Chapter 22
Questions and Problems
• 1. Using Exchange Rates
• Take a look back at Figure 22.1 to answer the following
questions:
• a. If you have $100, how many euros can you get?
• b. How many dollars is one euro worth?
• c. If you have five million euros, how many dollars do
you have?
• d. Which is worth more, a New Zealand dollar or a
Singapore dollar?
• e. Which is worth more, a Mexican peso or a Chilean
peso?
• f. How many Mexican pesos can you get for a euro?
What do you call this rate?
• g. Per unit, what is the most valuable currency of those
listed? The least valuable?
• 1.
•
•
•
•
•
•
•
•
•
•
Using the quotes from the table, we get:
a.
b.
c.
d.
e.
f.
g.
$100(€0.8206/$1) = €82.06
$1.2186
€5M($1.2186/€) = $6,093,103
Singapore dollar
Mexican peso
(P11.4850/$1)($1.2186/€1) = P13.9959/€
This is a cross rate.
Most valuable: Bahrain dinar = $3.3920
Least valuable: Turkish lira = $0.00000067
• 2. Using the Cross-Rate
• Use the information in Figure 22.1 to answer the
following questions:
• a. Which would you rather have, $100 or €100?
Why?
• b. Which would you rather have, 100 Swiss
francs or £100? Why?
• c. What is the cross-rate for Swiss francs in
terms of British pounds? For British pounds in
terms of Swiss francs?
• 2.
• a. You would prefer €100, since: (€100)($1.8301/€1) =
$54.642
• b. You would still prefer €100. Using the $/€ exchange
rate and the SF/€ exchange rate to find the amount of
Swiss francs €100 will buy, we get:
• (€100)($1.8301/€1)(SF .8008/$1) = SF 43.7572
• c. Using the quotes in the book to find the SF/€ cross
rate, we find:
• (SF .8008/$1)($1.8301/€1) = SF 0.4376/€1
• The €/SF exchange rate is the inverse of the SF/€
exchange rate, so:
• €1/SF0.4376 = €2.2853/SF 1
• 3. Forward Exchange Rates
• Use the information in Figure 22.1 to answer the
following questions:
• a. What is the three-month forward rate for the Japanese
yen in yen per U.S. dollar? Is the yen selling at a
premium or a discount? Explain.
• b. What is the six-month forward rate for Canadian
dollars in U.S. dollars per Canadian dollar? Is the dollar
selling at a premium or a discount? Explain.
• c. What do you think will happen to the value of the
dollar relative to the yen and the Canadian dollar, based
on the information in the figure? Explain.
• 3.
• a. F90 = ¥107.46 (per $). The yen is selling at a premium
because it is more expensive in the forward market than
in the spot market ($0.0092678 versus $0.0093058).
• b. F180 = $0.7409/C$1. The dollar is selling at a discount
because it is less expensive in the forward market than
in the spot market ($0.7425 versus $0.7409).
• c. The value of the dollar will fall relative to the yen, since
it takes more dollars to buy one yen in the future than it
does today. The value of the dollar will rise relative to the
Canadian dollar, because it will take fewer dollars to buy
one Canadian dollar in the future than it does today.
• 4. Using Spot and Forward Exchange Rates
• Suppose the spot exchange rate for the Canadian dollar
is Can$1.26 and the six-month forward rate is Can$1.29.
• a. Which is worth more, a U.S. dollar or a Canadian
dollar?
• b. Assuming absolute PPP holds, what is the cost in the
United States of an Elkhead beer if the price in Canada
is Can$2.49? Why might the beer actually sell at a
• different price in the United States?
• c. Is the U.S. dollar selling at a premium or a discount
relative to the Canadian dollar?
• d. Which currency is expected to
appreciate in value?
• e. Which country do you think has higher
interest rates—the United States or
Canada? Explain.
• 4.
• a. The U.S. dollar, since one Canadian dollar
will buy:
•
• (Can$1)/(Can$1.26/$1) = $0.7937
• b. The cost in U.S. dollars is:
•
(Can$2.49)/(Can$1.26/$1) = $1.9762
• Among the reasons that absolute PPP doesn’t
hold are tariffs and other barriers to trade,
transactions costs, taxes, and different tastes.
• c. The U.S. dollar is selling at a premium,
because it is more expensive in the forward
market than in the spot market (Can$1.29
versus Can$1.26).
• d. The Canadian dollar is expected to
depreciate in value relative to the dollar,
because it takes more Canadian dollars to buy
one U.S. dollar in the future than it does today.
• e. Interest rates in the United States are
probably lower than they are in Canada.
• 7. Interest Rates and Arbitrage
• The treasurer of a major U.S. firm has $30
million to invest for three months. The annual
interest rate in the United States is .45 percent
per month. The interest rate in Great Britain is .6
percent per month. The spot exchange rate is
£0.53, and the three-month forward rate is £0.56.
Ignoring transactions costs, in which country
would the treasurer want to invest the
company's funds? Why?
• 7.
