTIONS

1. Define globalization. How has it proceeded in trade in goods and services versus

capital markets?

Answer: Globalization refers to the increasing connectivity and integration of countries

and corporations and the people within them in terms of their economic, political, and

social activities. Because of globalization, multinational corporations dominate the

corporate landscape.

2. Describe fours ways that a company can supply its products to a foreign country.

How do they differ?

Answer: An MNC can supply a foreign market through exports, by licensing local firms

abroad to manufacture the company’s products, by setting up a joint venture with a

foreign company, or by foreign direct investment.

3. What is a greenfield investment?

Answer: MNCs engage in greenfield investments when they enter foreign markets by

simply establishing new operations in these countries without having a local partner and

without acquiring a local company.

4. What percentage ownership typically defines FDI?

Answer: Foreign direct investment (FDI) occurs when a company from one country

makes a significant investment that leads to at least a 10% ownership interest in a firm in

another country.

5. What is agency theory? How does corporate governance the issues raised by agency

theory?

2 Chapter 1 Globalization and the Multinational Corporation


Answer: Agency theory explores the problems that arise because the owners of the firm

do not typically manage the firm, and it devises ways to resolve these problems. This is

often called the separation of owneship and control. A manager of a firm, in particular

the chief executive officer (CEO), is viewed as an agent who contracts with various

principals—most importantly the firm’s shareholders but also the firm’s creditors,

suppliers, clients, and employees. The principals must design contracts that motivate the

agent to perform actions and make decisions that are in the best interests of the principals.

6. Why is ownership more concentrated in developing countries than in developed

countries?

Answer: In many developed countries, the rule of law is strong enough to discipline

managers through legal means, for example by takeovers and proxy contests or through

contractual compensation plans. Concentrated ownership is one way in which agency

problems are mitigated in developing countries. A block of stock is held by either a

wealthy investor, a family, or a financial intermediary, which might be a bank, a holding

company, a hedge fund or a pension fund. The large shareholder clearly has a vested

interest in monitoring management and has the power to implement changes in

management. Negative aspects of this approach include possible collusion between the

large shareholder and the management to expropriate wealth from smaller shareholders

and the fact that the stock may be more difficult to trade on the stock market if a

substantial block of shares is withdrawn from the market but is still available to be sold

should the large shareholder want to sell.

7. What is the IMF? What is its role in the world economy?

Answer: The International Monetary Fund (IMF) is an international organization of 187

member countries, based in Washington, DC, which was conceived at a United Nations

conference convened in Bretton Woods, New Hampshire, in 1944. The main goal of the

IMF is to ensure the stability of the international monetary and financial system—the

system of international payments and exchange rates among national currencies that

enables trade to take place between countries, to help resolve crises when they occur, and

to promote growth and alleviate poverty. To meet these objectives, the IMF offers

surveillance and technical assistance. Surveillance is the regular dialogue about a

country’s economic condition and policy advice that the IMF offers to each of its

members. Technical assistance and training are offered to help member countries

strengthen their capacity to design and implement effective policies, including fiscal

policy, monetary and exchange rate policies, banking and financial system supervision

and regulation, and statistics.

8. What is the World Bank? What is its role in the world economy?

Answer: The World Bank is an international institution created in 1944, as the

Chapter 1 Globalization and the Multinational Corporation 3


International Bank for Reconstruction and Development (IBRD) to facilitate postwar

reconstruction and development. Over time, the IBRD’s focus shifted toward poverty

reduction, and in 1960, the International Development Association (IDA) was established

as an integral part of the World Bank. Whereas the IBRD focuses on middle-income

countries, the IDA focuses on the poorest countries in the world. Together they provide

low-interest loans, interest-free credits, and grants to developing countries for

investments in education, health, infrastructure, communications, and other activities.

The World Bank also provides advisory services to developing countries and is actively

involved with efforts to reduce and cancel the international debt of the poorest countries.

9. What are the major multilateral development banks?

Answer: The term typically refers to the World Bank Group and four regional

development banks: the African Development Bank, the Asian Development Bank, the

European Bank for Reconstruction and Development, and the Inter-American

Development Bank. These banks have a broad membership that includes both developing

countries (borrowers) and developed countries (donors), and their membership is not

limited to countries from the region of the regional development bank. While each bank

has its own independent legal and operational status, their similar mandates and a

considerable number of joint owners lead to a high level of cooperation among MDBs.

The MDBs provide financing for development in three ways. First, they provide long-

term loans at market interest rates. To fund these loans, the MDBs borrow on the

international capital markets and re-lend to borrowing governments in developing

countries. Second, the MDBs offer long-term loans (often termed credits) with interest

rates set well below market rates. These credits are funded through direct contributions of

governments in donor countries. Finally, grants are sometimes offered mostly for

technical assistance, advisory services, or project preparation.

10. What is the WTO? What is its role in the world economy?

Answer: The World Trade Organization (WTO) was founded in 1995. It is headquartered

in Geneva, Switzerland, and had 153 member countries in 2010. Whereas GATT was a

set of rules, the WTO is an institutional body. The WTO expanded its scope from traded

goods to trade within the service sector and intellectual property rights. Various WTO

agreements set the legal ground rules for international commerce to hopefully ensure that

the multilateral trading system operates smoothly. They are negotiated and signed by a

large majority of the world’s trading nations, and the agreements are ratified in the

parliaments of the member countries. If there is a trade dispute between countries, the

WTO’s dispute settlement process helps interpret the agreements and commitments, and

it ensures that countries’ trade policies conform to them.

11. What is an institutional investor? Along with individual investors, what do they

detemine?

4 Chapter 1 Globalization and the Multinational Corporation


Answer: Institutional Investors are organizations that invest pools of money on behalf of

individual investors or other organizations. Examples include banks, insurance

companies, pension funds, mutual funds, and university endowments. Institutional

investors, together with individual investors, determine the prices of bonds and stocks

implicitly determining the expected rates of return on these assets thereby setting the

MNC’s cost of capital. The cost of capital, in turn, affects project valuations, which

determines a company’s investments.

12. What are anti-globalists?

Answer: Anti-globalization is an umbrella term encompassing separate social

movements, united in their opposition to the globalization of corporate economic activity

and the free trade with developing nations that results from such activity. Anti-globalists

generally believe that global laissez-faire capitalism is detrimental to poor countries and

to disadvantaged people in rich countries. Anti-globalists also criticize global financial

institutions such as the World Bank, the IMF, and the WTO. Especially under attack is

the so-called Washington consensus model of development, which, as promoted by

international financial institutions (especially the IMF), is interpreted as requiring

macroeconomic austerity, privatization, and a relatively laissez-faire approach to

economic management. Anti-globalists believe that these policies exacerbate

unemployment and poverty.

13. Who are Ante and Freedy Handel? How do their views on the world economy

differ?

Answer: Ante and Freedy Handel are two brothers who discuss various international

financial management problems and controversial issues in international finance in

Point–Counterpoint features. The brothers are enrolled in an international finance class.

Ante typically rails against free trade and free markets as he believes financial markets

are inefficient and that prices do not necessarily correctly reflect information about a

firm’s prospects. Freedy believes more in the power of the capitalist system to allocate

resources efficiently, and he consequently believes that financial markets by and large get

things right.

PROBLEMS

1. Go to the Web site of your favorite multinational firm and determine where it

operates thoughout the world. How many employees does it have worldwide? Has

it done any interesting cross-border mergers and acquisitions during the last year?

Answer: As an example, Siemens, http://www.siemens.com/investor/en/index.htm, has an

investor relations section in which you can find the current annual and quarterly reports.

Chapter 1 Globalization and the Multinational Corporation 5


Doing a Google search for acquisition will allow you to find the most current acquisitions

that the company has done. The company operates in over 190 countries around the

world listed on its Web site. There are over 340,000 employees.

2. Go to UNCTADstat at http://unctadstat.unctad.org. Update the data in Exhibit 1.6

on cross-border mergers and acquisitions for the most recent years.

Answer: UNCTAD provides lots of interesting data on FDI. As of publication of the

book in 2011, Exhibit 1.6 was as current as we could get.

3. Go to the IMF’s Web site at www.imf.org and download the 2011 World Economic

Outlook. Pick your favorite country and determine if this is a good time to invest in

it or not.

Answer: On the IMF’s Web site, click on Data and Statistics to find the WEO.

4. Go to the WTO’s Web site at www.wto.org and determine which goods or services

are the sources of trade disputes between countries this year.

Answer: In May 2011, China was appealing the resolution of a dispute with the United

States over passenger vehicle and light truck tires, and the Ukraine accused Moldova of

protectionism because of certain environmental regulations.


Chapter 2

The Foreign Exchange Market

QUESTIONS

1. What is an exchange rate?

Answer: An exchange rate is the relative price of two currencies, like the U.S. dollar price of

the euro, the Thai baht price of the Malaysian ringgit, or the Mexican peso price of the

Canadian dollar.

2. What is the structure of the foreign exchange market? Is it like the New York Stock

Exchange?

Answer: The interbank foreign exchange market is a very large, diverse, over-the-counter

market, not a physical trading place where buyers and sellers gather to agree on a price to

exchange currencies. Traders, who are employees of financial institutions in the major

financial cities around the world, deal with each other primarily over the phone or via

computer, with written or formal electronic confirmations of transactions occurring only

later.

3. What is a spot exchange rate contract? When does delivery occur on a spot contract?

Answer: When currencies in the interbank spot market are traded, certain business

conventions are followed. For example, when the trade involves the U.S. dollar, business

convention dictates that spot contracts are settled in 2 business days—that is, the payment of

one currency and receipt of the other currency occurs in 2 business days. One business day is

necessary because of the back-office paperwork involved in any financial transaction. The

second day is needed because of the time zone differences around the world.

Several exceptions to the 2-business-day rule are noteworthy. First, for exchanges

between the U.S. dollar and the Canadian dollar or the Mexican peso, the rule is 1 business

day. Second, if the transaction involves the dollar and the first of the 2 days is a holiday in

the United States but not in the other settlement center, the first day is counted as a business

day for settlement purposes. Third, Fridays are not part of the business week in most Middle

Eastern countries, although Saturdays and Sundays are. Hence, non–Middle Eastern

currencies settle on Fridays, and Middle Eastern currencies settle on Saturdays.

2 Chapter 2 The Foreign Exchange Market


4. What was the Japanese yen spot price of the U.S. dollar on December 21, 2010?

Answer: Examining Exhibit 2.5 for December 21, 2010 we find that the Japanese yen spot

price of the U.S. dollar was ¥84.12/$.

5. What was the U.S. dollar spot price of the Swiss franc on December 21, 2010?

Answer: Examining Exhibit 2.5 for December 21, 2010, we find that the U.S. dollar spot

price of the Swiss franc was $1.0289/CHF.

6. How large are the bid–ask spreads in the interbank spot market? What is their

purpose?

Answer: The purpose of the bid-ask spread is to allow traders to profit by buying a currency

at a low bid price and selling that currency at a higher ask price. Bid–ask spreads in the spot

foreign exchange market are quite small, often only two or three basis points. For example, a

yen–dollar trader might quote a bid price of yen per dollar at which she is willing to buy

dollars in exchange for yen of, say, ¥83.74/$. The trader would then quote a higher ask price

at which she is willing to sell dollars for yen, say, at an exchange rate of ¥83.76/$. This

percentage bid-ask spread is

¥83.76/$ - ¥83.74/$

100 0.02%¥83.76/$ + ¥83.74/$ / 2

7. What was the euro price of the British pound on December 21, 2010? Why?

Answer: We can find this information two ways. The cross-rate quote from Exhibit 2.6 is

€1.1818/£. The exchange rates of euros per dollar and dollars per pound from Exhibit 2.5 are

€0.7636/$ and $1.5477/£. We know that there would be a triangular arbitrage possibility if

the cross-rate differs from the indirect rate using the dollar as an intermediary. Thus, we find

the same value if we calculate

€0.7636/$ $1.5477/£ = €1.1818/£

8. If the direct euro price of the British pound is higher than the indirect euro price of the

British pound using the dollar as a vehicle currency, how could you make a profit by

trading these currencies?

Answer: If the direct euro price of the British pound is higher than the indirect euro price of

the British pound using the dollar as a vehicle currency, there would be a triangular arbitrage.

We would want to buy pounds at the indirect low price and sell pounds at the direct high

price. Suppose in Question 7 that the direct price euros per pound were €1.2115/£ and the

exchange rates versus the dollar are €0.7636/$ and $1.5477/£. The indirect euro price of the

pound is therefore

Chapter 2: The Foreign Exchange Market 3


€0.7636/$ $1.5477/£ = €1.1818/£

If we start with €10,000,000, we can convert euros to dollars and get

€10,000,000 / €0.7636/$ = $13,095,862

Converting these dollars into pounds gives

$13,095,862 / $1.5477/£ = £8,461,499

Converting these pounds into euros gives

€1.2115/£ £8,461,499 = €10,251,106

Thus, we make a profit of €251,106 or 2.51%.

9. What is an appreciation of the dollar relative to the pound? What happens to the dollar

price of the pound in this situation?

Answer: An appreciation of the dollar relative to the pound means that it takes fewer dollars

to buy a pound, so the dollar price of the pound falls. This situation is also described as the

dollar is stronger in the foreign exchange market, the pound has depreciated versus the dollar,

and the pound is weaker in the foreign exchange market.

10. What is a depreciation of the Thai baht relative to the Malaysian ringgit? What

happens to the baht price of the ringgit in this situation?

Answer: A depreciation of the Thai baht relative to the Malaysian ringgit means that it will

take more baht to buy one ringgit. Thus, the baht price of the ringgit is now higher after the

depreciation of the baht.

PROBLEMS

1. Mississippi Mud Pies, Inc. needs to buy 1,000,000 Swiss francs (CHF) to pay its Swiss

chocolate supplier. Its banker quotes bid–ask rates of CHF1.3990–1.4000/USD. What

will be the dollar cost of the CHF1,000,000?

Answer: The bank’s bid rate is CHF1.3990/$. That is the price at which the bank is willing to

buy $1 in return for CHF1.3990. The bank sells dollars at its ask price CHF1.4000/$.

Mississippi Mud Pies must sell dollars to the bank to buy CHF. Therefore Mississippi Mud

Pies will receive the bank’s bid rate of CHF1.3990/$. The dollar cost of CHF1,000,000 is

consequently

CHF 1,000,000 / CHF1.399/$ = $714,796



2. If the Japanese yen–U.S. dollar exchange rate is ¥104.30/$, and it takes 25.15 Thai bahts

to purchase 1 dollar, what is the yen price of the baht?

Answer: To prevent triangular arbitrage, the direct quote of the yen price of the baht (¥/THB)

must equal the yen price of the dollar times the dollar price of the baht (which is the

reciprocal of the baht price of the dollar):

¥104.30/$ 1/(THB25.15/$) = ¥104.30/$ $0.03976/THB = ¥ 4.1471/THB

3. As a foreign exchange trader, you see the following quotes for Canadian dollars (CAD),

U.S. dollars (USD), and Mexican pesos (MXN):

USD0.7047/CAD MXN6.4390/CAD MXN8.7535/USD

Is there an arbitrage opportunity, and if so, how would you exploit it?

Answer: The direct quote for the cross-rate of MXN6.4390/CAD should equal the implied

cross-rate using the dollar as an intermediary currency; otherwise there exists a triangular

arbitrage opportunity. The indirect cross rate is

MXN8.7535/USD USD0.7047/CAD = MXN6.1686/CAD

This indirect cross rate is less than the direct quote so there is an arbitrage opportunity to

exploit between the three currencies. In this situation, buying the CAD with MXN by first

buying USD with MXN and then buying the CAD with the USD and finally selling that

amount of CAD directly for MXN would make a profit because we would be buying the

CAD at a low MXN price and selling the CAD at a high MXN price.

4. The Mexican peso has weakened considerably relative to the dollar, and you are trying

to decide whether this is a good time to invest in Mexico. Suppose the current exchange

rate of the Mexican peso relative to the U.S. dollar is MXN9.5/USD. Your investment

advisor at Goldman Sachs argues that the peso will lose 15% of its value relative to the

dollar over the next year. What is Goldman Sachs’s forecast of the exchange rate in 1

year?

Answer: One way to think of this is to say that the investment advisor is referring to the fact

that the Mexican peso price of the dollar will be 15% higher next year. In this case, the

forecast of the MXN/USD exchange rate in year 1

MXN9.5/USD 1.15 = MXN 10.925/USD

A 15% loss of value of the Mexican peso versus the U.S. dollar technically means that dollar

price of the peso is 15% lower. We know that the current USD price of the peso is

1 / (MXN9.5/USD) = USD0.105263/MXN

If this exchange rate falls by 15%, the new exchange rate will be

0.85 USD0.105263/MXN = USD0.089474/MNX

In this case the forecast for the future exchange rate measured in pesos per dollar is

Chapter 2: The Foreign Exchange Market 5


1 / (USD0.089474/MXN) = MXN11.1765/USD

The difference arises because the simple percentage change in the exchange rate depends on

how the exchange rate is quoted.

5. Deutsche Bank quotes bid–ask rates of $1.3005/€ - $1.3007/€ and ¥104.30 - 104.40/$.

What would be Deutsche Bank’s direct asking price of yen per euro?

Answer: The direct asking price of yen per euro (¥/€) is the amount of yen that the bank

charges someone who is buying euros with yen. The bank would want this to be the same as

the price at which it sells dollars for yen (the bank’s ask price) times the price at which it

sells euros for dollars (also the bank’s ask price). Thus, the asking price of yen per euro

should be

(¥104.40/$) ($1.3007/€) = ¥135.79/€

6. Alumina Limited of Australia has called Mitsubishi UFJ Financial Group to get its

opinion about the Japanese yen–Australian dollar exchange rate. The current rate is

¥67.72/A$, and Mitsubishi thinks the Australian dollar will weaken by 5% over the next

year. What is Mitsubishi UFJ’s forecast of the future exchange rate?

Answer: If the Australian dollar weakens by 5% over the next year, it will take 5% fewer

Japanese yen to purchase the Australian dollar. Thus, the forecast is

¥67.72/A$ (1 – 0.05) = ¥64.334/A$

7. Go to www.fxstreet.com, find the “Live Charts Window,” and plot the exchange rate of

the dollar vs. the euro with a “candle stick” high-low chart at 5 minute intervals for one

day, daily intervals for one month, and weekly intervals for one year. Now, cover the

units and ask a classmate to identify the different graphs. Are you surprised?

Answer: The Web site, fxstreet.com, provides some interesting ways to look at the data. The

point of this exercise is that the dynamics of exchange rates look quite similar at the different

intervals. The eye easily sees “trends” and other “reversals.” These are often quite difficult

to detect with statistical analysis, and in real time one never knows when the “trend” will

stop.

8. Pick 3 currencies, and go to www.oanda.com to get their current bilateral exchange

rates. Is there an arbitrage opportunity?

Answer: Oanda is an excellent source of high quality data. When we checked prices, they all

satisfied the no arbitrage requirement.



9. Go to the CLS Bank web site, www.cls-group.com, and read about In/Out Swaps. How

do they help participants manage their risks?

Answer: Here is the quote from the Web site:

An In/Out Swap comprises two equal and opposite FX transactions that are

agreed as an intraday swap. One of the two FX transactions is input to CLS,

in order to reduce each Member's net position in the two currencies. The

other is settled outside CLS.

The combined effect of these two FX transactions is a reduction in the

intraday funding requirements of the two Members, whilst leaving the

institutions’ overall FX position unchanged. In/Out Swaps exploit the

likelihood that an institution with a large short position in CLS will almost

certainly have one or more large long positions in CLS.

As In/Out Swaps reduce these “in-CLS” cash positions as well as the

corresponding liquidity positions outside of CLS, banks can more easily

manage liquidity flows for their non-CLS needs, as well as in the CLS Bank

system.

CLS offers a full In/Out Swap service that identifies potential In/Out Swaps,

notifies participants and implements In/Out Swaps efficiently through the

CLS Bank system.

The multilateral netting effect together with the In/Out Swap process has

proved to be extremely efficient, resulting in a pay in requirement from

Settlement Members of less than 2% of the gross value of instructions being

settled through CLS Bank.


Chapter 3

Forward Markets and Transaction

Exchange Risk

QUESTIONS

1. What is a forward exchange rate? When does delivery occur on a 90-day forward

contract?

Answer: The forward exchange rate is a price quoted today for the exchange of currencies

at the maturity of the forward contract. To find the delivery date for a 90-day forward

contract, one first finds the spot value date, which is typically two business days in the

future relative to the day that the contract is made. Then, to find the forward value date, one

goes to the calendar date in three months corresponding to the calendar date of the spot

value date. If that calendar date in three months is a legitimate business day in both

countries, that date is the forward value date. If the banks in one of the countries are closed

on that date, because it is a weekend or holiday, the forward value date is the next available

business day without going out of the month. If going forward in time would take you out

of the month, you go backward in time. This rule is followed except when the spot value

day is the last business day of the current month, in which case the forward value day is the

last business day in both countries in three months (this is referred to as the end-end rule).

2. If the yen is selling at a premium relative to the euro in the forward market, is the

forward price of EUR per JPY larger or smaller than the spot price of EUR per JPY?

Answer: When the yen is selling at a premium in the forward market, the euro price of the

yen in the forward market, EUR per JPY, would be larger than the spot price of EUR per

JPY.

3. What do we mean by the expected future spot rate?

Answer: The expected future spot rate is the conditional mean of the probability

distribution of future spot rates. The probability distribution describes all of the possible

realizations (or ranges of realizations) of the future spot rate and assigns probabilities to

those values (or ranges of values). The conditional mean of the probability distribution of

future spot rates takes a probability weighted average of those possible realizations (or

Chapter 3: Forward Markets and Transaction Exchange Risk


2

ranges of realizations). We say that the expectation is conditional because we use all

available information at the time when we are describing the probability distribution.

4. How much of the probability distribution of future spot rates is between plus or

minus 2 standard deviations?

Answer: For a normal distribution, when we go from 2 standard deviations below the

conditional mean to 2 standard deviations above the conditional mean, we encompass

95.44% of the probability distribution.

5. If you are a U.S. firm and owe someone ¥10,000,000 in 180 days, what is your

transaction exchange risk?

Answer: Because you owe ¥10,000,000 in 180 days, you have a transaction exchange risk

because if you do nothing to hedge and the yen strengthens, it will take more dollars to

eliminate your yen liability.

6. What is a spot–forward swap?

Answer: A spot-forward swap involves either the purchase of foreign currency spot against

the sale of the same amount of foreign currency forward, or the sale of foreign currency

spot against the purchase of the same amount of foreign currency forward.

7. What is a forward–forward swap?

Answer: A forward-forward swap involves either the purchase of foreign currency at a

short maturity forward against the sale of the same amount of foreign currency at a longer

maturity forward, or the sale of foreign currency at the short maturity forward against the

purchase of the same amount of foreign currency at a longer maturity forward.

PROBLEMS

1. If the spot exchange rate of the yen relative to the dollar is ¥105.75, and the 90-day

forward rate is ¥103.25/$, is the dollar at a forward premium or discount? Express

the premium or discount as a percentage per annum for a 360-day year?

Answer: When the forward rate of yen per dollar is less than the spot rate of yen per dollar,

the dollar is said to be at a discount in the forward market. The magnitude of the discount is

expressed in percentage per annum by dividing the difference between the forward rate and

the spot rate by the spot rate and multiplying by reciprocal of the fraction of the year

corresponding to the maturity of the forward contract (360/N days) and by 100. Thus, the

Chapter 3: Forward Markets and Transaction Exchange Risk 3


annualized forward discount is 9.46% because

¥103.25/$ - ¥105.75/$ 360

100 9.46%¥105.75/$ 90

Notice that the word “discount” implies that the forward rate is less than the spot rate.

2. Suppose today is Tuesday, January 18, 2011. If you enter into a 30-day forward

contract to purchase euros, when will you pay your dollars and receive your euros?

(Hints: February 18, 2011, is a Friday, and the following Monday is a holiday.)

Answer: To determine the value date of the forward contract, which is the day on which the

exchange of currencies happens, one must first find the spot value date. For dollar-euro

contracts, the spot value date is two business days in the future. Thus, for a spot contract on

Tuesday, January 18, 2011, the exchange of currencies would take place on Thursday,

January 20, 2011. The 30-day forward contract settles on the calendar day in the next

month corresponding to the date of spot settlement if that is a legitimate business day. The

forward contract would therefore settle on February, 20, 2011 if that is a legitimate

business day, but that date is a Sunday. Furthermore, Monday, February 21, 2011, is a

holiday, so the settlement of the forward contract would be on Tuesday, February 22, 2011.

3. As a foreign exchange trader for JPMorgan Chase, you have just called a trader at

UBS to get quotes for the British pound for the spot, 30-day, 60-day, and 90-day

forward rates. Your UBS counterpart stated, “We trade sterling at $1.7745-50, 47/44,

88/81, 125/115.” What cash flows would you pay and receive if you do a forward

foreign exchange swap in which you swap into £5,000,000 at the 30-day rate and out

of £5,000,000 at the 90-day rate? What must be the relationship between dollar

interest rates and pound sterling interest rates?

Answer: The fact that you are swapping into £5,000,000 at the 30-day rate forward rate

means that you are paying dollars and buying pounds. You would do this transaction at the

bank’s 30-day forward ask rate. To find the forward ask rate, you must realize that the 30-

day forward points of 47/44 indicate the amounts that must be subtracted from the spot bid

and ask quotes to get the forward rates. We know to subtract the points because the first

forward point is greater than the second. Hence, the first part of the swap would be done at

$1.7750/£ - $0.0044/£ = $1.7706/£. Therefore, to buy £5,000,000 you would pay

$1.7706/£ £5,000,000 = $8,853,000

In the second leg of the swap, you would sell £5,000,000 for dollars in the 90-day forward

market. Because you are selling pound for dollars, you transact at the 90-day forward bid

rate of $1.7745/£ - $0.0125/£ = $1.7620/£. Therefore, you would receive

$1.7620/£ £5,000,000 = $8,810,000

Notice that you get back fewer dollars than you paid, but you had use of £5,000,000 for 60

days. Thus, the pound must be the higher interest rate currency.



4

4. Consider the following spot and forward rates for the yen–euro exchange rates:

Spot

30 days

60 days

90 days

180 days

360 days

146.30

145.75

145.15

144.75

143.37

137.85

Is the euro at a forward premium or discount? What are the magnitudes of the

forward premiums or discounts when quoted in percentage per annum for a 360-day

year?

Answer: The forward rates of yen per euro are lower than the spot rates. Therefore, the euro

is at a discount in the forward market. The annualized forward premium or discount for the

N day forward contract is

F - S

S n

360

N days = 100

If the value of this calculation is negative, say -2%, we say there is a 2% discount.

Therefore, the discounts are 4.51% for 30 days, 4.72% for 60 days, 4.24% for 90 days,

4.01% for 180 days, and 5.78% for 360 days.

5. As a currency trader, you see the following quotes on your computer screen:

Exch. Rate

Spot

1-month

2-month

3-month

6-month

USD/EUR

1.0435/45

20/25

52/62

75/90

97/115

JPY/USD

98.75/85

12/10

20/16

25/19

45/35

USD/GBP

1.6623/33

30/35

62/75

95/110

120/130

a. What are the outright forward bid and ask quotes for the USD/EUR at the 3-month

maturity?

Answer: The spot bid and ask quotes for USD/EUR are 1.0435/45. These quotes mean that the

bank buys euros with dollars spot at $1.0435/€, and the bank sells euros for dollars at

$1.0445/€. Because the forward points at the 3-month maturity are 75/90, we know that we

must add the points to get the outright forward bid and ask rates. Adding the points makes the

bid-ask spread in the forward market larger than the bid-ask spread in the spot market.

Consequently, the forward bid rate is $1.0435/€ + $0.0075/€ = $1.0510/€, and the forward ask

quote is $1.0445/€ + $0.0090/€ = $1.0535/€.

b. Suppose you want to swap out of $10,000,000 and into yen for 2 months. What are the

cash flows associated with the swap?


Answer: When you swap out of $10,000,000 into yen in the spot market, you are selling

dollars to the bank. The bank buys dollars at its low bid rate of ¥98.75/$, so you get

¥98.75/$ $10,000,000 = ¥987,500,000

When you contract to buy the $10,000,000 back from the bank in the 2-month forward

market, you must pay the bank’s ask rate of

¥98.85/$ - ¥00.16/$ = ¥98.69/$

You subtract the points because the 2-month forward quote is 20/16. Subtracting the

points makes the bid-ask spread in the forward market larger than the bid-ask spread in

the spot market. Hence, the amount of yen you pay is

¥98.69/$ $10,000,000 = ¥986,900,000

c. If one of your corporate customers calls you and wants to buy pounds with

dollars in 6 months, what price would you quote?

Answer: If the customer wants to buy pounds with dollars, the customer must pay the

bank’s 6-month ask rate. The spot quotes are 1.6623/33 which means the spot ask rate is

$1.6633/£. The 6-month forward points are 120/130. We add the points because the first

one, 120, is less than the second, 130. Hence, the outright forward quote would be

$1.6633/£ + $0.0130/£ = $1.6763/£

6. Intel is scheduled to receive a payment of ¥100,000,000 in 90 days from Sony in

connection with a shipment of computer chips that Sony is purchasing from Intel.

Suppose that the current exchange rate is ¥103/$, that analysts are forecasting that the

dollar will weaken by 1% over the next 90 days, and that the standard deviation of 90-

day forecasts of the percentage rate of depreciation of the dollar relative to the yen is

4%.

a. Provide a qualitative description of Intel’s transaction exchange risk.

Answer: Intel is a U.S. company, and it is scheduled to receive yen in the future. A

weakening of the yen versus the dollar causes a given amount of yen to convert to fewer

dollars in the future. This loss of value could be severe if the yen depreciates by a

significant amount.

b. If Intel chooses not to hedge its transaction exchange risk, what is Intel’s expected

dollar revenue?

Answer: If Intel chooses not to hedge, the expected dollar revenue is the expected dollar

value of the ¥100,000,000. The expected spot rate incorporates a 1% weakening of the

dollar. This means that the expected yen price of the dollar is 1% less than the current

spot rate of ¥103/$ or

Et[S(t+90,¥/$)] = 0.99 ¥103/$ = ¥101.97/$

Hence, Intel expects to receive ¥100,000,000 / ¥101.97/$ = $980,681

c. If Intel does not hedge, what is the range of possible dollar revenues that

incorporates 95.45% of the possibilities?



6

Answer: We are told that the standard deviation of the rate of depreciation of the dollar is 4%.

The standard deviation of the future spot rate is therefore 4% of the current spot rate or 0.04 ¥103/$ = ¥4.12/$. Thus, plus or minus 2 standard deviations around the conditional expected

future spot rate is

¥101.97/$ + ¥8.24/$ = ¥110.21/$

¥101.97/$ - ¥8.24/$ = ¥93.73/$

The range that encompasses 95.45% of possible future values for Intel’s receivable is therefore

¥100,000,000 / ¥110.21/$ = $907,359

¥100,000,000 / ¥93.73/$ = $1,066,894

7. Go to the Wall Street Journal’s Market Data Center and find New York closing prices for

currencies. Calculate the 180-day forward premium or discount on the dollar in terms of the

yen.

Answer: The correct calculation is ( ,180) ( )

200( )

F t S t

S t

.

8. Go to the St. Louis Federal Reserve Bank’s data base, FRED, at

http://research.stlouisfed.org/fred2/ and download data for the exchange rate of the Brazilian

real vs. the U.S. dollar. Calculate the percentage changes over a one month interval. What loss

would you take if you owed BRL 1 million in one month and the dollar depreciated by two

standard deviations.

Answer: Data on FRED for the Brazilian real per dollar start in January 1995 until the present. Our

data ended with April 2011. Using the full sample available to us, the monthly standard deviation of

the rate of appreciation of the dollar relative to the real was 4.49%. Thus, a 2 standard deviation

move would be 8.98%. The spot rate was BRL1.5833/USD. Thus, the exchange rate could change

to (BRL1.5833/ USD) (1 0.0898) BRL1.4411/ USD if the dollar weakened by 2 standard

deviations. The dollar cost of the BRL1 million could go from BRL1,000,000

USD631,592(BRL1.5833 / USD)

toBRL1,000,000

USD693,914(BRL1.4411/ )USD

. This is a loss of USD62,322 . Of course, this calculation

assumes that the spot rate is not expected to change so that the expected spot rate is the current spot

rate.


Chapter 4

The Balance of Payments

QUESTIONS

1. What are the major accounts of the balance of payments, and what transactions are

recorded on each account?

Answer: The three major account of the balance of payments are the current account, the

capital account, and the official settlements account.

The current account records the following:

1. Imports, which are purchases of goods and services from foreign residents, and

exports, which are sales of goods and services to foreign residents.

2. Transactions associated with the income flows from the ownership of foreign assets

(dividends and interest paid to domestic residents who own foreign assets as well as

dividends and interest paid to foreign residents who own domestic assets).

3. Unilateral transfers of money between countries (foreign aid, gifts, and grants given

by the residents or governments of one country to those of another).

The capital account records the following:

Purchases and sales of foreign assets by domestic residents as well as the purchases and

sales of domestic assets by foreign residents.

The definition of an asset is all inclusive: It is any form in which wealth can be held. It

encompasses both financial assets (bank deposits and loans, corporate and government

bonds, and equities) and real assets (factories, real estate, antiques, and so forth). Hence, the

capital account records all changes in the domestic ownership of the assets of other nations as

well as changes in the foreign ownership of the assets of the domestic country.

The official settlements account records the following:

Transactions involving the purchase or sale of official international reserve assets by a

nation’s central bank.

International reserves are the assets of the central bank that are not denominated in the

domestic currency. Gold and assets denominated in foreign currency are the typical

international reserves.

2. Why is it important for an international manager to understand the balance of

payments?

Answer: The balance of payments provides information that is useful in understanding the

determination of exchange rates and the growth prospects of a country. For example,

persistent, large current account deficits, especially ones that are primarily consumer driven,

are often associated with currency crises in which the currency of the country with the deficit

depreciates substantially and the country suffers a severe recession. Knowledge of the

Chapter 4: The Balance of Payments


2

official settlements account indicates whether the country is gaining or losing international

reserves, and sufficient losses of reserves indicate a loss of the ability to maintain a fixed

exchange rate. Massive increases in international reserves indicate that the central bank is

resisting pressure for the currency to appreciate in value. Large capital account surpluses that

are primarily driven by private sector investments indicate that foreigners find the assets of

the country to be attractive investment opportunities.

3. What are the rules that determine the residency requirements on the balance of

payments?

