INSTRUCTOR’S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9TH ED.
SUGGESTED SOLUTIONS TO CHAPTER 7 PROBLEMS
1.
The $: € exchange rate is €1 = $1.45, and the €/SFr exchange rate is SFr 1 = €0.71. What is the SFr/$ exchange
rate?
ANSWER. SFr1 = €0.71 x 1.45 = $1.0295.
2.
Suppose the direct quote for sterling in New York is 1.9110-5. What is the direct quote for dollars in London?
ANSWER. The direct quote for the dollar in London is just the reciprocal of the direct quote for the pound in New
York or 1/1.9115 - 1/1.9110 = 0.5231-3.
3.
Using the data in Exhibit 7.5, calculate the 30-day, 90-day, and 180-day forward discounts for the Canadian
dollar.
ANSWER. Here are the relevant rates for the Canadian dollar:
Spot:
C$1 = $1.0078
30-day forward:
C$1 = $1.0073
90-day forward:
C$1 = $1.0069
180-day forward:
C$1 = $1.0066
The 30-day forward discount is:
[($1.0073 - $1.0078)/$1.0078] x 12 = -0.60%
The 90-day forward discount is:
[($1.0069 - $1.0078)/$1.0078] x 4 = -0.36%
The 180-day forward discount is:
[($1.0066 - $1.0078)/$1.0078] x 2 = -0.24%
In this case, the forward discounts at these maturities are relatively small, indicating that Canadian and U.S. interest
rates are close to each other.
4.
An investor wishes to buy euros spot (at $1.3908) and sell euros forward for 180 days (at $1.3996).
a.
What is the swap rate on euros?
ANSWER. A premium of 88 points.
b.
What is the premium on 180-day euros?
ANSWER. The 180-day premium is (1.3996 - 1.3908)/1.3908 x 2 = 1.27%.
5.
Suppose Credit Suisse quotes spot and 90-day forward rates on the Swiss franc of $0.7957-60, 8-13.
a.
What are the outright 90-day forward rates that Credit Suisse is quoting?
ANSWER. The outright forwards are: bid rate = $0.7965 (0.7957 + 0.0008) and ask rate = $0.7973 (0.7960 +
0.0013).
b.
What is the forward discount or premium associated with buying 90-day Swiss francs?
ANSWER. The annualized forward premium = [(0.7973 - 0.7960)/0.7960]x 4 = 0.65%.
c.
Compute the percentage bid-ask spreads on spot and forward Swiss francs.
ANSWER. The bid-ask spread is calculated as follows:
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CHAPTER 7: THE FOREIGN EXCHANGE MARKET
Percent spread =
Ask price - Bid price
x 100
Ask price
Substituting in the numbers yields a spot bid-ask spread of (0.7960 - 0.7957)/0.7960 = 0.04%. The corresponding
forward bid-ask spread is (0.7973 - 0.7965)/0.7973 = 0.10%.
6.
Suppose Dow Chemical receives quotes of $0.009369-71 for the yen and $0.03675-6 for the Taiwan dollar
(NT$).
a.
How many U.S. dollars will Dow Chemical receive from the sale of ¥50 million?
ANSWER. Dow must sell yen at the bid rate, meaning it will receive from this sale $468,450 (50,000,000 x
0.009369).
b.
What is the U.S. dollar cost to Dow Chemical of buying ¥1 billion?
ANSWER. Dow must buy at the ask rate, meaning it will cost Dow $9,371,000 (1,000,000,000 x 0.009371) to buy ¥1
billion.
c.
How many NT$ will Dow Chemical receive for U.S. $500,000?
ANSWER. Dow must sell at the bid rate for U.S. dollars (which is the reciprocal of the ask rate for NT$, or
1/0.03676), meaning it will receive from this sale of U.S. dollars NT$13,601,741 (500,000/0.03676).
d.
How many yen will Dow Chemical receive for NT$200 million?
ANSWER. To buy yen, Dow must first sell the NT$200 million for U.S. dollars at the bid rate and then use these
dollars to buy yen at the ask rate. The net result from these transactions is ¥784,334,649.45 (200,000,000 x
0.03675/0.009371).
e.
What is the yen cost to Dow Chemical of buying NT$80 million?
ANSWER. Dow must sell the yen for dollars at the bid rate and then buy NT$ at the ask rate with the U.S. dollars.
The net yen cost to Dow from carrying out these transactions is ¥313,886,220.51 (80,000,000 x 0.03676/0.009369)
7.
Suppose the euro is quoted at 0.6064-80 in London, and the pound sterling is quoted at 1.6244-59 in Frankfurt.
a.