• If we invest in the U.S. for the next three months, we will
have:
•
$30M(1.0045)3 = $30,406,825.23
• If we invest in Great Britain, we must exchange the
dollars today for pounds, and exchange the pounds for
dollars in three months. After making these transactions,
the dollar amount we would have in three months would
be:
• ($30M)(£0.53/$1)(1.0060)3/(£0.56/$1) = $28,907,001.13
• We should invest in U.S.
• 8. Inflation and Exchange Rates
• Suppose the current exchange rate for the
Polish zloty is PLN 3.84. The expected
exchange rate in three years is PLN 4.02. What
is the difference in the annual inflation rates for
the United States and Poland over this period?
Assume that the anticipated rate is constant for
both countries. What relationship are you relying
on in answering?
• 8.
• Using the relative purchasing power parity equation:
•
Ft = S0 × [1 + (hFC – hUS)]t
•
We find:
•
PLN 4.02 = PLN3.84[1 + (hFC – hUS)]3
•
hFC – hUS = (PLN4.02/PLN3.84)1/3 – 1
•
hFC – hUS = .0154
•
• Inflation in Poland is expected to exceed that in the U.S.
by 1.54% over this period.
• 10. Exchange Rates and Arbitrage
• Suppose the spot and six-month forward rates
on the Norwegian krone are NOK 6.43 and NOK
6.52, respectively. The annual risk-free rate in
the United States is 5 percent, and the annual
risk-free rate in Norway is 7 percent.
• a. Is there an arbitrage opportunity here? If so,
how would you exploit it?
• b. What must the six-month forward rate be to
prevent arbitrage?
• 10.
• a. If IRP holds, then:
•
F180 = (NOK 6.43)[1 + (.07 – .05)]1/2
•
F180 = NOK 6.494
• Since given F180 is NOK 6.52, an arbitrage
opportunity exists; the forward premium is too
high.
• Borrow NOK1 today at 7% interest. Agree to a
180-day forward contract at NOK 6.52. Convert
the loan proceeds into dollars:
• NOK 1 ($1/NOK 6.43) = $0.15552
• Invest these dollars at 5%, ending up with
$0.15931. Convert the dollars back into
krone as
• $0.15931(NOK 6.52/$1) = NOK 1.03869
• Repay the NOK 1 loan, ending with a profit
of:
• NOK1.03869 – NOK1.07180/365 = NOK
0.00476
• b. To find the forward rate that eliminates
arbitrage, we use the interest rate parity
condition, so:
• F180 = (NOK 6.43)[1 + (.07 – .05)]1/2
• F180 = NOK 6.494
• 12. Spot versus Forward Rates Suppose
the spot and three-month forward rates for
the yen are ¥131.30 and ¥129.76,
respectively.
• a. Is the yen expected to get stronger or
weaker?
• b. What would you estimate is the
difference between the inflation rates of
the United States and Japan?
• 12.
• a. The yen is expected to get stronger, since it
will take fewer yen to buy one dollar in the future
than it does today.
• b. hUS – hJAP  (¥129.76 – ¥131.30)/¥131.30
•
hUS – hJAP = – .0117 or –1.17%
•
(1 – .0117)4 – 1 = –.0461 or –4.61%
•
• The approximate inflation differential between
the U.S. and Japan is – 4.61% annually.
• 13. Expected Spot Rates
• Suppose the spot exchange rate for the
Hungarian forint is HUF 215. Interest rates
in the United States are 4.2 percent per
year. They are 8.6 percent in Hungary.
What do you predict the exchange rate will
be in one year? In two years? In five years?
What relationship are you using?
• 13.
• We need to find the change in the exchange rate
over time so we need to use the relative
purchasing power parity relationship:
• Ft = S0 × [1 + (hFC – hUS)]t
• Using this relationship, we find the exchange
rate in one year should be:
• F1 = 215[1 + (.086 – .042)]1
• F1 = HUF 224.46
•
•
•
•
The exchange rate in two years should be:
F2 = 215[1 + (.086 – .042)]2
F2 = HUF 234.34
And the exchange rate in five years should
be:
• F5 = 215[1 + (.086 – .042)]5
• F5 = HUF 266.65
• 14. Capital Budgeting
• You are a U.S. firm that is evaluating a proposed
expansion of an existing subsidiary located in
Switzerland. The cost of the expansion would be
27.0 million francs (CHF). The cash flows from
the project would be CHF 7.5 million per year for
the next five years. The dollar required return is
12 percent per year, and the current exchange
rate is CHF 1.72. The going rate on Eurodollars
is 8 percent per year. It is 6 percent per year on
Euroswiss.
• 14.
• a. Implicitly, it is assumed that interest
rates won’t change over the life of the
project, but the exchange rate is projected
to decline because the Euroswiss rate is
lower than the Eurodollar rate.