Answer: The rules for residency are that the entity has a primary economic interest in the

country. Thus, it is not citizenship that is being measured. These concepts are discussed in

detail in the IMF’s Balance of Payments manual available online at

http://www.imf.org/external/np/sta/bop/BOPman.pdf.

4. Which items on the balance of payments are recorded as credits, and which items are

recorded as debits? Why?

Answer: The balance of payments uses a double-entry system. Each transaction gives rise to

two entries: One entry is a credit, and the other entry is a debit of equal value. Any

transaction resulting in a payment to foreigners is entered in the BOP accounts as a debit.

Any transaction resulting in a receipt of funds from foreigners is entered as a credit. In the

double entry system, the flow of money from a domestic resident to a foreign resident is a

credit and the item that gives rise to the flow (either an import of a good or service or the

purchase of a foreign asset) is a debit.

5. How are gifts and grants handled in the balance of payments?

Answer: Gifts and grants are handled as imports and exports of goodwill. If a domestic

resident gives a gift to a foreign resident, the value of the gift is a debit (an import of

goodwill) and the value of the gift is a credit on the domestic balance of payments because it

results in payment of funds to foreigners.

6. What does it mean for a country to experience a capital inflow? Is this associated with a

surplus or a deficit on the country’s capital account?

Answer: When a country experiences a capital inflow, foreign residents are investing in

domestic assets and domestic residents are selling foreign assets. These transactions are

credits on the balance of payments because the country is effectively exporting assets. If

capital inflows exceed capital outflows, there is a surplus on the country’s capital account.

This surplus would be offsetting a combined deficit on the current account and the official

settlements account.

7. If you add up all the current accounts of all countries in the world, the sum should be

zero. Yet this is not so. Why?

http://www.imf.org/external/np/sta/bop/BOPman.pdf

Chapter 4: The Balance of Payments 3


Answer: There is a large, consistently negative sign for the global balance of payments which

suggests that the discrepancy cannot simply be due to measurement errors because if it were,

the balance would be positive about as often as it is negative. One reason why there is a

consistent negative sign in the aggregate errors has to do with tax evasion. Many individuals

try to escape taxes on the income from their investments. Hence, they may fail to report the

interest income they earn on their foreign securities, which would constitute a credit for their

home country’s current account balance. Unrecorded earnings in the international shipping

business may also account for a large part of the missing surplus. Once again, these would be

credits on the service account of the balance of payments. Countries that receive foreign aid

may fail to fully account for official aid disbursements. Freer trade has made it more difficult

for governments to measure sales accurately, and sales over the Internet may also escape

detection.

8. What is the investment income account of the balance of payments?

Answer: The investment income account of the balance of payments is a sub-account of the

current account. It records the dividend and interest receipts that domestic residents receive

as income from their ownership of foreign assets. These flows are credits. The dividend and

interest payments that domestic residents make to foreigners who own domestic assets are

recorded as debits on the investment income account.

9. What is the official settlements account of the balance of payments? How are official

settlements deficits and surpluses associated with movements in the international

reserves of the balance of payments?

Answer: The official settlements account records the purchases and sales of the country’s

international reserves. Just as on the private sector’s capital account, if the central bank

increases its ownership of international reserves, this is recorded as a debit, whereas a sale of

international reserves is a credit. Thus, if the official settlements account is in surplus, the

country is losing international reserves.

10. What is the meaning of an account labeled “statistical discrepancy” or “errors and

omissions”? If this account is a credit, what does that imply about the measurement of

other items in the balance of payments?

Answer: The “statistical discrepancy” or “errors and omissions” account is the value of the

measured items on all other accounts with the sign reversed. Thus, if the sum of all other

accounts is a negative number, indicating that the other accounts are in deficit, the statistical

discrepancy must be a credit (a positive number). The statistician missed some credit items

on the other accounts, because we know that the sum of all accounts should be zero due to

the double entry nature of the balance of payments.

11. Why must the national income of a closed economy equal the national expenditures of

that economy? What separates the two concepts in an open economy?



4

Answer: In a closed economy, the value of the final expenditures on all goods and services

must be the income of the factors of production in the economy. In an open economy, final

expenditures can fall on foreign goods and factors of production can earn income abroad.

Net factor income from abroad plus net unilateral transfers from abroad provide flows of

resources that separate the income of the country from the value of final goods and services

produced in a country.

12. Explain why private national saving plus government saving equals the current

account of the balance of payments.

Answer: Saving is the difference between the income of an entity and what that entity

consumes. In a closed economy, the value of what is produced, the country’s gross domestic

product or GDP, must equal its expenditures and its income. Thus, investment expenditures

must be financed by national savings. In the case of an open economy, this does not have to

be the case. By definition, national savings are equal to national income minus the

consumption of the private (C) and public sectors (G):

National savings = Gross national income – Consumption of the private and public sectors

Symbolically,

S = GNI – C – G

We know that gross national income is GDP plus net foreign income, so

S = GDP + NFI – C – G

Substituting the components of GDP gives

S = C + I + G + NX + NFI – C – G

Upon canceling out the consumption terms and rearranging terms, we find

S – I = NX + NFI = CA

National saving – National investment = Current account

If a country’s purchases of investment goods are more than its savings, the country must

run a current account deficit; that is, the country’s investment spending must be financed

from abroad with a capital account surplus.

13. It has been argued that the high correlation between national saving and national

investment that Feldstein and Horioka first measured in 1980 is not evidence of

imperfect capital mobility. What arguments can you offer for why they might have

misinterpreted the data, and what do recent investigations of this issue imply about the

degree of capital mobility throughout the world?

Answer: There are several important caveats to the Feldstein and Horioka interpretation that

have been noted in the literature. One line of argument asserts that the high correlation

between savings and investment could be produced by common forces that move both

variables even though the international capital market is open and competitive. For example,

Baxter and Crucini (1993) and Mendoza (1991) argue that economic shocks affecting

productivity can increase both saving and investment over the business cycle. The argument



goes like this: An increase in productivity causes output and income to increase. Some of the

increase in income is consumed, but some of it is saved because the shock is not expected to

be permanent. But because productivity is temporarily high and is expected to be high for

awhile, it is also a good time to invest. Hence, investment and saving both increase. Bai and

Zhang (2010) argue that financial frictions, such as default risk, prevent people in different

countries from sharing risk adequately, leading to the positive correlation between savings

and investment.

Finally, Jeffrey Frankel (1991) has argued that high correlations between national

investment rates and national saving rates should not really be surprising because the world

economy during the 1960s, 1970s, and even much of the 1980s and 1990s was not

characterized by perfect capital mobility. That is, capital markets were not completely open

around the world. For example, there were significant barriers to international investment in

many European countries and Japan that persisted well into the 1980s. (See also Chapter 1.)

Hence, it would stand to reason that in countries in which saving rates are high, investment

rates would be high as well because there is nowhere else for the capital to go. Frankel argues

that to assess how integrated the world’s capital markets are, we must look at the various

rates of return offered around the world and not merely the flows of saving and investment

stressed by Feldstein and Horioka.

More recent investigations of this issue, such as Bai and Zhang (2010) find that the

correlations between savings and investment are going down, which implies that capital

mobility is increasing.

PROBLEMS

1. Suppose that the following transactions take place on the U.S. balance of payments

during a given year. Analyze the effects on the merchandise trade balance, the

international investment income account, the current account, the capital account, and

the official settlements account.

a. Boeing, a U.S. aerospace company, sells $3 billion of its 747 airplanes to the People’s

Republic of China, which pays with proceeds from a loan from a consortium of

international banks.

Answer: Boeing’s sale of planes is an export on the U.S. balance of payments, which is a

credit. The fact that China borrows from international banks is difficult to assess but

ultimately, it means that U.S. ownership of foreign assets is going up. The Chinese must

ultimately be borrowing from U.S. residents. This is a debit on the U.S. balance of

payments.

U.S. BOP Credit Debit

Sale of airplanes by a U.S. exporter to China

(Current account; U.S. goods export, trade balance)

$3 billion

Reduction of Ownership of U.S. assets by the

Consortium of International Banks

(Capital account; U.S. Capital outflow)

$3 billion



6

b. Mitsubishi UFJ Financial Group purchases $70 million of 30-year U.S. Treasury

bonds for one of its Japanese clients. Mitsubishi draws down its dollar account with

Bank of America to pay for the bonds. Answer: The purchase of Treasury bonds by a foreign company is a credit on the U.S.

balance of payments just like an export of goods is a credit. The reduction in Mitsubishi’s

bank account is a reduction in foreign ownership of U.S. assets and is a corresponding

debit.


Mitsubishi draws down its account with Bank of

America


$70 million

Mitsubishi purchases U.S. Treasury bonds

(Capital account; U.S. Capital inflow)

$70 million

c. Eli Lilly, a U.S. pharmaceutical company, sends a dividend check for $25,255 to a

Canadian investor in Toronto. The Canadian investor deposits the check in a U.S. dollar-

denominated bank account at the Bank of Montreal.

Answer: The dividend check is a debit on the U.S. balance of payments because it is a payment to

a foreigner. The corresponding credit is the increase in foreign ownership of U.S. assets that

occurs when the dollars are deposited in the bank and not spent on goods or services in the U.S.


Dividend check to a Canadian investor

(Current account; dividend payout in international

investment account)

$25,255

Canadian investor deposits the check in a U.S. dollar-

denominated foreign bank account


$25,255

d. The U.S. Treasury authorizes the New York Federal Reserve Bank to intervene in the

foreign exchange market. The New York Fed purchases $5 billion with Japanese yen and

euros that it holds as international reserves.

Answer: When the New York Fed purchases $5 billion in the foreign exchange market and thus

sells international reserves, this is a credit on the official settlements account of the U.S. balance

of payments just as if the private sector were selling goods or assets. The corresponding debit is a

decrease in the foreign ownership of U.S. assets because the New York Fed bought dollars.


$5 billion increase in foreign holdings of U.S. assets


$5 billion

The New York Fed sells $5 billion worth of international

reserves

(Official Settlements Account; decrease in international

reserves)

$5 billion

e. The president of the United States sends troops into a Latin American country to establish a

democratic government. The total operation costs U.S. taxpayers $8.5 billion. To show their



support for the operation, the governments of Mexico and Brazil each donate $1 billion to

the United States, which they raise by selling U.S. Treasury bonds that they were holding as

international reserves.

Answer: It is not entirely clear how much, if any, of the $8.5 billion of military expenditures

would be part of the balance of payments. Any expenditures on soldiers would not be, as the

soldiers are considered U.S. residents for balance of payments purposes. Any equipment that was

damaged or destroyed would also be U.S. equipment, and would not be part of the U.S. balance

of payments. Only purchases made in the Latin American country would be imports. We assume

these expenditures are zero, as we know how to deal with imports from previous questions.

The $2 billion donations by Mexico and Brazil are unilateral transfers from foreigners, which

corresponds to an export of goodwill. The transfers are thus credits on the U.S. balance of

payments. The reduction in the ownership of U.S. assets by Mexico and Brazil are the

corresponding debits.


The governments of Mexico and Brazil each donate $1

billion to the United States (U.S. export of goodwill)

(Current account; Brazilian & Mexican donations)

$2 billion

Mexico & Brazil Sale of U.S. Treasury bonds

(Capital account, U.S. Capital outflow)

$2 billion

f. Honda of America, the U.S. subsidiary of the Japanese automobile manufacturer, obtains

$275 million from its parent company in Japan in the form of a loan to enable it to

construct a new state-of-art manufacturing facility in Ohio.

Answer: The loan is considered a credit on the U.S. balance of payments because foreigners are

increasing their ownership of U.S. assets. The reduction in the parent company’s ownership of

U.S. assets is a corresponding debit.


Honda’s American Subsidiary obtains a foreign loan


$275 million

Reduction in Honda Japan’s ownership of U.S. assets


$275 million

2. Consider the situation of La Nación, a hypothetical Latin American country. In 2010, La

Nación was a net debtor to the rest of the world. Assume that all of La Nación’s foreign debt

was dollar denominated, and at the end of 2010, its net private foreign debt was $75 billion and

the official foreign debt of La Nación’s treasury was $55 billion. Suppose that the interest rate

on these debts was 2.5% per annum (p.a.) over the London Interbank Offering Rate (LIBOR),

and no principal payments were due in 2011. International reserves of the Banco de Nación, La

Nación’s central bank, were equal to $18 billion at the end of 2010 and earn interest at LIBOR.

There were no other net foreign assets in the country. Because La Nación is growing very

rapidly, there is great demand for investment goods in La Nación. Suppose that residents of La

Nación would like to import $37 billion of goods during 2011. Economists indicate that the

value of La Nación’s exports is forecast to be $29 billion of goods during 2011. Suppose that the

Banco de Nación is prepared to see its international reserves fall to $5 billion during 2011. The

LIBOR rate for 2011 is 4% p.a.



8

a. What is the minimum net capital inflow during 2011 that La Nación must have if it wants to

see the desired imports and exports occur and wants to avoid having its international

reserves fall below the desired level?

Answer: We know that the balance of payments always sums to zero:

Current account + Regular capital account + Official settlements account = 0

The current account records exports minus imports plus interest inflows minus interest outflows.

Interest outflows are required to service the $75 billion of private debt and $55 billion of public

debt. The interest payments will be at a rate of 6.5% (LIBOR of 4% plus a spread of 2.5%), or

total interest payments of 0.065 ($75 billion + $55 billion) = $8.45 billion. There will be

interest income on the $18 billion of interest reserves which earn interest at 4%. Thus, interest

income is 0.04 ($18 billion) = $0.72 billion. Hence, the deficit on the interest income account

will be $8.45 billion - $0.72 billion = $7.73 billion. Because La Nación wants to import more

than it exports, it will have a trade deficit of $37 billion - $29 billion = $8 billion. The current

account deficit will be the sum of the trade account deficit and the interest income deficit or $8

billion + $7.73 billion = $15.73 billion. This deficit must be balanced by a surplus on the official

settlements account and a private sector capital account surplus. If the central bank draws down

its international reserves from $18 billion to the minimum of $5 billion, they can provide $13

billion of the $15.73 billion that must be financed. Thus, the private sector would need to have a

capital inflow of $2.73 billion.

b. If this capital inflow occurs, what will La Nación’s total net foreign debt be at the end of

2011?

Answer: The total net foreign debt is the sum of private and public foreign debts minus public

assets. At the end of 2010, net foreign debt was

$75 billion + $55 billion - $18 billion = $112 billion

At the end of 2011, the new net foreign debt is

$75 billion + $55 billion + $2.73 billion - $5 billion = $127.73

The increase in net foreign debt is the current account deficit of $15.73 billion.

3. True or false: If a country is a net debtor to the rest of the world, its international investment

service account is in deficit. Explain your answer.

Answer: The statement is false. The situation of the U.S. in the late 1990s is a good counter example.

As long as the income that a country receives on its foreign assets is providing a higher rate of return

than the payments that country is making to foreigners who own domestic assets, the country can be a

net debtor (that is, have a negative net international investment position) but still have a surplus on its

international investment service account.

4. Choose a country and analyze its balance of payments for the past 10 years. Good sources of

data include official bulletins of the statistical authority of a country or its central banks;

International Financial Statistics, which is a publication of the IMF (www.imf.org), and the

Main Economic Indicators, which is a publication of the Organization for Economic Co-

operation and Development (www.oecd.org).



a. Examine how trade in goods and services has evolved over time. Is the country becoming

more or less competitive in world markets?

b. Consider the relationship between the country’s net foreign asset position and its

international investment income account.

c. If the country has run a current account deficit, what capital inflows have financed the

deficit? If the country has run a current account surplus, how have the capital outflows

been invested?

5. Pick a country and search the internet for newspaper or magazine articles that contain

information related to the balance of payments of the country and corresponding movements in

the foreign exchange value of the country’s currency. Does an unexpectedly large current

account deficit cause the country’s currency to strengthen or weaken on the foreign exchange

market?

6. What are the effects on the British balance of payments of the following set of transactions?

U.K. Videos imports £24 million of movies from the U.S. firm Twenty-First Century Wolf

(TFCW). The payment is denominated in pounds, is drawn on a British bank, and is deposited

in the London branch of a U.S. bank by TFCW because TFCW anticipates purchasing a film

studio in the United Kingdom in the near future.

Answer: The import of movies is a debit of £24 million on the British balance of payments. The

offsetting credit is the increase in foreign ownership of British assets – the increase in the TFCW

bank account in London of £24 million.

7. What are the effects on the French balance of payments of the following set of transactions? Les

Fleurs de France, the French subsidiary of a British company, The Flowers of Britain, has just

received €4.4 million of additional investment from its British parent. Part of the investment is

a €0.9 million computer system that was shipped from Britain directly. The €3.5 million

remainder was financed by the parent by issuing euro denominated Eurobonds to investors

outside of France. Les Fleurs de France is holding these euros in its Paris bank account.

Answer: The €4.4 million of additional investment from the British parent to the French subsidiary is

an increase in the foreign ownership of French assets, which is a credit on the French balance of

payments. There is an import of €0.9 million for the computer system that is a debit on the French

balance of payments. The remaining €3.5 million, corresponding to the funds that were borrowed

abroad by Flowers of Britain and are now being held by Fleur de France, represents a decrease in

foreign ownership of French assets.

French BOP Credit Debit

Increase in the direct foreign ownership of French assets

by Flowers of Britain

(Capital account; French Capital inflow)

€4.4 million

Computer system that was shipped from Britain to France

(Current account; French import)

€0.9 million

Decrease in Foreign ownership of French assets by

Flowers of Britain

(Capital account; French Capital outflow)

€3.5 million



10

8. In December 1994, a major earthquake rocked Kobe, Japan, destroying the housing stock of

more than 300,000 people and ruining bridges, highways, and railroad tracks. What impact, if

any, do you think this event had on the Japanese current account deficit? Why?

Answer: This major disaster destroys capital and infrastructure and causes an increase in desired

investment spending relative to income. It is likely that the earthquake reduces the economy’s ability

to produce income and that wealth falls leading to a reduction in consumption spending. Private

savings will likely fall as people try to maintain their standard of living. It is also likely that the

government reacts by increases spending on infrastructure without increasing taxes. Thus, overall

investment should rise relative to savings, and there should be less of a current account surplus.

9. After running high current account surpluses in the second half of the 1980s, Germany ran

sizable deficits in the early 1990s. The most important reason for the current account deficit

was the surge in demand from eastern Germany after reunification, causing imports to rise

sharply. At the same time, Germany went from being a net creditor country to being a net

debtor. Explain why this is a logical implication of the current account deficits. Interest rates in

Germany were historically high during this period. Why might that have been the case? Could

East Germany have been developed without running a current account deficit? How?

Answer: The reunification of Germany caused a surge in demand because the public and private

capital stock of East Germany was well below western standards. To equip the whole country with

better capital required massive investment spending. The country could have cut its consumption and

shifted its purchases to investment goods, but this would not have been logical. Instead, the country

maintained its consumption level and borrowed from abroad to finance the increased investment

spending. The high interest rates attract foreign capital and serve to ration the investment projects.

The current account deficits also implied that Germany increased its debts to the rest of the world,

eventually moving from a net creditor position to a net debtor position. (Recall that the change in net

foreign assets equals the current account balance.)


Chapter 5 Exchange Rate Systems

QUESTIONS

1. How can you quantify currency risk in a floating exchange rate system?

Answer: To characterize the risk of a currency position, you must try to characterize the

conditional distribution of the future exchange rate changes. With floating exchange rates,

historical information provides useful information about this distribution. For example, you

can use data to measure the average historical dispersion (standard deviation or volatility) of

the distribution. The higher this volatility, the riskier are positions in this currency. It is also

possible to rely on more forward-looking information using the options markets (see Chapter

20). Finally, we should point out that volatility is an adequate indicator of risk when

exchange rate changes are approximately normally distributed. In reality, the distribution of

exchange rate changes displays fat tails, even in floating exchange rate systems, and this

increases the risk of currency positions.

2. Why might it be hard to quantify currency risk in a target zone system or a pegged

exchange rate system?

Answer: If the peg or target zone holds for a long time, historical volatility appears to be zero

or very limited, but this may not accurately reflect underlying tensions that may ultimately

result in a devaluation or revaluation of the currency. Hence, the true currency risk does not

show up in day-to-day fluctuations of the exchange rate. It is hard to quantify this “latent

volatility.”

3. What is likely to be the most credible exchange rate system?

Answer: Among fixed exchange rate systems, a monetary union with a common currency is

likely the most credible exchange rate system. But even here, we see tensions within the

Economic and Monetary Union in Europe that could lead to a breakup of the euro. The

inability of Greece and the other peripheral countries to devalue their currencies is leading to

a protracted period of high unemployment with associated fiscal deficits and an inability to

regenerate growth. Ultimately, one of the problem countries might withdraw from the EMU

or the strong countries, like Germany and Finland, might withdraw rather than subsidize their

inefficient neighbors.

4. How can a central bank create money?

Chapter 5: Exchange Rate Systems

©2012 Pearson Education, Inc

2

Answer: First, because the central bank operates the only authorized printing press in the

country, it can actually print money to pay its bills or to acquire assets, thereby increasing the

money supply. Second, the central bank can create money by increasing the reserve accounts

financial institutions hold with it. For example, if the central bank buys an asset (a

government bond say) from a financial institution, it credits the financial institution’s reserve

account at the central bank for the purchase price of the bond. Because this financial

institution can now use this credit to its account to lend money to individuals and businesses,

the central bank has, essentially, created money.

5. What are official international reserves of the central bank?

Answer: Official reserves consist of three major components: foreign exchange reserves, gold

reserves, and IMF-related reserve assets, with the first being by far the most important

component. Foreign exchange reserves are all the foreign currency denominated assets the

central bank holds, and mostly consist of foreign government bonds.

6. What is likely to happen if a central bank suddenly prints a large amount of new

money?

Answer: Whereas there are theories that predict that changes in the supply of money have

real effects on the economy in the short run, it is likely that if the central bank showers the

economy suddenly with money, the only result will be higher inflation. This is because the

demand for money ultimately depends on the amount of real transactions in the economy and

how much money is needed to facilitate these transactions. Additional supply of money is

unlikely to make people consume more or work harder.

7. What is the effect of a foreign exchange intervention on the money supply? How can a

central bank offset this effect and still hope to influence the exchange rate?

Answer: When a central bank buys (sells) foreign currency, its international reserves increase

(decrease), and the money supply increases (decreases) simultaneously. To offset the effect

on the money supply, the foreign exchange intervention can be sterilized; that is, the central

bank can perform an open market operation that counteracts the effect on the money supply

of the original foreign exchange intervention. The direct effects of a sterilized intervention

are two-fold. First, it forces a portfolio shift on private investors, by replacing foreign bonds

with domestic bonds (or vice versa). This may affect expectations and prices. Second, the

actions of the central bank in the foreign exchange markets, while very small relative to the

nominal trading volumes, may still manage to squeeze foreign exchange inventories at dealer

banks and generate pricing effects. Indirectly, the central bank can signal its opinion on the

fundamental value of the exchange rate through an intervention that consequently affects

market expectations. There is no consensus on how effective sterilized interventions are in

affecting the level and volatility of exchange rates.



3

8. How can a central bank peg the value of its currency relative to another currency?

Answer: To peg the value of its currency to another currency, the government must make a

market in the two currencies. If there is excess supply of the foreign currency (which is

equivalent to excess demand for the domestic currency) that would drive down the domestic

currency price of the foreign currency, the government must buy the private excess supply of

foreign currency and deliver domestic currency to those demanding it. On the contrary, if

there is excess demand for foreign currency (which is equivalent to excess supply of

domestic currency) that would drive up the domestic currency price of the foreign currency,

the government must supply the foreign currency and demand the domestic currency to

prevent the foreign currency from appreciating in value.

9. Describe two channels through which foreign exchange interventions may affect the

value of the exchange rate.

Answer: There is a direct and an indirect channel. As indicated in question 7, the direct effect

of forex purchases or sales is likely small, because trading volumes are so large in the forex

market, but there may be some short-term effects if the inventories of dealer banks are

adversely affected by the intervention. If not sterilized, interventions affect the money

supply, but that effect too, is likely to be small relative to the size of the money supply. The

indirect channel refers to the fact that an intervention can alter peoples’ expectations and

affect their investments, thus helping to push the exchange rate in the direction the central

bank desires. For example, the intervention may be a signal to the public of the central bank’s

monetary policy intentions, or it may signal the central banks inside information about future

market fundamentals, or it may signal to investors that a currency’s exchange rate is

deviating too far from its long-run equilibrium value. The signal is costly and therefore

potentially more credible, because if the central bank is wrong and, for example, buys an

“undervalued” currency, which keeps depreciating, the intervention will lose money.

10. What was the Bretton Woods currency system?

Answer: In the Bretton Woods System, in place between 1944 and 1971, the participating

countries agreed to an exchange rate regime that linked their exchange rates to the dollar.

They could fluctuate in a 1% band around a fixed parity. The dollar itself had a fixed gold

parity ($35 per ounce). When a country ran into a temporary balance of payments problem (a

current account deficit) that threatened the currency peg, it could draw on the lending

facilities of the IMF, also established at Bretton Woods in 1944, to help it defend the

currency. Countries were also allowed to change their parities when their balances of

payments were considered to be in “fundamental disequilibrium.” The system broke down

when President Nixon abandoned the U.S. commitment to exchange dollars for gold in

August 1971.



4

11. How do developing countries typically manage to keep currencies pegged at values that

are too high? Who benefits from such an overvalued currency? Who is hurt by an

overvalued currency?

Answer: Such a situation is difficult to maintain, because if the exchange rate overvalues the

local currency on the foreign exchange markets, there will be an excess supply of the local

currency—everybody will want to turn in local currency to the central bank, receive foreign

currencies, and invest them abroad. If this situation persists, the central bank’s foreign

reserves will dwindle quite fast. The only way to sustain such a system is to impose exchange

controls. The central bank of the developing country must ration the use of foreign exchange,

manage who gets access to it, and restrict capital flows; in short, it must strictly control

financial transactions involving foreign currencies. That currencies of developing countries

are primarily traded by the central bank of the country or by a number of financial

institutions with strict controls on their use of foreign currency (i.e. the currencies are

inconvertible), is helpful to maintain such a system.

It is clear who benefits and who loses from this situation. The fixed exchange rate

undervalues the foreign currency and overvalues the domestic currency, thereby subsidizing

buyers of foreign currency (such as importers and those investing abroad) and taxing sellers

of foreign exchange (such as exporters and foreign buyers of domestic assets). Not

surprisingly, one main reason for the popularity of over-valued exchange rates is that such

situations increase the external purchasing power of the political elite.

12. What are the potential benefits of a pegged currency system?

Answer: Some believe that fixed exchange rate systems bring with it policy discipline and

stability. A fixed exchange rate should discourage over-expansionary fiscal or monetary

policies, which would cause inflation and a loss of competitiveness under a fixed exchange

rate system. Hence, fixed exchange rates should induce the kind of policies that help control

inflation. The absence of day-to-day exchange rate volatility in such a system should

eliminate the uncertainty that comes with floating exchange rates and which might hamper

international trade. Note that the argument that exchange rate volatility hampers international

trade is far from generally accepted. For example, it ignores the possibility to hedge currency

fluctuations. Moreover, pegged exchange rate systems are not without risks, and may show

considerable “latent variability,” see Question 2. Such devaluation risk also complicates

international trade.

13. Describe two different currency systems that have been introduced in countries such as

Hong Kong and Ecuador to improve the credibility of pegged exchange rate systems.

Answer: Hong Kong has a currency board system. A currency board is a monetary institution

that issues base money (notes and coins, and required reserves of financial institutions) that is

fully backed by a foreign reserve currency and fully convertible into the reserve currency at a

fixed rate and on demand. Hence, the domestic currency monetary base is 100% backed by



5

assets payable in the reserve currency. In practical terms, this requirement bars the currency

board from extending credit to either the government or the banking sector. Ecuador instead

has officially adopted the U.S. dollar as its currency. This is an example of (“Official”)

dollarization, which occurs when a foreign currency has exclusive or predominant status as

full legal tender in a particular country.

14. What is the difference between a target zone and a crawling peg?

Answer: In a target zone, the currency is allowed to fluctuate in a percentage band around a

“central value.” One can view a pegged system as a target zone system with a very narrow

band. In a crawling peg system, the fixed rate or band is adjusted over time, typically in a

pre-determined way as a function of the inflation differential between the crawling peg

country and the country to whose currency the peg is set. Such a system is often used in

developing countries, where the “crawl” of the band prevents the country from losing too

much competitiveness when its inflation rate is higher than that of the benchmark country.

15. How can central banks defend their currency—for example, if the currency is within a

target zone or pegged at a particular value?

Answer: The monetary authorities in the countries with weaker currencies have three basic

defense mechanisms available: interventions, interest rate increases, and capital controls.

Interventions (see Questions 7 and 9) to support the local currency may result (when not

sterilized) in a lower money supply, reduced liquidity in the money market, and therefore

higher interest rates. Central banks can also directly raise the interest rates they control

(typically, the rate at which banks can borrow from the central bank), both to make currency

speculation more costly and to signal commitment to the central rate. Finally, the authorities

can limit foreign exchange transactions through capital controls, which may include taxes on

(or outright prohibition of) the purchases of most foreign securities by the country’s

residents.

16. What was the EMS?

Answer: EMS stands for European Monetary System, a target zone system that operated in

Europe between 1979 and 1999. Exchange rates were, for most of the time, maintained

between bands of 2.25% around central rates. The countries participating in the EMS were a

gradually increasing number of European Union countries.

17. What is a basket currency?

Answer: A basket of currencies is a composite currency consisting of various units of other

currencies. Examples include the ECU (European Currency Unit) in the EMS and the SDR

(Special Drawing Right) of the IMF.



6

18. What did the Maastricht Treaty try to accomplish?

Answer: The 1991 Maastricht Treaty mapped out the road to economic and monetary union

within the European Union to be finalized by 1999. The Treaty called for eliminating all

remaining restrictions on the movement of capital and payments between member states and

between member states and third countries; the creation of a European central bank, and the

introduction of a new currency, the euro, in 1999. The monetary union was indeed

established (but not all EU countries participate).

19. What is an optimum currency area?

Answer: An optimum currency area is an area that balances the microeconomic benefits of

perfect exchange rate certainty against the costs of macroeconomic adjustment problems. The

area is therefore suitable for the introduction of a single currency and monetary union.

Sharing a currency across a border enhances price transparency (that is, makes prices easier

to understand and compare across countries), lowers transactions costs, removes exchange

rate uncertainty for investors and firms, and enhances competition. The potential cost of a

single currency is the loss of independent monetary policies for the participating countries. If

countries experience adverse shocks, such as a sudden fall in demand for a country’s main

export product or a sudden increase in the price of one of the main inputs for a country’s

manufacturing sector, it can no longer stave off a recession or unemployment through

monetary policy actions when it has a common currency. It also cannot devalue its currency

to try to regain competitiveness.

20. Do you believe its monetary union will be beneficial for Europe?

Answer: The gains are already being realized throughout Europe—for example, car prices

have decreased and converged across Europe. Academic research documents sizable

economic benefits following the introduction of the euro in terms of price convergence,

lower costs of capital, and increased trade. For example, the European Commission has

estimated the microeconomic gains of monetary union to amount to 0.5% of GDP of the

entire EU—a substantial sum. On the other hand, the sovereign debt crises in Greece, Ireland,

and Portugal, and potentially in Spain, and the persistent high unemployment rates in these

countries while Germany thrives suggest that asymmetric macroeconomic adjustment costs

are present and are causing strain within Europe.

21. Do you think the euro will survive?

The survival of the euro will depend on the political will of the strong countries to bail out

the weaker countries. It is difficult to image that a weak country will abandon the euro and

reissue its own money. This would surely be quite inflationary and could not be done without



7

also adopting severe capital controls. A more likely scenario is that strong countries decide

that they can no longer afford to bailout the weaker countries, which causes a crisis of

confidence in the European banking system and a call for the reissuance of the Deutsche

mark. Things would have to get very bad before the political process would lead to the

breakdown of the euro.

PROBLEMS

1. Toward the end of 1999, the central bank (Reserve Bank) in Zimbabwe stabilized the

Zimbabwe dollar, the Zim for short, at Z$38/USD and privately instructed the banks to

maintain that rate. In response, at the end of 1999, an illegal market developed wherein

the Zim traded at Z$44/USD. Are you surprised at rumors that claim corporations in

Zimbabwe were “hoarding” USD200 million? Explain.

Answer: The existence of an illegal exchange market indicates that the Zim is incorrectly

valued at Z$38/USD. Clearly, the Zim is over-valued at the official rate (See Exhibit 5.10 for

an example of such a situation). At this “artificial” exchange rate everybody wants to turn in

Zim to the central bank, receive foreign currency and invest them abroad. To maintain the

overvalued rate without losing all its international reserves, the government must control the

use of foreign exchange (impose exchange controls). It likely forces exporters to convert

their foreign exchange at the official rate, which is too low. Given this situation, hoarding

foreign exchange is a rational response. Anyone who earns foreign exchange has an incentive

to hold on to the foreign exchange until the Zim is valued correctly, i.e. after it is devalued.

Moreover, given high inflation in Zimbabwe and a highly unstable political regime, U.S.

dollars are a better store of value than Zimbabwe dollars. The situation in Zimbabwe

subsequently deteriorated into hyperinflation, and the abandonment of the Zim.

2. In Chapter 3, we described how exchange rate risk could be hedged using forward

contracts. In pegged or limited-flexibility exchange rate systems, countries imposing

capital controls sometimes force their importers and exporters to hedge. First,

assuming that forward contracts are to be used, and an exporter has future foreign

currency receivables, what will the government force him to do? Second, how does this

help the government in defending their exchange rate peg?

Answer: Exporters, who have foreign currency receivables, have an incentive to lag the

foreign currency payments (e.g. by giving generous trade credit), if they think their domestic

currency is under pressure and may be devalued. Doing so allows them to potentially profit

from an impending devaluation of the local currency. Of course, extending trade credit

involves an opportunity cost, but the interest rates reflect some probability that the peg will

hold. Hence, if the currency is actually devalued, lagging the payment is beneficial ex-post.

Lagging foreign currency payments causes further pressure on the local currency as

the exporter’s demand for local currency is postponed. A forced hedge would require the

exporter to sell the foreign currency forward for the local currency. Hence, there is

immediate positive demand for the local currency. That the demand is in the forward market



8

is inconsequential. Because of covered interest rate parity, if the forward rate decreases (in

local currency per foreign currency) it would result in lower local interest rates. This is

because the spot rate is fixed and the foreign interest rate is not likely affected. Hence, this

relieves the speculative pressure.