Is there a profitable arbitrage situation? Describe it.
ANSWER. Sell pounds for €1.6447/£ (1/0.6080) in London. Use the Euros to buy pounds for €1.6259/£ in Frankfurt.
There is a net profit of €0.0188 per pound bought and sold–a percentage yield of 1.15% (0.0188/1.6447).
b.
Compute the percentage bid-ask spreads on the pound and euro.
ANSWER. The percentage bid-ask spreads on the pound and euro are calculated as follows:
£ bid-ask spread = (1.6259 - 1.6244)/1.6259 = 0.09%
Euro bid-ask spread = (0.6080 - 0.6064)/0.6080 = 0.26%
8.
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
¥101.37-85/U.S.$1
30-day
15-13
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INSTRUCTOR’S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9TH ED.
A$1.2924-44/U.S.$1
a.
20-26
What bid and ask yen cross rates would you quote on spot Australian dollars?
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.
b.
What outright yen cross rates would you quote on 30-day forward Australian dollars?
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
¥101.37-85/U.S.$1
A$1.2924-44/U.S.$1
30-day
15-13
20-26
30-day outright forward 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$1 = ¥78.58. This is the yen ask price for the forward
Australian dollar.
c.
What is the forward premium or discount on buying 30-day Australian dollars against yen delivery?
ANSWER. As shown in parts a and b, the ask rate for 30-day forward Australian dollars is ¥78.58 and the spot ask
rate is ¥78.81. Thus, the Australian dollar is selling at a forward discount to the yen. The annualized discount equals
-3.43%, computed as follows:
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CHAPTER 7: THE FOREIGN EXCHANGE MARKET
Forward premium
or discount
9.
=
Forward rate Spot rate
360
78.58 - 78.81 360
x
=
x
= - 3.43%
Forward contract
Spot rate
78.81
30
number of days
Suppose Air France receives the following indirect quotes in New York: €0.92 - 3 and £0.63 - 4. Given these
quotes, what range of £/ € bid and ask quotes in Paris will permit arbitrage?
ANSWER. Triangular arbitrage can take place in either of two ways: (1) Convert from euros to dollars (at the ask
rate), then from dollars to pounds (at the bid rate), or (2) convert from pounds to dollars (at the ask rate), then from
dollars to euros (at the bid rate). The first quote will give us the bid price for the euro in terms of the pound and the
second quote will yield the ask price. Using the given rates, Air France would end up with the following amounts:
(1) Euros to pounds
=
=
=
€/$ (ask)
x
0.93
x
€ 1.4762/£ or £0.6774/ €
$/£ (bid)
1/0.63
(2) Pounds to euros
=
£/$ (ask)
x
0.64
x
£0.6957/€ or €1.4375/£
$/ € (bid)
1/0.92
=
The import of the figures in method (1) is that Air France can buy pounds in New York for €1.4762/£, which is the
equivalent of selling euros at a rate of £0.6774/ €. So, if Air France can buy euros in Paris for less than £0.6774/ €
(which is the equivalent of selling pounds for more than €0.6774/£), it can earn an arbitrage profit. Similarly, the
figures in method (2) tell us that Air France can buy euros in New York at a cost of £0.6957/ €. Given this exchange
rate, Air France can earn an arbitrage profit if it can sell these euros for more than £0.6957/FF in Paris. Thus, Air
France can profitably arbitrage between New York and Paris if the bid rate for the euro in Paris is greater than
£0.6957/ € or the ask rate is less than £0.6774/ €.
10. On checking the Telerate screen, you see the following exchange rate and interest rate quotes:
Currency
90-day interest rates annualized
Dollar
4.99% - 5.03%
Swiss franc
3.14% - 3.19%
a.
Spot rates
90-day forward rates
$0.711 - 22
$0.726 - 32
Can you find an arbitrage opportunity?
ANSWER. Yes. There are two possibilities: Borrow dollars and lend in Swiss francs or borrow Swiss francs and lend
in dollars. The profitable arbitrage opportunity lies in the former: Lend Swiss francs financed by borrowing U.S.
dollars.
b.
What steps must you take to capitalize on it?
ANSWER. Borrow dollars at 1.2575% for 90 days (5.03%/4), convert these dollars into francs at the ask rate of
$0.722, lend the francs at 0.785% for 90 days (3.14%/4), and immediately sell the francs forward for dollars at the
buy rate of $0.726.
c.
What is the profit per $1,000,000 arbitraged?
ANSWER. The profit is $1,000,000 x [(1.00785/0.722) x 0.726 - 1.012575] = $858.66.
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