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50. PPP and Hedging with Call Options. Visor Inc. (a U.S. firm) has agreed to purchase supplies
from Argentina and will need 1 million Argentine pesos in one year. Interest rate parity presently
exists. The annual interest rate in Argentina is 19%. The annual interest rate in the U.S. is 6%. You
expect that annual inflation will be about 11% in Argentina and 4% in the U.S. The spot rate of the
Argentine peso is $.30. Call options on pesos are available with a one-year expiration date, an
exercise price of $.29, and a premium of $0.03 per unit. Determine the expected amount of dollars
that you will pay from hedging with call options (including the premium paid for the options) if you
expect that the spot rate of the peso will change over the next year based on purchasing power parity
(PPP).
ANSWER: Expected % change in peso = (1.04)/(1.11) – 1 = -.0631
51. Long-term Forward Contracts. Assume that interest rate parity exists. The annualized interest
rate is presently 5% in the U.S. for any term to maturity, and is 13% in Mexico for any term to
maturity. Dokar Co. (a U.S. firm) has an agreement in which it will develop and export software to
Mexico’s government two years from now, and will receive 20 million Mexican pesos in two years.
The spot rate of the peso is $.10. Dokar uses a 2-year forward contract to hedge its receivables in two
years. How many dollars will Dokar Co. receive in two years? Show your work.
ANSWER:
Country Two - Year Compounded Return
U.S. (1.05)2 – 1 = 10.25%
Mexico (1.13)2 – 1 = 27.69%
52. Money Market Versus Put Option Hedge. Narto Co. (a U.S. firm) exports to Switzerland and
expects to receive 500,000 Swiss francs in one year. The one-year U.S. interest rate is 5% when
investing funds and 7% when borrowing funds. The one-year Swiss interest rate is 9% when investing
funds, and 11% when borrowing funds. The spot rate of the Swiss franc is $.80. Narto expects that the
spot rate of the Swiss franc will be $.75 in one year. There is a put option available on Swiss francs
with an exercise price of $.79 and a premium of $.02.
a. Determine the amount of dollars that Narto Co. will receive at the end of one year if it implements
a money market hedge.
b. Determine the amount of dollars that Narto Co. expects to receive at the end of one year (after
accounting for the option premium) if it implements a put option hedge.
ANSWER:
a. Narto Co. could borrow the amount of Swiss francs so that the 500,000 Swiss francs to be
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Managing Transaction Exposure 2
b. Given an exercise price of $.79, Narto Co. can exercise the put option and sell its Swiss francs for
53. Forward Versus Option Hedge. Assume that interest parity exists. Today, the one-year interest
rate in Japan is the same as the one-year interest rate in the U.S. You use the international Fisher
effect when forecasting how exchange rates will change over the next year. You will receive Japanese
yen in one year. You can hedge receivables with a one-year forward contract on Japanese yen or a
one-year at-the-money put option contract on Japanese yen. If you use a forward hedge, will your
expected dollar cash flows in one year be higher than, lower than, or the same as if you had used put
options? Explain.
ANSWER: Because the two countries have equal one-year interest rates, there is no expected change
in the spot rate based on the international Fisher effect. When hedging receivables with a forward
54. Long-term Hedging. Rebel Co. (a U.S. firm) has a contract with the government of Spain and
will receive payments of 10,000 euros in exchange for consulting services at the end of each of the
next 10 years. The annualized interest rate in the U.S. is 6% regardless of the term to maturity. The
annualized interest rate for the euro is 6% regardless of the term to maturity. Assume that you expect
that the interest rates for the U.S. and for the euro will be the same at any future time, regardless of
the term to maturity. Assume that interest rate parity exists. Rebel considers two alternative strategies:
Strategy (1) - It can use forward hedging one year in advance of the receivables, so that at the
end of each year, it creates a new one-year forward hedge for the receivables,
Strategy (2) - It can establish a hedge TODAY for ALL future receivables (a one-year forward
hedge for receivables in one year, a two-year forward hedge for receivables in two years, and so on).
a. Assume that the euro depreciates consistently over the next 10 years. Will strategy 1 result in
higher, lower, or the same cash flows for Rebel Co. as strategy 2?
b. Assume that the euro appreciates consistently over the next 10 years. Will strategy 1 result in
higher, lower, or the same cash flows for Rebel Co. as strategy 2?
ANSWER:
a. Lower, because if the euro depreciates over time, so will the one-year forward rate. Thus, the
amount of dollars received from using strategy 1 declines each year. Conversely, if strategy 2 is used,
b. Higher, because if the euro appreciates over time, so will the one-year forward rate. Thus, the
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Managing Transaction Exposure 3
55. Long-term Hedging. San Fran Co. imports products. It will pay 5 million Swiss francs for
imports in one year. Mateo Co. will also pay 5 million Swiss francs for imports in one year. San Fran
Co. and Mateo Co. will also need to pay 5 million Swiss francs for imports arriving in 2 years.
Today, Mateo Co. uses a one-year forward contract to hedge its payables in one year. A year from
today, it will use a one-year forward contract to hedge the payables that it must pay two years from
today.