3. In years past, Belgium, a participant of the former EMS, and South Africa operated a

two-tier, or dual, exchange rate market. The two-tier market was abolished in March

1990 in Belgium and in March 1995 in South Africa. Import and export transactions

were handled on the official market, and capital transactions were handled on the

financial market, where the “financial” exchange rate was freely floating. Discuss why

such a system may prevent speculators from profiting when betting on devaluation.

Answer: Speculators will try to profit by buying foreign exchange forward, deposit money in

foreign accounts or buy foreign securities, hoping to repatriate capital after the devaluation

happens. All these transactions imply selling local currencies in the foreign exchange market.

With the double tier market, the “financial” exchange rate immediately reacts to the selling

pressure and the local currency instantly depreciates so that the speculators cannot profit

from their actions. Of course, exporters and importers can still engage in leading and lagging

operations, and they massively did so.

4. The Kuna is the currency of Croatia. Find the web site of Croatia’s central bank, and

determine the exchange rate system Croatia runs? Suppose the Kuna weakens

substantially relative to the euro. Which action can the central bank take to keep its

currency system functioning properly?

Answer: The web site of Croatia’s central bank, called the Croatian National Bank, is at

http://www.hnb.hr/eindex.htm. Under the Tab entitled Exchange Rate List, there is another

Tab entitled About the Exchange Rate. Here is what was written on June 2, 2011:

HOW IS THE KUNA EXCHANGE RATE SET? Croatia implements the exchange rate regime of managed floating, where the

exchange rate of the domestic currency is not fixed against another foreign

currency or basket of currencies, but is rather freely determined by the foreign

exchange market. The exchange rate thus floats depending on the foreign

exchange supply and demand on the foreign exchange market. However, the

Croatian National Bank prevents too excessive exchange rate fluctuations by

occasional market interventions in an attempt to maintain relative stability of the

exchange rate.

Hence, if the currency weakens substantially, the central bank can intervene directly on the

foreign exchange market. It may also increase the domestic interest rate.

http://www.hnb.hr/eindex.htm



9

5. Type “People’s Bank of China” into your favorite search engine and go to the English

versions of the web site. Under “Statistics” find the Balance Sheet of the Monetary

Authority. Calculate the growth rate of base money and the growth rate of

international assets for the last few years. How much foreign exchange intervention is

China doing? Are they sterilizing it?

Answer: The URL for the English version of the People’s Bank of China is

http://www.pbc.gov.cn/publish/english/963/index.html where you will find a Tab entitled

“The Balance Sheet of the Monetary Authority.” The base money supply corresponds to the

row entitled Reserve Money, which is the sum of Currency and Deposits of Financial

Corporations. During 2010, Reserve Money grew by 29.75% from 142,815.58 to 185,311.08

or by 42,491.50, where the units are 100 million yuan. The line labeled Foreign Assets grew

by 14.59% from 188,021.75 to 215,419.60 or by 27,397.85, also in units of 100 million yuan.

The fact that Reserve Money grew by more than Foreign Assets indicates that the foreign

exchange intervention is likely not sterilized.

http://www.pbc.gov.cn/publish/english/963/index.html


Chapter 6

Interest Rate Parity

QUESTIONS

1. Explain the concepts of present value and future value.

Answer: These concepts relate to the time value of money. Because interest rates are positive,

a given amount of money in the future is not worth as much today. If you want to know how

much a future amount of money is worth, you take the present value. This is the amount that

you could borrow against the future amount while using the future amount to pay the interest

plus principal on the loan. Analogously, the future value of an amount of money available

today is the value that would be available in the future if you invested today and received the

principal plus interest on the investment in the future.

2. If the dollar interest rate is positive, explain why the value of $1,000,000 received every

year for 10 years is not $10,000,000 today.

Answer: If you were to borrow against each of the annual $1,000,000 payments, the bank

would lend you progressively smaller amounts. The present value of the 10 payments could

be found by using the spot interest rates, i(t,k), at time t for year t+k in the future. The present

value would be

10

kk=1

$1,000,000PV =

1 + i(t,k)

3. Describe how you would calculate a 5-year forward exchange rate of yen per dollar if

you knew the current spot exchange rate and the prices of 5-year pure discount bonds

denominated in yen and dollars. Explain why this has to be the market price.

Answer: The 5-year forward rate would be equal to the spot rate of yen per dollar times the

ratio of the future value in 5 years of one yen to the future value in 5 years of one dollar. The

logic is the following. If you can invest directly in yen for 5 years, you can convert one yen

into the future value of one yen in 5 years. Alternatively, you can convert the one yen into

dollars in the spot foreign exchange market, invest that dollar principal for 5 years to get the

future value of dollars, and contract today to sell those dollars in the forward market to get

back to future yen in 5 years. If the two amounts of future yen differ, there would be an

Chapter 6: Interest Rate Parity


2

arbitrage available in which you would borrow future yen where they are cheap and invest in

future yen where they are expensive. Hence, the 5 year forward rate should satisfy

5

5

1 + i(t,5,¥)F(t,5,¥/$) = S(t,¥/$) ×

1 + i(t,5,$)

4. If interest rate parity is satisfied, there are no opportunities for covered interest

arbitrage. What does this imply about the relationship between spot and forward

exchange rates when the foreign currency money market investment offers a higher

return than the domestic money market investment?

Answer: If the foreign currency money market investment offers a higher return (in the

foreign currency) than the domestic money market investment, the foreign currency must be

at a discount in terms of the domestic currency in the forward market. The forward discount

locks in a capital loss when the transaction exchange risk is offset, which reduces the higher

return of the foreign currency back to the lower return offered in the domestic money market.

5. It is often said that interest rate parity is satisfied when the differential between the

interest rates denominated in two currencies equals the forward premium or discount

between the two currencies. Explain why this is an imprecise statement when the

interest rates are not continuously compounded.

Answer: Interest rate parity requires the equality of returns from investing directly in the

domestic money market versus converting domestic currency into foreign currency, investing

the foreign currency, and selling the foreign currency forward. Symbolically, we have

1

1 + i(t,DC) = × 1 + i(t,FC) × F(t,DC/FC)S(t,DC/FC)

If we divide by 1 + i(t,FC) on both sides and subtract one from both sides, we get

i(t,DC) - i(t,FC) F(t,DC/FC) - S(t,DC/FC)

= 1 + i(t,FC) S(t,DC/FC)

The left-hand side is the interest differential between the domestic and foreign rates adjusted

for the denominator term and the right-hand side is the forward premium or discount on the

foreign currency in terms of the domestic currency.

6. What do economists mean by the external currency market?

Answer: The external currency market is an interbank market for deposits and loans that are

denominated in currencies that are not the currency of the country in which the bank is

operating. Its settlement procedures are identical to those of the foreign exchange market.

The first currency for which these deposits and loans began to trade was the dollar, and the



3

deposits were called Eurodollars because they were dollar-denominated deposits at European

banks. The market for other currencies came to be called the Eurocurrency market, even

though the trading might be done in Asia or the Americas. With the advent of the euro as a

currency, the term external currency market seems less confusing.

7. What determines the bid–ask spread in the external currency market? Why is it usually

so small?

Answer: The bid-ask spread in the external currency market is the difference between the bid

rate, which is the interest rate that the bank pays on its deposits and the ask rate, which is the

interest rate that the bank charges on its loans. The market is very competitive, and the bid-

ask spreads are small. The reason is because the banks accepting the deposits and making the

loans are subject only to the regulations of the government of the country in which the bank

is operating, not the government of the country that issues the money in which the deposits

and loans are denominated. These regulations include how much banks must keep on reserve

with their nation’s central bank. Because reserve requirements are often lower for foreign

currency deposits than for domestic currency deposits, banks can lend out a larger part of

these deposits. Thus, the foreign currency deposits are potentially more profitable.

8. Explain why the absence of covered interest arbitrage possibilities can be characterized

by two inequalities in the presence of bid–ask spreads in the foreign exchange and

external currency markets.

Answer: Because there are bid-ask spreads in the foreign exchange market and in the external

currency market, we do not convert from one currency to another at the same spot or forward

exchange rates, and we do not borrow at the same rate at which we lend. The absence of

covered interest arbitrage therefore is characterized by two inequalities. We cannot profit by

borrowing the domestic currency (at the ask domestic interest rate), converting to the foreign

currency (at the ask spot rate of domestic currency per unit of foreign currency), lending the

foreign currency (at the foreign bid interest rate), and converting to the domestic currency in

the forward market (at the bid forward rate of domestic currency per unit of foreign

currency). Similarly, we cannot profit by borrowing the foreign currency (at the ask foreign

interest rate), converting to domestic currency (at the bid spot rate of domestic currency per

unit of foreign currency), lending the domestic currency (at the domestic bid interest rate),

and converting to the foreign currency forward (at the ask forward rate of domestic currency

per unit of foreign currency).

9. Describe the sequence of transactions required to do a covered interest arbitrage out of

Japanese yen and into U.S. dollars.

Answer: To do a covered interest arbitrage out of Japanese yen and into U.S. dollars, one

would borrow yen from the bank at the bank’s ask interest rate. You would owe interest on

the yen and would have to return the yen principal at the end of the investment horizon. You



4

would then convert the yen principal into dollars at the ask spot exchange rate of yen per

dollar. You would pay the ask rate because you are buying dollars from the bank with yen.

You would then invest the dollar principal at the bank’s bid dollar interest rate. Because you

would know how much the dollar interest plus principal would be at the end of the

investment horizon, you would contract to sell that amount of dollars forward for yen. This

forward contract would be made at the bank’s forward bid rate of yen per dollar. If the

amount of yen that you get from the forward contract exceeds the amount of yen that you

owe the bank from the initial borrowing, you have successfully done a covered interest

arbitrage.

10. Suppose you saw a set of quoted prices from a U.S. bank and a French bank such that

you could borrow dollars, sell the dollars in the spot foreign exchange market for euros,

deposit the euros for 90 days, and make a forward contract to sell euros for dollars and

make a guaranteed profit. Would this be an arbitrage opportunity? Why or why not?

Answer: It could be an arbitrage opportunity, but it could also reflect the fact that

counterparty risk differs across banks. It may be that the market knows that the default risk of

the French bank is higher than other banks, which has induced the French bank to increase its

promised deposit rates above rates charged by other banks with lower default risk. The

perceived arbitrage opportunity would be illusory in this case.

11. The interest rates on U.S. dollar–denominated bank accounts in Mexican banks are

often higher than the interest rates on bank accounts in the United States. Can you

explain this phenomenon?

Answer: Mexico has periodically gotten into balance of payments difficulties and suffered

severe depreciations of the peso. During these periods of crisis, the Mexican government

converted dollar-denominated bank deposits into peso-denominated accounts at exchange

rates that were unfavorable to the depositor, effectively expropriating some of an investor’s

principal. If there is a possibility of this type of risk or just higher default risk by the Mexican

banks than at U.S. banks, the higher dollar-denominated Mexican deposit rates would be

required to induce depositors to invest in Mexican banks.

12. What is a money market hedge? How is it constructed?

Answer: In a money market hedge you offset the underlying transaction exchange risk with

borrowing or lending in the foreign money market rather than with a forward market

transaction. For example, if the underlying business transaction gives you a liability in

foreign currency, you can borrow domestic currency, convert the principal from the

borrowing into foreign currency, and invest the foreign currency thereby acquiring a foreign

currency asset that is equivalent in value to the underlying foreign currency liability. You

would want to borrow an amount of domestic currency equal to the present value of the

foreign currency liability when converted at the spot exchange rate.



5

13. Suppose you are the French representative of a company selling soap in Canada.

Describe your foreign exchange risk and how you might hedge it with a money market

hedge.

Answer: As a French company, you are interested in euro profits. Selling soap in Canada will

give you Canadian dollar revenues. The euro value of these Canadian dollar revenues will

fall in value if the Canadian dollar weakens relative to the euro. To offset this loss in value,

your company should borrow in Canadian dollars.

14. What is a pure discount bond?

Answer: A pure discount bond only has one cash flow at the maturity of the bond. Hence, the

bond’s price is less than its face value, and this discount of the price from the face value

provides the return to holding the bond.

15. What is the term structure of interest rates? How are spot interest rates determined

from coupon bond prices?

Answer: The term structure of interest rates is the relation between the maturities of bonds

and the pure discount bond yields, which are the spot interest rates for the various maturities.

At the shortest maturities, one typically has spot interest rates from pure discount bond

prices. One can then begin to use coupon bonds at longer maturities, discounting the early

coupons at the known spot interest rates for those maturities and determining the final spot

interest rate by finding the discount rate such that discounting the final coupon and principal

payment provides a present value equal to the bond price minus the present value of the

intervening coupon payments.

16. How does a coupon bond’s yield to maturity differ from the spot interest rate that

applies to cash flows occurring at the maturity of the bond? When are the two the

same?

Answer: A coupon bond’s yield to maturity is the internal rate of return that sets the present

value of the promised coupon payments and principal payment equal to the bond price. The

yield to maturity is therefore a kind of average of the spot interest rates at various maturities.

The yield to maturity equals the spot interest rates at various maturities only when the term

structure of interest rates is flat, that is, when the spot interest rates at various maturities are

all identical.



6

PROBLEMS

1. In the entry forms for its contests, Publisher’s Clearing House states, “You may have

already won $10,000,000.” If the Prize Patrol visits your house to inform you that you

have won, it offers you $333,333.33 each and every year for 30 years. If the interest rate

is 8% p.a., what is the actual present value of the $10,000,000 prize?

Answer: The present value of 30 annual payments of $333,333.33 when discounted at 8% is 30

1

$333,333.33$3,752,594.41

1.08kk

This value can be found in Excel by using the function NPV(rate, cashflows), where rate =

8% and cashflows refers to a sequence of 30 cells that all have the value $333,333.33.

2. Suppose the 5-year interest rate on a dollar-denominated pure discount bond is 4.5%

p.a., whereas in France, the euro interest rate is 7.5% p.a. on a similar pure discount

bond denominated in euros. If the current spot rate is $1.08/€, what is the value of the

forward exchange rate that prevents covered interest arbitrage?

Answer: We know that the 5-year forward rate must satisfy

5 5

5 5

1+i(t,5,$) 1.045F(t,5,$/€) = S(t,$/€)× = $1.08/€ × = $0.9375/€

1.0751+i(t,5,€)

3. Carla Heinz is a portfolio manager for Deutsche Bank. She is considering two

alternative investments of EUR10,000,000: 180-day euro deposits or 180-day Swiss

francs (CHF) deposits. She has decided not to bear transaction foreign exchange risk.

Suppose she has the following data: 180-day CHF interest rate, 8% p.a., 180-day EUR

interest rate, 10% p.a., spot rate EUR1.1960/CHF, 180-day forward rate,

EUR1.2024/CHF. Which of these deposits provides the higher euro return in 180 days?

If these were actually market prices, what would you expect to happen?

Answer: The euro return to investing directly in euros is 180

5% 10%360

, so the euros

available in 180 days is EUR10,000,000 1.05 = EUR10,500,000. Alternatively, the

EUR10,000,000 can be converted into Swiss francs at the spot rate of EUR1.1960/CHF. The

Swiss francs purchased would equal EUR10,000,000 / EUR1.1960/CHF = CHF8,361,204.

This amount of Swiss francs can be invested to provide a 180

4% 8%360

return over the

next 180 days. Hence, interest plus principal on the Swiss francs is CHF8,361,204 1.04 =

CHF8,695,652. If we sell this amount of Swiss francs forward for euros at the 180-day

forward rate of EUR1.2024/CHF, we get a euro return of CHF8,695,652 EUR1.2024/CHF

= EUR10,455,652. This is less than the return from investing directly in euros.



7

If these were the actual market prices, you should expect investors to do covered interest

arbitrages. Investors would borrow Swiss francs, which would tend to drive the CHF interest

rate up; they would sell the Swiss francs for euros in the spot foreign exchange market,

which would tend to lower the spot rate of EUR/CHF; they would deposit euros, which

would tend to drive the EUR interest rate down; and they would contract to buy CHF with

EUR in the 180-day forward market, which would put upward pressure on the forward rate of

EUR/CHF. Each of these actions would help bring the market back to equilibrium.

4. If the 30-day yen interest rate is 3% p.a., and the 30-day euro interest rate is 5% p.a., is

there a forward premium or discount on the euro in terms of the yen? What is the

magnitude of the forward premium or discount?

Answer: We know that the high interest rate currency must sell at a forward discount when

priced in the low interest rate currency to prevent a covered interest arbitrage. Therefore the

euro is at a discount in the forward market. To determine the magnitude of the discount,

recognize that interest rate parity requires equality of the return to investing in yen versus

converting the yen principal into euros, investing the euros, and selling the euro principal

plus interest in the forward market for yen:

1

1 + i(¥) = × 1 + i(€) × F(¥/€)S(¥/€)

Solving this expression for the forward premium, we find

F(¥/€) - S(¥/€) i(¥) - i(€)

= S(¥/€) 1 + i(€)

The de-annualized interest rates are 0.0025 = (3/100) (30/360) for the yen and

0.004167 = (5/100) (30/360) for the euro. The right-hand side of the above expression is

therefore -0.00166. The annualized value is -0.00166 (100) (360/30) = -1.99%. We

therefore say that the euro sells at an annualized discount of 1.99%.

5. Suppose the spot rate is CHF1.4706/$ in the spot market, and the 180-day forward rate

is CHF1.4295/$. If the 180-day dollar interest rate is 7% p.a., what is the annualized

180-day interest rate on Swiss francs that would prevent arbitrage?

Answer: Interest rate parity requires equality of the return to investing in CHF versus

converting the CHF principal into dollars, investing the dollars, and selling the dollar

principal plus interest in the forward market for CHF:

1

1 + i(CHF) = × 1 + i($) × F(CHF/$)S(CHF/$)

If we de-annualize the dollar interest rate, we find that the 180 day interest rate is 0.035.

Hence, the Swiss franc interest rate that prevents arbitrage is

1i(CHF) = × 1.035 × CHF1.4295/$ - 1 = 0.0061

CHF1.4706/$



8

If we annualize this value, we find 0.0061 (100) (360/180) = 1.21%.

6. As a trader for Goldman Sachs you see the following prices from two different banks:

1-year euro deposits/loans: 6.0% – 6.125% p.a.

1-year Malaysian ringgit deposits/loans: 10.5% – 10.625% p.a.

Spot exchange rates: MYR 4.6602 / EUR – MYR 4.6622 / EUR

1-year forward exchange rates: MYR 4.9500 / EUR – MYR 4.9650 / EUR

The interest rates are quoted on a 360-day year. Can you do a covered interest

arbitrage?

Answer: We need to check the two inequalities that characterize the absence of covered

interest arbitrage. In the first, we will borrow euros at 6.125%, convert to ringgits in the spot

market at MYR4.6602 / EUR, invest the ringgits at 10.5%, and sell the ringgit principal plus

interest forward for euros at MYR4.9650 / EUR. We find that

MYR4.6602 11.06125 > × 1.105 × = 1.0372

EUR MYR4.9650/EUR

Thus, it is not profitable to try to arbitrage in this direction as the amount that we would

owe is greater than the amount that we would gain.

Let’s try the other direction, arbitraging out of ringgits into euros and covering the

foreign exchange risk. We will borrow ringgits at 10.625%, convert to euros in the spot

market at MYR4.6622 / EUR, invest the euros at 6.0%, and sell the euro principal plus

interest forward for ringgits at MYR4.9500 / EUR. We find that

1 MYR4.95001.10625 < × 1.06 × = 1.1254

MYR4.6622/EUR EUR

Thus, there is a possible arbitrage opportunity because the amount that we owe from

borrowing ringgits is less than the amount that we gain by converting from ringgits to euros,

investing the euros, and covering the transaction exchange risk with a forward sale of euros

for ringgits.

7. As an importer of grain into Japan from the United States, you have agreed to pay

$377,287 in 90 days after you receive your grain. You face the following exchange rates

and interest rates: spot rate, ¥106.35/$, 90-day forward rate ¥106.02/$, 90-day USD

interest rate, 3.25% p.a., 90-day JPY interest rate, 1.9375% p.a.

a. Describe the nature and extent of your transaction foreign exchange risk.

Answer: As a Japanese grain importer, you are contractually obligated to pay $377,287 in

90 days. Any weakening of the yen versus the dollar will increase the yen cost of your

grain. The possible loss is unbounded.



9

b. Explain two ways to hedge the risk.

Answer: You could hedge your risk by buying dollars forward at ¥106.02/$.

Alternatively, you could determine the present value of the dollars that you owe and buy

that amount of dollars today in the spot market. You could borrow that amount of yen to

avoid having to pay today.

c. Which of the alternatives in part b is superior?

Answer: If you do the forward hedge, you will have to pay

¥106.02/$ $377,287 = ¥39,999,967.74

in 90 days. If you do the money market hedge, you first need to find the present value of

$377,287 at 3.25%. The de-annualized interest rate is (3.25/100) (90/360) = 0.008125.

Thus, the present value is

$377,287 / 1.008125 = $374,246.25

Purchasing this amount of dollars in the spot market costs

¥106.35/$ $374,246.25 = ¥39,801,088.69

To compare this value to the forward hedge, we must take its future value at 1.9375% p.a.

The de-annualized interest rate is (1.9375/100) (90/360) = 0.00484375, and the future

value is

¥39,801,088.69 (1.00484375) = ¥39,993,875.21

The cost of the money market hedge is essentially the same as the cost of the forward

hedge because interest rate parity is satisfied.

8. You are a sales manager for Motorola and export cellular phones from the United

States to other countries. You have just signed a deal to ship phones to a British

distributor. The deal is denominated in pounds, and you will receive £700,000 when the

phones arrive in London in 180 days. Assume that you can borrow and lend at 7% p.a.

in U.S. dollars and at 10% p.a. in British pounds. Both interest rate quotes are for a

360-day year. The spot exchange rate is $1.4945/£, and the 180-day forward exchange

rate is $1.4802/£.

a. Describe the nature and extent of your transaction foreign exchange risk.

Answer: As a U.S. exporter, you have a contract to receive £700,000 in 180 days. Any

weakening of the pound versus the dollar will decrease the dollar value of your pound-

denominated receivable. Large losses are possible as the dollar value could go to zero,

although that is highly unlikely.



10

b. Describe two ways of eliminating the transaction foreign exchange risk.

Answer: You could hedge by selling pounds forward for dollars. Alternatively, you could

do a money market hedge in which you borrow the present value of the pounds, and

convert the loan principal to dollars in the spot market, and then use the pound receivable

to pay off the interest plus principal on the loan at maturity.

c. Which of the alternatives in part b is superior?

Answer: The forward hedge gives

$1.4802/£ £700,000 = $1,036,140

in 180 days. The money market hedge requires the present value of the £700,000. The

interest rate is (10/100) (180/365) = 0.0493. Thus, the present value is

£700,000 / 1.0493 = £667,111.41

The dollar value of this is

$1.4945/£ £667,111.41 = $996,998

To compare this to the forward hedge we must take its future value at 7% p.a. The

interest rate is (7/100) (180/360) = 0.035. Therefore the future value is

$996,998 1.035 = $1,031,892.93

The forward hedge provides slightly more dollar revenue.

d. Assume that the dollar interest rate and the exchange rates are correct. Determine

what sterling interest rate would make your firm indifferent between the two

alternative hedges.

Answer: We know that if interest rate parity is satisfied, the money market hedge and the

forward hedge will provide the same revenue. The pound interest rate that satisfies

interest rate parity is

1

1 + i(£) = S($/£) × 1 + i($) × F($/£)

The value of the right-hand side is $1.4945/£ 1.035 / $1.4802/£ = 1.0450. Thus the

annualized pound interest rate that would make the firm indifferent between the forward

hedge and the money market hedge is 0.0450 100 (365/180) = 9.12%.

9. Suppose that there is a 0.5% probability that the government of Argentina will

nationalize its banking system and freeze all foreign deposits indefinitely during the



11

next year. If the dollar deposit interest rate in the United States is 5%, what dollar

interest would Argentine banks have to offer in order to attract deposits from foreign

investors?

Answer: If the freezing of deposits is an idiosyncratic event, then the expected value of the

return should equal the risk free return of 5%. If investors effectively get a return of zero with

0.5% probability, they must get a return of (1 + X%) with 99.5% probability, such that

[(1 + X%) 0.995] + [0 0.005] = 1.05

When we solve this equation for X%, we find X% = 5.53%. Of course, the more that you

eventually recover in the event of a freeze of deposits, the smaller the interest rate can be.

10. Suppose the market price of a 20-year pure discount bond with a face value of $1,000 is

$214.55. What is the spot interest rate for the 20-year maturity expressed in percentage

per annum?

Answer: We know that the relationship between the price of a pure discount bond and the

spot interest rate at the 20 year maturity satisfies

20

$1,000P(t) =

1 + i(t,20)

Substituting the price of $214.55 and solving for i(t,20), we find 1/20

$1,000i(t,20) = - 1 = 0.08

$214.55

Therefore, the spot interest rate for the 20-year maturity expressed in percentage per annum

is 8%.

11. Consider a 2-year euro-denominated bond that has a current market price of €970, a

face value of €1,000, and an annual coupon of 5%. Suppose the 1-year euro-

denominated spot interest rate is 5.5%. What is the 2-year euro-denominated spot

interest rate?

Answer: The present value of a coupon paying bond is found by discounting each annual

coupon and the final principal payment at the appropriate spot interest rates for those

maturities. Thus, to find the 2-year euro-denominated spot interest rate we must solve for the

two-period spot interest rate in the following equation:

2

€50 €1050€970 = +

1.055 1+i(t,2)

The answer is i(t,2) = 6.68%.



12

12. Consider some data drawn from Exhibit 6.5. The 1-year rates can be viewed as spot

interest rates, and the 2-year rates are yields to maturity in annualized percent. The

spot exchange rate is ¥132.192/£.

U.K. Japan

1 year 1.105 0.370

2 year 1.770 0.430

What should be the 2-year forward rate to prevent arbitrage?

Answer: We know that if the coupon on a bond is equal to the yield to maturity on the bond, then

the bond is selling for face value. Therefore,without loss of generality, we assume that a two-

year coupon bond has a coupon of 1.77% in the U.K. and 0.43% in Japan. Thus, in the U.K. the

two-year spot interest rate satisfies

2

0.0177 1.01771

(1 0.01105) (1 (2))i

Solving for i(2) gives 0.01776. Doing the same for the yen, we have

2

0.0043 1.00431

(1 0.0037) (1 (2))i

Solving for i(2) gives 0.004301. Hence, the 2-year forward rate that prevents arbitrage would

satisfy

2

2

¥132.192 1.004301 ¥128.719( ,2)

£ 1.01776 £F t

13. Go to the website of the British Bankers’ Association (BBA). Find out which banks are

on the panel for the dollar, the euro, the yen and the Australian dollar.

Answer: The information can be found at http://www.bbalibor.com/panels/. The composition of

the panels on June 2, 2011 was the following:

US Dollar Panel

Please find a complete list below for all the 20 banks that currently contribute to the fixing of US Dollar bbalibor. This panel was last reviewed in November 2010.

Bank of America Bank of Nova Scotia

http://www.bbalibor.com/panels/



13

Bank of Tokyo-Mitsubishi UFJ Ltd Barclays Bank plc BNP Paribas Citibank NA Credit Agricole CIB Credit Suisse Deutsche Bank AG HSBC JP Morgan Chase Lloyds Banking Group Rabobank Royal Bank of Canada Société Générale Sumitomo Mitsui Banking Corporation The Norinchukin Bank The Royal Bank of Scotland Group UBS AG West LB AG

Euro Panel

Please find a complete list below for all the 16 banks that currently contribute to the fixing of Euro bbalibor. This panel was last reviewed in November 2010.

Abbey National plc Bank of Tokyo-Mitsubishi UFJ Ltd Barclays Bank plc Citibank NA Credit Suisse Deutsche Bank AG HSBC JP Morgan Chase Lloyds Banking Group Mizuho Corporate Bank Rabobank Royal Bank of Canada Société Générale The Royal Bank of Scotland Group UBS AG West LB AG

Japanese Yen Panel

Please find a complete list below for all the 16 banks that currently contribute to the fixing of Japanese Yen bbalibor. This panel was last reviewed in November 2010.



14

Bank of Tokyo-Mitsubishi UFJ Ltd Barclays Bank plc Citibank NA Credit Agricole CIB Deutsche Bank AG HSBC JP Morgan Chase Lloyds Banking Group Mizuho Corporate Bank Rabobank Société Générale Sumitomo Mitsui Banking Corporation The Norinchukin Bank The Royal Bank of Scotland Group UBS AG West LB AG

Australian Dollar Panel

Please find a complete list below for all the 8 banks that currently contribute to the fixing of Australian Dollar bbalibor. This panel was last reviewed in November 2010.

Barclays Bank plc Commonwealth Bank of Australia Deutsche Bank AG JP Morgan Lloyds Banking Group National Australia Bank Ltd The Royal Bank of Scotland Group UBS AG

Only Barclays Bank, Deutsche Bank AG, JP Morgan Chase, Lloyds Banking Group, The Royal Bank of Scotland, and UBS AG are on all four panels.


Chapter 8 Purchasing Power Parity and Real

Exchange Rates

QUESTIONS

1. What does the purchasing power of a money mean? How can it be measured?

Answer: The purchasing power of a money is also known as its real value and indicates the

amount of goods and services that can be purchased with a given amount of the money. We

measure purchasing power by first calculating the price level, which is a weighted average of

the prices of the goods and services that people consume. The weights in the price level

reflect the shares of these goods and services in the consumption bundle of a typical

individual. The purchasing power of the money is then found by taking the reciprocal of the

price level. The units of the price level are an amount of money per consumption bundle, and

the units of purchasing power are consumption bundles per unit of money.

2. Suppose the government releases information that causes people to expect that the

purchasing power of a money in the future will be less than they previously had

expected. What will happen to the exchange rate today? Why?

Answer: Typically, when people think that the purchasing power of a money is going to

decline in the future, due to higher expected inflation, they try to sell that currency today to

get into a currency that will have more stable purchasing power. This reduced demand for the

currency causes that currency to weaken or depreciate immediately.

3. What is the difference between a price level and a price index?

Answer: The price level is a weighted average of the prices of the goods and services that

people consume. The price index is a ratio of a price level at one point in time to the price

level in some base year, with the ratio usually multiplied by 100. Thus, if the price level in a

given year is 30% higher than the price level in the base year, the price index would be 130.

Price levels give you information about the purchasing power of a currency. Price indexes

give you information about the rate of inflation between two points in time.

4. What do economists mean by the law of one price? Why might the law of one price be

violated?

Chapter 8: Purchasing Power Parity and Real Exchange Rates


2

Answer: The law of one price says that the price of a good, when denominated in a particular

currency, is the same wherever in the world the good is being sold. The law of one price

relies on arbitrage in the goods market. If the good is being sold in one place at a low price

and is being sold in a different place at a high price, people have an incentive to arbitrage the

two markets. Therefore, anything that makes it difficult or costly to arbitrage in the goods

market can create a deviation from the law of one price. Clearly, transaction costs, such as

the costs of shipping, generate deviations from the law of one price that cannot be arbitraged.

Tariffs and quotas on imports and exports also create deviations. If markets are not

competitive and firms have some monopoly power, the corporation may decide to charge

different prices in different countries, but it must be able to segment the markets to prevent

arbitrage. If arbitrage cannot be done instantaneously, there will be a speculative element that

enters the calculations and the speculator may have to be compensated for the risk of loss

with an expected profit from buying in one market and selling in another market at a later

point in time. Finally, various goods markets are subject to a certain amount of price

stickiness because of the costs of changing prices. Because exchange rates are asset prices

and freely flexible, unanticipated changes in exchange rates will create deviations from the

law of one price if goods prices are sticky.

5. What is the value of the exchange rate that satisfies absolute PPP?

Answer: Absolute purchasing power parity requires that the internal purchasing power of a

currency equals its external purchasing power. The internal purchasing power is calculated

by taking the reciprocal of the price level, and the external purchasing power is calculated by

first exchanging the domestic money into the foreign money in the foreign exchange market

and then calculating the purchasing power of that amount of foreign currency in the foreign

country. Hence, the prediction of absolute PPP for the exchange rate of domestic currency

per unit of foreign currency is found by equating the internal purchasing power of the

domestic currency to the external purchasing power of the domestic currency:

PPP

1 1 1 = ×

P DC S P FC

where P(DC) is the domestic price level, P(FC) is the foreign price level, and SPPP

signifies

the exchange rate of domestic currency per unit of foreign currency that satisfies the PPP

relation. By solving for SPPP

, we find

PPPP DC

S = P FC

6. If the actual exchange rate for the euro value of the British pound is less than the

exchange rate that would satisfy absolute PPP, which of the currencies is overvalued

and which is undervalued? Why?

Answer: The terminology of “overvalued” and “undervalued” refers to the relationship of the

exchange rate to the PPP theory. If the actual exchange rate of euros per pound is less than



3

the PPP prediction, the euro is overvalued and the pound is undervalued. We know this is the

correct answer because if the actual exchange rate were to move to the PPP prediction, the

euro would have to weaken, and the pound would correspondingly have to strengthen, on the

foreign exchange market. The weakening of the euro would correct its overvaluation, and the

strengthening of the pound would correct its undervaluation.

7. What market forces prevent absolute purchasing power parity from holding in real

economies? Which of these represent unexploited profit opportunities?

Answer: Any of the forces that create a deviation from the law of one price can also cause a

deviation from PPP. See the answer to question 4. In addition, even if the law of one price

were satisfied for all goods, if the consumption bundles in the two countries put different

weights on the goods because of taste differences across countries, relative price changes

would be reflected in deviations from PPP. It is our opinion that deviations from PPP do not

represent unexploited profit opportunities.

8. Why is it better to use a PPP exchange rate to compare incomes across countries than

an actual exchange rate?

Answer: When comparing incomes across countries, one is interested in comparing the

quality of life that occurs from earning such incomes and consuming in those countries. One

way to do such a comparison is to examine the real values of the nominal incomes, that is, to

multiply each of the nominal incomes times the respective purchasing powers of the

currencies (which is equivalent to dividing the nominal income by the price level). The real

value of the income tells you the command over goods and services that the nominal income

provides when you consume in that country. If the real incomes in countries A and B were

the same, we would have

nominal income in country A nominal income in country B

price level in country A price level in country B

If we multiply this expression by the price level in country A, we get

price level in country Anominal income in country A nominal income in country B

price level in country B

In the above expression, the ratio of the price level in country A to the price level in country

B is the purchasing power parity exchange rate. Hence, if we multiply the nominal income in

country B by the purchasing power parity exchange rate we get a nominal income that is in

the units of the currency of country A and that can be compared to the nominal income in

country A. If the nominal income in country A is higher than the purchasing power exchange

rate multiplied by nominal income in country B, people in country A are better off in terms

of their ability to consume than those in country B.

