FINS5516 FINS5516 International Corporate Finance
International Corporate Finance
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FINS5516 FINS5516 International Corporate Finance
Week 2 Reading Guide & Practice Questions Solution
Chapters 2, 6: Exchange Rate Determination and Foreign Exchange Markets Week
2 Readings (Shapiro, 11E)
Chapter 2 – The Determination of Exchange Rates
2.1 Setting the Equilibrium Spot Exchange Rate
2.2 Expectations and the Asset Market Model of Exchange Rates - only content covered in
lecture
2.3 The Fundamentals of Central Bank Intervention - only content covered in lecture
Chapter 6 – The Foreign Exchange Market
6.1 Organization of the Foreign Exchange Market
6.2 The Spot Market
6.3 The Forward Market
Note: only content covered in lecture does not imply you can skip these parts of the book – it means
you only have to know the concepts and theories explained in the lectures.
FINS5516 Week 02 Practice Problems
Week 2 Practice Questions (Note: some, but not all problems are from Shapiro)
Appreciation & Depreciation:
Problem 01 (From Shapiro Chapter 2, Questions 2.3)
For each of the following six scenarios, say whether the value of the dollar will appreciate, depreciate,
or remain the same relative to the Japanese yen. Explain each answer. Assume that exchange rates
are free to vary and that other factors are held constant.
a. The growth rate of national income is higher in the United States than in Japan.
ANSWER. The value of the dollar should rise as more rapidly rising GNP in the United States leads to a relative
increase in demand for dollars.
b. Inflation is higher in the U.S. than in Japan.
ANSWER. The value of the dollar should fall in line with purchasing power parity.
c. Prices in Japan and the United States are rising at the same rate.
ANSWER. According to PPP, the exchange rate should remain the same.
d. Real interest rates are higher in the United States than in Japan.
ANSWER. The value of the dollar should rise as the higher real rates attract capital from Japan that must first be
converted into dollars.
e. The United States imposes new restrictions on the ability of foreigners to buy American companies and real
estate.
ANSWER. The value of the dollar should fall as foreigners find it less attractive to own U.S. assets.
f. U.S. wages rise relative to Japanese wages, and American productivity falls behind Japanese productivity.
ANSWER. Higher U.S. wages and declining relative productivity weaken the American economy and make it less
attractive for investment purposes. Assuming that a weak economy leads to a weak currency, the dollar will fall.
From a somewhat different perspective, when a nation's productivity growth lags behind that of its major trading
partners, the other countries will become more depreciating currency is the market's way of restoring balance.
The lagging country regains its balance, but only by accepting a lower real price for its goods. In effect, the
cheaper currency is the market's way of cutting wages in the lagging country.
Problem 02
What does it mean for there to be an appreciation of the dollar relative to the pound? Use
example exchange rates to show what happens to the dollar price of the pound in this
situation.
ANSWER. An “appreciation of the dollar relative to the pound” means that the dollar
is now worth more (than it previously was) against the pound.
This strengthening of the dollar can be thought of as either:
I. Each dollar can now be sold for more pounds than previously
II. Each dollar will now cost more pounds to purchase. An example of this change
could be:
FINS5516 Week 02 Practice Problems
• An original spot rate of S0 = GBP 0.7278/USD
• A new spot rate of S0 = GBP 0.8010/USD
Problem 03
On August 8, 2000, Zimbabwe changed the value of the Zim dollar from ZWD38/USD to ZWD50/USD.
What was the original USD value of the Zim dollar? What is the new USD value of the ZWD?
ANSWER. The U.S. dollar value of the Zim dollar prior to devaluation was $0.0263
(1/38). Subsequent to devaluation, the Zim dollar was worth $0.02 (1/50).
By what percent has the Zim dollar devalued or revalued relative to the U.S. dollar?
ANSWER. The U.S. dollar value of the Zim dollar has changed by (0.02 - 0.0263)/0.0263
= -24%. Thus, the Zim dollar has devalued by 24% against the U.S. dollar.
By what percent has the U.S. dollar appreciated or depreciated relative to the Zim dollar?
ANSWER. The U.S. dollar has appreciated against the Zim dollar by an amount equal
to (50 - 38)/38 = 31.58%.
Problem 04
In 1995, one dollar bought ¥80. In 2000, it bought about ¥110.
What was the dollar value of the yen in 1995? What was the yen’s dollar value in 2000?
ANSWER. The dollar value of the yen in 1995 was $0.0125 (1/80). By 2000, the yen
had fallen to $0.00909.
By what percent has the yen fallen in value between 1995 and 2000?
ANSWER. Between 1995 and 2000, the yen fell by 27.27%, calculated as (0.00909 -
0.0125)/0.0125.
By what percent has the dollar risen in value between 1995 and 2000?
ANSWER. During this same period, the dollar appreciated by 37.5%, calculated as (110
- 80)/80.