Today, San Fran Co. uses a one-year forward contract to hedge its payables due in one year. Today, it
also uses a two-year forward contract to hedge its payables in two years.
Assume that interest rate parity exists and it will continue to exist in the future. You expect that the
Swiss franc will consistently depreciate over the next two years.
Switzerland and the U.S. have similar interest rates, regardless of their maturity, and they will
continue to be the same in the future. Will the total expected dollar cash outflows that San Fran Co.
will pay for its payables be higher than, lower than, or the same as the total expected dollar cash
outflows that Mateo Co. will pay? Explain.
ANSWER: The dollar cash outflows will be higher for San Fran Co. than for Mateo Co. Because
both countries have similar interest rates, the forward rate of the franc will contain neither a discount
nor premium according to IRP. So when San Fran Co. buys the two forward contracts, it will buy
56. Comparison of Hedging Techniques. Today, the spot rate of the euro is $1.20. The one-year forward
rate is $1.16. A one-year call option on euros exists with a premium of $.04 per unit and an exercise
price of $1.17. You think the spot rate is the best forecast of future spot rates. You will need to pay 10
million euros in one year. Determine whether a money market hedge or a call option hedge would be
more appropriate to hedge your payables.
ANSWER: Money market hedge: Invest in euros today so that you have enough to pay 10 million
euros in 1 year: 10,000,000 euros/1.09=9,174,311 euros.
57. IRP, PPP, and the Hedging Decision. The one-year U.S. interest rate is presently higher than the
Japanese interest rate. Assume a real rate of interest of zero percent in each country. Assume that
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Managing Transaction Exposure 4
interest rate parity exists. You believe in purchasing power parity (PPP). You have receivables of 10
million Japanese yen that you will definitely receive in one year. Should you hedge? Briefly explain.
ANSWER: Since the real rate of interest is zero in each country, the expected rate of inflation is
58. Cross-Hedging Strategy. Assume that the country of Dreeland has a currency (called the dree) that
tends to move in tandem with the Chile peso and is expected to continue to move in tandem with the
Chilean peso in the future. Indianapolis Co., a U.S. firm, has a large amount of receivables in the
dree. It expects that the dree will depreciate against the dollar over time. There are no derivatives
available on the dree. Indianapolis Co. considers the following strategies to reduce its exchange rate
risk: (a) use a money market hedge in which it converts dollars into dree and maintains a deposit in
the dree for one year, (b) use a forward contract to purchase Chilean pesos forward, (c) sell a put
option hedge on Chilean pesos, (d) purchase a call option on Chilean pesos, and (e) use a forward
contract in which it sells Chilean pesos forward. Which strategy is most appropriate?
ANSWER: Indianapolis Co. should sell Chile pesos forward. The Chile peso is correlated with the
59. Estimating the Hedged Cost of Payables. Grady Co. is a manufacturer of hockey equipment in
Chicago, and will need 3 million Swiss francs (SF) in one year to pay for imported supplies. The U.S.
one-year interest rate is 2% while Switzerland's one-year interest rate is 7%. The spot rate of the SF is
$.90. The one-year forward rate of the SF is $.88. A one-year call option on SF exists with an exercise
price of $.90 and a premium of $.03 per unit. As the Treasurer of Grady Co., you think the spot rate of
the SF is the best forecast of the future spot rate of the SF.
a. If you use a money market hedge, determine the amount of dollars that you will pay for the
payables.
b. If you use a call option hedge, determine the expected amount of dollars that you will pay for the
payables (account for the option premium within your estimate).
ANSWER:
a. Invest in SF today so that you have enough to pay SF3 million in 1 year.
b. Cost per unit = Exercise price of $.90 + premium of $.03 = $.93.
Solution to Continuing Case Problem: Blades, Inc.
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Managing Transaction Exposure 5
1. Using a spreadsheet, compare the hedging alternatives for the Thai baht with a scenario under which
Blades remains unhedged. Do you think Blades should hedge or remain unhedged? If Blades should
hedge, which hedge is most appropriate?
ANSWER: (See spreadsheet attached.) Based on the analysis, it appears that Blades should hedge its
Calculation of Net Baht Paid or Received in 90 Days:
Baht-denominated inflow:
Pairs sold 45,000
Forward Hedge:
Sell baht 90 days forward:
Money Market Hedge:
Borrow baht, convert to $, invest $, use receivables to pay off loan in 90
days:
Remain Unhedged:
Total Dollars Received
Possible Spot Rate in 90 Days ($) from Converting Baht
0.0200 3,054,600
2. Using a spreadsheet, compare the hedging alternatives for the British pound receivables with a
scenario under which Blades remains unhedged. Do you think Blades should hedge or remain
unhedged? Which hedge is the most appropriate for Blades?