If you use the actual exchange rate rather than the PPP exchange rate to convert the nominal

income in country B into currency of country A, you are effectively saying you would like to



4

earn the income in country B, but you want to consume it in country A. This can create

incorrect inferences about where is the best place to live. Suppose currency B is overvalued

relative to PPP. Then, the market exchange rate of currency A per unit of currency B,

denoted S, is greater than the PPP prediction,

SPPP

= price level in country A

price level in country B

That is S > SPPP

. In such a situation, it can happen that PPPnominal income in country A > S nominal income in country B

in which case we know from the above discussion that we would prefer to earn income in

country A and consume there. Yet, when we compare incomes with the actual exchange rate,

we might find that the nominal income in country A < S nominal income in country B

The overvaluation of currency B causes us to think that the income in country B is preferred.

But, this is only correct if we earn the income in country B but consume in country A after

converting our income into the currency of country A.

9. What is relative PPP, and why does it represent a weaker relationship between

exchange rates and prices than absolute PPP?

Answer: The theory of relative PPP specifies that exchange rates adjust in response to

differences in inflation rates across countries to leave the deviation of the actual exchange

rate from absolute PPP unchanged. Intuitively, inflation is the rate of loss of the internal

purchasing power of a currency. Thus, if two currencies are losing internal purchasing power

at different rates because the rates of inflation in the two countries are not equal, the rate of

change of the exchange rate can offset the differential rates of inflation to leave the same

absolute relationship between the internal and external purchasing powers of the currencies.

The relative PPP theory is weaker than absolute PPP because relative PPP could be satisfied

even though there are deviations from absolute PPP. The requirement for relative PPP to hold

is that the deviations from absolute PPP do not change over time.

10. What is the real exchange rate, and how are fluctuations in the real exchange rate

related to deviations from absolute PPP?

Answer: The real exchange rate, say, of the dollar relative to the euro, is denoted RS(t,$/€). It

is defined to be the nominal exchange rate multiplied by the ratio of the price levels:

S(t,$/€) P(t,€)RS(t,$/€) =

P(t,$)

Notice that the real exchange rate would be 1 if absolute purchasing power parity held

because the nominal exchange rate, S(t,$/€), would equal the ratio of the two price levels,

P(t,$)/P(t,€). Similarly, if absolute PPP is violated, the real exchange rate is not equal to 1.



5

Thus, fluctuations in the deviations from absolute PPP are fluctuations in the real exchange

rate.

11. If the nominal exchange rate between the Mexican peso and the U.S. dollar is fixed, and

there is higher inflation in Mexico than in the United States, which currency

experiences a real appreciation and which experiences a real depreciation? Why? What

is likely to happen to the balance of trade between the two countries?

Answer: If the peso is pegged to the dollar and the rate of inflation in Mexico is greater than

in the rate of inflation in the United States, the peso is appreciating in real terms and the

dollar is experiencing a real depreciation. The logic is that the rate of inflation in Mexico

measures the loss of internal purchasing power, while because the exchange rate is pegged,

the loss of the peso’s external purchasing power is measured by the U.S. rate of inflation. If a

currency’s loss of internal purchasing power is greater than its loss of external purchasing

power, that currency experiences a real appreciation.

The real appreciation of the peso tends to make Mexican residents think that U.S. goods are

relative bargains, while the real depreciation of the dollar relative to the peso, makes U.S.

residents think that Mexican goods are relatively expensive. Thus, the balance of trade

between Mexico and the United States on the Mexican balance of payments should

deteriorate with an increase in imports from the United States and a decrease in exports to the

United States.

PROBLEMS

1. If the consumer price index for the United States rises from 350 at the end of a year to

365 at the end of the next year, how much inflation was there in the United States

during that year?

Answer: Price indexes are ratios of the price level in a given year to the price level in a base

year. Because the base year is the same in the two price indexes under consideration, we can

take the ratio of the two price indexes and find the rate of inflation over that year. The ratio is

365/350 = 1.0429 or an inflation rate of 4.29%.

2. As a wheat futures trader, you observe the following futures prices for the purchase

and sale of wheat in 3 months: $3.00 per bushel in Chicago and ¥320 per bushel in

Tokyo. Delivery on the contracts is in Chicago and Tokyo, respectively. If the 3-month

forward exchange rate is ¥102/$, what is the magnitude of the transaction cost

necessary to make this situation not represent an unexploited profit opportunity?

Answer: The forward dollar price of wheat in Tokyo is the ratio of the futures price, ¥320 per

bushel, to the forward exchange rate, ¥102/$. This ratio is ¥320 per bushel / (¥102/$) = $3.14

per bushel. Since we can buy wheat for delivery in Chicago at $3 per bushel, if transaction



6

costs of shipping wheat from Chicago to Tokyo are smaller than $0.14 per bushel, we could

make an arbitrage profit. Thus, the minimum magnitude of the transaction cost necessary to

make this situation not represent an unexploited profit opportunity is $0.14 per bushel.

3. Suppose that the price level in Canada is CAD16,600, the price level in France is

EUR11,750, and the spot exchange rate is CAD1.35/EUR.

a. What is the internal purchasing power of the Canadian dollar?

Answer: It is probably best to calculate the purchasing power of CAD10,000. If we divide

this amount by the price level in Canada of CAD16,600, we find

CAD10,000=0.6024 consumption bundles

CAD16,600 / consumption bundle

b. What is the internal purchasing power of the euro in France?

Answer: Performing a similar calculation to the one in part a., we find

EUR10,000 = 0.8511 consumption bundles

EUR11,750 / consumption bundle

c. What is the implied exchange rate of CAD/EUR that satisfies absolute PPP?

Answer: The implied PPP exchange rate equates the internal purchasing power of the

CAD to its external purchasing power. This implies that the PPP exchange rate is the

ratio of the Canadian price level in Canadian dollars to the French price level in euros:

PPP CAD16,600 CAD1.4128S CAD/EUR = =

EUR11,750 EUR

d. Is the euro overvalued or undervalued relative to the Canadian dollar?

Answer: Because the actual exchange rate of CAD1.35/EUR is less than the PPP

exchange rate, the euro is undervalued on the foreign exchange market because it would

have to strengthen to move from CAD1.35/EUR to CAD1.4128/EUR.

e. What amount of appreciation or depreciation of the euro would be required to

return the actual exchange rate to its PPP value?

Answer: The exchange rate moves from the actual value of CAD1.35/EUR to the PPP

value of CAD1.4128/EUR for a percentage change of1.4128/1.35– 1 = 0.0466. This is a

4.66% appreciation of the euro versus the Canadian dollar.



7

4. Suppose that the rate of inflation in Japan is 2% in 2011. If the rate of inflation in

Germany is 5% during 2011, by how much would the yen strengthen relative to the

euro if relative PPP is satisfied during 2011?

Answer: The approximately correct answer is that the yen should strengthen by the

differential in the rates of inflation or 5% - 2% = 3%. The exact answer is found from

equation (8.4) of the text, which incorporates a denominator correction, and we get

π t+1,DC - π t+1,FCDCs t+1, =

FC 1 + π t+1,FC

Since we are concerned about the strengthening of the yen, let the yen be the foreign

currency (FC), and let the euro be the domestic currency (DC). Then, the relative PPP

formula states that the rate of appreciation of the yen is

0.05 - 0.02

0.0294 or 2.94%1+ 0.02

5. One of your colleagues at Deutsche Bank thinks that the dollar is severely undervalued

relative to the yen. He has calculated that the PPP exchange rate is ¥140/$, whereas the

current exchange rate is ¥105/$. Because interest rates are 3% p.a. lower in Japan than

in the United States, he thinks that this is a good time to speculate by borrowing yen

and lending dollars. What do you think?

Answer: Deviations from PPP are a weak reason to engage in speculation. While the data in

the problem indicate that the dollar is 33.33% undervalued, because that is the amount of

dollar appreciation that would be required to take the actual exchange rate from ¥105/$ to the

PPP prediction of ¥140/$, we know that the return to PPP will not be an overnight event.

The empirical analysis of the issue indicates that the half-life of PPP deviations is around 5

years. Thus, you might expect that the dollar will appreciate by 16.67% over the next 5 years.

But, uncovered interest rate parity actually suggests that the yen will appreciate in the short

run, because the yen interest rate is 3% less than the dollar interest rate. Notice, though, that

the correction back toward PPP can take place with differential rates of inflation in the two

countries. If Japanese rate of inflation falls below the U.S. rate of inflation, the PPP

prediction will begin falling toward the actual exchange rate. Finally, although the dollar is

33.33% undervalued, there is no guarantee that the undervaluation will begin to be corrected

now. It may, in fact, get worse. If the undervaluation of the dollar goes to 50% over the next

2 years, you would lose 16.67% in the foreign exchange market which would not be

compensated by the approximate 6% that you would earn by borrowing yen and lending

dollars. Finally, do not forget that your boss in proprietary trading at Deutsche Bank would

not be happy with such a situation.

6. Suppose that you are trying to decide between two job offers. One consulting firm

offers you $150,000 per year to work out of its New York office. A second consulting



8

firm wants you to work out of its London office and offers you £100,000 per year. The

current exchange rate is $1.65/£. Which offer should you take, and why? Assume that

the PPP exchange rate is $1.40/£ and that you are indifferent between working in the

two cities if the purchasing power of your salary is the same.

Answer: We know from the extensive discussion in Question 8 that we should use the PPP

exchange rate to compare the pound salary to the dollar salary. If we do so, we find

$1.40/£ £100,000 = $140,000. This is less than the $150,000 that you are being offered in

New York. The fact that the dollar is undervalued on the foreign exchange markets makes the

perceived salary of $1.65/£ £100,000 = $165,000, calculated with the spot exchange rate,

seem more attractive. But, the key point is that to achieve $165,000 of spending in the United

States, you would have to work in London and consume in New York.

7. Suppose that in 2011, the Japanese rate of inflation is 2%, and the German rate of

inflation is 5%. If the euro weakens relative to the yen by 10% during 2011, what would

be the magnitude of the real depreciation of the euro relative to the yen?

Answer: The real exchange rate is

//

S(t, ) P(t, )RS(t, ) =

P(t, )

¥ € €¥ €

¥

We also know that a real depreciation of the euro means that this real exchange rate

decreases. The new real exchange rate will be the old real exchange rate with each term

multiplied by one plus the respective percentage rate of change. Thus, one plus the

percentage rate of change of the real exchange rate is

//

1 + s(t, ) 1 + (t, ) 1 - 0.10 1 + 0.051 + rs(t, ) = 0.9265

1 + (t, ) 1 + 0.02

¥ € €¥ €

¥

So, we conclude that the real depreciation of the euro is 7.35%.

8. Pick a particular brand of appliance, like a Bosch dishwasher with certain features, and

use the internet to compare its prices across countries. Be sure to have exactly the same

style of appliance in each country. How different are the prices when expressed in a

common currency?

We found the Bosch Ascenta series Model SHX6AP05UC on sale at Sears-Canada for

CAD1,149.99. The exact same model in the United States was available from Amazon

through AJ Madison for $728.10. The exchange rate on June 4, 2011 was CAD0.9772/USD.

Thus, a Canadian could purchase the U.S. dishwasher for CAD0.9772/USD x $728.10 =

CAD711.50. Buying the dishwasher from Sears-Canada would have cost 61.6% more.



9

9. Go to the IMF’s web site at www.imf.org, find the Data and Statistics tab, locate World

Economic Outlook (WEO) data, and download the “Implied PPP conversion rate” for

the Indonesian rupiah and the Philippines peso versus the dollar. Calculate a rupiah per

peso PPP rate and compare it to the actual exchange rate. Which currency is

overvalued, and by how much?

Go to the IMF’s WEO site at

http://www.imf.org/external/pubs/ft/weo/2010/02/weodata/index.aspx

Request data for Indonesia and the Philippines on their Implied PPP rates versu the U.S.

dollar. The 2011 rates were 6,402.79 for Indonesia and 25.143 for the Philippines. The ratio

of these two gives the Implied PPP rate of IDR/PHP:

IDR6,402.79/USD IDR254.65

= PHP25.143/USD PHP

The actual exchange rate was IDR197.153/PHP. Hence, the Philippines peso is undervalued

relative to the Indonesian rupiah because the peso would have to strengthen if the actual

exchange rate were to go to the Implied PPP rate. The peso would have to strengthen by

29.16%.

http://www.imf.org/external/pubs/ft/weo/2010/02/weodata/index.aspx


Chapter 9 Measuring and Managing Real Exchange

Risk

QUESTIONS

1. As the vice president of finance for a U.S. firm, what do you say to your production

manager when he states, “We shouldn’t let foreign exchange risk interfere with our

profitability. Let’s simply invoice all our foreign customers in dollars and be done with

it.”

Answer: The production manager is poorly informed. Whenever goods are sold across

borders of countries that use different currencies, there will be foreign exchange risk that

must be born by someone. If your firm invoices only in dollars, you may lose export sales

that would go to importers that are not willing to bear the risk. Other competitors of yours

may be more flexible and willing to invoice in the local currency. The important point is that

the foreign exchange risk is present and must be managed by someone. Why not by you – the

trained international finance expert!

2. What do economists mean by pricing-to-market?

Answer: Pricing-to-market means that a producer charges different prices in different

markets for the same good. Clearly, this requires the markets to be segmented to prevent

arbitrage in the goods market, and the producer must have some degree of monopoly power

in the sense that the demand curve that it faces in each of the markets is not perfectly elastic.

3. Why does a monopolist not charge the same price for the same good in two different

countries?

Answer: The monopolist sets the prices in the two markets such that the marginal revenue in

each market equals the common marginal cost of producing the good. If the elasticities of

demand differ in the two markets, the producer optimally charges a higher price in the market

with the less elastic demand curve.

4. What determines how much a foreign producer allows the dollar price of a product sold

in the United States to be affected by a change in the real exchange rate?

Chapter 9: Measuring and Managing Real Exchange Risk


2

Answer: Pricing-to-market interacts with changes in the real exchange rate to prevent the full

pass-through of the change in the exchange rate to the change in the price of the good. If the

real exchange rate moves in a favorable direction for the monopolist, the foreign price of the

good could be allowed to fall one-for-one with the appreciation of the foreign currency. But,

while the monopolist will allow the price to fall to allow the sale of more goods, the

monopolist will not let the price fall one-for-one with the exchange rate because the

monopolist has the opportunity to take enhanced profitability on all sales. Conversely, if the

real exchange rate moves in an unfavorable direction for the monopolist, the foreign price of

the good will be allowed to rise to decrease the amount sold, but the monopolist will also

accept some reduced profitability on all sales.

5. Why is the pass-through from changes in exchange rates to changes in the prices of

products not one-for-one?

Answer: Imperfect pass-through ultimately reflects imperfections in the competitiveness of

goods markets. If markets were perfectly competitive, pass-through would be full. For

additional discussion, see the answer to Question 5. These are really the same question.

6. Given that real exchange rates fluctuate, when would be the best time to enter the

market of a foreign country as an exporter to that market?

Answer: Firms often introduce new products in foreign markets when the foreign currencies

are strong in real terms. Doing so allows the new entrant to the market to set a comparatively

low foreign currency price for a product so that it can better compete and become an

established player in the market. This strategy allows the exporter to develop loyal customers

who will then potentially tolerate increases in the foreign currency price that the exporter

feels compelled to introduce when the foreign currency eventually depreciates relative to the

exporter’s currency.

7. You have been asked to evaluate possible sites for an Asian production facility that will

manufacture your firm’s products and sell them to the Asian market. What real

exchange rate considerations should you entertain in your evaluation?

Answer: You must be aware of the strength or weakness of the real exchange rates in the

various countries. Because your firm will be exporting from the country in which the plant is

located, your profits will be hurt by a future real appreciation of the currency of that country

relative to the currencies of countries to which you export. Your costs would rise with no

corresponding benefit in sales. Thus, if the potential production country currency is currently

severely undervalued on foreign exchange markets, this country may appear to be a low cost

production center, but it is likely that this cost advantage will be eroded by a real

appreciation in the future.

8. Why is it important for an exporter to understand the distinction between a temporary

change in the exchange rate and a permanent change in determining whether to



3

respond to a real depreciation of the home currency with increased production or sales

out of inventories?

Answer: Exporters benefit when their home currencies depreciate in real terms. If the

depreciation is temporary, drawing down inventory stocks without changing the production

process can meet the short-term increase in demand in the lowest cost way. The more

permanent is the perception of the real depreciation, the more likely it is that the firm’s

demand will be permanently higher, in which case it is more appropriate to increase

production as this is the lowest cost long-run response.

PROBLEMS

1. If there is 10% inflation in Brazil, 15% inflation in Argentina, and the Argentine peso

weakens by 21% relative to the Brazilian real, by how much has the peso strengthened

or weakened in real terms. What effect do you expect that this change in the real

exchange rate would have on trade between the two countries?

Answer: If s denotes the rate of change of the nominal exchange rate measured as Brazilian

real per Argentine peso, π(A) denotes the rate of Argentine inflation, and π(B) denotes the

rate of Brazilian inflation, the percentage change in the real exchange rate measured as

Brazilian real per Argentine peso is

1 1 ( ) 1 0.21 1 0.151 1 0.1741

1 ( ) 1 0.10

s Ars

B

Thus, the Argentine peso has weakened by 17.41% in real terms. This is less than the 21%

by which it weakened in nominal terms because the Argentine rate of inflation was 5%

greater than the Brazilian rate of inflation.

2. Suppose that you have one domestic production facility that supplies both the domestic

and foreign markets. Assume that the demand for your product in the domestic market

is Q = 2,000 – 3P and in the foreign market, demand is given by Q* = 2,000 – 2P*.

Assume that your domestic marginal cost of production is 600. If the initial real

exchange rate is 1, what are your optimal prices and quantities sold in the two markets?

By how much will you change the relative prices of your product if the foreign currency

appreciates in real terms by 10%? What will you do to production?

Answer: From the domestic demand curve, we find that P = (2,000 – Q) / 3, and revenue

from domestic sales is

P × Q = [(2,000 × Q) – Q2] / 3

We know that when the monopolist sells output in the foreign market, the domestic real value

of revenue from foreign sales is the real exchange rate, RS, multiplied by the foreign relative



4

price, multiplied by foreign sales, or by substituting P* = (2,000 – Q*) / 2, we find that

domestic real revenue from foreign sales equals

RS × P* × Q* = [(RS × 2,000 × Q*) – RS × Q*2] / 2

The domestic marginal cost of production is constant at 600, and the total cost of production

is the per-unit cost multiplied by the total quantity produced for sale in each of the two

markets, or 600 × (Q + Q*).

A profit-maximizing monopolist produces an amount of the good such that the marginal

revenues earned from sales in each market are each equal to the common marginal cost. The

domestic marginal revenue is (2,000 – 2Q) / 3. Thus, the monopolist should sell a quantity in

the domestic market that satisfies

(2,000 – 2Q) / 3 = 600

or, by solving for Q, we find Q = 100. The monopolist charges P = 633.33 to achieve sales of

100.

The marginal revenue from the foreign market is

(RS × 2,000 – RS × 2Q*) / 2.

The optimal quantity in the foreign market satisfies

RS × 1,000 – RS × Q* = 600

or, once again solving for Q*, we find

Q* = [1,000 – (600 / RS)]

At the initial real exchange rate of 1, the monopolist should sell 400 in the foreign market by

charging the relative price of 800. The total real profit would be

(633.33 × 100) + (800 × 400) – [600 × (100 + 400)] = 83,333

Now, if there is a 10% real appreciation of the foreign currency, the new real exchange rate is

1.1. The real appreciation of the foreign currency benefits an exporting monopolist because

the domestic value of real revenue in the foreign country is now

1.1 × [(2,000 – Q*) × Q*] / 2

1.2 By equating the foreign marginal revenue to the unchanged domestic marginal cost of 600

and solving for Q*, we find

Q* = [1,000 – (600 / 1.1)] = 454.55



5

In order to sell the 454.55 units in the foreign market, the monopolist must lower the foreign

price per unit to

P* = (2,000 – 454.55) / 2 = 772.73

Because the marginal cost of production is constant, the domestic price per unit remains at

633.33, and the domestic sales remain at 100. Notice that although the foreign currency

appreciates by 10%, the monopolist only decreases the relative price in the foreign market by

3.4% because the ratio of the new foreign price to the old foreign price is

772.73 / 800 = 0.966

3. How would you respond in Problem 2 if the marginal cost of production were

increasing? Why?

Answer: If the marginal cost of production is increasing, it costs more to produce larger

quantities. After the real appreciation of the foreign currency, the monopolist would still

want to increase the quantity sold in the foreign market, but not by as much. Hence, the

foreign relative price would not fall as much. The monopolist would also increase the

domestic relative price to sell less in that market, and he would shift some sales from the

domestic market to the foreign market.

4. Suppose you are a monopolist who faces a domestic demand curve given by Q = 1,000 –

2P. Your domestic cost of production involves domestic costs per unit of 300 and a

foreign cost per unit produced of 150. If the real exchange rate is 1.1, what would be the

price you would charge and the quantity you would sell? How do these variables change

when the real exchange rate increases by 10%?

Answer: The monopolist will operate where marginal revenue equals marginal cost. Price is

(1,000 – Q) / 2, and total revenue is P × Q = (1,000 Q – Q2) / 2. Marginal revenue is therefore

(1,000 – 2Q) / 2 = 500 – Q.

Marginal cost has a domestic component of 300 and a foreign component of RS × 150. The

initial real exchange rate is 1.1. Therefore, marginal cost is 300 + 1.1 × 150 = 465. Equating

marginal revenue to marginal cost gives the optimal production:

500 – Q = 465

Q = 35.

In order to sell a quantity of 35, the monopolist must charge

P = (1,000 – 35) / 2 = 482.5.



6

If there is a 10% real appreciation of the foreign currency, the new real exchange rate is 1.1 ×

(1 + 10%) = 1.21. Marginal cost increases to 300 + 1.21 × 150 = 481.5, and the optimal

quantity falls to

500 – Q = 481.5

Q = 18.5.

The relative price in the domestic market increases to

P = (1,000 – 18.5) / 2 = 490.75.

The 10% increase in the real exchange rate causes marginal cost to increase by 3.55% from

465 to 481.5. The price of the product increases by a smaller percentage, 1.71%, from 482.5

to 490.75. Thus, pass-through from the change in the exchange rate to the product price is

less than one-for-one.

5. Use a program like Crystal Ball to generate Monte Carlo simulations of the profits of

Safe Air and Metallwerke under various contracting clauses.

These graphics indicate the profit margin with no inflation in either country and a standard

deviation of the dollar-euro exchange rate equal to 10%.



7

6. In 2008 Endo Pharmaceuticals, a U.S. firm, signed a five-year contracted with Novartis,

a Swiss firm, to obtain the exclusive U.S. marketing rights for Voltaren Gel, an anti-

inflammatory useful in treating osteoarthritis. Search the internet for information

about the contract. Who bore the real exchange risk?



8

Searching for “Voltaren Gel aggreement” turned up this assessment from www.mmm-

online.com:

Under the terms of the five-year agreement with Novartis, Endo will make an upfront cash

payment of $85 million. Novartis is also eligible to receive a one-time milestone payment of

$25 million if annual sales exceed $300 million. Under the deal, Novartis will receive

royalties on the net sales of Voltaren Gel in the US and will supply this product to Endo.

Thus, it appears that Novartis is bearing the real foreign exchange risk as Endo will receive

dollars from its customers and pay dollars to Novartis.

66

Chapter 10 Exchange Rate Determination and Forecasting QUESTIONS 1. What is the difference between the ex ante and the ex post real interest rate?

Answer: The ex post interest rate corrects the nominal interest rate with the realized or ex post rate of inflation; whereas the ex-ante (or expected) real interest rate corrects the nominal interest rate for expected inflation.

As a lender, you care about the real return on your investment, which is the return that measures your increase in purchasing power between two periods of time. If you invest $1, you sacrifice

$1P(t)

real goods now, where P(t) is the price level. In 1 year, you get back1 + i

P(t+1), where i is the

nominal rate of interest. We calculate the real return by dividing the real amount you get back by the real amount that you invest. Thus, if rep is the ex post real rate of return and ex post real interest rate, we have

( )ep

1 + i1 + iP(t+1)

1 + r = = 1 P(t+1)

P(t) P(t)

⎛ ⎞⎜ ⎟⎝ ⎠⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Notice that the real rate of interest depends on the realization of the rate of inflation because P(t + 1)/P(t) = 1 + π(t + 1), where π(t + 1) is the rate of inflation between time t and t + 1. For simplicity, we drop the time notation and simply write

ep (1 + i)1 + r = (1 + π)

If we subtract 1 from each side, we have ep (1 + i) (1 + π) i - πr = - =

(1 + π) (1 + π) (1 + π)

which is often approximated as rep = i – π

The approximation involves ignoring the term (1 + π) in the denominator, which is close to 1 if inflation is not too high. Thus, the ex post real interest rate equals the nominal interest rate minus the actual rate of inflation.

Because the inflation rate is uncertain at the time an investment is made, the lender cannot know with certainty the real rate of return on the loan. By taking the expected value of both sides of the equation, conditional on the information set at the time of the loan, we derive the lender’s expected real rate of return, which is also called the expected real interest rate, or the ex ante real interest rate, which we denote re:

e ept tr = E [r ] = i(t) - E [π(t+1)]

Chapter 10: Exchange Rate Determination and Forecasting 67

2. Suppose that the international parity conditions all hold and a country has a higher nominal

interest rate than the United States. Characterize the country’s inflation rate compared to the United States, the country’s expected exchange rate change versus the dollar, the country’s currency forward premium (or discount) versus the dollar, and the country’s real interest rate compared to the U.S. real interest rate.

Answer: When all the parity conditions hold, real interest rates are equalized across countries, so the country’s real interest rate should equal that of the United States. The country’s higher nominal interest rate therefore must reflect a higher expected rate of inflation relative to the United States. Since the parity conditions hold, a higher expected rate of inflation implies that country’s currency should be expected to depreciate relative to the dollar, and the currency will trade at a forward discount relative to the dollar.

3. How do fundamental analysis and technical analysis differ?

Answer: Fundamental analysis typically uses formal economic models of exchange rate determination and macroeconomic fundamental data such as money supplies, inflation rates, productivity growth rates, and the current account to predict exchange rates. Technical analysis uses only past exchange rate data, and perhaps some other financial data, such as the volume of currency trade, to predict future exchange rates.

4. Would technical analysis be useful if the international parity conditions held? Why or why not? Answer: If the parity conditions held, technical analysis would not be useful in the sense of providing profitable trading information or information about expected exchange rates that could not be obtained elsewhere. If the parity conditions held, the best predictor of the future exchange rate would be the forward rate, and exchange rate forecasts based on other indicators would not lead to systematic profits on currency speculation.

5. Describe three statistics you should obtain from a currency-forecasting service in order to judge

the quality of its currency forecasts.

Answer: Three important statistics are the Root Mean Squared Error (RMSE) or Mean Absolute Deviation of its forecasting record, which would provide information on accuracy; the percentage of times they were on the correct side of the forward rate, which would provide useful information on the profitability, and a risk–return statistic (such as the Sharpe ratio), which would provide a characterization of the profitability of using their forecasts in a real time trading strategy.

6. Does a large increase in the domestic money supply always lead to a depreciation of the currency?

Answer: Most theories of the determination of exchange rates would predict that a large increase in the money supply would imply a depreciation of the currency, definitely in the long run, and especially as economists say when “everything else is equal.” However, it is possible that the change in the money supply is accompanied by an increase in real income that increases the demand for money and thus offsets the money supply’s effect on the exchange rate.

Chapter 10: Exchange Rate Determination and Forecasting

68

7. Is a current account deficit always associated with a strong real exchange rate (that is, one that is overvalued compared to the PPP prediction)?

Answer: Not necessarily. It is best to view the current account and the real exchange rate as being determined in an equilibrium that depends on many forces, such as movements in net foreign assets, government spending, productivity growth, and the expectations and risk tolerances of domestic and foreign investors.

8. Describe how three macroeconomic fundamentals affect exchange rates.

Answer: According to the monetary exchange rate model, the domestic currency weakens (strengthens) if the domestic (foreign) money supply increases today or if news arrives that leads people to believe that the future domestic (foreign) money supply will increase. The domestic currency also weakens if domestic real income falls, if foreign real income rises, or if news arrives that causes people to expect lower domestic real growth or faster foreign real growth. Finally, according to the equilibrium theory regarding the real exchange rate and the current account, an increase in government spending or a decrease in taxes that causes a budget deficit should increase the real exchange rate (and hence likely also the nominal exchange rate). This is because an increase in government spending increases aggregate demand in the economy, which causes the real interest rate to rise. The rise in the interest rate reduces investment and encourages private saving

9. Which simple statistical model yields some of the best exchange rate predictions available?

What does this imply for the value of models of exchange rate determination to multinational businesses?

Answer: It is surprisingly difficult to beat the forecasts of the random walk model. This model uses the current exchange rate as the predictor of the future exchange rate. If this model provided the best forecast, the unbiasedness hypothesis (which says the forward rate is the best predictor) would be violated. If there were a forward premium on the foreign currency, the forward rate would be above the expected future spot rate, and you would want to sell the foreign currency in the forward market.

10. What is chartism?

Answer: Chartists graphically record the actual trading history of an exchange rate and then try to infer possible future trends based on that information alone.

11. What is an x% filter rule?

Answer: An x% rule states that you should go long in the foreign currency (buy) after the foreign currency has appreciated relative to the domestic currency by x% above its most recent trough (or support level) and that you should go short in the foreign currency (sell) whenever the currency falls x% below its most recent peak (or resistance level). Common x% filter rules are 1% or 2%.


12. What is a moving-average crossover rule?

Answer: Moving-average crossover rules use moving averages of the exchange rate to indicate trade directions. An n-day moving average is just the sample average of the last n trading days, including the current rate. A (y, z) moving-average crossover rule uses averages over a short period (y days) and over a long period (z days). The strategy states that you should go long (short) in the foreign currency when the short-term moving average crosses the long-term moving average from below (above). Common rules use 1 and 5 days (1, 5), 1 and 20 days (1, 20), and 5 and 20 days (5, 20).

13. Have forecasting services been successful in forecasting exchange rates?

Answer: The direct evidence on the forecasting prowess of forecasting services is rather dated by now (see, for example, a 1987 study by Robert Cumby and David Modest), but the results of these studies suggested that most forecasting services were more often wrong than correct, but that most did make profits. Academic studies have suggested that it has become more difficult to forecast currency movements based on technical signals more recently relative to the 1980s; but it is possible that other models may do better.

14. Are devaluations of pegged exchange rates totally unexpected?

Answer: While there is a debate about their predictability, some theories suggest that devaluations may be partially predictable. These models argue that growing budget deficits, fast money growth, and rising wages and prices usually precede devaluations. Increases in nominal interest rates typically reflect a combination of the probability and magnitude of a possible devaluation.

15. Construct a list of a country’s economic statistics you would assemble to help determine the

probability of a devaluation of its currency within the coming year.

Answer: Based on theoretical and empirical work, the following economic variables should prove useful predictors: PPP-based measures of currency overvaluation, current account balances and monetary growth rates. In addition, if liquid financial markets exist, information about forward rates or interest rates, currency option prices, and so on may prove useful in terms of forecasting devaluations.


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PROBLEMS 1. Suppose the 1-year nominal interest rate in Zooropa is 9%, and Zooropa’s expected inflation

rate is 4%. What is the real interest rate in Zooropa? Answer: The expected real interest rate is approximately 9% - 4% = 5%. The correct computation is: (1 + 0.09) / (1 + 0.04) – 1 = 0.0481 or 4.81%.

2. You were recently hired by the Doolittle Corporation corporate treasury to help oversee its expansion into Europe. Blake Francis, the CFO, wants to hire a foreign exchange forecasting company. Blake has asked you to evaluate three different companies, and he has obtained information on their past performances. Out of a total of 50 forecasts for the $/€ rate, the companies reported the number of times they correctly forecast appreciations and depreciations:

Correct Down Forecasts Correct Up Forecasts Morrissey Forex Advisors 20 5

Pixie Exchange Land 20 4 FOREX Cures 12 12

There are a total of 35 dollar appreciations (down periods) and 15 dollar depreciations (up periods) in the sample. Blake wants to know two things:

a. Can anything be said about the companies’ forecasting ability with the available data?

Answer: Yes, one can compute the number of correct “directional” forecasts. Morrissey has the highest correct proportion with 25 out of 50 correct, whereas the other firms have less than 50% correct. However, note that the dollar over this period was relatively strong and appreciations (down forecasts for the $/€ rate) dominate. Hence, forecasts in the down period may be more useful (see footnote 3 in the chapter). If we look at correct conditional forecasts, we see that Morrissey is correct 20/35 or 57.14% of the time when the dollar appreciates, but only 5/15 or 33.33% of the time when the dollar depreciates. According to the Henriksson–Merton test, the sum of these two proportions should be over 1 for a firm to have market timing ability. However, the sum in this case is only 90.47%. While Morrissey obviously dominates Pixie Land Exchange, it is not clear that it is better than FOREX Cures. The proportions of correct conditional forecasts of FOREX Cures are 12/35 (34.29%) and 12/15 (80%) for a sum of 114.29%. Consequently, only FOREX Cures shows directional forecasting ability. b. What additional information should Blake try to obtain in order to form a better

judgment?

Answer: Directional forecasting ability in the foreign exchange market is not particularly useful if the forecasts are to be used in speculative strategies. To this end, it would have been more useful to know whether the forecasting firms were on the correct side of the forward rate. Ideally, a full record of forecasts would be obtained. Then, accuracy statistics (like the RMSE) and profitability statistics (like the Sharpe ratio) could be computed.


3. Mini-Case: Currency Turmoil in Zooropa Fad Gadget has never worked so hard in his entire life. It is near midnight, and he is

still poring over statistics and tables. Fad recently joined Smashing Pumpkins, a relatively young but fast-growing British firm. Smashing Pumpkins produces and distributes an intricate device that turns fresh pumpkins into pumpkin pie in about 30 minutes. Recently, the firm has started exporting to Zooropa. Some of the largest and tastiest pumpkins are grown in Zooropa, and Zooropa’s population boasts the highest per capita pumpkin consumption in the world. A recent analysis of the pumpkin market in Zooropa has left the company’s senior managers very impressed with the profit potential.