Problem 05
Suppose the current exchange rate of the Mexican peso relative to the U.S. dollar is MXN 9.5000/USD.
Your advisor argues that the peso will lose 15% of its value relative to the dollar over the next year.
What is your advisor’s forecast of the peso price of the dollar in 1 year’s time?
ANSWER. The first thing to observe is that the question states that the peso is the
currency that will change by some percentage. Thus we should put that currency in
the denominator of our quotes if it is not already there.
Next, we can change the value of the peso by the percentage stated in the question.
If the value of the peso falls by 15%, it will go from being worth USD0.10526 to
FINS5516 Week 02 Practice Problems
Now that we have the t=1 dollar price of the peso, we can convert it back to the peso
price of the dollar:
Problem 06 (From Shapiro Chapter 2, Problem 2.4)
In early August 2002 (the exact date is a state secret), North Korea reduced the official value of the
won from $0.465 to $0.0067. The black market value of the won at the time was $0.005.
By what percent did the won devalue?
ANSWER. Using Equation 2.1, the won devalued ($0.067-$0.465)/$0.465)=98.56%
Following the initial devaluation what further percentage devaluation would be necessary for
the won to equal its black market value?
ANSWER. 25.4% = ($0.0067 – $0.005)/$0.0067
Cross Exchange Rates
Problem 07 (From Shapiro Chapter 6, Problem 6.1)
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 = $1.0295.
Working with Bid-Ask Spreads
Problem 08
Alabama Chocolate Fudge, Inc. needs to buy 2,000,000 Swiss francs (CHF) to pay its Swiss chocolate
supplier. Its banker quotes bid–ask rates of CHF1.3990/USD – CHF1.4000/USD.
What will be the dollar cost of the CHF2,000,000 invoice?
ANSWER. The company wants to buy CHF, which means they’re selling USD. If they’re
selling USD, they’ll have to do that at the lower CHF/USD price, which is the bank’s bid
of CHF1.3990/$. If the firm is purchasing CHF2,000,000 at a price of CHF1.3990/USD,
they will pay 2,000,000/(CHF1.3990/USD) = USD 1,429,592.57.
Problem 09 (From Shapiro Chapter 6, Problem 6.7)
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?
FINS5516 Week 02 Practice Problems
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)
Cross Exchange Rates & Triangular Arbitrage
Problem 10
You can trade Canadian dollars (CAD), U.S. dollars (USD), and Mexican pesos (MXN) at these rates:
USD0.7047/CAD MXN6.4390/CAD MXN8.7535/USD
Is there an arbitrage opportunity, and if so, how would you exploit it?
ANSWER. We must flip the MXN........./CAD quote to CAD………/MXN so we can follow
the test rules:
As it is less than 1, sell the currencies in the numerator to buy the currencies in the
denominator.
I. Sell USD 1.00 in order to buy CAD 1.4190.
II. Sell CAD 1.419 in order to buy MXN 9.1372.
III. Sell MXN 9.1372 in order to buy USD 1.0438.
IV. You now have USD 0.0438 more than the USD 1.00 you started with, which is
a 4.38% profit.
What would be your arbitrage profit in USD if the first step of your arbitrage transaction was
the purchase or sale of USD 1,000,000?
ANSWER. 0.0438 x USD 1,000,000 = USD43,800
Cross Exchange Rates with Bid/Ask Spreads
Problem 11
FINS5516 Week 02 Practice Problems
Société Générale quotes bid–ask rates of ¥104.30-104.40/$ and $1.3005/€–$1.3007/€.
What would be Société Générale’s direct asking price of yen per euro (¥/€)?
ANSWER. You should think of the logic underpinning these cross-rate calculations as
us using the currency that’s going to be eliminated (in this case, the $) as a vehicle
currency for separate two transactions.
One pair of transactions will be to 1) Sell euros to buy dollars then 2) Sell those dollars
to buy yen. The other pair will be where we 1) Sell yen to buy dollars and then 2) Sell
those dollars to buy euro.
In this question’s case, we are after the latter. The direct asking price of yen per euro
(¥………/€) is the price at which you the customer will buy euros from (and sell yen to)
the bank. So first, we identify the rates at which you can:
1) Sell yen for dollars (…which is ¥104.40/$)
2) Buy euros with those dollars (….which is $1.3007/€).
Then eliminate the USD in order to find the ¥........./€ cross rate.
Problem 12 (From Shapiro Chapter 7, Problem 6.8)
The euro is quoted at 0.6064-80 in London and the pound sterling is quoted at 1.6244-59 in Paris.
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).
Problem 13
Below are the bid & ask rates for trading between the Euro, the Japanese Yen, and the Aussie Dollar:
BID ASK
YEN 128.71/EUR YEN 128.74/EUR
YEN 92.50/AUD YEN 92.52/AUD
AUD 1.3912/EUR AUD 1.3915/EUR
Is there an arbitrage profit available? How did you arrive at this conclusion?