• b. We can use relative purchasing power
parity to calculate the dollar cash flows at
each time. The equation is:
• E[St] = (CHF 1.72)[1 + (.06 – .08)]t
• E[St] = 1.72(.98) t
• So, the cash flows each year in U.S. dollar
terms will be:
t
CHF
E[St]
US$
0
–27.0M
1.7200
–$15,697,674.42
1
+7.5M
1.6856
$4,449,454.20
2
+7.5M
1.6519
$4,540,259.39
3
+7.5M
1.6189
$4,632,917.74
4
+7.5M
1.5865
$4,727,467.08
5
+7.5M
1.5547
$4,823,946.00
• And the NPV is:
• NPV = –$15,697,674.42 +
$4,449,454.20/1.12 + $4,540,259.39/1.122
+ $4,632,917.74/1.123 +
$4,727,467.08/1.124
+$4,823,946.00/1.125
• NPV = $933,766.18
• c. Rearranging the relative purchasing
power parity equation to find the required
return in Swiss francs, we get:
•
• RSFr = 1.12[1 + (.06 – .08)] – 1
• RSFr = 9.76%
• So the NPV in Swiss francs is:
• NPV= CHF 1,606,077.83
•
• Converting the NPV to dollars at the spot
rate, we get the NPV in U.S. dollars as:
• NPV = (CHF 1,606,077.83)($1/CHF 1.72)
• NPV = $933,766.18
Additional Questions
• 1. Suppose the euro is quoted at
0.7064-80 in London, and the pound
sterling is quoted at 1.6244-59 in Frankfurt.
• Is there a profitable arbitrage situation?
Describe it.
• Answer. Sell euros for £0.7080/€ in
London. Use the pounds to buy euros for
€1.6244/£ in Frankfurt. This is equivalent
to buying pounds for £0.6156. There is a
net profit of £0.0924 per pound bought and
sold–a percentage yield of 13.05%
(0.0924/0.7080).
•
•
•
•
2. As a foreign exchange trader at
Sumitomo Bank, one of your customers
would like a yen quote on Australian
dollars. Current market rates are:
Spot
30-day
¥101.37-85/U.S.$1
15-13
A$1.2924-44/U.S.$1
20-26
• a. What bid and ask yen cross rates
would you quote on spot Australian dollars?
• b. What outright yen cross rates would
you quote on 30-day forward Australian
dollars?
• c. What is the forward premium or
discount on buying 30-day Australian
dollars against yen delivery?
• Answer. By means of triangular arbitrage, we
can calculate the market quotes for the
Australian dollar in terms of yen as
•
¥78.31-81/A$1
• These prices can be found as follows. For the
yen bid price for the Australian dollar, we need to
first sell Australian dollars for U.S. dollars and
then sell the U.S. dollars for yen. It costs
A$1.2944 to buy U.S.$1. With U.S.$1 we can
buy ¥101.37. Hence, A$1.2944 = ¥101.37, or
A$1 = ¥78.31. This is the yen bid price for the
Australian dollar
• The yen ask price for the Australian dollar can be found
by first selling yen for U.S. dollars and then using the
U.S. dollars to buy Australian dollars. Given the quotes
above, it costs ¥101.85 to buy U.S.$1, which can be sold
for A$1.2924. Hence, A$1.2924 = ¥101.85, or A$1 =
¥78.81. This is the yen ask price for the Australian dollar.
• As a foreign exchange trader, you would try to buy
Australian dollars at slightly less than ¥78.31 and sell
them at slightly more than ¥78.81. Buying and selling
Australian dollars at the market price will leave you with
no profit. How much better than the market prices you
can do depends on the degree of competition you face
from other traders and the extent to which your
customers are willing to shop around to get better quotes.
• Answer. Given the swap rates, we can
compute the outright forward direct quotes
for the yen and Australian dollar by adding
or subtracting the forward points as follows
• Spot
30-day
¥101.37-85/U.S.$1
15-13
A$1.2924-44/U.S.$1
20-26
30-day outright rates
¥101.22-72/U.S.$1
A$1.2944-70/U.S.$1
• By means of triangular arbitrage, we can then calculate
the market quotes for the 30-day forward Australian
dollar in terms of yen as
•
¥78.04-58/A$1
• These prices can be found as follows. For the yen bid
price for the forward Australian dollar, we need to first
sell Australian dollars forward for U.S. dollars and then
sell the U.S. dollars forward for yen. It costs A$1.2970 to
buy U.S.$1 forward. With U.S.$1 we can buy ¥101.22.
Hence, A$1.2970 = ¥101.22, or A$1 = ¥78.04. This is the
yen bid price for the forward Australian dollar.
• The yen ask price for the Australian dollar
can be found by first selling yen forward
for U.S. dollars and then using the U.S.
dollars to buy forward Australian dollars.
Given the quotes above, it costs ¥101.72
to buy U.S.$1, which can be sold for
A$1.2944. Hence, A$1.2944 = ¥101.71, or
A$1 = ¥78.58. This is the yen ask price for
the forward Australian dollar.
Forward premium
or discount
=
Forward rate Spot rate
360
78.58 - 78.81 360
x
=
x
= - 3.43%
Forward contract
Spot rate
78.81
30
number of days