Although Zooropa consists of 10 politically independent countries, their currencies are linked through a system called the Currency Rate Linkage System (CRLS) that works exactly like the former Exchange Rate Mechanism (ERM) of the EMS worked before the currency turmoil started in September 1992. The anchor currency is the banshee of Enigma, the leading country in Zooropa.

Initial contacts with importers in Zooropean countries indicated that they typically insist on payment in their own local currency. About a week ago, Cab Voltaire, the CEO of Smashing Pumpkins, expressed concerns about this development and asked Fad to lead a research team to further examine the present state of the currency system of Zooropa. Cab viewed the outlook for the banshee relative to the pound quite favorably and did not predict any substantial depreciation of the banshee against any other major currency. However, the precarious economic situation of some of the countries in Zooropa and the growing importance of speculative pressures in Zooropa’s currency markets last week suddenly made him suspicious about the possibility of realignments within the system. He even doubted the long-term viability of the system. Cab instructed Fad to examine the following issues:

Which currencies in the system exhibit the highest realignment risk? If a currency realigns and gets devalued, what are the effects on our sales and profit

margins in this particular country? Can we take the realignment possibility into account in our pricing?

Suppose a currency is forced to leave the CRLS. What are the effects on exchange rates, interest rates, and the outlook for sales in that country? What is the likelihood of this occurring for the different countries?

Fad Gadget felt nervous. A meeting was scheduled with Cab the day after tomorrow. He wanted to write a thorough and insightful report. At the last management meeting, he had the uneasy feeling that some senior managers doubted his abilities. Some managers were naturally suspicious of a young Australian newcomer with his MBA. His earring and punk hairdo did not exactly help either. His team of analysts had already assembled a table with relevant macroeconomic and financial data (see Exhibit 10.11). “If only I could use this to rank the different countries according to realignment risk,” he thought.

a) Realignment rankings

The data provided are a scrambled version of an Exhibit that appeared in the Economist of September 19, 1992, when a currency crisis in Europe had just erupted. The Exhibit presented macro-economic statistics for all the countries participating in the European system. To prevent students guessing where the data are from, we scrambled the country names two ways. First, we gave each European country another name that did provide a vague hint on the actual European country of origin. However, we then randomly assigned the actual data to the fictitious countries. Here is the “key:”


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Zooropa Country Reference to European Country Data from European country Sinead Ireland (Irish singer) Ireland Carmen Carmen (Spanish opera) France Marquee UK (club in London) Spain Fries Belgium (French fries are Belgian!) Portugal Ney Denmark (No in Danish) Denmark HelpIsink the Netherlands (below sea level) Belgium Benfica Portugal (soccer team) the Netherlands Che Ora Italy (only Italian Geert knows) UK Vachement France (French stop word) Italy Enigma Germany (pop band) Germany

We now reproduce the original Economist table from the article “A Ghastly Game of Dominoes.” Who’s Next? Legend for Chart: A - Currency's ERM position Sept 15th (*) B - Currency's over/under valuation, % (A) C - Reserves, import cover (**) D - Budget deficit as % of GDP, 1992 (B) E - Inflation rate %, latest F - GDP growth, %, 1992 (B) G - Devaluation risk (AA)

A B C D E F G

Italy 27 2 0.5 -11.3 5.2 1.3 1 Britain -90 3 2.6 -4.6 3.6 -0.8 2 Spail 16 11 8.2 -4.9 5.7 2.0 3 Portugal -3 11 11.7 -5.4 9.5 2.8 4 Denmark -22 -2 2.5 -2.1 2.2 2.1 5= Belgium 31 -18 1.3 -5.5 2.1 1.6 5= Holland 30 -16 1.5 -3.4 3.5 1.6 5= France -36 -12 3.1 -2.3 2.7 2.0 8 Ireland -6 -10 2.9 -1.9 3.6 2.4 9 Germany 36 -- 1.7 -3.4 3.5 1.3 --

Sources: OECD; IMF; government statistics; NatWest; The Economist poll of forecasters (*) % of permitted divergence from central rate (A) Central rate against DM relative to PPP (**) Foreign-exchange (mid September estimates), number of months' imports (B) Forecast (AA) 1=greatest risk, 9=least risk

Based on this article, we can actually use the data given to come up with a realignment ranking. For example, the position in the CRLS system (the divergence indicator in the EMS, a summary measure of the currency’s position in its bands relative to all other currencies), and the reserves import cover are direct indicators of devaluation pressure. An overvalued currency, a large budget deficit, high inflation,


and low GDP growth are “bad” economic fundamentals that may contribute to speculative pressure on the currency. The Economist did a very simple exercise. It ranked all the countries on these criteria from “worst” (most speculative pressure) to “best” (least speculative pressure). It then added up the ranks and came up with an overall devaluation risk ranking. Using the information provided on fundamentals leads to a surprisingly accurate realignment risk ranking. These ranks are reproduced in the last column of the Economist table. Italy and Britain were actually forced out of the EMS during the September currency crisis. Spain was forced to devalue and Portugal later followed suit. The other countries with better fundamentals duly survived. Whether the currency crisis in 1992 was actually predictable is still a topic of academic debate. Some important scholars in the area have argued that the crisis was almost completely unpredictable. Our case seems to indicate otherwise, although more formal analysis is necessary (and is still being conducted by many scholars). Finally, while some countries, such as France, still looked relatively “safe,” another currency crisis erupted in July August 1993, which led to rather drastic changes in the operation of the EMS, including a widening of the bands to 15%.

b) Effects of Realignments/Exits for the Firm

Since the British firm agrees to local currency pricing, the risk is that the Zooropa currencies get devalued. Two cases must be considered: (1) The price remains fixed. In this case, the revenue per unit sold in pounds decreases and the profit

margin is squeezed because the firm's costs are local (in pounds). Except for "dynamic effects" (see below), there need not be any effect on the number of units sold. Sales may remain unchanged in local currency, but sales go down in pounds.

(2) The firm tries to "pass through" the exchange rate change and raises the price of the pumpkin device as in Chapter 9. The optimal response will be to raise the domestic price because the firm does not want to sell as much quantity in that market. The amount of the price increase depends on the elasticity of the demand curve. The price will rise less, the more elastic is the demand – that is, the larger the percentage change in quantity with a given percentage change in price.

These are the immediate effects. The realignment restores the general competitiveness of the Zooropean country. If the devaluation is successful, it accomplishes a decrease in real wages locally and shifts resources to the export sector. It should also make potential local competitors to Smashing Pumpkins more competitive. However, the case seems to indicate that these are non-existent. Initially, this may lower the demand for all imports (the whole idea of the devaluation in the first place). If the economy was not producing at full capacity, the increased competitiveness may spur considerable additional economic growth. This, in fact, happened in Britain and Sweden after the 1992 devaluations. Higher growth may then lead to higher imports and increase the demand for the pumpkin device. These are potential dynamic effects. Eventually, this may cause inflationary pressures to creep back into the economy. Unsuccessful devaluations will let higher import prices (if there is some pass through or most import products are priced in foreign currency) affect wages and the general price level. In this case, there may be only small effects for the British firm. Hence, the dynamic effects depend on the success of the devaluation. All of this analysis goes through for exits from the target zone. In fact, the effects for realignments are probably considerably smaller, since an exit may lead to much lower exchange rates and in some cases to lower interest rates, which further help the Zooropa economy become more competitive. It has to be said that these are all "elaborate guesses," since in reality new shocks to the economy may cause completely different outcomes.


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c) Incorporating Realignment Risk into Pricing/Hedging The market will anticipate the realignment. In fact, if UIRP holds, the interest differential with Britain and the forward rate relative to the pound will reflect the expected currency depreciation (the probability of a devaluation multiplied by the magnitude of the devaluation). Hence, hedging the risk will automatically lead to lower pound revenue in the future. Ideally, one establishes a pricing scheme that takes potential realignments into account, for example using forward rates. Your personal view on realignment risk may differ from the forward rates though. Alternatively, a dynamic real exchange rate risk sharing formula as in the SAFE AIR case could be proposed. d) Effects of devaluation/exits on exchange and interest rates

Exchange rates fall, by definition. The effect on the interest rate however may be different in both cases. With devaluation it is very likely that the interest rate will drop. That is because the interest rate was most probably very high during the speculative attack preceding the realignment and it now drops back to normal levels, which are still likely to be above the interest rate of the anchor currency. With an exit, the pressure of a speculative attack gets relieved as well, and now the interest rate need not exceed the rate on the anchor currency. However, the exiting currency loses its "inflation credibility mechanism" by leaving the target zone, and hence, interest rates may go up reflecting higher expected inflation in the future. When Britain exited the ERM, its interest rates dropped substantially at the short end, but they remained quite high at the long end. In Mexico, after the December 1994 crisis, peso interest rates rose reflecting fears of future depreciation and inflation. Both market responses seem justified both by the data at the time of the event and the subsequent experiences of the economies.

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Chapter 11 International Debt Financing QUESTIONS 1. What are the three main sources of financing for any firm?

Answer: Corporations rely on three primary types of financing for their capital expenditures: internally generated funds, debt financing, and equity financing.

2. What is the difference between a centralized and decentralized debt denomination for

an MNC?

Answer: Under a decentralized debt-denomination model, MNCs issue debt in different currencies to hedge the cash flows they earn in these currencies from their foreign subsidiaries. Under a centralized model, debt is issued in the currency of the country in which the MNC has its headquarters.

3. Will an MNC issuing debt in low–interest rate currencies necessarily lower its cost of

funds? Why?

Answer: No. The ultimate cost of the debt will also depend on currency movements. If uncovered interest rate parity holds, the cost of the low interest rate debt, expressed in the home currency, is expected to be identical to the cost of high interest rate debt. After the fact, the debt will be either less expensive than corresponding debt denominated in the domestic currency, if the foreign currency appreciates less than predicted by UIRP; or it will be more expensive if the foreign currency appreciates more than predicted by UIRP.

4. Should an MNC borrow primarily short term when short-term interest rates are lower

than long-term interest rates? Or should it keep the maturity the same but use a floating-rate loan rather than a fixed-rate loan? Explain.

Answer: First, if short-term interest rates are lower than long-term interest rates, this may be an indication of impending increases in interest rates. In fact, if the expectations hypothesis of the term structure of interest rates holds, the long rate is simply an appropriately weighted average of short term rates. This implies that “timing” the loan by having a floating interest rate that allows for low interest payments when short rates are low and high interest payments when short rates are high does not add value. Second, the difference between simply borrowing short-term and using a floating rate note is that the latter approach also locks in the MNC’s credit spread. If the firm thinks its credit rating will improve over time, it may not want to issue a floating rate note, preferring instead to borrow short-term and borrow again at a better credit spread after the information is incorporated by the market.


5. What is financial disintermediation?

Answer: This concept refers to the phenomenon in which firms issue securities directly to investors in the capital markets, rather than borrowing from financial institutions that in turn raise funds from the capital markets.

6. What are the two main segments of the international bond market, and what types of

regulations apply to them?

Answer: One segment of the international bond market is the foreign bond market, where a foreign issuer issues bonds in a particular domestic bond market, subject to local regulations. The other segment is the Eurobond market, where bonds are issued simultaneously in various markets, outside the specific jurisdiction of any country. Hence, these bonds are not subject to the regulations of any particular country.

7. What is the difference between a foreign bond and a Eurobond?

Answer: See the answer to Question 6. 8. Why might U.S. investors continue to purchase Eurobonds, despite the fact that the

U.S. corporate bond market is well developed?

Answer: The Eurobond market gives them access to bonds of firms that are not available in the US market thereby providing valuable diversification of default risk. Recall that the Eurobond market is a highly liquid, unregulated, convenient market to issue bonds, which has lead to a wide array of available bonds from which investors can choose. Also, Eurobonds are not registered (ownership is anonymous), and it may therefore allow certain tax avoidance benefits to non-scrupulous investors.

9. What is a global bond, and what role does the global bond market play in the blurring

of the distinctions in the international bond market?

Answer: Global bonds are issued simultaneously in a domestic market and in the Eurobond market, and they therefore straddle the two segments of the international bond market, making distinctions between them more difficult to draw.

10. What are the differences between a straight bond, a floating-rate note, and a

convertible bond?

Answer: A straight bond has no special features. It has a fixed coupon payment and a final principal payment at maturity. A floating-rate note carries a floating interest rate that typically varies with short-term LIBOR. Convertible bonds allow the holder to convert the bonds into a certain amount of stock and therefore have an option feature.

11. What is a dual-currency bond?


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Answer: Dual-currency bonds are issued in one currency and pay interest in that currency, but the final principal payment is denominated in another currency.

12. What kind of activities do international banks engage in?

Answer: International banks typically develop a complete line of financial services to facilitate the overseas trade of their customers. In addition to commercial credit, these ancillary financial services include market making and trading in spot and forward currencies, international trade financing, and risk management services. Unlike domestic banks, international banks participate in the Eurocurrency market and are frequently members of international loan syndicates, lending out large sums of money to MNCs or governments. An international bank might also engage in the underwriting of Eurobonds and foreign bonds, which are investment-banking activities.

13. Why is there a need for international banking regulation?

Answer: First, central banks are concerned that without an international regulatory framework to ensure that an adequate level of capital is maintained in the international banking system, bank failures could lead to a global financial crisis or at least domestic crises could spill over into other countries. Second, the variety of different national regulations potentially gives an unfair advantage to banks from countries with laxer regulatory standards, and this could decrease the soundness and safety of the international banking system overall. International regulations can create a more level playing field that avoids potential under-regulation if individual regulators compete to see who can be the least strict.

14. What are the differences between credit risk, market risk, and operational risk?

Answer: Credit risk is the risk that a company or government will default on its promised payments on a loan or a bond. Market risk is the risk of losses in trading positions when prices move adversely. Operational risk is the risk of direct or indirect loss resulting from inadequate or failed internal processes, people, and systems or from external events, such as computer failure, poor documentation, or fraud.


15. Which activity would require the largest capital charge under the 1988 Basel Accord: a loan to another bank or a loan to a large MNC? Would this necessarily be true under the Basel II?

Answer: Under Basel I, claims on other banks receive only a 20% weighting, meaning that only 20% of the claim is counted against the 8% capital requirement. Some claims receive a 50% weighting, but virtually all claims on the non-bank private sector receive a 100% weight and hence the full capital charge. Hence, the charge for the loan to the MNC would be larger. Under Basel II, other risks are taken into account (market risk and operational risk), and credit risk is measured differently, primarily to better reflect the true creditworthiness of the borrower. Consequently, it is conceivable that the capital charge for the bank loan is larger than for the MNC under Basel II.

16. What is VaR?

Answer: VaR stands for Value at Risk and measures the dollar loss that a given portfolio position can experience with 5% probability over a given length of time.

17. What is the difference between a foreign branch and a subsidiary bank?

Answer: A foreign branch of a bank is legally a part of the parent bank, but it operates like a local bank. Foreign branch banks are subject to both the banking regulations of their home countries and the countries in which they operate. However, foreign branches of U.S. banks are not subject to U.S. reserve requirements and are not required to have federal deposit insurance. A subsidiary bank is also wholly or partly owned by a parent bank, but it is incorporated in the foreign country in which it is located. Subsidiary banks are therefore subject to the banking laws of the countries in which they are incorporated.

18. What is an offshore center?

Answer: Offshore banking centers conduct international banking activities in a “lightly” regulated setting. Most of the transactions involve nonresidents as counterparties; the transactions are typically initiated outside the financial center, and the majority of the financial institutions involved are controlled by nonresidents who do business primarily with nonresidents. Offshore banking centers can be found in places such as Aruba, the Cayman Islands, and parts of the West Indies.


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19. What is the difference between an Edge Act bank and an international banking facility?

Answer: Edge Act banks are federally chartered subsidiaries of U.S. banks that are physically located in the United States but are allowed to engage in a full range of international banking activities. Such activities include accepting deposits from foreign customers, trade financing, and transferring international funds. Edge Act banks are not prohibited from owning equity in U.S. corporations, as are domestic commercial banks. Consequently, U.S. parent banks own foreign subsidiaries and affiliate banks through an Edge Act setup. An international banking facility (IBF) is a separate set of asset and liability accounts that is segregated on the parent bank’s books, so it is not a unique physical or legal entity. Any U.S.-chartered depositary institution (including a U.S. branch, a subsidiary of a foreign bank, or a U.S. office of an Edge Act bank) can operate an IBF. An IBF operates as a foreign bank in the United States and is consequently not subject to domestic reserve requirements or FDIC insurance regulation. However, IBFs may only accept deposits from non-U.S. citizens and make loans to foreigners. The bulk of an IBF’s activities relate to interbank business. 20. What is the difference between a Eurocredit, a Euronote, and a Euro-medium-term

note?

Answer: Eurocredits are typically very large international loans extended by a consortium or syndicate of banks that share the risk of the loan. Eurocredits are typically issued at floating interest rates. Euronotes are short-term, negotiable promissory notes, established by a Euronote facility. Typically, in such a facility, a syndicate of banks commits to distribute for a specified period, typically 5 to 7 years, the borrower’s notes (the “Euronotes”), with maturities ranging between 1 month, 3 months, 6 months, and 12 months. In case the notes cannot be placed in the market, the syndicate banks in many Euronote facilities stand ready to buy them at previously guaranteed rates. Euro-Medium-Term Notes (Euro-MTN) are securities issued directly to the market and bridge the maturity gap between Euronotes and the longer-term international bond, with maturities as short as 9 months to as long as 10 years. Like Euronotes, the Euro-MTN is a facility with notes offered continuously or periodically rather than all at once, like a bond issue. Unlike conventional underwritten debt securities, medium-term notes can be issued in relatively small denominations and issuing costs are low, but they are not underwritten.

21. Why are Eurocredits not extended by one bank but by a large syndicate of banks?

Answer: Eurocredits are typically very large so that banks appreciate the opportunity to share the risk of default on the loan with other banks.

22. What is the all-in cost of a 5-year loan? What are its main components?

Answer: The all-in cost (AIC) has three components: The “default free” interest rate, the credit spread, and transaction costs. The default free interest rate is the rate available on risk-free government securities of the same maturity. The credit spread is the difference between the borrowing cost of the company and the borrowing cost of the government and reflects the market’s assessment of the ability of the company to repay its debt. Finally,


transaction costs reflect the fees that a company pays to arrange the bond, which also effectively raise the interest rate payable on the loan.

23. What is a credit rating? What is a credit spread?

Answer: For credit spread, see the answer to Question 23. The credit spread a company faces in the market place is typically closely related to its credit rating. Companies that supply credit ratings, such as Moody’s Investors Service and Standard & Poor’s (S&P), provide information on the credit worthiness of companies across the world by producing a “rating” for the securities they issue. They classify bond issues into categories based on the creditworthiness of the borrower. The ratings are based on an analysis of current information regarding the likelihood of default and the specifics of the debt obligation. The ability of a firm to service its debt depends on the firm’s financial structure, its profitability, the stability of its cash flows, and its long-term growth prospects.

24. Should corporations issue bonds in countries where they face the lowest credit

spreads? Be very specific about the concept of credit spread you use.

Answer: The answer here is potentially yes. When expressed in a multiplicative sense (by dividing one plus the interest rate the company faces by one plus the rate on a comparable government bond), lower credit spreads do indeed translate into lower borrowing costs, provided the company can cheaply hedge the cash flows involved into its desired borrowing currency .


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PROBLEMS 1. In 1985, R.J. Reynolds (RJR for short) acquired Nabisco Brands and financed the deal

with a variety of financial instruments, including three dual-currency Eurobonds. The first dual-currency bond, lead-managed by Nikko, raised JPY25 billion (which was equivalent to USD105.5 million at the time of issue). Coupons were paid in yen, but the required final principal payment was not JPY25 billion but USD115.956 million. The coupon was 7.75%, even though a comparable fixed-rate Euroyen bond at that time carried only a 6.375% coupon. The actual 5-year forward rate at the time was around JPY200/USD. a. Given the “fat” coupon, is this bond necessarily a great deal for the investors?

Answer: No, it isn’t a particularly great deal for the investor because the payment at the end is worth substantially less than the face amount of the bond. To see this, note that the yen value of final payment can be found by multiplying the USD115.956 million by the forward rate:

USD115.956 million × JPY200/USD = JPY23.191 billion which is less than JPY25 billion, the original principal. Of course, the coupon is higher than the coupon on a straight Euroyen bond, so we shouldn’t expect the final principal payment to be JPY25 billion otherwise the rate of return on the bond would be 7.75%. If we hedge the dual currency bond and find the internal rate of return on the yen cash flows, we find the value, y, which sets the discounted yen payoffs equal to the cost of the bonds:

( ) ( )5

i 5i=1

0.0775 × ¥25billion (¥200/$) × $0.115956 billion¥25 billion = + 1 + y 1 + y

∑

Using Excel’s IRR command, we find that the internal rate of return on the bond is 6.48%, which is greater than the rate of return offered by the straight Euroyen bond. Thus, the bond is a good deal for investors if they can hedge at the forward rate of ¥200/$.

b. At maturity, in August 1990, the exchange rate was actually JPY144/USD. Was the

bond a good deal for investors?

Answer: We need to calculate the return to investors if the investors were unhedged. Investors received

USD115.956 million × JPY144/USD = JPY16.698 billion which is almost ¥7 billion less than if they had sold the face amount forward at the forward rate prevailing in August 1985. This loss happened because the yen appreciated by much more than was predicted by the forward rate. It is therefore also unlikely that the “fat coupon” would have made up for this huge capital loss. In fact, it is straightforward to compute the actual internal rate of return investors made on an unhedged investment in this bond. It is the rate that solves:

( ) ( )5

i 5i=1

0.0775 × ¥25billion ¥16.698 billion¥25 billion = + 1 + y 1 + y

∑

We find y = 1.28%. This is a much lower return than the yield offered in 1985 by a regular Euroyen bond! This is not so hard to understand considering that the payment at the end represents a capital loss of approximately 30%!


2. GBA Company wishes to raise $5,000,000 with debt financing. The funds will be repaid with interest in 1 year. The treasurer of GBA Company is considering three sources: i. Borrow USD from Citibank at 1.50% ii. Borrow EUR from Deutsche Bank at 3.00% iii. Borrow GBP from Barclays at 4.00% If the company borrows in euros or British pounds, it will not cover the foreign exchange risk; that is, it will change foreign currency for dollars at today’s spot rate and buy foreign currency back 1 year later at the spot rate prevailing then. The GBA Company has no operations in Europe. A representative of GBA contacts a local academic to provide projections of the spot rates 1 year in the future. The academic comes up with the following table:

Currency Spot Rate Projected Rate 1 Year in the

Future USD/GBP 1.5 1.55 USD/EUR 0.95 0.85

a. What is the expected interest rate cost for the loans in EUR and GBP?

Answer: For the EUR, the expected cost is

(1 + .03) × (0.85/0.95) - 1 = -0.0784 or -7.84% For the GBP, the expected cost is

(1 + 0.04) x (1.55/1.50) - 1 = 0.0747 or 7.47% These costs reflect both the interest costs and the expected capital gains or losses on the currency positions. If the academic’s projections prove accurate, the interest cost in GBP is higher than the GBP interest because the pound is expected to appreciate relative to the dollar, and GBA will need more than $5,000,000 to repay the pound loan. In contrast, the EUR is expected to decrease in value by more than 10% relative to the dollar, providing a large capital gain to GBA, which borrows in a depreciating currency and hence must use much less than the initial $5,000,000 to repay the euro loan.

b. What are the projected USD/GBP rate and USD/EUR rate for which the expected

interest costs would be the same for the three loans? Answer: These are the exchange rates that satisfy Uncovered Interest Rate Parity,

[ ] ( )( )t

1 + i($)E S(t+1,$/FC) = S(t,$/FC) ×

1 + i(FC)

where FC indicates either the EUR or the GBP. For the euro we find

[ ]t$0.95 1.015 $0.9362E S(t+1,$/FC) = × =

€ 1.03 €

Hence, the euro must depreciate only a little bit for the euro loan to be as cheap as the USD loan. For the pound, we obtain

[ ]t$1.50 1.015 $1.4639E S(t+1,$/FC) = × =

£ 1.04 £


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c. Should the company borrow in the currency with the lowest interest rate cost? Why or why not? Would your answer change if GBA did generate cash flows in the UK and continental Europe?

Answer: When using the forecasts of the academic, the lowest interest cost occurs in EUR. However, the academic’s forecast is quite far away from the “break-even” rates computed in part b., which may be closely related to the market determined forward rates. Moreover, currency forecasters do not have the best of records (see Chapter 10). Consequently, it is not at all clear that the “expected” low interest cost will actually be realized. If anything, the empirical evidence suggests that borrowing in low interest countries (in this case the US) may eventually save money (see Chapter 7 on the deviations from Unbiasedness). What a company can do is to investigate in what country its (multiplicative) credit spread is minimized, borrow in that country and hedge back to dollars when there is no reason, as in this case, to hold foreign exchange risk. If GBA generates cash flows in Europe, borrowing in currencies there may provide a natural hedge.

3. FE Company wishes to raise $1,000,000 with debt financing. The treasurer of FE

Company considers two possible instruments: i. A 2-year floating-rate note at 1% above 1-year dollar LIBOR on which interest is

paid once a year ii. A 2-year bond with an interest rate of 5% Currently, the dollar LIBOR is 1.50%.

a. Is it obvious which security the Treasurer should pick?

Answer: It is not at all obvious which debt to pick. While the two-year floating rate starts out at a lower rate (2.50% versus 5%), it is not clear at all what the eventual cost of the note will be to the company. The cost will also depend on the reset of the interest rate in the second year. If that interest is high enough, the 2-year bond may ex-post prove to be the cheapest financing vehicle. Typically, an upward sloping yield curve suggests the market does indeed expect that short-term interest rates will rise in the future.

b. Suppose the Treasurer believes that 1-year LIBOR, 1 year from now, will rise to

4.50%. Which security has the lowest expected AIC if borrowing fees are similar for the two instruments?

Answer: The AIC for the two-year bond is simply 5%. For the two-year floating rate note, we must compute the y that satisfies:

( ) ( ) ( )2 2

25,000 55,000 1,000,0001,000,000 = + + 1 + y 1 + y 1 + y

where we computed the coupon payments as 2.5% for year 1 and 5.5% (4.5% +1%) for year 2 on the $1,000,000 principal. The solution for y is 3.97%. Hence, at this forecast, the floating rate note is cheaper than the bond.


4. K3 Company wants to borrow $100 million for 5 years. Investment bankers propose to either do a syndicated Eurocredit or issue a Eurobond. The Eurocredit would be denominated in dollars, but the Eurobond would be denominated in different currencies for different markets (these issues are called tranches):

Terms: Syndicated Eurocredit Amount: USD100 million Upfront fees: USD1.25% Interest rate: Interest payable every 6 months; LIBOR plus 1.00% Terms: Eurobond Tranche 1: USD 50 million, Interest rate: 3.50% Tranche 2: ¥ 5,952 million (equivalent of USD50 million), Interest rate 1.5%

a. What are the net proceeds in USD for K3 for the Eurocredit loan?

Answer: The net proceeds for the Euro credit are (1 - 0.0125) × $100 million = $98.75 million (the fees amount to $1.25 million).

b. Assuming that the 6-month LIBOR in USD is currently at 2.00%, what is the

effective annual interest cost for K3 for the first 6 months of the loan?

Answer: The LIBOR convention is simple interest, so the 6-month interest rate is [2% + 1%] / 2 = 1.5%. To obtain the effective annual interest rate, we must annualize using compounding, (1 + 0.015)2 - 1 = 0.0302 or 3.02%

c. Compute an effective annualized interest rate cost (all-in cost) for the USD tranche

of the Eurobond.

Answer: The interest rate is 3.5% and is likely payable just once a year. Hence, this would also be the AIC for the loan. Of course, the question omits mentioning the costs of issuing the bond, and these costs should be taken into account in a proper AIC computation.

d. What information would you need to obtain the dollar all-in cost of the yen

tranche?

Answer: In addition to the transaction costs associated with the loan, we must know the terms for converting yen payments into dollar payments. For example, we could use the swap market (see Chapter 21), and we would need the terms for that, or we could use forward contracts, and we would need to know the available forward rates to convert dollars into yen for 1, 2, 3, 4, and 5 years into the future.


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e. What elements would you take into account to choose between the two possibilities?

Answer: With all the information given above (interest rate costs, loan issuance costs, and information on yen conversion rates), we can compute the AIC on the two tranches of the Eurobond issue. K3 can then compare its fixed borrowing costs with the Eurobond relative to the variable costs involved in the Eurocredit. While it appears that the floating rate Eurocredit will have interest expenses that are less than the Eurobond’s in the first year or so, this by no means guarantees that it will ex-post have the lowest costs. K3 should think of why it is optimal for the firm to incur interest rate risk. Perhaps its cash flows are cyclical and increase when short term interest rates increase, mitigating the interest rate risk embedded in the floating rate loan.

5. Suppose Intel wishes to raise USD1 billion and is deciding between a domestic dollar

bond issue and a Eurobond issue. The U.S. bond can be issued at a 5-year maturity with a coupon of 4.50%, paid semiannually. The underwriting, registration, and other fees total 1.00% of the issue size. The Eurobond carries a lower annual coupon of 4.25%, but the total costs of issuing the bond runs to 1.25% of the issue size. Which loan has the lowest all-in cost?

Answer: To keep things simple, we express the cash flows on bonds with a face value of 100, instead of $1 billion. We use a cash flow diagram similar to the one used in the Point-Counterpoint. The U.S. bond is special as it features semi-annual coupon payments (of 4.5%/2 = 2.25%). It is best to simply compute the AIC using 10 half-years. This AIC is then a semi-annual rate which must be annualized to be comparable to the annual AIC of the Eurobond. Because there are so many periods, we only show the first few and the last few. Negative numbers are in parentheses.

1. US Bond Half-Year Dollar Cash Flows

0 100 – 1.00 = 99.001 -2.25 2 -2.25

…. …. 9 -2.25

To annualize this AIC, we compute (1 + 0.0236)2 – 1 = 0.0478 or 4.78%. For the Eurobond, the computations are more standard:

2. Eurobond Year Euro Cash Flows

0 100 – 1.25 = 98.751 -4.25 2 -4.25 3 -4.25 4 -4.25


Hence, we see that, on an annualized basis, the Eurobond is substantially cheaper (by 24 basis points) than the U.S. bond.

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Chapter 12 International Equity Financing QUESTIONS 1. What are the differences between public, private, and banker’s bourses?

Answer: In public bourses the government appoints brokers, typically ensuring them a monopoly over all stock market transactions. With the deregulation wave in the 1980s and 1990s, most stock markets are now private. A private bourse is owned and operated by a corporation founded for the purpose of trading securities. Sometimes these corporations are publicly traded, or they may be owned by a set of financial institutions, in which case they are known as banker’s bourses.

2. What is the difference between a price-driven trading system and an order-driven trading system? Which system lends itself most easily to automation? Answer: In a price-driven system, dealers who act as market markers for certain stocks stand ready to buy at a bid price and sell at an ask price. In an order-driven system, share prices are determined in an auction that brings together the supply and demand of shares. The order-driven system can be most easily automated, as it is easy to let a computer store demand and supply schedules, and determine the equilibrium price.

3. Do we have a global stock market, as we have a global foreign exchange market? Answer: In the global foreign exchange markets, it is possible to trade any currency almost anywhere in the world at any time in the day. This is not true in the stock market, even though globalization has had profound effects on stock market trading. First, there has been increased cross listing of firms on exchanges throughout the world, with London and the US as important listing markets. Second, exchanges have extending their trading hours to make their markets more accessible to foreign traders located in other time zones. In addition, some exchanges have merged or created alliances with foreign exchanges to automatically cross-list their stocks. For example, Euronext in Europe combines the stock exchanges of Amsterdam, Brussels, Paris, Lisbon and LIFFE, the London derivatives market. Very recently (in 2007), the NYSE and Euronext merged to form a new company called NYSE Euronext, Inc., getting ever closer to a truly global stock market.

4. What is turnover?

Answer: Turnover is the total volume traded on an exchange during a year (or some other period) divided by the exchange’s market capitalization. It is often viewed as a liquidity indicator.

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5. What are the three primary components of transaction costs in trading stocks? Answer: Trading costs consist of direct costs such as brokerage commissions, the bid–ask spread, and market impact (the fact that the price may move against you when you trade a large order).

6. Does high turnover always signal lower transaction costs? Answer: No, the tables in the Chapter indicate a clear negative relation between the two, but it is not perfect. There are a number of high turnover emerging markets (such as Taiwan) that may have higher transaction costs than some lower turnover developed markets. The Illustration Box on the Casablanca exchange provides another example of an imperfect relation between turnover and trading costs.

7. What is the difference between an ADR and a GDR? Answer: An American depositary receipt (ADR) is used to list shares in the American market. It represents a certain number of original shares issued in the home stock market, and held in custody by a depositary bank. Global depositary receipts (GDRs) are similar to ADRs, but can be traded on many exchanges in addition to U.S. exchanges.

8. What motivates companies to cross-list their shares? Answer: Cross-listing a stock can lower a company’s cost of capital through several channels, including improved liquidity and better corporate governance. It can heighten the awareness of the firm’s brands, provide direct access to foreign capital, and make future capital access easier.

9. Has cross listing been beneficial for most listed companies? If yes, why doesn’t every

company cross-list? Answer: It appears that indeed cross-listing has mostly brought benefits for the firms that cross-list. However, firms for which cross listing is not beneficial should, of course, not do so. The costs associated with cross-listing have to do with the direct costs of registration, the potentially higher costs of more demanding accounting and reporting requirements, and the increased scrutiny and corporate governance that may erode the private benefits of controlling managers. Clearly, not every firm will have an incentive to cross-list.

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10. What is the difference between a GDR and a GRS? Answer: A GDR, like an ADR, represents negotiable claims on home-market ordinary shares (in bearer or registered form) and is issued by a depositary bank. Settlement of cross-border trades takes place daily through ADR issuances or cancellations (“conversions”) conducted by the depositary bank, and there are fees for such transactions. Finally, the depositary bank maintains ownership records and processes corporate actions. Global registered shares (GRSs) trade simultaneously in different markets around the world, in different currencies, with the shares being completely fungible across markets. They do not require the intervention of a depositary bank, but of course, shares can then also not be bundled or unbundled to facilitate trading in different markets. Finally, share ownership is more direct with a GRS than with a GDR. Holding a GRS gives investors the same voting privileges, rights to receive dividends, and so forth, as a regular shareholder has, whereas the depositary intermediary may impose certain restrictions.

11. What is a strategic alliance? Answer: A strategic alliance is an agreement between legally distinct companies to share the costs and benefits of a particular investment.