ANSWER. Method 1: Manually try going each way around the triangle
First direction (EUR -> YEN -> AUD -> EUR)
• Start with EUR 1.00
• Sell your EUR 1.00 at YEN 128.71/EUR to get YEN 128.71
FINS5516 Week 02 Practice Problems
• Spend your YEN 128.71 to purchase AUD at YEN 92.52/AUD to get AUD
1.391159
• Spend your AUD 1.391159 to purchase EUR at AUD 1.3915/EUR to get EUR
0.99975
• You’ve finished with LESS than the EUR 1.00 you started with. No arbitrage.
Second direction (EUR -> AUD -> YEN -> EUR)
• Start with EUR 1.00
• Sell your EUR 1.00 at AUD 1.3912/EUR to get AUD 1.3912
• Sell your AUD 1.3912 at YEN 92.50/AUD to get YEN 128.686
• Spend your YEN 128.686 to purchase EUR at YEN 128.74/EUR to get EUR
0.99958
• You’ve finished with LESS than the EUR 1.00 you started with. No arbitrage
again.
Method 2: Find an implied cross-rate bid/ask spread & compare it to the quoted
market bid/ask spread.
Use the 1st and 3rd lines of the table to work out what the YEN cross-rates SHOULD
be:
• If I was to buy one EUR using AUD, I would pay AUD 1.3915 to get it
• If I was to sell one EUR using YEN, I would receive YEN 128.71
• Therefore the effective calculated cross-exchange rate (BID) is:
• If I was to buy one EUR using YEN, I would pay YEN 128.74 to get it
• If I was to then sell that one EUR to get AUD, I would receive AUD 1.3912
• Therefore the effective calculated cross-exchange rate (ASK) is:
Forward Rates
Problem 14
You enter into a one-year forward contract to purchase GBP1,000,000 at a forward rate of
AUD1.7346/GBP.
Draw a time-line of the cash flows of this transaction (from your perspective).
ANSWER.
FINS5516 Week 02 Practice Problems
Problem 15
TRUE OR FALSE:
If the closing spot rate is $0.5800/C$ at the expiration of a forward contract, a party that has sold
dollars at a forward rate of $0.5754/C$ has an incentive to default.
ANSWER. False. If we’re “selling $” forward, we’re simultaneously “buying C$” at that same
$0.5754/C$ forward rate. So if you have committed to buy C$ at $0.5754 each on the maturity
date, but you can actually resell those C$ into the spot market at $0.5800 each.
Problem 16
As a FX trader for Dimon Bank, you have just called a trader at WeberAxel Bank to get quotes for the
British pound for the spot, 30-day, 60-day, and 90-day forward rates.
Your WeberAxel Bank 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?
ANSWER. To calculate the cash flows, we must first calculate the actual forward rates
from the spot & forward points. Given that the forward points are DECLINING when
read left to right (i.e. 47>44, 88>81, 125>115), we subtract the points.
Because the forward points are BIGGER/SMALLER we SUBTRACT them from the spot
rate in order for the bid-ask spread to widen as maturity lengthens.
The forward points for 30 days are 47/44, so subtracting:
Similarly with the 90-day points:
To “swap into” £5,000,000 at the 30-day rates, we BUY £5,000,000 at an ask of
$1.7706/£ = We PAY $8,853,000 in 30 days.
To “swap out of” £5,000,000 at the 90-day rates, we SELL £5,000,000 at a bid of
$1.7620/£ = We RECEIVE $8,810,000 in 90 days.
What must be the relationship between dollar interest rates and pound sterling interest rates?
ANSWER. As we’ll discuss more in the Interest Rate Parity chapter:
• The currency with the SMALLER interest rate trades at a forward PREMIUM
• The currency with the LARGER interest rate trades at a forward DISCOUNT
FINS5516 Week 02 Practice Problems
As the pound is trading at a forward discount relative to the dollar, it MUST have the
higher interest rate.
If the pound did not have the higher interest rate, there would be guaranteed
covered-interest arbitrage opportunities that we could make against the bank quoting
the above spot & forward rates.
So absent any other information and assuming that this bank is sane, it is safe to
assume the pound has the larger interest rate.
Problem 17 (From Shapiro Chapter 6, Problem 8)
As a FX trader at Sumitomo Bank, your customer would like a ¥ quote on AUD.
Current market rates are:
SPOT 30-Day
¥101.37-85/$ 15-13
A$1.2924-44/$ 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.
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 30-day 30-day outright forward rates
¥101.37-85/U.S.$1 15-13 ¥101.22-72/U.S.$1
A$1.2924-44/U.S.$1 20-26 A$1.2944-70/U.S.$1
FINS5516 Week 02 Practice Problems
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.
What is the forward premium or discount on buying 30-day Australian dollars against yen
delivery?