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Managing Transaction Exposure 6
ANSWER: (See spreadsheet attached.) Based on the analysis, it appears that Blades should hedge its
pound exposure. The money market hedge appears to be the most appropriate for Blades, because it
Calculation of Pounds Received in 90 Days:
Pound-denominated inflow:
Forward Hedge:
Sell pounds 90 days forward:
Money Market Hedge:
Borrow pounds, convert to $, invest $, use receivables to pay off loan in 90
days:
Put Option Hedge:
Purchase put option:
Total Dollars Total Dollars
Premium Received per Received from
Possible Spot per Unit Unit (after Converting
Rate in 90 Paid for Exercise accounting for 4,000,000
Days ($) Option ($) Option? the premium) Pounds Probability
$1.45 $0.02 Y $1.45 $5,800,000 5%
1.47 0.02 Y 1.45 5,800,000 20%
Remain Unhedged:
Possible Spot Total Dollars
Rate in 90 Received from
Days ($) Converting Pounds Probability
$1.45 $5,800,000 5%
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Managing Transaction Exposure 7
3. In general, do you think it is easier for Blades to hedge its inflows or its outflows denominated in
foreign currencies? Why?
ANSWER: In general, it is easier for Blades to hedge its inflows denominated in foreign currencies.
This is because Blades’ outflows are subject to two uncertain variables, the amount of the payables
4. Would any of the hedges you compared in question 2 for the British pounds to be received in 90 days
require Blades to overhedge? Given Blades’ exporting arrangements, do you think it is subject to
overhedging with a money market hedge?
ANSWER: In this case, none of the hedges would require Blades, Inc. to overhedge. Usually, the put
Given Blades’ exporting arrangements, it is not subject to overhedging using the money market
hedge. Both the British and Thai retailers have entered into arrangements with Blades under which
5. Could Blades modify the timing of the Thai imports in order to reduce its transaction exposure? What
is the tradeoff of such a modification?
ANSWER: Blades could import sufficient materials to completely offset the baht-denominated
inflows this period. Since Blades will generate baht-denominated revenue of 45,000 × 4,594 =
The tradeoff of accelerating the purchases from Thailand in order to reduce Blades’ transaction
6. Could Blades modify its payment practices for the Thai imports in order to reduce its transaction
exposure? What is the tradeoff of such a modification?
ANSWER: Yes, Blades could modify its payment practices in order to reduce its transaction exposure
in Thailand. Currently, Blades pays the Thai suppliers sixty days earlier than its competitors. If the
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Managing Transaction Exposure 8
7. Given Blades’ exporting agreements, are there any long-term hedging techniques Blades could benefit
from? For this question only, assume that Blades incurs all of its costs in the United States.
ANSWER: Blades has fixed-price exporting arrangements with both the Thai and British customers
for the next two years. Furthermore, the timing of the resulting foreign currency inflows is known.
Solution to Supplemental Case: Blackhawk Company
This case uses actual data to show how inaccurate forecasts can be.
a. Using the regression model in which FSR is the dependent variable and FR is the independent
variable, the slope coefficient is about .857 and the standard error of the coefficient is .0825.
Therefore, the t-statistic in testing for a bias is:
t = .857 - 1
.0825
-1.733
b. There appears to be a bias, in that the use of the forward rate resulted in negative forecast errors
c. The average absolute forecast error when using the forward rate is .02963.
d. Using the regression model in which FSR is the dependent variable and SR is the independent
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Managing Transaction Exposure 9
e. There appears to be a bias, in that the use of the spot rate resulted in negative forecast errors
h. The probability distribution for FSR is:
Probability FSR
i. The probability distribution for payments if Blackhawk does not hedge is:
$ Amount
Probability Needed
j. The probability distribution for the real cost of hedging is determined below:
$ Amount $ Amount
Needed if Needed if Real Cost
Probability Hedged Unhedged of Hedging
k. The probability distribution of payments when owning a call option is shown below:
Exercise
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Managing Transaction Exposure 10
Probability FSR Option? $ Needed (incl. prem.)
l. Money market hedge
Amount of NZ$ to invest = NZ$800,000
(1.021)
= NZ$783,545
Small Business Dilemma
Hedging Decisions by the Sports Exports Company
1. Determine the amount of dollars received by the Sports Exports Company if the receivables to be
received in one month are not hedged under each of the two exchange rate scenarios.
ANSWER:
Scenario I: A 3% rate of depreciation reflects a future spot rate (in one month) of:
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Managing Transaction Exposure 11
2. Determine the amount of dollars received by the Sports Exports Company if a put option is used to
hedge receivables in one month under each of the two exchange rate scenarios.
ANSWER:
Scenario I: The put option would be hedged, resulting in the conversion of 10,000 pounds at an
exchange rate of $1.645:
Scenario II: The put option would not be exercised, so that the pounds could be converted at the
future spot rate of $1.683:
3. Determine the amount of dollars received by the Sports Exports Company if a forward hedge is used
to hedge receivables in one month under each of the two exchange rate scenarios.
ANSWER: The forward rate is $1.645. Therefore, the amount of dollars to be received regardless of
4. Summarize the results of dollars received based on an unhedged strategy, a put option strategy, and a
forward hedge strategy. Select the strategy that you prefer based on the information provided.
ANSWER:
Results Based Results Based
on Scenario I on Scenario II
Unhedged Strategy $16,005 $16,830
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Managing Transaction Exposure 12
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