12. What is a joint venture? Answer: A joint venture is a type of strategic alliance where two or more independent firms form and jointly control a different entity, which is created to pursue a specific objective. The new entity tries to combine the strengths of each partner.

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PROBLEMS 1. The following table shows how average share prices jump (in percentage) after the

announcement that the stocks will be cross-listed (see Miller, 2000). The price response should be interpreted as corrected for risk and market movements that happened on the same day:

2. 3. All ADR

Issues 4. Capital

Raising 5. Non-Capital

Raising 6. Emerging markets 7. 1.5 8. 0.9 9. 2.8 10. Developed markets 11. 0.9 12. 0.7 13. 0.9 14. Total 15. 1.2 16. 0.8 17. 1.4

Although these numbers appear small, it is important to realize that announcements of equity issues, which are by definition capital raising, in a domestic context lead to an average negative return response of 2% to 3% (see, for instance, Masulis and Korwar, 1986). The main reason is that capital-raising equity issues are viewed as a signal of the managers that the firm may be overvalued in the stock market. Given what you learned in chapter, answer the following: a. Why is there a positive price response when a company’s shares are cross-listed?

Answer: The positive response likely reflects the reduction of the cost of capital (which increases the valuation of the firm) associated with cross listing. As indicated in Question 7, there are a variety of channels that may lead to a lower cost of capital, such as improved liquidity, a wider shareholder base, improved corporate governance, and effective integration within global capital markets.

b. Why might the response for emerging-market firms be larger than for developed-

market firms?

Answer: Because their own stock markets have poorer liquidity and corporate governance, the benefits may be relatively larger for emerging market firms. In particular, while most firms from developed markets are subject to “global pricing,” most emerging markets are still “segmented” from global capital markets, and listing in a developed market effectively integrates the firm into global capital markets. The move from segmented to global pricing tends to increase valuations because global discount rates tend to be lower than discount rates in segmented emerging markets.

c. Without knowing that equity issues in a domestic context are associated with

negative price responses, is the difference between capital-raising and non-capital-raising ADRs a surprise? Why or why not? Answer: Ignoring the negative signal of raising capital through the equity market, it is surprising that capital-raising ADRs would lead to a smaller price response than non-capital raising ADRs. That is because the fact that companies raise capital through the international capital market would suggest they have substantial growth opportunities that should raise the value of the firm.

2. Suppose you are a U.S.-based investor, and you would like to diversify your stock portfolio internationally. What advantages do ADRs offer you? Would it be wise to restrict your international portfolio to only ADRs?

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Answer: As we will discuss in Chapter 13, diversifying your portfolio internationally will offer significant benefits. However, since not all international firms have ADRs, the set of firms to invest in may not be large enough to exhaust the benefits of international diversification. In particular, it would tend to be the larger, more internationally oriented firms that will first cross-list, and these firms may be exactly the ones that are more heavily correlated with domestic firms (see Chapter 13 for more discussion on correlation and diversification benefits).

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Chapter 13 International Capital Market Equilibrium QUESTIONS 1. Is the volatility of the dollar return to an investment in the Japanese equity market the

sum of the volatility of the Japanese equity market return in yen plus the volatility of yen/dollar exchange rate changes? Why or why not?

Answer: It is not. Even though the dollar return on investing in Japanese equity is approximately the yen return on the Japanese equity market plus the rate of change in the dollar/yen exchange rate, the volatility of this sum is not the sum of the volatilities. Intuitively, because the equity risk and currency risk are not highly correlated, part of the volatility of the individual components is diversified away. Technically, the variance of the dollar returns can be written as follows:

Var[r(t + 1,¥) + s(t + 1)] = Var[r(t + 1,¥)] + Var[s(t + 1)] +2ρVol[r(t + 1, ¥)]Vol[ s(t + 1)] where r(t + 1,¥) is the yen-denominated equity return, s(t+1) is the rate of change in the dollar/yen exchange rate, and ρ is the correlation between the yen equity return and dollar/yen exchange rate changes. Because volatility, Vol, is the square root of the variance, we know that the volatility of the dollar return on a Japanese equity investment is

Vol[r(t + 1,¥) + s(t + 1)] = {Vol[r(t + 1,¥)]2 + Vol[s(t + 1)] 2 + 2ρVol[r(t + 1, ¥)]Vol[ s(t + 1)]}0.5

Clearly, only when the correlation is exactly 1 will the right-hand side have the form (A2 + 2AB + B2)0.5 = [(A + B)2]0.5 = (A + B)

and hence, only then will the volatility of the sum be the sum of the volatilities. Because of the perfect correlation, there is no natural diversification advantage to having exposure to two sources of risk. However, as long as ρ < 1, the total dollar volatility will be less than the sum of the two volatilities.

2. Why is the variance of a portfolio of internationally diversified stocks likely to be

lower than the variance of a portfolio of U.S. stocks?

Answer: With international stocks, the investor can diversify away U.S.-specific sources of volatility (e.g. U.S.–specific business cycle movements, changes in U.S. monetary policy, changes in U.S. interest rates, etc.). Technically, the variance of an equally weighted portfolio converges to the average covariance between these stocks when the number of stocks gets very large. The average covariance among U.S. stocks is higher than the average covariance among a set of U.S. and international stocks.

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3. How can you increase the Sharpe ratio of a portfolio? What type of stocks would you have to add to it in order to do so?

Answer: To increase the Sharpe ratio on your portfolio, you must add stocks that increase the expected return on your portfolio and/or reduce the volatility of the portfolio (for instance, because the stocks exhibit low correlation with the portfolio you already have). One way to think of the problem is to compute the following hurdle rate,

Hurdle rate = f*E[r]r + ρ Vol [r ]

Vol[r]× ×

In this equation rf is the risk free rate, ρ is the correlation between the portfolio you have and the stock you want to add to the portfolio, E[r] and Vol[r] are the expected return and volatility of the portfolio you are holding, and Vol[r*] is the volatility of the stock you want to add. The hurdle rate is higher when the existing portfolio has a high Sharpe ratio, the stock you are adding is more volatile, or there is high correlation between the return on the portfolio and the return on the stock you are adding to the portfolio.

4. Why is the hurdle rate in Section 13.2 lower for Japan than for Canada? Should U.S.

investors still invest in Canada?

Answer: From the formula in the answer to Question 3, we see that the two main drivers of the hurdle rates are the correlations between Canadian and U.S. returns and between Japanese and U.S. returns (reported in Exhibit 13.6), and the volatilities of Canadian and Japanese returns (reported in Exhibit 13.1). The most important number is the correlation. Of the G7 countries, the Canadian market returns have the highest correlation with U.S. returns, whereas the Japanese returns have the lowest correlation. It is this difference that makes Japan have the lowest hurdle rate and Canada the highest. Whether U.S. investors should still invest in Canada depends on their opportunity set. The hurdle rate for Canada, reported in Exhibit 13.7, suggests that even if the expected return on Canadian stock is a bit lower than that of the U.S., it is still a valuable investment that increases the Sharpe ratio. However, if the U.S. investor can invest in Japanese securities first, it is quite likely that the Canadian hurdle rate will exceed the expected return of the U.S.-Japan diversified portfolio. In that case, it may not be optimal to go long Canadian securities. Note that this answer depends on the historical numbers reported in the Exhibits. Some theories of portfolio choice (such as the CAPM) postulate that investors should hold portfolios that are well diversified and include all securities in line with their market capitalizations.

5. What is the mean standard deviation frontier, and what is the mean-variance-efficient

(MVE) portfolio?

Answer: The mean standard deviation frontier is the locus of the portfolios in expected return–standard deviation space that have the minimum variance for each expected return. It is therefore also often referred to as the minimum-variance frontier. The MVE is the portfolio on that frontier that maximizes the Sharpe ratio. It can be found by drawing a line emanating from the risk free rate that is just tangent to the mean standard deviation frontier. The tangency point represents the MVE’s expected return and standard deviation. The MVE is therefore also referred to as the tangency portfolio.


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6. What is the prediction of the CAPM with respect to optimal portfolio choice?

Answer: All investors should hold the same portfolio for risky assets, the market portfolio. The market portfolio contains all securities, and the proportion of each security is its market value as a percentage of total market value.

7. What is it prediction of the CAPM with respect to the expected return on any security?

Answer: The CAPM implies that the expected return of any security equals the risk-free rate plus the beta of the security multiplied by the market risk premium. The beta of the security is the covariance of its return with the return on the market portfolio divided by the variance of the market portfolio return. Hence, the risk premium on an individual security is a function of its covariance with the market portfolio.

8. What is the beta of a security?

Answer: As indicated in Question 7, the beta of the security is the covariance of its return with the return on the market portfolio divided by the variance of the market portfolio return. This beta can be estimated from a regression of excess returns on the security in question onto excess returns on the market portfolio (proxied by the world market portfolio return, for example). Sometimes, industry portfolios are used to reduce the sampling error in estimating the betas.

9. Why might it be useful to estimate the beta for a stock from returns on stocks within

its industry rather than from the stock itself?

Answer:Estimating a beta using a regression is often imprecise because a firm’s returns exhibit considerable idiosyncratic volatility. That is, much of the variation in a firm’s return is driven by firm-specific events. This idiosyncratic volatility reduces the fit of the regression and increases the standard errors of the estimates. If firms in the same industry have about the same systematic risk, which is a reasonable assumption, their betas will be about the same as well. A portfolio of firms diversifies away a lot of idiosyncratic risk and is consequently much less variable than an individual firm’s stock returns. Therefore, beta estimates from industry portfolios are more precise, and provide reasonable estimates for a firm’s beta.

10. What does it mean for an equity market to be integrated or segmented from the world

capital market?

Answer: Markets are integrated when assets of identical risk command the same expected return, irrespective of their domicile. Hence, in an integrated equity market, stocks are priced using global discount rates. In a segmented market, discount rates are country–specific. Segmentation usually arises through governmental interference with free capital markets. For example, if foreign investors are taxed or otherwise prohibited from holding the equities of a country, then that country’s assets are not part of the world market portfolio, and that country is said to be segmented from international capital markets. It is also conceivable that


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other factors (such as poor corporate governance or liquidity) keep foreigners from investing in an equity market, causing it to be effectively segmented.

11. What would you expect to happen to the risk-free rate and equity returns when a

segmented country opens its capital markets to foreign investment?

Answer: When a country unexpectedly opens its capital markets to foreign investors, we expect the real interest rate to decrease, and the stock market to rise in value. The real interest rate in the country should fall because the country’s residents are now free to borrow and lend internationally (which may reduce domestic demand for local funds), and there is additional foreign supply of capital. It is conceivable that before the liberalization, the government may have kept interest rates artificially low—for instance, through interest rate ceilings—in which case the interest rate may rise upon liberalization.

The equities of the country will now be priced globally, rather than locally. Using the intuition from the CAPM, equity discount rates will now be based on their covariances with the return on the world market portfolio and no longer on their covariances with the local market. The latter covariances are likely to be much larger than the covariances with the world market; hence the liberalization should lead to a lower risk premium for domestic stocks. Together with the lower risk free rate, the discount rates for local stocks should decrease, and, consequently, their valuations should increase. Simply put, foreign investors will bid up the prices of local stocks in an effort to diversify their portfolios, while all investors will shun inefficient sectors. Thus, equity prices should rise (as expected returns decrease) when a market moves from a segmented to an integrated state.

12. What accounts for the home bias phenomenon?

Answer: Home bias refers to the phenomenon that investors, even in the developed world, have not fully internationally diversified their portfolios which are consequently heavily invested in their own stock markets. No well-accepted explanation for why investors forego the benefits of international diversification exists.

Home bias is definitely declining over time, which suggests that the direct barriers to international investment did play a role in the past. For most countries, these barriers have been dismantled and can no longer explain why investors do not invest abroad.

Arguments such as the idea that currency risk increases the riskiness of foreign investments or that foreign investments are costlier than domestic ones are unlikely to be valid explanations. Because currency changes show little correlation with local equity markets, they add little to the volatility that U.S. investors face when investing in foreign equity markets. Moreover, currency volatility can be hedged. Transaction costs may play a role, but in order to generate the observed portfolio proportions of U.S. investors, U.S. investors would have to think that the average returns on foreign stocks were 2% to 4% per annum less than the realized average returns on foreign assets. It may be that these figures represent U.S. investors’ perceived transaction costs of foreign investing, but it is unlikely. Moreover, the huge volume of international capital flows is also inconsistent with the transaction costs story, as is the fact that foreign countries are home biased.

Perhaps the most popular explanation of home bias is that international investors have an informational disadvantage relative to local investors, which cause international investors to invest less abroad, or to not invest at all in unknown foreign markets. For public investments, this story also is not entirely appealing. It is easy enough to obtain information on foreign companies or to set up or use local investment managers. However, it may be that the quality of the information and a poor regulatory framework in terms of investor protection and corporate governance keep out U.S. institutional investors. This may explain


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why foreign companies like to list ADRs, which can thus be more easily included in institutional investors’ portfolios. Again, such an explanation would not explain why even investors in countries with poor corporate governance are still home biased. Ultimately, it appears that the main variable most negatively and robustly correlated with the degree of home bias is “distance,” suggesting that people invest more in countries with which they are more familiar.

13. Explain the basic principle of the APT.

Answer: The arbitrage pricing theory (APT) recognizes that the return on the market portfolio may not be the only potential source of systematic risks that affect the returns on equities. The APT postulates that other economy-wide factors can systematically affect the returns on a large number of securities. These factors might include news about inflation, interest rates, gross domestic product (GDP), or the unemployment rate. Changes in these factors will affect the future profitability of corporations, and they may affect how investors view the riskiness of future cash flows. This, in turn, will affect how investors discount future uncertain cash flows. When there are economy-wide factors that affect the returns on a large number of firms, the influences of these factors on the return to a well-diversified portfolio are still present. The influences of these factors cannot be diversified away. Consequently, the risk premiums on particular securities are determined by the sensitivities of their returns to the economy-wide factors and by the compensations that investors require because of the presence of each of these different risks.

14. Suppose AZT is a small value stock and that you use both the CAPM and the Fama-

French model to compute its cost of capital. Under which model is the cost of capital for AZT likely to be higher?

Answer: It is likely to be higher under the Fama-French model. The reason is that the Fama-French model has two additional factors in addition to the return on the value-weighted market portfolio in excess of the risk-free return, as in the CAPM. These factors are the difference in the return on a portfolio of small firms and the return on a portfolio of big firms (small minus big [SMB]) and the difference between the return on a portfolio of firms with high values of book equity to market equity (BE/ME) and the return on a portfolio of firms with low values of BE/ME (high minus low [HML]). These two factors carry positive risk premiums. As a small value stock, AZT stock will have positive exposures to these two factors and therefore likely have a higher cost of capital, than if only the CAPM were used.


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PROBLEMS 1. The EAFE is the international index comprising markets in Europe, Australia, and the

Far East. Consider the following annualized stock return data: Average U.S. index return: 14% Average EAFE index return: 13% Volatility of the U.S. return: 15.5% Volatility of the EAFE return: 16.5% Correlation of U.S return and EAFE return: 0.45

a. What would be the return and risk of a portfolio invested half in the EAFE (Europe,

Australia and Far East index) and half in the U.S. market? Answer: Using standard formulas for the expected return and volatility of a portfolio of two assets, we find:

P

1P 2 2 2 2 2 2

12 2 2

E[r ] = (0.5)×14% + (0.5)×13% = 13.5%

VOL[r ] = [(0.5) (15.5%) + (0.5) (16.5%) + 2(0.5) 0.45(15.5%)(16.5%)]

= 0.5[(15.5%) + (16.5%) + 2 0.45 15.5% 16.5%]13.63%

× × ×=

Note that this is lower than the volatility of either of the two indexes. b. Market watchers have noticed slowly increasing correlations between the United

States and the EAFE index, which some ascribe to the increasing integration of markets. Given that the volatilities remain unchanged, is it possible that the volatility of a portfolio that is equally weighted between the two indexes has higher volatility than the U.S. market?

Answer: Yes. For example, when ρ = 1.00, the variability of the equally weighted portfolio would just be the average volatility. There would be no risk reduction through diversification.

2. Let the expected pound return on a UK equity be 15%, and let its volatility be 20%.

The volatility of the dollar/pound exchange rate is 10%.

a. Graph the (approximate) volatility of the dollar return on the UK equity as a function of the correlation between the UK equity’s return in pounds and changes in the dollar–pound exchange rate.

Answer: The formula to use is:

Vol[r($)] = [{Vol[r(£)]}2 + {Vol[s]}2 + 2 ρ Vol[r(£)] Vol[s]]1/2

where ρ is the correlation. It is easy to see that the dollar volatility will be an increasing function of ρ. In particular:

Vol[r($), ρ = -1] = 10% Vol[r($), ρ = 0] = 22.36%

Vol[r($), ρ = 1] = 30% This formula assumes away the “cross-term.”


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b. Suppose the correlation between the UK equity return in pounds and the exchange rate change is 0. What expected exchange rate change would you expect if the UK equity investment is to have a Sharpe ratio of 1.00? (Assume that the risk-free rate is 0 for a U.S. investor.) Does this seem like a reasonable expectation?

Answer: The Sharpe ratio = E[r($)]

Vol[r($)], and Vol(r($)) = 22.36%, see Question a.

We also have: E[r($)] ≈ E[r(£)] + E[s] = 15% + E[s], as the expected pound return was given, but the expected exchange return must be computed to make the Sharpe ratio equal to one. That is, we must have

15% + E[s] 122.36%

= , or E[s] = 7.36%.

It seems rather unreasonable for the expected exchange rate change to be 7.36% unless there is a large interest differential between the two currencies (with the U.K. interest rate substantially lower than the U.S. interest rate).

3. Suppose General Motors managers would like to invest in a new production line and

must determine a cost of capital for the investment. The beta for GM is 1.185, the beta for the automobile industry is 0.97, the equity premium on the world market is assumed to be 6%, and the risk-free rate is 3%. Propose a range of cost-of-capital estimates to consider in the analysis.

Answer: The formula to use is the following:

Cost of GM equity capital = risk free rate + beta times market risk premium. We compute two estimates, using the two available beta estimates, one for GM and one for the automobile industry, which may be more precise (assuming GM’s financial leverage is not too different from that of the industry as a whole). Using GM’s beta, we obtain 3% + 1.185 x 6% = 10.11%. Using the industry beta, we obtain 3% + 0.97 x 6% =8.82%. So, considering a range between 8.80% and 10.20% is a reasonable range of cost-of-capital estimates to consider. In fact, there is also considerable uncertainty about the size of the equity premium on the world market, which may call for an ever-wider range of cost of capital estimates.


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4. Thom Yorke is a typical mean-variance investor. He likes high-expected returns and hates high variability in his portfolio returns. He is currently invested 100% in a diversified U.S. equity portfolio. The expected return on the portfolio is 12.46%, and the portfolio’s volatility (standard deviation) is 15.76%. Thom is considering adding some alternative investments to his portfolio. One investment he is considering is the STCMM fund, which invests in U.S. small-capitalization, high technology firms. Yorke has determined that the expected return on the fund is 14.69%, that its volatility is 32.5%, and that its correlation with his current portfolio is 0.7274. He is also intrigued by the LYMF fund, which invests in several emerging markets. The expected return on the fund is only 12%; it has 35% volatility and a correlation of 0.2 with his portfolio. The correlation of the LYMF fund with the STCMM fund is 0.15. Assume that the risk-free rate is 5%. a. If Yorke is interested in improving the Sharpe ratio of his portfolio, will he invest a

positive amount in one of the funds? Which one? Carefully explain your reasoning. Answer: We established that you will add an asset to your portfolio if

f fE[r*] - r E[r] - r > corr[r, r*]×Vol[r*] Vol[r]

with * indicating the new funds. Plugging in the numbers, we obtain:

Sharpe Ratios Investment Threshold

(Hurdle Rate) U.S. portfolio 0.4734 STCMM fund 0.2982 0.3444 LYMF 0.2 0.0947

For example, 0.2982 = [14.69% - 5%]/0.325 and 0.3444 = 0.4734 x 0.7274. Although the LYMF (“Lose Your Money Fast”) fund has a much lower Sharpe ratio than the STCMM (“Short-Term Money Mis-Management”) fund, it will get added to the portfolio, because of its low correlation with Thom's portfolio. The STCMM fund pretty much looks like a levered version of the portfolio Thom already has and seems not to eliminate much systematic risk.

b. Suppose Yorke is moderately risk averse (meaning he hates variability quite a bit),

but his friend, Nick Cave, is really quite risk tolerant and focuses primarily on expected returns. Both cannot short-sell securities, and both are thinking of splitting their entire portfolio between the U.S. portfolio that Yorke is currently holding, the STCMM fund, and the LYMF fund. They also do not invest in the risk-free asset and do not consider levering up risky portfolios. Compare the two investors’ optimal holdings. Who will invest more in the LYMF fund, and who will invest more in the STCMM fund? Why? Answer: While it is impossible to answer this question precisely without more information about how the two funds correlate, some outcomes are very likely. Maybe somewhat surprisingly the "risky" emerging markets fund will be held by the least risk-tolerant investors. Although very risky by itself, when added in small proportions to the portfolio Thom already has, the emerging market fund is a wonderful diversifier. He will surely hold


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the fund, since he can lower his risk without lowering expected returns much. Nick Cave on the other hand may actually invest a bit in the STCMM fund. If his preferences are such that he requires more than 12.46% return, he must hold some of the fund, since he cannot reach a better return with the two other investments. Needless to say, he will move along the mean-standard deviation frontier in riskier territory.

5. International economists continue to be puzzled by the phenomenon that investors

worldwide seem to be plagued by the home asset bias. Economists have pointed out that investors with mean-variance preferences (that is, they like higher expected returns and dislike higher volatility) ought to allocate much more of their wealth to foreign equities and bonds. Three explanations for the phenomenon are given below, all of them based on empirical facts. For each one of them, discuss whether the statements are true or false and in what sense they help rationalize or fail to rationalize the home bias puzzle. In answering the questions, assume that investors indeed have mean-variance preferences.

a. Investors should not hold foreign equities because they are more volatile and have

been yielding lower returns than U.S. stocks in recent years. Answer: This explanation is totally false. We established that you should add foreign securities to your portfolio as soon as the foreign Sharpe ratio exceeds the American Sharpe ratio times the correlation between the U.S. portfolio return and the foreign security return. Since these correlations are quite low, foreign securities definitely belong in your portfolio (at even rather low expected returns). The dimension totally forgotten in the statement here is correlation! Moreover, the statement seems to suggest that returns from the recent past will extrapolate into the future, whereas what drives optimal asset allocations is the expected return.

b. Home bias arises because investors face an additional risk when investing

internationally—namely, currency risk. Because currency risk makes returns more volatile but does not lead to a higher expected return, investing more in domestic assets is rational.

Answer: This is a much more subtle and rather sensible statement at first. Currency volatility drives up the volatility of foreign investment returns, although not by as much as one would think because the correlations between currency returns and equity returns are small. The problem is worse for bond returns though. Is the additional risk rewarded? Well, if the unbiasedness hypothesis holds, the foreign expected return on a hedged and unhedged investment is the same, so it is not rewarded. Moreover, most of the currency risk can be hedged away using forward contracts. This latter point makes this statement an unlikely explanation for the home bias phenomenon under UIRP, because one can eliminate the unrewarded risk using a rather "cheap" hedge. If UIRP does not hold, investors in some countries will earn risk premiums by investing internationally, which should make international investing attractive for at least a number of investors.

c. Home bias arises because investors have a non-traded domestic asset that they

care about as well—namely human capital. The returns to this asset can be thought of as labor income. It has been empirically determined that labor income correlates quite highly with U.S. stock returns.


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Answer: If the empirical statement about the correlation is true, human capital makes the home asset bias worse! This was the conclusion of an article by Marianne Baxter and Urban Jermann, published in the American Economic Review. To improve your portfolio's risk profile, you want to add assets, which have low correlations with your domestic assets. If investors turn out to have another domestic asset that correlates high with U.S. stocks (and which they really cannot get rid of!), they will be looking even harder for assets with low correlation with these domestic assets, which are to be found in the international securities markets.


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6. Consider Softmike, a software company. Softmike’s world market beta is 1.75. When a regression is run of Softmike’s return on the world market return and the global HML factor, the betas are 1.50 and –1.2, respectively. Assume that the world equity premium is 6%, the HML premium is 3%, and the risk-free rate is 5%. Compute the cost of equity capital using both the CAPM and the Fama-French model. Is Softmike a value company or a growth company? Answer: According to the CAPM, Softmike’s cost of equity capital is:

5% + 1.75 x 6% = 15.50%. According to the two-factor international Fama-French model, the cost of capital is:

5% + 1.50 x 6% -1.2 x 3% = 10.40%. The Fama-French model yields a much smaller cost of capital because Softmike is a growth company and loads negatively on the value factor, which in the Fama-French model is assumed to carry a positive premium.

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Chapter 14 Political and Country Risk QUESTIONS 1. Describe the differences between country risk and political risk. What is sovereign

risk?

Answer: Political risk is the risk that a government action will negatively affect a company’s cash flows. In the most extreme form of political risk, governments seize property without compensating the owners in a total expropriation (or nationalization). Country risk is a broader concept that encompasses both the potentially adverse effects of a country’s political environment and its economic and financial environment. For example, a recession in a country that lowers its aggregate demand and reduces the revenues of exporters to that nation is a realization of country risk. Labor strikes by a country’s dockworkers, truckers, and transit workers that disrupt production and distribution of products, thus lowering profits, also qualify as country risks. Clashes between rival ethnic or religious groups that prevent people in a country from shopping can also be considered country risks. In international bond markets, country risk refers to any factor related to a country that can cause a borrower to default on a loan. When country risk is taken in a narrow sense to be the risk associated with a government defaulting on its bond payments, it is called sovereign risk.

2. What economic variables would give some indication of the country risk present in a

particular country?

Answer: To help investors discriminate between financially and economically sound and financially and economically troubled countries, a number of economic variables are used, including the following: The ratio of a country’s external debt to its GDP The ratio of a country’s debt service payments to its exports The ratio of a country’s imports to its official international reserves A country’s terms of trade (the ratio of its export to import prices) A country’s current account deficit

These variables are directly related to the ability of the country to generate inflows of foreign exchange. Factors such as inflation and real economic growth are useful as well.

Chapter 14: Political and Country Risk 67

3. Suppose an MNC is considering investing in Bolivia. Will an overall assessment of Bolivia’s country risk suffice to understand the political risk present in the investment?

Answer: First, an analysis of country risk may definitely be informative about political risk in a narrow sense. The better a country’s economic situation, the less likely it is to face political and social turmoil that will inevitably harm foreign and domestic companies. However, as the answer to question 1 notes, country risk is broader than political risk. Consequently, the MNC should try to find measures and analyses that focus more narrowly on political risk in Bolivia (such as the political risk ratings from the PRS group).

Second, the industry in which a multinational corporation operates can affect its exposure to political risk. Calculating a company’s industry-specific risk is not as straightforward as calculating more general political risks. The MNC should consider issues such as whether it has primarily local competitors (more subject to political risk) rather than primarily foreign competitors (less subject to political risk). Analogously, if the MNC is the source of considerable foreign exchange earnings for the host country or is the vehicle for important technology transfer, it might be less subject to government interference than one without such advantages. The MNC must also ask whether the region in which it operates has more or less political risk than Bolivia as a whole. This raises questions such as: How much power do the country’s regional governments have versus the national government? What is the attitude of local communities to the MNC’s proposed projects? Are there any armed opposition groups in the area, and how do they view the presence of a foreign company?

4. What are three political risk factors?

Answer: Political risk factors include the risk of expropriation (see Question 1), contract repudiation (when government revoke contracts without compensating companies for their existing investments in projects or services), currency controls that prevent the conversion of local currencies to foreign currencies, and laws that prevent MNCs from transferring their earnings out of the host country. Corruption, civil strife, and war are also factors.

5. When, where, and why did the Debt Crisis start?

Answer: The Debt Crisis started in Mexico on August 12, 1982 when Mexico announced that it could no longer make the scheduled payments on its foreign debt. Mexico requested loans from foreign governments and the IMF, and it started negotiating with its commercial bank creditors. This constituted the start of the Debt Crisis. By the end of the year, 24 other countries had requested restructuring on their commercial bank debts.

The Debt Crisis indirectly resulted from the large oil price increases that occurred in the 1970s. The OPEC countries saved their windfall income in the form of Eurocurrency deposits at international banks (usually denominated in dollars) at floating interest rates. The banks in turn loaned these “petrodollars,” as they were called at the time, to developing countries, typically in the form of Eurocredits that were quoted at a spread above the floating interest rate they paid to the OPEC countries.

Banks viewed the lending as profitable and relatively riskless for three reasons. First, the loans were made at a spread over the banks’ borrowing costs. Thus, the banks were not exposed to changes in interest rates, as they would have been if they had borrowed short term and loaned at long-term fixed rates. Second, the banks eliminated exchange rate

Chapter 14: Political and Country Risk

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exposure as the debts were denominated in dollars, which was the currency the OPEC countries had deposited. Third, the banks syndicated the loans, taking diversified exposures to a number of countries to avoid too much exposure to a single country. As a result, during the 1970s, the debt of non-OPEC developing countries owed to banks in industrialized countries, especially banks in the United States, increased significantly. A mix of external shocks affecting industrialized countries and developing countries in the 1980s and macroeconomic mismanagement in developing countries triggered the actual Debt Crisis. The steep increase in the oil price in the late 1970s was met with a staunchly anti-inflationary monetary policy in a number of countries, particularly in the United States under Federal Reserve Bank Governor Paul Volcker. The macroeconomic situation in the developed world was now totally different than it had been in the early 1970s: Real interest rates were high, the global economy was in recession, and the dollar was strong. This situation contributed to low prices of commodities on the world markets and low demand for the exports of developing countries. With the huge dollar appreciation and high dollar interest rates, the developing countries faced steep interest payments in dollars at the same time as their export revenues were falling. Suddenly, the default risk of the loan portfolios of international banks had greatly increased. The situation was exacerbated by the fact that developing countries often had not used the money they borrowed very productively and had run what were ultimately seen to be unsustainable economic policies.

6. What is debt overhang?

Answer: Debt overhang is the notion that a country saddled with a huge debt burden has little incentive to implement economic reforms or stimulate investment because the resulting increase in income will simply be appropriated by the country’s creditors to pay an outstanding large debt. From this perspective, it may be better in certain situations for countries to stop or severely restrict repaying their debts.

7. What is a debt buyback? Why was a program of debt buybacks not sufficient to

resolve the Debt Crisis?

Answer: A debt buyback is one example of the policies that many countries attempted to employ in an effort to reduce their debt burden. In a debt buyback, the country repays a loan at a discount. Such efforts did not suffice to resolve the Crisis for various reasons. First, programs such as debt buybacks require monetary resources, which were in limited supply. Second, such programs may not be very effective in reducing the outstanding debt. Several economists argue that when a country uses its own resources to buy back its troubled debt at a discount, the country’s creditors are the only ones that benefit. Essentially, the debt buyback program drives up the secondary market price of the debt, reducing its effectiveness. For example, in the famous case of the 1988 Bolivia debt buyback, Bolivia used $34 million in donations to reduce the market value of its debt by only $8.8 million. It is ultimately more effective to deal with a solvency problem by taking a comprehensive approach that involves debt relief. That is essentially what the Brady plan set out to do.


8. What were the main characteristics of the Brady Plan?

Answer: The 1989 Brady Plan, developed by then U.S. Treasury Secretary Nicholas Brady, had the following important characteristics: 1) It put pressure on banks to offer some form of debt relief to developing countries. 2) It called for an expansion in secondary market transactions aimed at debt reduction. 3) The IMF and the World Bank were urged to provide funding for these “debt or debt service reduction purposes.” 4) It offered banks a menu of different debt-reduction methods, including providing new loans. Each bank could choose the restructuring option that it found most suitable from a menu of possibilities established in a debt-reduction agreement between the debtor-country government and its creditor banks. In order to mitigate free-rider problems, no bank could opt out. Among the options available to the banks were the following: Buybacks: The debtor country was allowed to repurchase part of its debt at an agreed

discount (a debt-reduction option). Discount bond exchange: The loans could be exchanged for bonds at an agreed

discount, with the bonds yielding a market rate of interest. Par bond exchange: The loans could be exchanged at their face value for bonds

yielding a lower interest rate than that one on the original loans. Conversion bonds combined with new money: Loans could be exchanged for

bonds at par that yielded a market rate of return, but banks had to provide new money in a fixed proportion of the amount converted (an option for banks unable or unwilling to participate in debt reduction or debt service reduction).

Because the bond options were particularly popular choices, the Brady Plan ended up securitizing the debt into easily tradable bonds, called Brady Bonds. Quite a few Brady bonds have “official enhancements” attached to them, such as collateral provisions funded by international organizations and certain governments.

9. Why should the discount rate not be adjusted for political risk?

Answer: Consider a multinational corporation with a shareholder base that is globally diversified. In this case, the discount rate should reflect only international, systematic risks. Chapter 13 showed that systematic risks are typically related to how an MNC’s return in a particular country covaries with the world market return. If the risk of loss from political risk does not covary with the world market return, no adjustment to the discount rate is necessary. Positive covariation between the cash flows from the project and the world market return increases the required global discount rate. Consequently, unless political risk, which adversely affects the MNC’s investment returns, is systematically high when the world market return is low, political risk should not enter the calculation of the discount rate. Instead, the company’s cash flows should be adjusted for the presence of political risk.

To fully understand this argument, suppose a company takes out an insurance policy against political risk and that the policy covers all contingencies and has no deductible. In this case, a company would simply compute its expected cash flows as if there were no political risk and then subtract the insurance premium it must pay each year from the cash flows of the project. The cash flows would then be discounted at the usual discount rate. While it is possible to purchase political risk insurance, it is seldom the case that an investment can be fully insured. If a company chooses not to purchase political risk insurance, it must incorporate into its forecasts of future cash flows how they might be affected by various political risks, such as expropriation, unexpected taxation, and so forth.


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10. What are some examples of organizations that provide country risk ratings?

Answer: Organizations such as Euromoney, Institutional Investor, the Economist Intelligence Unit, and Political Risk Services Group produce country risk ratings for most countries in the world. Both quantitative information from countries and qualitative information obtained from experts are used to evaluate country and political risks.

11. How can we use current quantitative information to predict future political events,

such as expropriation?

