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Contract Valuation and Hedging in International Business

Problem 1: Valuing a 10-Year Contract for Air Tanks

1. SweetAir, Inc. is a U.S. corporation that sells compressed air tanks. Loelife, A.G. is a German firm that manufactures air tanks, and submitted an attractive contract that offered dollar pricing. SweetAir is intrigued by the possibility of locking in long-term dollar prices from a low-cost foreign supplier.

Consider the discounted expected value of the 10-year contract that Loelife may sign with SweetAir. In the initial year of the deal, Lowlife sells an air tank to SweetAir for $400. It costs e696 to produce an air tank. The current exchange rate is e2/$. Assume that 15,000 air tanks will be sold the first year. For simplicity, also assume that accepting the SweetAir project will not require any major capital expenditures by Loelife. The other relevant information is:

• 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.

• Euro-denominated costs are expected to increase at the euro rate of annual inflation of 2%.

• The base dollar price of the air tank will be increased at the U.S. rate of inflation, which is expected to be 4% annually.

• The German corporate income tax rate is 50%.

• The appropriate euro weighted average cost of capital for the project is 17% annually.

• Loelife 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.

Can you determine the net present value (NPV) of the contract to the Loelife? Show all the steps you think necessary.

2.Subsandwich Inc. is a U.S. company that is considering expanding its operations into Japan. Subsandwich has located a possible site for a Japanese subsidiary in Tokyo. The cost to purchase and equip the facility is U765,000,000. Perform an adjusted present value (APV) analysis to determine whether this is a good investment, under the following assumptions:

• Economic life is 10 years. The terminal value is U65 million. The firm will take a straight-line depreciation for these 10 years. Net working capital will average 6% of total sales revenue. The Japanese corporate income tax rate is 37.5%.

• The average per-unit sales price will initially be U400. First-year sales will be 15 million units, and 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 afterwards.

Problem 2: Adjusted Present Value Analysis for a Japanese Subsidiary

• First-year variable costs of production will be U225 per unit of labor and $1.75 per unit of imported parts. Administrative costs will be U300 million. Retail prices, labor costs, and administrative expenses are expected to rise at the Japanese yen rate of inflation, which is forecast to be 1% annually. Dollar prices of imported parts are expected to rise at the U.S. dollar rate of inflation, which is expected to be 4% annually. The yen/dollar exchange rate is currently S0(U/$) = 85.

• The yen-denominated unlevered equity discount rate for the project is 13% annually. The firm decides to borrow U300 million to finance the project, and the yen-denominated borrowing rate for the project is 6% annually. 2 Use the second recipe (p.23 of ch18 notes part 1) to find out the adjusted present value of this project in $. Should the firm accept or reject? Show all the steps you think necessary.

3.Let’s consider a Belgian manufacturing company Grasshopper, which engages in international business with Japan and currently has the following Japanese U commitments:

(a) A/R of U300,000 for ninety days.

(b) A/P of U100,000 for thirty days.

(c) Sales contract (six months) of U100,000,000.

(d) A/R of U500,000 for thirty days.

(e) A deposit that at maturity, in twelve months, pays U5,000,000.

(f) A loan for which Grasshopper will owe U800,000 in half a year.

(g) A/P of U300,000 in three months.

(h) A/R of U100,000 for thirty days.


(a) What is Grasshopper’s net exposure for each maturity? 

(b) How would Grasshopper hedge the exposure for each maturity on the forward market? Each forward contract can only have one specified maturity.

(c) Assume that the compound per month interest rate is 0.5 percent. How would the company hedge its exposure on the spot market and the U money market? Describe all money-market transactions in detail. 

(d) Your answer to (a) may involve exposures for maturity of different month. If so, how would the company hedge all the exposures on the forward market if it is allowed to use one forward contract only (again, a forward contract can only have one specific maturity)? Please give details for each relevant maturity in consideration (i) A purchase contract for U500,000 for twelve months.

4.Let’s consider a fictitious country Frankenstan, where a UK firm has just set up a subsidiary. In the next period, assume that the subsidiary’s cashflow (CF), in terms of theFrankenstan currency (FRK), can take of the two possible values, 70% chances FRK 150 or 30% chances FRK 100, depending on whether the Frankenstan economy is booming or in a recession. Let there also be two possible next period spot rate, GBP/FRK 1.2 (28.5714% chances if the economy is in boom, 66.6667% chances if the economy is in recession) and 0.75 (71.4286% chances if the economy is in boom and 33.3333% chances if the economy is in recession). For simplicity, just assume the forward rate is 1.0GBP/FRK.

(a) To hedge against exchange rate exposure, the UK parent should buy or sell how much forward for the next maturity? 

(b) What is the expected cashflow when next period spot rate is high? When next period spot rate is low? Can the forward contract do a good job hedging exchange rate movement? 

(c) How many forward should the parent buy or sell to ensure that the expected cashflow is the same when the economy is either in boom or in recession? 

(d) If you hedge so, what is the expected cashflow when the economy is in boom? When in recession? Can the forward contract do a good job hedging the economy uncertainty? 

5.Suppose the forward expectation parity does not hold. In other words, the forward premium is not really equal to the expected rate of appreciation. Then, we can write the forward premium as the expected rate of appreciation plus a remainder term. If you regress the expected rate of appreciation on the forward premium, what does a negative beta (slope coefficient) imply about the magnitude of variance of the remainder term relative to the magnitude of variance of expected rate of appreciation? Which one is larger, or they are equal to each other? You don’t really need any mathematics/statistics beyond chapter 9 of our class.

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