Answer: Most risk-rating services look for measurable attributes and indicators that, in the past, have been correlated with future risk events. For example, left-wing governments may be associated with actions that harm foreign investors, such as stricter labor regulations or outright nationalization. Countries with unstable governments and frequent, forced elections have a higher probability of electing left-wing officials within a particular period than countries with stable governments. This is true even if a right-wing government may be in power currently. Consequently, the frequency of government changes is used as a risk attribute. Generally, political risk services examine indicators of political risk, such as the following: Political stability (for example, the number of different governments in power over time) Ethnic and religious unrest; the strength and organization of radical groups The level of violence and armed insurrections; the number of demonstrations Property rights enforcement The extent of xenophobia (fear of foreigners); the presence of extreme nationalism

The different political variables are then weighted and added to provide one country score. Such overall scores may be the best indicators of an extreme political risk event, such as expropriation. Some services, such as the PRS Group, do provide subcomponents that may be more correlated with the specific political risk event, such as “democratic accountability” and “government stability.” In particular, one subcomponent, Investment Profile, specifically considers risk factors that directly affect the risk of expropriation.

12. Suppose a multinational corporation is particularly worried about ethnic warfare in a

few countries in which it is considering investing. Do country risk ratings have information on this particular risk?

Answer: Yes, some rating services, such as the PRS Group’s ICRG (International Country Risk Guide) system have subcomponents within their overall political risk rating. It so happens that “ethnic tensions” is one such subcomponent, providing assessment of disagreements and tensions between various ethnic groups that may lead to political unrest or civil war. Other subcomponents that may also be worthwhile investigating are “internal conflicts” (an assessment of internal political violence in the country) and “religious tensions” (an assessment of the activities of religious groups and their potential to evoke civil dissent or war).


13. Can Brazil issue a bond denominated in dollars at the same terms (that is, at the same yield) as the U.S. government? Why or why not?

Answer: When a sovereign borrower issues bonds in its own currency, there is technically no default risk because the government can typically simply print money to pay back the debt holders. When a sovereign borrower issues bonds in a different currency, though, a default is possible because the government must earn foreign exchange to pay off the bondholders. This possibility of default will be priced into the yield on the bond. Hence, Brazil will face a higher yield on its dollar borrowings than the U.S. government does. The difference between the two yields is called the country credit spread. For example, if the yield on a 5-year U.S. Treasury bond is 5%, and the yield on a 5-year dollar bond issued by the Brazilian government is 10%, the Brazilian country credit spread is 5%. These spreads, which vary over time as the bonds trade in secondary markets, are, of course, an indication of country risk.

14. What stops governments from defaulting on loans or bonds held by foreigners?

Answer: Sovereign defaults are different from a company going bankrupt because it is very difficult to take a country to court, and there are no formal bankruptcy proceedings in place for sovereigns. Nonetheless, sovereigns still must worry about the consequences of defaulting because of the following issues: The assets of the country located in the jurisdiction of a creditor may be seized. The country will not be able to borrow as readily in the future, which can have grave

economic consequences. The country could find its ability to engage in international trade severely curtailed.

These costs of defaulting must be weighed against the benefit that the debt must no longer be serviced. Governments have defaulted on bonds periodically throughout history, a recent example being Argentina in 2001.

15. What is a Brady bond?

Answer: Brady bonds were created as a consequence of the Brady plan which aimed at resolving the Debt Crisis for many countries. In February 1990, Mexico became the first country to issue Brady bonds, and Brady deals were subsequently done by Argentina, Brazil, Bulgaria, Costa Rica, the Dominican Republic, Jordan, Nigeria, Philippines, Poland, Uruguay, and Venezuela.

The vast majority of outstanding Brady bonds are U.S. dollar denominated, and they tend to have very long maturities (20 to 30 years). The bonds are evenly divided between fixed and floating-rate instruments.

Brady bonds have a number of special features: Principal collateral: All par and discount bonds are collateralized by U.S. Treasury

zero-coupon securities having similar maturities. Interest collateral: For some bonds, the government issuing the Brady bonds deposits

money with the New York Federal Reserve Bank in amounts covering 12 to 18 months’ of interest payments on a “rolling” basis.

Sovereign portion: The remaining cash flows are subject to sovereign risk. Bonds sometimes also include detachable warrants or recovery rights predicated on

a country’s economic performance. Mexico’s Value Recovery Rights (VRRs), for example,


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were based on numerous variables, including oil prices, GDP, and oil production levels. In June 2003, Mexico retired the last of $35 billion in Brady bonds.

16. Should the “stripped” yield on a Brady bond typically be higher or lower than the

regular yield? Explain.

Answer: It should be higher as the stripped yield removes the effect of the collateral enhancements. It is the yield-to-maturity of the unenhanced interest stream after removing the present value of the U.S. Treasury zero-coupon bond that collateralizes the principal and the present value of the guaranteed interest stream. This stripped yield is truly based on the credit quality, or sovereign risk, of the issuing nation. The collateral enhancements imply that the difference between the yield-to-maturity on the Brady bond and a U.S. Treasury bond of comparable maturity (sometimes called the “blended” yield) cannot really be viewed as a country spread.

17. How is a political risk probability related to a country spread?

Answer: First, recall that the country spread is an indication of the default risk of a bond. However, although a government might default on its bonds as a result of a political event, this does not necessarily mean that it will also expropriate the assets of the MNCs that lie within its borders. Hence, the correlation between political risk and sovereign default risk is far from perfect.

Second, even when we assume that the political risk probability is perfectly correlated with the probability of default, the probability of default is not easily recovered from the yield spread. In fact, the information needed is not the spread itself but the bond’s price, coupon rate, U.S. interest rates (assuming the bond is dollar denominated) and potentially information on collateral enhancements. We can then estimate this probability by making some additional assumptions: the political risk probability is constant over time. the recovery value in the case of default is zero (although computations could be made

assuming a particular recovery value). default is an idiosyncratic risk.

The computations should also take into account any collateral enhancements. As a simple example, assume a bond with price equal to $92 (per $100 par value).

Assume that the coupon rate is 7%, that the bond has only 2 years to go, and that the one-year and two-year U.S. dollar interest rates are 5%. We denote the probability of default by p. The first year, the probability that $7 is paid to the bondholders is 1 – p. The second year, there is a probability of (1 – p)2 that the bond will not be in default, and there is a probability of (1 – p) p that there will be a default. It therefore must be the case that

<DM> 22

7 10792 = (1 - p) + (1 - p)1.05 1.05

Here, we equate the value investors assign to the bond with the present value of the expected cash flows, discounted at U.S. risk-free rates. We can do this because the possibility of default is taken into account in the probabilities, and we assume that default is an idiosyncratic risk. This equation can be solved for p, the probability of default. We find p = 6.01%. If we believe sovereign risk as reflected in this default probability is perfectly correlated with the political risk embedded in a cash flow analysis for capital budgeting, this is the probability we should use.


18. What are Cetes? What are Tesobonos?

Answer: Cetes are treasury bills issued by the Mexican government, denominated in Mexican peso. Tesobonos are also treasury bills issued by the Mexican government, but they are effectively U.S. dollar denominated. That is, while both the purchase amount and the principal payment are denominated and made in pesos, the principal payment is fully indexed to the change in the exchange rate between the dollar and the peso.

Let’s consider an example using a 3-month Tesobonos. Suppose the yield on the Tesobonos is 5%. If the Mexican peso exchange rate didn’t change in value, the investor would receive

<DM>0.051 + = MXN1.0125

4

after 3 months. Suppose though that the Mexican peso devalues by 5% over the 3-month period. Then, the amount paid to the investor will be

<DM>0.051 + 1.05 = MXN1.063125.

4⎛ ⎞⎜ ⎟⎝ ⎠

Note that this represents a 25.25% (6.3125% × 4) return on an annualized basis. Hence, Tesobonos provided investors with protection against peso devaluation.

19. What are the three main types of political risk covered by political risk insurance?

Answer: Insurance is typically available for currency inconvertibility (when a company is unable to convert its foreign earnings to its home currency or otherwise transfer the earnings out of the host country), expropriation (protects MNCs and lenders against confiscation, expropriation, nationalization, and other acts by the host government that adversely affect the MNC’s cash flows, including “creeping expropriation” – a series of acts that cumulatively result in some expropriation of value – discriminatory legislation, the deprivation of assets or collateral, the repudiation of a concession, and the failure of a sovereign entity to honor an arbitration award issued against it), and war and political violence (compensates a company when war or civil disturbances cause damage to the MNC’s assets or cash flows).

20. What are some organizations or firms that provide political risk insurance?

Answer: There are three potential sources of political risk insurance: international organizations aimed at promoting foreign direct investment (FDI) in developing countries, government agencies, and the private market. Among international organizations providing insurance, the World Bank’s Multilateral Investment Guarantee Agency (MIGA), the Inter-American Development Bank (IDB), and the Asian Development Bank (ADB) are the best known. Most OECD countries have national agencies that provide domestic companies with political risk insurance. Examples include the Overseas Private Investment Corporation (OPIC; United States), Nippon Export and Investment Insurance (formerly EID/MITI; Japan), the Export Development Corporation (EDC; Canada), the Export Credits Guarantee Program (ECGD; United Kingdom), and the Export Finance and Insurance Corporation (EFIC; Australia). The private market has grown significantly and now includes firms such as Lloyd’s, American International Group (AIG), Sovereign Risk Insurance Ltd., and Zurich Emerging Markets Solutions.


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21. How is it possible to embed political risk insurance in a capital budgeting analysis?

Answer: Assuming that political risk insurance would be complete and perfect, it is straightforward to embed political risk insurance in capital budgeting analysis because such insurance simply generates an annual cost. The cost of the premium must be deducted from the cash flows, and the discount rate should only reflect systematic, not political risk. Of course, political risk insurance is typically somewhat incomplete, so it may be necessary to consider cash flow scenarios in which political risk events still lead to loss of cash flows in computing the expected cash flows from a project.

22. What is project finance?

Answer: Project financing is a method of financing that is specific to a particular project, typically industrial in the nature, in which the providers of the funds are repaid primarily from the cash flows generated by the project.

PROBLEMS 1. In February 1994, Argentina’s currency board was in place, and 1 peso was

exchangeable into 1 dollar. The following interest rates were available: U.S. LIBOR 90 days: 3.25% Peso 90-day deposits: 8.99% Dollar interest rate in Argentina, 90-day deposits: 7.10%

The latter two rates were offered by Argentine banks. What risk does the difference between the 7.10% dollar interest and 3.25% LIBOR reflect? What risk does the difference between the rate on 90-day pesos and 90-day dollar deposits by Argentine banks reflect? Answer: The difference between the 7.10% dollar interest rate and the 3.25% LIBOR rate reflects country risk, the chance that the Argentine banks will not repay the loan. Both deposits are in dollars so the interest rate difference does not reflect currency risk. The difference between the rate on 90-day pesos and 90-day dollar deposits by Argentine banks reflects currency risk. The deposits are offered by Argentine banks (so the credit risk is the same), but if the currency board is abandoned, the peso may no longer be worth 1 dollar.

2. Consider the numbers in the previous question. Assume that if the peso were to

depreciate, investors figure it will depreciate by 25%. Also, assume that if the Argentine bank were to default on its dollar obligations, it would pay nothing to investors. Compute the probability that the peso will devalue and the probability that there will be a default.

Answer: We can follow the analysis done on the Tesobonos case in Chapter 14 to compute the default probability. We equate the return of the LIBOR rate [iLIBOR] with the return for dollar deposits in Argentina [iARG], taking into account a default probability of p.

LIBOR ARG1 + i = (1 + i )(1 - p) + 0×p Consequently:


0.03251+4p = 1 - = 0.95%0.07101 + 4

, or almost 1%.

The devaluation probability computation was first illustrated in chapter 7. Under Uncovered Interest Rate Parity, the expected return on the peso and dollar deposits at Argentine banks should offer the same expected return. Consequently, we should have

E[S(t+1)] 0.0899 0.07101 + = 1 + S(t) 4 4

⎡ ⎤⎢ ⎥⎣ ⎦

(*)

where S(t+1) is the spot exchange rate at time t+1 in dollars per peso. Hence, E[S(t+1)] is the expected exchange rate. Let q be the probability of devaluation. We have

E[S(t+1)] = (1 - q) S(t) + q S(t) (1 - 0.25) = S(t)[1 - 0.25×q] where S(t)=1. Substituting in Equation (*), we obtain

0.07101 + 1 4q = 1 - 0.08990.25 1 + 4

⎡ ⎤⎢ ⎥

× ⎢ ⎥⎢ ⎥⎣ ⎦

= 1.85%

The probability of a 25% devaluation is 1.85%. However, these computations implicitly assume that the devaluation and default

events are independent. In this case, they very likely are not. As long as the currency board is in place, Argentine banks are much less likely to default on the dollar deposits. Let’s see what happens under the following assumptions. There are three possible states: 1. No default occurs, and the currency board remains in place. 2. The peso depreciates, but the Argentine banks do not default. 3. Both the currency board collapses and the banks default on all their deposits and pay depositors nothing.

We know the probability of scenario 3 occurring, as it is simply the probability of default, p = 0.95%. Given the correlation between default and depreciation, what is the probability of the second scenario? Let’s call it q*. The total probability of the peso depreciating is consequently q*+p. However, when scenario 3 materializes, holders of peso deposits receive nothing. So the expected gross dollar return on peso deposits is:

0.0899 0.0899(1 - p - q*)(1 + ) + q*(1 + )0.75 + p×04 4

where we used the fact that if the currency devalues it devalues to $0.75 / peso. This return must equal the return on dollar deposits in the U.S. Therefore, we obtain:

0.0899 0.03251 + (1 - p) - 1 + 4 4q* =

0.08990.25 1 + 4

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

⎡ ⎤⎢ ⎥⎣ ⎦

Using p = 0.95%, we find: q* = 1.81%.

Consequently, the total chance of some bad event happening (scenarios 2 or 3) is slightly reduced under this assumption.


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3. Consider a 10-year Brady bond issued by Brazil. The coupon payment is 6.50%, and the par value has been collateralized by a U.S. Treasury bond. The current price of the bond is $98 (per $100 in par value). Compute the (blended) yield-to-maturity for the bond. What is the stripped yield? Assume that the spot rates on the dollar are the ones reported in Exhibit 14.8.

Answer: We list the cash flows as in Exhibit 14.8:

Year Dollar Cash Flows Dollar Spot Rates

1 6.5 3.50 2 6.5 4.10 3 6.5 4.65 4 6.5 5.05 5 6.5 5.55 6 6.5 5.85 7 6.5 6.05 8 6.5 6.25 9 6.5 6.35

10 106.5 6.50

The (blended) yield to maturity for the bond is the solution to the following equation:

2 10

6.5 6.5 106.598 = + + ... + 1 + y (1 + y) (1 + y)

Using Excel, we find: y = 6.78%

The stripped yield takes into account that part of the bond value is collateralized by U.S. Treasuries, in this case the par value of the bond. The current value of $100 worth of par value is:

Collateral value = 10

$100 $53.27.(1 0.065)

=+

This means that the “stripped” price equals $98.00 - $53.27 = $44.73. The stripped yield, y , then follows from re-doing the computation above, adjusting the price and stripping out the par value repayment:

2 10

6.5 6.5 6.544.73 = + + ... + 1 + y (1 + y) (1 + y)

It follows that y = 7.45%. The stripped yield is substantially higher than the blended yield.


4. Right at the height of the Mexican peso crisis in January 1995, the default probabilities on U.S. dollar-denominated emerging-market bonds were quite high. A British investment bank, assuming that these bonds would pay 15 cents on the dollar upon default, calculated a 61% chance of default on Venezuelan bonds. Consider a bond with 5 years left to maturity, paying a coupon of 12%. The par value is 80% collateralized by American Treasury bonds. Assume that the U.S. interest rate is 5% for all maturities. What is the price of a bond with $100 par? Answer: The first step in the computation is to compute the value of the collateral,

Value collateral 5

80$= = $62.68.(1.05)

To figure out the value of the remaining cash flows, we list the cash flows and probabilities in an exhibit:

No Default Case Default Case Year Discount Factor Cash

Flow Probability Cash

Flow Probability

1 0.9524 12 0.39 15 0.61 2 0.9070 12 (0.39)2 15 0.61(0.39) 3 0.8638 12 (0.39)3 15 0.61(0.39)2

4 0.8227 12 (0.39)4 15 0.61(0.39)3

5 0.7835 32 (0.39)5 15 0.61(0.39)4

The cash flow in year 5 reflects the coupon of 12 and the non-collateralized part of the par value (20). Note that the probability of retrieving this $32 in full in year 5 is (0.39)5 = 0.009 < 1%. The current value of these cash flows is now simply the probability-weighted sum of the cash flows, discounted using U.S. discount rates (see the formula in Equation (14.4)). The

discount factor in the 2nd column reflects these interest rates and is given as 1

1.05⎛ ⎞⎜ ⎟⎝ ⎠

n

for the

n-th year in the future. The present value of the “no default” cash flow is $7.18. The value of the “default” cash flows is $13.77. Hence, the total value of the bond is:

$62.68 + $7.18 + $13.77 = $83.63. The collateral represents the most important part of the value.


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5. Badwella United Company (BUC) is worried that its banana plantation in El Salvador will be expropriated during the next 2 years. However, BUC, through an agreement with El Salvador’s central bank, knows that compensation of $100 million will be paid if the plantation is expropriated. If the expropriation does not occur, the plantation will be worth $400 million 2 years from now. A wealthy El Salvadoran has just offered $160 million for the plantation. BUC would have used a discount rate of 23% to discount the cash flows from its Honduran operations if the threat of expropriation were not present. Evaluate whether BUC should sell the plantation now for $160 million. (Hint: Set up a cash flow diagram.)

Answer: Let’s first make the simplifying assumption that the probability of expropriation is constant and let’s denote it by p. There are three possible scenarios as indicated in the following diagram:

Scenario Probability Value Discount Factor

No expropriation (1 – p)2 400 2

1 = 0.66101.23

Expropriation in year 1

p 100 1 0.81301.23

=

Expropriation in year 2

(1 - p) p 100 2

1 = 0.66101.23

We assume that the 23% discount rate applies to the expected cash flows of the project, and we account for the possibility of expropriation in computing expected cash flows. Hence, we have:

Value project = 2

2 2

400 (1 ) 100 100 (1 )1.23(1.23) (1.23)

p p p p× − × × −+ +

Because the problem does not mention the probability of expropriation, we cannot come up with a final answer. BUC should evaluate the probability of expropriation in El Salvador and check whether the value of the project is more or less than 160 million. A useful computation is to find that value of p for which the value of the project is exactly 160 million. Using trial and error, we find that p = 33.05%. This looks like a rather high probability of expropriation, implying that there is only a (1 – p)2 = 44.82% chance that the full value of the project will be realized two years from now.


6. You are the chief financial officer of Clad Metal, a U.S. multinational with operations throughout the world. Your capital budgeting department has presented a proposal to you for a 5-year ore-extraction project in Mexico. The expected year-end net dollar cash flows are as follows:

Year Net Cash Flow 1 $100,000 2 200,000 3 250,000 4 250,000 5 250,000

The initial required investment in plant and equipment is $500,000, and the cost of capital is 16%.

a. What is the present value of the project? Should the project be undertaken?

Answer: We can construct the following cash flow diagram:

Year Dollar Cash Flows

Discount Factors

Present Value of the Cash

Flows

1 100,000 0.8621 86,207 2 200,000 0.7432 148,633 3 250,000 0.6407 160,073 4 250,000 0.5523 138,073 5 250,000 0.4761 119,028

Consequently, the present value of the project is 652,105 and the NPV 152,105. The project should be undertaken.

b. You notice that the proposal does not include any analysis of political risk, but

you are concerned about potential expropriation of the investment. You therefore decide to call a meeting to discuss political risk. Who would you invite to this meeting? What information or data would you need? How would you arrive at a political risk probability estimate?

Answer: You could invite people familiar with the local political and economic situation or, if you do not have the in-house expertise, consult political ratings and the accompanying information from any one of the political ratings services discussed in this chapter. If available, you may also consult price information on Mexican bonds (preferably issued in dollars) and information on premiums for political risk insurance for projects in Mexico. As discussed at length in this chapter, it is not straightforward to convert information on country spreads into expropriation probabilities but under certain assumptions, it can be done (see Question 17 for an example). Political insurance premiums directly give an idea of how much should be subtracted each year from expected cash flows to account for political risk.


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c. Assume that, at the end of the meeting, you decide that the probability of expropriation is between 5% and 7%. Also assume that there is no compensation in the case of expropriation. Would you approve the project?

Answer: Let p be the probability of expropriation. We recompute the present value of the cash flows, taking the probability of expropriation into account. This implies multiplying the cash flow in year t by (1 – p)t. Doing this reduces the present value to 557,921 in the case of p = 5% and 532,822 in the case of p = 7%. In both cases, you should continue to approve the project!

d. Given the possibility of expropriation, might you want to reconsider converting

Mexican peso expected cash flows at forward rates?

Answer: It depends how these forward rates were derived. If the forward exchange rates come from the Chicago Mercantile Exchange, they only reflect currency risk (as the CME is an AAA organization). If the cash flow computations take into account expropriation risk, these are the appropriate forward rates to use. If, however, the forward exchange rates were derived using local interest rates, they will also partially reflect country and political risk. Taking into account expropriation risk in the cash flow computations would therefore account for the political risk twice.

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Chapter 15 International Capital Budgeting QUESTIONS 1. Can an investment project of a foreign subsidiary that has a positive net present value when

evaluated as a stand-alone firm ever be rejected by the parent corporation? Assume that the parent accepts all projects with positive adjusted net present values.

Answer: Yes, we know that countries impose withholding taxes on the dividends that are repatriated from subsidiaries to parent corporations. These taxes lower the value of the project to the parent. The parent must also be aware of the possibility of future problems accessing the foreign exchange market from the subsidiary’s country. In general, political risk could be different for a subsidiary of a multinational corporation versus a local stand-alone firm.

2. How do licensing agreements, royalties, and overhead allocation fees affect the value of a foreign project?

Answer: Licensing agreements, royalties, and overhead allocation fees are true costs to the subsidiary or to the stand-alone firm that would be operating in the foreign country producing and selling the products of the multinational corporation. Thus, licensing agreements, royalties, and overhead allocation fees reduce the income in the foreign country. Nevertheless, these cash flows provide profit to the parent corporation. Licensing agreements and royalties provide pure profit to the parent as no costs are incurred, and overhead fees provide net profit as they cover costs incurred by the parent. Thus, these cash flows are quite valuable to the parent.

3. Why does an adjusted net present value analysis treat the present value of financial side effects

as a separate item? Isn’t interest expense a legitimate cost of doing business?

Answer: The adjusted net present value approach to capital budgeting starts by valuing the free cash flows to the all-equity cash firm. It then adds other sources of value associated with how the firm is financed. Compared to the weighted average cost of capital approach, the numerator cash flows are the same – the free cash flow to the all equity firm. In contrast to WACC analysis which discounts these cash flows with a discount rate that is a weighted average of the after-tax required return on the debt and the rate of return on the levered equity, the ANPV analysis uses the rate of return on the unlevered assets to get the all-equity value. Students sometimes think that the deductibility of interest as a business expense is therefore missing, and they want to reduce the all-equity free cash flows by the after-tax interest payments. This misses the fact that the value of the interest tax shields is being added as a separate source of value in ANPV, whereas it is included in WACC. Also, it misses the fact that when the equity holders lever the firm, they get the principal on the debt up front and don’t have to put as much equity into the firm for its investments. The present value of the future cash outflows for interest payments and repayment of principal equal the initial value of the principal, in which case it is only the tax shield that needs to be valued. ANPV does this separately.

Chapter 15: International Capital Budgeting

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4. What is meant by the net present value of the financial side effects of a project?

Answer: Generally, these effects arise from the costs of issuing securities, the taxes or tax deductions associated with the type of financing instrument used (including the tax deductibility of the interest paid on the debt), the costs of financial distress, and the availability of subsidized financing from governments.

5. Why is it costly to issue securities?

Answer: The investment bankers who handle the issuing of securities either to the public or to private investors are financial intermediaries, and they must be compensated for the use of their scarce resources. This compensation includes a monetary fee, but it also often includes an underwriting discount, or spread. The underwriting discount between what the corporation receives from issuing the securities and what the public pays for the securities is often a large part of the compensation of the investment bank that underwrites the issue.

6. What is an interest tax shield? How do you calculate its value?

Answer: The interest tax shield on a debt is the deduction for interest expense. Therefore, it is equal to the corporate tax rate times the amount of interest, Dτ r D . This tax deduction is discounted at the stated debt rate, which is the market debt rate associated with that debt. Thus, the discounted present value of a perpetual interest tax shield is

( ) ( ) ( )D D D

2 3D D D

τ r D τ r D τ r D+ + + ... = τ D1 + r 1 + r 1 + r

7. What is an interest subsidy? How do you calculate its value?

Answer: Interest subsidies arise when governments are willing to lend to corporations at below market interest rates. Such subsidies add value to a project. The appropriate discount rate for an interest subsidy is the market’s required rate of return on the debt of the corporation because the corporation is just as likely to default on a subsidized loan from the government as it is on a normal loan at market interest rates. Suppose that the government lets a corporation borrow a principal of D for one period at a subsidized interest rate of rS < rD, which is the market’s required rate of return on the corporation’s debt. The corporation borrows D in the first period, and it repays (1 + rS)D in the second period. Because the actual interest payment is deductible, the corporation also gets a tax deduction of τ rS D in the second period. The present value of the cash flows of the subsidized debt discounted at the market’s required rate of return on the corporation’s debt is therefore

( )( ) ( )

( )( ) ( )

S D SS S

D D D D

1 + r D r - r Dτ r D τ r DD - + = + 1 + r 1 + r 1 + r 1 + r

The value of a loan at a subsidized, below-market, interest rate has two components: the present value of the interest subsidy, which is the difference between the interest paid on a market loan and the interest on the subsidized loan, plus the present value of the actual interest tax shield. In both cases, the present value is taken at the market’s required rate of return on the debt.


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8. What are growth options? Provide an example of one in an international context.

Answer: A growth option arises when a firm undertakes a project and obtains an option to do another project in the future. The option to do the second project adds value to the first project. A growth option might include a firm’s ability to sell a new product that is successful in the domestic market in the international marketplace. Growth options are specific examples of real options that also include the ability of a firm to shut down a plant or a mine until operating conditions improve or to delay an important operating decision until more information can be gathered. Real options are valuable.

9. What is the difference between EBIT and NOPLAT?

Answer: The acronym EBIT is earnings before interest and taxes. It represents the before-tax operating profit of the firm. The acronym NOPLAT is net operating profit less adjusted taxes. It is found by taking the taxes out of EBIT that would be paid by the all-equity firm. It is therefore the after-tax operating profit of the all-equity firm.

10. Why is it important to understand and manage net working capital?

Answer: The stock of net working capital is the amount of inventory, cash, and accounts receivable minus accounts payable that the firm must have on hand to run its business. If the business can be run with a lower net working capital, this amount of assets could be given to investors. Conversely, increases in net working capital use after-tax profits that the firm could otherwise use to finance capital expenditures or pay to investors. As such, changes in net working capital are investments that the firm makes in its future profitability.

11. What does CAPX mean, and why is it a firm’s engine of growth?

Answer: CAPX is an acronym that is short for capital expenditures. These are investments that the firm is making in physical plant and equipment that will produce output in the future. Consequently, if the firm wants to grow, it will have to do CAPX, and in this sense, CAPX is the firm’s engine of growth.

12. Why is it sometimes assumed that CAPX equals depreciation in the later stages of a project?

Answer: As a project matures, there are no more planned investments in which case the scale of the project is fixed. But, the physical plant and equipment have an economic lifetime and must be replaced. If accounting depreciation matches economic depreciation, setting CAPX equal to depreciation is appropriate. You should be aware that accounting depreciation often fails to match economic depreciation because of inflation. The higher the rate of inflation, the more severe this problem is unless the accounting depreciation is indexed to inflation in some way. Because CAPX will be spent on real plant and equipment, the nominal amount of expenditures may be somewhat greater than the amount the accounts are allowed to deduct for the book value of depreciation.


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13. What is the terminal value of a project? How is it calculated?

Answer: The terminal value of a project is the present discounted value of all future free cash flows in the years beyond an explicit forecasting horizon. If we generate explicit forecasts of free cash flows for the next 10 years, the terminal value is the present discounted value of free cash flows in years 11 to infinity. One typically assumes that future free cash flows will grow at the rate g, and the discount rate for these perpetual cash flows is r. The starting value in year 11 is (1+ g) higher than the expected free cash flows in year 10. From the perpetuity formula for a growing cash flow, we know that

( )( )

tE [FCF(t+10)] 1 + gTerminal value in year 10 =

r - g

After calculating the terminal value in year 10, that quantity must then be discounted to year 0 by multiplying by the appropriate discount factor, which is 1 / (1 + r)10:

( )10

Terminal value in year 10Terminal value in year 0 = 1 + r

The growth rate g should reflect the expected rate of inflation in the currency of the forecasts because the project’s real capacity from its CAPX assumptions will be fully utilized, and new real investments would have to be made for there to be additional real growth. These real investments are typically not in the forecasts, so the only source of growth in nominal terms is expected inflation.

14. What is meant by the cannibalization of an export market?

Answer: When you choose to change how you service a market to which you are exporting, either because you are building a new plant in the foreign country or you are expanding production in an existing plant, you would like to know the incremental profitability of this new project. Cannibalization of exports refers to the lost exports in this market that you are now serving differently if no market can be found for the goods that were formerly being exported to that country. These lost exports could be from the parent or from another one of its foreign subsidiaries in a different country. The lost profits on these exports must be considered to be a cost of accepting the new project. If the exports that were formerly being sent to the country can be sold elsewhere in the world, there is no cannibalization.

15. What are the primary sources of value to IWPI-U.S. in establishing a Spanish subsidiary?

Answer: The primary sources of value for IWPI-U.S. are the dividends that will be received by the parent that represent the after-tax free cash flows of the subsidiary, the profits from royalties and licensing fees, and the profits on intermediate parts that are sold to the Spanish subsidiary.

16. Why are the profits on exports of intermediate goods by IWPI-U.S. to IWPI-Spain included as

part of the value of the project? Answer: Even though the intermediate goods are sold by IWPI-U.S. to IWPI-Spain at an internally determined transfer price, this price should incorporate profit to the parent. We explicitly discuss transfer pricing issues in Chapter 19 where we argue that the government authorities require that transfer prices be done at market prices that would be observed between third parties. If IWPI-U.S. sells replacement parts for its hinges and handles, it will have a retail price for these intermediate parts, and those prices will determine the transfer prices.


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17. What risks are present in the IWPI-Spain project? How do they affect the value of the project?

Answer: The primary source of risk is the business risk of selling wooden furniture in Europe. The expected free cash flows of the project are taken from a probability distribution that represents the possible ups and downs of the business due to cyclical fluctuations in Europe as well as idiosyncratic events particular to IWPI. The systematic business risk of the project is reflected in the fact that the beta of the project is 1.1. The beta is the perceived covariance of the return on the project with the return on the world market portfolio divided by the variance of the return on the world market portfolio. Thus, assuming an equity risk premium of 8.5%, the expected free cash flows are discounted by an all-equity required rate of return that is 9.35 percentage points above the risk free interest rate.

PROBLEMS 1. What percentage of the adjusted net present value of the IWPI-Spain project arises from cash

flows that will occur more than 10 years in the future?

Answer: The present value of the cash flows from years 11 to infinity is €32.06 million. The total ANPV of the project is €84.64 million. Thus, the terminal value of the project contributes 37.9% of the ANPV of the project.

2. How sensitive is the value of IWPI-Spain to the assumed discount rate of 20%? What happens

to the value of the project if the rate is 22% instead?

Answer: When the project was discounted with 20%, upon adding together all the costs and benefits of the project, we found ANPV of IWPI-Spain = – €78.40 million in initial costs + €70.66 million from dividends + €62.64 million from royalties and fees + €27.60 million from exports + €0.38 million from the interest tax shield + €1.76 million from the interest subsidy = €84.64 million When the project is discounted at 22%, the values change to

ANPV of IWPI-Spain = – €78.40 million in initial costs + €59.31 million from dividends + €53.43 million from royalties and fees + €23.60 million from exports + €0.38 million from the interest tax shield + €1.76 million from the interest subsidy = €60.08 million A 10% increase in the discount rate from 20% to 22% causes the value of the project to fall by 29%. Furthermore, if there is cannibalization of exports, the value of the project becomes negative because the present value of lost exports is €64.05 million.


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3. What would be the terminal values of the profits from IWPI-Spain if they were expected to grow in real terms at 1% rather than 0%?

Answer: We know that the ability of the project to grow in real terms requires additional real investments, that is, additional capital expenditures. If these capital expenditures are zero NPV projects, the terminal value will increase by the amount of the investment.

4. How much does the value of IWPI-Spain, viewed as a stand-alone firm, change if the royalty fee

is increased by 1% and the overhead allocation fee is reduced by 1%? What is the change in value to IWPI-U.S.? What is the source of this change in value?

Answer: We know that because the royalty and the overhead fee are costs to the stand-alone firm and are calculated as a percentage of revenue, the profitability of the stand-alone firm is not affected by lowering the fee from 2% to 1% and raising the royalty rate from 5% to 6%. The present value of the after-tax royalties and fees also doesn’t change because the firm gets a tax credit for the withholding tax paid, and it can fully utilize the tax credit. Therefore, the after-tax value of the royalties and fees remains €62.64 million even though the royalty is taxed at a lower rate.

5. Valuing Metallwerke’s Contract with Safe Air, Inc.

Consider the discounted expected value of the 10-year contract that Metallwerke may sign with Safe Air in Chapter 9. In the initial year of the deal, Metallwerke sells an air tank to Safe Air for $400. It costs €696 to produce an air tank. The current exchange rate is €2/$. Assume that 15,000 air tanks will be sold the first year. Make the following other assumptions in your valuation: a. The demand for air tanks is expected to grow at 5% for the second year, 4% for the third

and fourth years, and 3% for the remaining life of the contract. b. Euro-denominated costs are expected to increase at the euro rate of inflation of 2%. c. The base dollar price of the air tank will be increased at the U.S. rate of inflation plus one-

half of any real depreciation of the dollar relative to the euro, but the base dollar price will be reduced by one-half of any appreciation of the dollar relative to the euro. The U.S. rate of inflation is expected to be 4%.

d. The dollar is currently not expected to strengthen or weaken in real terms relative to the euro.

e. The German corporate income tax rate is 50%. f. The appropriate euro discount rate for the project is 17%. g. Metallwerke typically establishes an account receivable for its customers. At any given time,

the stock of the account receivable is expected to equal 10% of a given year’s revenue. h. Accepting the Safe Air project will not require any major capital expenditures by

Metallwerke. Can you determine the value of the contract to Metallwerke?

Answer: The value of the project can be determined by discounting the expected incremental free cash flows from the project. The following spreadsheet demonstrates how to do this.

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Valuing Metallwerke's 10-year Contract with Safe Air Year 0 1 2 3 4 5 6 7 8 9 10 US Inflation 4% 4% 4% 4% 4% 4% 4% 4% 4% 4%Euro Inflation 2% 2% 2% 2% 2% 2% 2% 2% 2% 2%Euros per dollar 2.0000 1.9615 1.9238 1.8868 1.8505 1.8149 1.7800 1.7458 1.7122 1.6793 1.6470 Retail Price per tank (dollars) 400 416 433 450 468 487 506 526 547 569Cost per tank (euros) 696 710 724 739 753 768 784 799 815 832 Growth in demand 5% 4% 4% 3% 3% 3% 3% 3% 3%tanks sold 15,000 15,750 16,380 17,035 17,546 18,073 18,615 19,173 19,748 20,341 All cash flows below are in euros Revenue 11,769,231 12,604,846 13,371,221 14,184,191 14,901,911 15,655,948 16,448,139 17,280,415 18,154,804 19,073,437Cost of goods sold 10,440,000 11,181,240 11,861,059 12,582,212 13,218,872 13,887,747 14,590,467 15,328,744 16,104,379 16,919,260EBIT 1,329,231 1,423,606 1,510,161 1,601,979 1,683,039 1,768,201 1,857,672 1,951,670 2,050,425 2,154,176NOPLAT @ 50% tax 664,615 711,803 755,081 800,990 841,520 884,101 928,836 975,835 1,025,212 1,077,088 Working Capital 1,176,923 1,260,485 1,337,122 1,418,419 1,490,191 1,565,595 1,644,814 1,728,041 1,815,480 1,907,344Change in Working Capital 1,176,923 83,562 76,637 81,297 71,772 75,404 79,219 83,228 87,439 91,863 Free Cash Flow -512,308 628,242 678,443 719,693 769,748 808,697 849,617 892,608 937,774 985,225 Discount factors @ 17% 0.8547 0.7305 0.6244 0.5337 0.4561 0.3898 0.3332 0.2848 0.2434 0.2080 Present value of FCF -437,870 458,939 423,600 384,064 351,091 315,261 283,088 254,199 228,258 204,964 Value of Project 2,465,593

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The first lines establish the background data. U.S. inflation is forecast to be 4% and German inflation is forecast to be 2%. The real exchange rate is forecast to be constant, so the nominal euro/dollar exchange rate is forecast to satisfy relative PPP. The first year nominal exchange rate is therefore

€2 1.02 €1.9615× = $ 1.04 $

The first year retail price is set at $400, and it is assumed to grow at the U.S. rate of inflation because there are no forecasts of real appreciation or real depreciation of the dollar. The first year unit cost of production is €696, and it is expected to grow at the German rate of inflation. Demand in the first year is 15,000 tanks, and demand is expected to grow at 5% in year 2, 4% in years 3 and 4, and 3% in all remaining years. Revenue is the €/$ exchange rate times the dollar retail price times the number of units sold. Cost of goods sold is the euro cost per unit times the number of units. EBIT (Earnings before interest and taxes) is revenue minus costs of goods sold. NOPLAT (Net operating profit less adjusted taxes) subtracts the 50% tax rate times EBIT from EBIT. The only investment that the project requires is an increase in the firm’s working capital. The stock of working capital is forecast to be 10% of revenue, and the change in working capital in the first year is therefore €1,176,923. Subtracting the change in net working capital from NOPLAT gives expected free cash flow because there is no incremental depreciation and no capital expenditures. This expected free cash flow is discounted at 17%, a rate that reflects the riskiness of the project. The value of the 10-year project is therefore €2,465,593. This valuation assumes that Metallwerke has the spare capacity to produce the extra tanks, and that it does not incur any additional capital expenditures because of the increased use of its capital. It also assumes that Metallwerke does not issue any debt to finance the project.

6. Deli-Delights Inc. Deli-Delights Inc. is a U.S. company that is considering expanding its operations into Japan. The company supplies processed foods to storefront delicatessens in large cities. This requires Deli-Delights to have a centralized production and warehousing facility in each of these cities. Deli-Delights has located a possible site for a Japanese subsidiary in Tokyo. The cost to purchase and equip the facility is ¥765,000,000. Perform an ANPV analysis to determine whether this is a good investment, under the following assumptions: a. The average per-unit sales price will initially be ¥400. b. First-year sales will be 15 million units, and physical sales will then grow at 10% per annum

for the next 3 years, 5% per annum for the 3 years after that, and then stabilize at 3% per annum for the indefinite future.

c. First-year variable costs of production will be ¥225 per unit of labor and $1.75 per unit of imported semi-finished goods. Administrative costs will be ¥300 million.

d. Depreciation will be taken on a straight-line basis over 20 years. e. Retail prices, labor costs, and administrative expenses are expected to rise at the Japanese

yen rate of inflation, which is forecast to be 1%. Dollar prices of semi-finished goods are expected to rise at the U.S. dollar rate of inflation, which is expected to be 4%.

f. The yen/dollar exchange rate is currently ¥85/$, and the yen is expected to appreciate at a rate justified by the expected inflation differential between the yen and dollar rates of inflation.

g. There will be a 4% royalty paid by the Japanese subsidiary to its U.S. parent. h. The Japanese corporate income tax rate is 37.5%, and there is a 10% withholding tax on

dividends and royalty payments. i. The yen-denominated equity discount rate for the project is 13%.


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j. Net working capital will average 6% of total sales revenue. k. Capital expenditures will offset depreciation. l. All of the Japanese subsidiary’s free cash flow will be paid to the parent as dividends. m. The corporate income tax rate for the United States is 34%. n. Deli-Delights Inc. has sufficient other foreign income that will allow it to fully utilize any

excess foreign tax credits generated by its Japanese subsidiary. o. Deli-Delights Inc. does not plan to issue any debt associated with this project.

Answer: The solution is presented in the following spread sheet pages. The first lays out the facts. Inflation is expected to be 4% in the United States and 1% in Japan. The current exchange rate is ¥85/$ and is expected to satisfy relative purchasing power parity in which case the yen is expected to appreciate. Deli-Delights expects to sell 15 million units at ¥400 per unit, and its retail price is expected to grow at the Japanese rate of inflation. Expected growth in volume is given as 10% for three years, then 5% for three years after that, and then 3%. The imported part initially costs $1.75 per part, and that price is expected to grow at the U.S. rate of inflation.

The next Exhibit builds the value of the subsidiary as a stand-alone firm. Revenue is retail price time quantity. Costs of goods sold is total labor and material costs. The royalty payment is a cost to the stand-alone firm of 4% of revenue. Depreciation is 5% of the initial investment of ¥765 million. Administrative costs are ¥300 million and growing at 1%. Revenue minus costs is EBIT. Notice that the project is unprofitable for the first 6 years, in which case the stand-alone firm will not owe any tax, and it will be able to avoid future taxes by taking advantage of tax loss carry forwards. Thus, NOPLAT equals EBIT. Working capital is 6% of revenue, and we get the subsidiary’s free cash flow by subtracting the change in net working capital from NOPLAT under the assumption that expected future capital expenditures equal depreciation. With the low Japanese rate of inflation, this is not a terrible assumption. Notice that free cash flows are forecast to be negative until year 10.

The discount rate is 13%, and the terminal value is calculated as a perpetuity beginning in year 11, growing at 1%, and discounted at 13%. Thus, the terminal value is

( ) ( )10

¥10 million × 1.01 = ¥24 million0.13 - 0.01 × 1.13

While we are told that the demand will be growing in real terms, we have chosen the conservative assumption that growth is equal to inflation because we have not included any additional capital expenditures that would be necessary to finance the additional real growth. The initial investment is ¥765 million, in which case we find that the value of the stand-alone firm is negative ¥1,492 million. Thus, no one would want to license the Deli-Delights name and pay a royalty to the U.S. corporate headquarters to operate in Japan. The third exhibit takes the Deli-Delights parent perspective. The first thing to determine is the present value of any dividends that will be received from the subsidiary. The dividends are the positive free cash flow from the subsidiary. These only arrive in year 10. The firm must pay a 10% withholding tax on the dividend, and it will receive that amount as a tax credit to offset U.S. taxes. The grossed-up dividend is just the gross dividend because there is no credit given for Japanese income taxes paid, because the Japanese subsidiary is not sufficiently profitable to have to pay tax. Thus, the U.S. parent owes 34% of the gross value of the dividend, but it only has to pay that amount minus the tax credit that it receives for the withholding tax. The real value to the parent from the subsidiary comes in the form of royalty payments. These are also subject to a Japanese withholding tax of 10%, and it will receive that amount as a tax credit to offset U.S. taxes. The grossed-up royalty is just the gross royalty. Thus, the U.S. parent owes 34% of the gross value of the royalty, but it only has to pay that amount minus the tax credit that it receives for the withholding tax. The after-tax value of the royalty starts at ¥158 million in year 1 and grows to ¥292 million in year 10. The terminal value of future royalty payments, discounted to the present is ¥723 million.


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The net present value of the project adds the present value of the after-tax dividends and the present value of the after-tax royalties, and subtracts the initial investment and the present value of the negative free cash flows in years 1-9 that the parent will have to send to the subsidiary as additional investments. The net present value of the project is ¥565 million or $7 million at the current exchange rate. This analysis understates the value of the project if there is profit on the intermediate parts. Since no information was given on the profit to the parent from these parts, we assumed that this source of value was zero.

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Valuing Deli-Delights Japanese Subsidiary as a Stand-alone Firm: Basic Data

Year 0 1 2 3 4 5 6 7 8 9 10

USD Inflation 4% 4% 4% 4% 4% 4% 4% 4% 4% 4%JPY Inflation 1% 1% 1% 1% 1% 1% 1% 1% 1% 1%Yen per dollar 85.00 82.55 80.17 77.85 75.61 73.43 71.31 69.25 67.25 65.31 63.43 Retail Price (yen) 400 404 408 412 416 420 425 429 433 437Growth in Unit Sales 10% 10% 10% 5% 5% 5% 3% 3% 3%Unit Sales (in millions) 15.00 16.50 18.15 19.97 20.96 22.01 23.11 23.81 24.52 25.26Labor Cost per unit (yen) 225 227 230 232 234 236 239 241 244 246Total Labor Cost (millions of yen) 3,375 3,750 4,166 4,628 4,908 5,205 5,520 5,743 5,974 6,215Imported Part Cost (dollars) 1.75 1.82 1.89 1.97 2.05 2.13 2.21 2.30 2.39 2.49Imported Part Cost (yen) 144.46 145.90 147.36 148.84 150.32 151.83 153.35 154.88 156.43 157.99Total Part Cost (millions of yen) 2,167 2,407 2,675 2,972 3,151 3,342 3,544 3,687 3,836 3,990


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Valuing Deli-Delights Japanese Subsidiary as a Stand-alone Firm: The Cash Flows

All cash flows below are in millions of yen Revenue 6,000 6,666 7,406 8,228 8,726 9,254 9,814 10,209 10,620 11,048 Cost of goods sold 5,542 6,157 6,840 7,600 8,060 8,547 9,064 9,430 9,810 10,205 Royalty 240 267 296 329 349 370 393 408 425 442 Depreciation 38 38 38 38 38 38 38 38 38 38 Administrative Costs 300 303 306 309 312 315 318 322 325 328 EBIT -120 -99 -75 -48 -33 -17 0 11 23 35 Potential Tax @ 37.5% -45 -37 -28 -18 -12 -6 0 4 9 13 Actual Tax 0 0 0 0 0 0 0 0 0 0 NOPLAT -120 -99 -75 -48 -33 -17 0 11 23 35 Working Capital 360 400 444 494 524 555 589 613 637 663 Change in Working Capital 360 40 44 49 30 32 34 24 25 26 CAPX = Depreciation Free Cash Flow -480 -139 -119 -98 -63 -49 -34 -12 -2 10 Discount factors @ 13% 0.88 0.78 0.69 0.61 0.54 0.48 0.43 0.38 0.33 0.29 Present value of FCF years 1-10 -425 -109 -83 -60 -34 -23 -14 -5 -1 3 Terminal Value 24 Initial Investment 765 NPV of Stand-alone Subsidiary -1,492 NPV of Stand-alone Sub (in $s) -18


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Valuing Deli-Delights Japanese Subsidiary - The Parent Perspective

Year All cash flows below are in millions of yen 0 1 2 3 4 5 6 7 8 9 10 Dividends Declared 0 0 0 0 0 0 0 0 0 10 Withholding Tax @ 10% 0 0 0 0 0 0 0 0 0 1 Net of Tax Dividends Received 0 0 0 0 0 0 0 0 0 9 Foreign Tax Credit 0 0 0 0 0 0 0 0 0 1 Grossed Up Dividend 0 0 0 0 0 0 0 0 0 10 Potential U.S. Tax @ 34% 0 0 0 0 0 0 0 0 0 3 Actual U.S. Tax 0 0 0 0 0 0 0 0 0 2 After-Tax Dividends 0 0 0 0 0 0 0 0 0 7 Discount factors @ 13% 0.88 0.78 0.69 0.61 0.54 0.48 0.43 0.38 0.33 0.29 PV of Dividends yrs 1-10 0 0 0 0 0 0 0 0 0 2 Terminal Value 18 Royalty Cash Flows 240 267 296 329 349 370 393 408 425 442 Withholding Tax @ 10% 24 27 30 33 35 37 39 41 42 44 Net of Tax Royalty Received 216 240 267 296 314 333 353 368 382 398 Foreign Tax Credit 24 27 30 33 35 37 39 41 42 44 Grossed Up Royalty 240 267 296 329 349 370 393 408 425 442 Potential U.S. Tax @ 34% 82 91 101 112 119 126 133 139 144 150 Actual U.S. Tax 58 64 71 79 84 89 94 98 102 106 After Tax Royalty 158 176 196 217 230 244 259 270 280 292 Discount factors @ 13% 0.88 0.78 0.69 0.61 0.54 0.48 0.43 0.38 0.33 0.29 PV of Royalty yrs 1-10 140 138 136 133 125 117 110 101 93 86 Terminal Value 723 Initial Investment 765 Aditional investments 425 109 83 60 34 23 14 5 1 PV of additional investments 376 85 57 37 19 11 6 2 0 NPV to Parent 563 NPV of Stand-alone Sub (in $s) 7

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Chapter 17 Risk Management and the Foreign Currency Hedging Decision QUESTIONS 1. Why would an entrepreneur find it desirable to hedge his or her foreign exchange risk?

Answer: An entrepreneur would find it desirable to hedge foreign exchange risk because the profits from the entrepreneurial venture are a significant part of the entrepreneur’s wealth. Unlike regular investors, entrepreneurs are unable to diversify away such risks through transactions in their own portfolios. Hence, if forward rates are unbiased predictors of future spot rates, risk-averse entrepreneurs will choose to hedge their future foreign currency cash flows because doing so will reduce the variance of the flows without changing their expected values in the domestic currency. Therefore, reducing the variance of future profits would increase the entrepreneur’s expected utility.

2. Explain Modigliani and Miller’s argument that hedging is irrelevant. What are the most

likely violations of Modigliani and Miller’s assumptions in actual markets?

Answer: Modigliani and Miller argued that a corporation’s financial policies, such as issuing debt, hedging foreign exchange risk, and other purely financial risk management activities, do not change the value of the firm’s assets unless these financial transactions lower the firm’s taxes, affect its investment decisions, or can be done more cheaply than individual investors’ transactions can be done.

The reason that reducing the uncertainty of future cash flows, per se, does not lead to a rationale for hedging is that it may not change investors’ perceptions of the firm’s systematic risk. We know from modern portfolio theory that the required rate of return on the equity cash flows of a corporation does not depend on the standard deviation of the firm’s cash flows but only on the systematic risk associated with those cash flows. The fact that a firm’s cash flows are uncertain is a necessary but not a sufficient condition for discounting the cash flows at a discount rate higher than the risk-free interest rate. Hence, unlike in the case of an entrepreneurial firm, if hedging merely reduces the unsystematic risk of the corporation’s cash flows while leaving unchanged both the systematic risk and the expected value of the cash flows, hedging will not have any effect on the firm’s value. Investors will still discount the same expected cash flows at the same required rate of return that is appropriate for the firm’s systematic risk.

The assumptions of Modigliani and Miller are strong. The investment policy of the firm is probably not invariant to the hedging decisions of the firm because of the asymmetric information environment in which the firm operates. A primary argument for hedging is to assure the management of a sufficiently large internally generated cash flow so that the investment decisions of the firm are not affected by adverse fluctuations in exchange rates. Hedging also probably can reduce the taxes that a firm pays by shifting income from good states of the world in which the firm is profitable to bad states of the world in which the firm would otherwise be unprofitable.

Chapter 17: Risk Management and the Foreign Currency Hedging Decision

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3. Suppose that after joining the treasury department of a large corporation, you find out that

it avoids hedging because the cost of hedging comes out of the treasury department’s budget. What argument could you make to the CFO to get the firm interested in letting you be the firm’s hedging guru?

Answer: There is something wrong with the firm if losses on hedges are booked to treasury whereas the gains on the underlying assets that are being hedged are booked somewhere else. You should explain to the CFO that hedging is about avoiding losses that would adversely affect the performance of the firm. Hedging involves investing in derivative securities whose values go down when the underlying assets of the firm go up in value, while the values of the derivative securities rise when the underlying assets of the firm fall in value.

It is appropriate for the costs of hedging to be borne by the treasury department, but these costs should be the personnel costs for those who are involved in the process.

4. Your CFO thinks that the value of your firm fluctuates enormously with the yen–dollar

exchange rate, but he does not want to hedge because he thinks it is an impossible risk to hedge. Can you convince him otherwise?

Answer: If the value of the firm fluctuates with the yen-dollar exchange rate, the firm must first determine the sign of the covariance. Suppose that the value of the firm goes up when the yen strengthens relative to the dollar and the value of the firm is low when the yen is weak versus the dollar. Then, the firm effectively has yen assets whose dollar value increases when the yen appreciates. An appropriate hedge would be to denominate some of the firm’s debt in yen, thereby getting yen liabilities which increase in value when the yen strengthens. The firm could also sell yen forward. The profits or losses on these contracts would be

1 1- × yen sold forwardF(t,¥/$) S(t+k,¥/$)⎡ ⎤⎢ ⎥⎣ ⎦

There would be profit when the future exchange rate of yen per dollar rose unexpectedly, that is, when the yen weakened and the value of the firm was low. Finally, the firm could buy yen puts, which would give the firm the right but not the obligation to sell yen at a fixed strike price of dollars per yen. These contracts would also provide profits when the dollar strengthened relative to the yen.

5. What does it mean for a tax code to be convex? If a country’s corporate tax rate is flat,

does it make sense for a firm to hedge?

Answer: A convex tax code imposes a larger tax rate on higher incomes and a smaller tax rate on lower incomes. If a country’s tax rate is flat, a key question is how losses are treated. If losses are subsidized immediately at the same rate that gains are taxed, there is no tax advantage to hedging. But, losses are usually not subsidized, as losses are typically only allowed to be deducted against future income. These tax-loss carry-forwards usually do not grow with the time value of money; nor are they indexed to inflation. Thus, the subsidy associated with a loss is less than the tax associated with a profit, and the tax code is effectively convex. There are also other legitimate reasons to hedge that are not tax related.


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6. If the tax code is convex and the forward rate equals the expected future spot rate, why would a firm prefer to pay taxes on the hedged value of a foreign currency cash flow rather than wait to pay the taxes on the realized foreign currency cash flow?

Answer: In the presence of a convex tax code and if the forward rate equals the expected future spot rate, a firm would prefer to pay tax on its expected income with certainty rather than paying its expected tax by taking the probability weighted average of the taxes on possible incomes in the uncertain future states of the world. This is because hedging allows the firm to shift income across different states of the world. Increasing income in states with losses avoids the low subsidy rates and thus hedging reduces expected taxes. This increases the firm’s value.

7. Why is the gain in a firm’s value greater when more of its future foreign currency income is

in the low tax region of the tax code?

Answer: This question is somewhat poorly phrased. If all of the firm’s foreign currency income accrued in the low tax region of the tax code, there would be no gain to hedging. The gain in a firm’s value (from hedging) arises from the ability to shift income from states in which it is subject to high taxes to states in which it is subject to low taxes.

8. Why would the managers of a firm take a foreign project with a lower domestic currency

NPV and a higher return variance rather than a foreign project with a higher domestic currency NPV but a lower return variance?

Answer: This is an example of the asset substitution issue that we covered in Chapter 16. Because shareholders only gain in good states of the world, they like the variance of the firm to be high. When the variance of the firm is higher, the shareholders gain more in the good states of the world. The bondholders get paid their full amount in good states of the world, and they get the value of the firm in the bad states of the world. By accepting a high variance project, managers may be able to shift some value from bondholders to shareholders in an asset substitution.

9. Why would a firm ever forgo a positive NPV project? How can hedging help prevent this

situation from arising?

Answer: If the firm has debt in its capital structure, we know that the managers may forego a positive NPV investment that must be financed by shareholders because too much of the increase in firm value accrues to bondholders. A hedging policy can help to avoid such as situation by avoiding the losses that may plunge the firm into financial distress and make the debt risky in the first place. By reducing the variance of income, the hedging policy makes the debt less risky in which case it sells for a price closer to face value.


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10. Suppose the cash flows from financial hedging are pooled with the cash flows from a firm’s operations and that the shareholders cannot ascertain the ultimate sources of profits and losses. Would the managers of the firm want to hedge or to speculate in the forward foreign exchange market?

Answer: The Peter DeMarzo and Darrell Duffie (1995) argument is the following. Shareholders must gauge the quality of the firm’s managers based on their observations of the firm’s profitability and its earnings, as disclosed in its accounting data. From this perspective, hedging makes good sense at first glance. Hedging reduces the amount of “noise” in earnings data that is not due to actions of the managers. That is, hedging increases the informational content about a manager’s ability that is conveyed by the firm’s reported profits. DeMarzo and Duffie demonstrate that in this situation, the accounting treatment of hedging and the optimal hedging policy are intimately linked. Because managers are better able to gauge the different financial risks the company faces, they have an incentive to hedge these risks to reduce the variability of the firm’s earnings and, with that, the variability of their own income stream, which will be linked to the firm’s earnings. A manager does not want to face an unexpected currency depreciation that adversely affects the firm’s profits.

The disclosure of information, though, interacts with the ability of shareholders to gauge the true ability of a manager. With additional precision, shareholders can make the managers’ compensation more sensitive to the firm’s performance. To avoid this additional variability in their income, managers may chose not to hedge. If the additional informational content of hedged earnings is sufficiently high, the shareholders may optimally decide not to disclose the firm’s hedging activities, to give managers an incentive to hedge.

11. Why is an internally generated cash flow of such importance to Merck? Can’t Merck use the

financial markets as a source of funds?

Answer: Merck realized that it was operating in an environment of asymmetric information. They needed to be assured of generating sufficiently large internal cash flows such that they could finance their research and development projects over the course of many years. An alternative would be to potentially suffer losses in foreign exchange markets and try to fund its investment projects in the external capital markets. They key question to address is the following: Can the firm successfully raise the funds that it needs at reasonable required rates of return in those states of the world? The answer appears to be no, because the firm will be going to the financial markets when it is unprofitable. As a result, participants in the financial markets must assess why the firm is unprofitable. They will attribute some of the losses to adverse fluctuations in exchange rates, but they might also assign some of the blame to poor managerial decisions. In such a case, the firm’s managers will find it difficult to pursue the projects they believe will keep the firm competitive. Hedging would prevent this from happening.


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12. True or false: The cost or benefit of hedging foreign exchange risk when a firm is selling the foreign currency forward is accurately measured by the forward discount or premium on the foreign currency.

Answer: We know that if the firm sells the foreign currency in the forward market when the foreign currency is at a discount, it will generate less domestic currency revenue than if the foreign currency had been sold at the spot rate. But, the important point is that the cash flows are in the future. They cannot be valued directly with the spot rate because the spot rate is for current cash flows or the present values of foreign currency amounts. When the foreign currency is at a discount, we know that the foreign currency interest rate is higher than the domestic currency interest rate. Thus, we must use this high foreign currency interest rate to get a present value if we are going to use the spot rate to value the cash flow. Alternatively, we can convert the foreign currency into domestic currency in the forward market and then discount it to the present with the domestic interest rate. In either case, we end up with the same amount of domestic currency if covered interest rate parity is satisfied. Thus, a forward discount does not represent a true cost of hedging, and, by analogy, a forward premium does not supply a benefit to hedging.

PROBLEMS 1. Chapeau Rouge has a Swiss project that will return either CHF300 million or CHF250

million per year of free cash flow indefinitely. Each of the possible CHF cash flows is equally likely. Chapeau Rouge’s CHF discount rate for these cash flows is 13% per annum, the cost of the project is €1,100 million, and the current exchange rate is CHF1.67/EUR. Should Chapeau Rouge accept the project? Suppose that Chapeau Rouge has a €400 million line of credit with its bank. Will Chapeau Rouge have trouble hedging the CHF cash flows?

Answer: We need to take the present value of the project in Swiss francs and then convert to euros at the current spot rate. Since the project’s cash flow is a perpetuity with an expected value of CHF275 million per year, we know that the present value, when discounted at 13%, is

CHF275 millionPresent value in Swiss francs = = CHF2,115 million0.13

Converting this present value into euros at the current spot exchange rate of CHF1.67/EUR gives CHF2,115 million / (CHF1.67/EUR) = €1,266.70 million. Since this exceeds the cost of the investment of €1,100 million, Chapeau Rouge should accept the project. If Chapeau wanted to hedge the cash flows, they would want to sell CHF275 million for euros in each year out into the indefinite future. Their credit line of €400 million would not be adequate to allow such a substantial exchange-rate exposure. Moreover, we know that the transactions costs of entering into longer term forward contracts increase substantially, which would significantly increase the cost of hedging if they contract to sell more than a few years forward. Consequently, Chapeau Rouge would continue to have a large exposure of the value of the project to a depreciation of the Swiss franc relative to the euro.

2. Fleur de France has a project that will provide £20 million in revenue in 1 year. The project

has a euro cost of €30 million that will be paid in 1 year. The cost of the project is certain, but the future spot exchange rate is not. Assume that there are only two possible future spot exchange rates. Either the spot rate in 1 year will be €1.54/£ with 55% probability, or it will be €1.48/£ with 45% probability. Assume that the French tax rate on positive income is 45%, that a firm’s losses are immediately refunded at a rate of 35%, and that the forward


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rate of euros per pound equals the expected future spot rate. a. If Fleur de France chooses not to hedge its foreign exchange risk, what is the expected

value of its after-tax income on the unhedged project? Answer: If Fleur de France is unhedged, it will either experience a positive after-tax income of €0.44 million that will be taxed at 45% with 55% probability because

{[(€1.54/£) × £20 million] – €30 million} × (1 – 0.45) = €0.44 million or Fleur de France will experience an after-tax loss, which is subsidized at 35%, of €0.26 million with 45% probability because

{[(€1.48/£) × £20 million] – €30 million} × (1 – 0.35) = - €0.26 million The expected euro value of Fleur de France’s after-tax income on the unhedged project is therefore the probability weighted average of the two possibilities:

[0.55 × €0.44 million] + [0.45 × (- €0.26 million)] = €0.125 million

b. If Fleur de France chooses to hedge its foreign exchange risk, what is the expected value of its after-tax income on the hedged project? Answer: The expected future spot rate is the probability weighted average of the two possible realizations:

(0.55 × €1.54/£) + (0.45 × €1.48/£) = €1.513/£ If the forward rate equals the expected future spot rate, Fleur de France will sell the £20 million forward and will have a sure income. Its after-tax income on the hedged project is

{[(€1.513/£) × £20 million] – €30 million} × (1 – 0.45) = €0.143 million

c. How much does Fleur de France gain by hedging? Answer: By hedging, Fleur de France shifts income from the good state of the world with pound appreciation to the bad state of the world with pound depreciation. It also avoids the loss that is only subsidized at the 35% rate. Its after-tax income in the good state falls from €0.44 million to €0.143 million, while its after-tax income in the bad state rises from a loss of €0.26 million to €0.143 million. If Fleur de France hedges, its gain is the difference between its after-tax income and its expected after-tax income, which is

€0.143 million - €0.125 million = €0.018 million The gain is due to the convexity of the tax schedule. It can be demonstrated that the gain is the probability of the bad state, multiplied by the income in the bad state, multiplied by the difference in the tax rates or

(0.45) × {[(€1.48/£) × £20 million] – €30 million} × (0.35 – 0.45) = €0.018 million


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3. How would your answer to problem 2 change if instead of allowing refunds at 35%, the refund rate were only 25%?

Answer: We know that the larger the difference between the tax rates, the larger the gain to hedging. If the subsidy rate is only 25%, Fleur de France will experience an after-tax loss if it does not hedge of €0.30 million with 45% probability because


[0.55 × €0.44 million] + [0.45 × (- €0.30 million)] = €0.107 million If Fleur de France hedges, its gain is the difference between its after-tax income and its expected after-tax income, which is

€0.143 million - €0.107 million = €0.036 million Notice that this is double the gain in Problem 2 because the gain is the probability of the bad state, multiplied by the income in the bad state, multiplied by the difference in the tax rates or

(0.45) × {[(€1.48/£) × £20 million] – €30 million} × (0.25 – 0.45) = €0.036 million 4. How would your answer to problem 2 change if the possible exchange rates in the future

were €1.56/£ and €1.46/£? We know that with a larger variance of the possible future exchange rates, the gain to

hedging is increased. Here are the numbers: a. If Fleur de France chooses not to hedge its foreign exchange risk, what is the expected

value of its after-tax income on the unhedged project?

Answer: If Fleur de France is unhedged, it will experience a positive after-tax income of €0.66 million that will be taxed at 45% with 55% probability because

{[(€1.56/£) × £20 million] – €30 million} × (1 – 0.45) = €0.66 million or Fleur de France will experience an after-tax loss, which is subsidized at 35%, of €0.52 million with 45% probability because


[0.55 × €0.66 million] + [0.45 × (- €0.52 million)] = €0.129 million

b. If Fleur de France chooses to hedge its foreign exchange risk, what is the expected value of its after-tax income on the hedged project? Answer: The expected future spot rate is the probability weighted average of the two possible realizations:

(0.55 × €1.56/£) + (0.45 × €1.46/£) = €1.515/£ If the forward rate equals the expected future spot rate, Fleur de France will sell the £20 million forward and have a sure income. Its after-tax income on the hedged project is

{[(€1.515/£) × £20 million] – €30 million} × (1 – 0.45) = €0.165 million

c. How much does Fleur de France gain by hedging?

Answer: If Fleur de France hedges, its gain is the difference between its after-tax income and its expected after-tax income, which is

€0.165 million - €0.129 million = €0.036 million


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5. Assume that U.S. Machine Tool has $50 million of debt outstanding that will mature next year. It currently has cash flows that fluctuate with the dollar–pound exchange rate. Over the next year, the possible exchange rates are $1.50/£ and $1.90/£, and each exchange rate is equally likely. The company thinks that it will generate $30 million of cash flow from its U.S. operations, and its expected pound cash flow is £12 million. a. If U.S. Machine Tool does not hedge its foreign exchange risk, what will be the current

market value of its debt and equity, assuming, for simplicity, that the appropriate discount rates are 0? Answer: If U.S. Machine Tool does not hedge, the dollar value of its pound revenue will be either $1.50/£ × £12 million = $18 million or $1.90/£ × £12 million = $22.8 million. With $30 million of cash flow from its U.S. operations, the company will therefore only be able to pay off its debt in the good state of the world. Bondholders will either receive $48 million = $18 million + $30 million, in which case equity will be worthless, or the firm will have enough to pay the bondholders the full $50 million, in which case equity will be worth $2.8 million = $22.8 million + $30 million - $50 million. Since the two states of the world are equally likely, and assuming a zero discount rate for simplicity, the debt will sell at

0.5 × $48 million + 0.5 × $50 million = $49 million and the equity will sell for

0.5 × $0 + 0.5 × $2.8 million = $1.4 million

b. Suppose that U.S. Machine Tool has access to forward contracts at a price of $1.70/£. What is the value of the firm’s debt and equity if it hedges its foreign exchange risk? Would the shareholders want the management to hedge? Answer: If the firm hedges its pound revenue, the dollar value is $1.70/£ × £12 million = $20.4 million. There would be no additional uncertainty associated with the firm, so its revenues would be $50.4 million = $20.4 million + $30 million. Debt would be riskless and would sell for $50 million, and equity would be the residual claimant to the $0.4 million. Shareholders would therefore not want the firm to hedge as they would prefer the “high variance” project.

c. Suppose U.S. Machine Tool could invest $1 million today in a project that returns £1 million next period. Is this a good project for the firm?

Answer: If the firm invests $1 million and gets £1 million next period, the dollar value of the pounds would be either $1.5 million or $1.9 million. So, the project is certainly a positive NPV project for the firm.

d. Suppose that U.S. Machine Tool is unhedged, that its managers are trying to maximize the value of the firm’s equity, and that the $1 million must be raised from current shareholders. Will the managers accept the project?

Answer: If U.S. Machine Tool does not hedge, the dollar value of its pound revenue will be either $1.50/£ × £13 million = $19.5 million or $1.90/£ × £13 million = $24.7 million. With $30 million of cash flow from its U.S. operations, the company will still only be able to pay off its debt in the good state of the world. Bondholders will either receive $49.5 million = $19.5 million + $30 million, in which case equity will be worthless, or the firm will have enough to pay the bondholders the full $50 million, in which case equity will be worth $4.7 million = $24.7 million + $30 million - $50 million. Since the two states of the world are equally likely, and assuming a zero discount rate for simplicity, the debt will sell for

0.5 × $49.5 million + 0.5 × $50 million = $49.75 million


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and the equity will sell for 0.5 × $0 + 0.5 × $4.7 million = $2.35 million

Because the value of the equity increases from $1.4 million to $2.35 million, which is less than the $1 million cost of the project, the shareholders would want the management to reject the project.

e. If U.S. Machine Tool hedges its foreign exchange risk, would the firm accept the project?

Answer: Yes, if the firm is hedged, the debt is riskless and the equity is worth $0.4 million. The return on the positive NPV project would therefore accrue totally to the shareholders. They would invest $1 million and get $1.7/£ × £1 million = $1.7 million in return. Thus, their equity would increase in value by $0.7 million.

International FInancial Management 2nd Edition Solution Manual

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Transcript of International FInancial Management 2nd Edition Solution Manual