Trident, a U.S.-based MNC, has just signed a contract to buy agricultural equipment from Plains Manufacturing for euro 1,250,000. The purchase was made in June with payment due six months later in December. Because this is a sizable contract for the firm, Trident is considering several hedging alternatives to reduce the exchange rate risk arising from the purchase. To help the firm make a hedging decision you have gathered the following information.

The spot exchange rate is $1.40/euro
Trident’s cost of capital is 11% p.a. (or 5.5% for 6 months)
The six-month forward rate is $1.38/euro
The Eurozone 6-month borrowing rate is 9% p.a. (or 4.5% for 6 months)
The Eurozone 6-month lending rate is 7% p.a. (or 3.5% for 6 months)
The U.S. 6-month borrowing rate is 8% p.a. (or 4% for 6 months)
The U.S. 6-month lending rate is 6% p.a. (or 3% for 6 months)
December put options for euro 625,000; strike price $1.42, premium price is 1.5%
December call options for euro 625,000; strike price $1.41, premium price is 1.3%
Trident’s forecast for 6-month spot rates is $1.43/euro

If Trident hedges the euro payable in the money market, what's the dollar cost to the firm on the date of purchase?

Question

Trident, a U.S.-based MNC, has just signed a contract to buy agricultural equipment from Plains Manufacturing for euro 1,250,000. The purchase was made in June with payment due six months later in December. Because this is a sizable contract for the firm, Trident is considering several hedging alternatives to reduce the exchange rate risk arising from the purchase. To help the firm make a hedging decision you have gathered the following information.

The spot exchange rate is $1.40/euro
Trident’s cost of capital is 11% p.a. (or 5.5% for 6 months)
The six-month forward rate is $1.38/euro
The Eurozone 6-month borrowing rate is 9% p.a. (or 4.5% for 6 months)
The Eurozone 6-month lending rate is 7% p.a. (or 3.5% for 6 months)
The U.S. 6-month borrowing rate is 8% p.a. (or 4% for 6 months)
The U.S. 6-month lending rate is 6% p.a. (or 3% for 6 months)
December put options for euro 625,000; strike price $1.42, premium price is 1.5%
December call options for euro 625,000; strike price $1.41, premium price is 1.3%
Trident’s forecast for 6-month spot rates is $1.43/euro

If Trident hedges the euro payable in the money market, what's the dollar cost to the firm on the date of purchase?

BlackTom AI · Accepted Answer

For a payable in foreign currency, the money-market hedge is implemented by borrowing domestic dollars today, converting them to euros at the spot rate, and depositing those euros at the euro deposit (lending) rate so they grow to the required euro payment in six months.

1) Relevant knowledge points and concepts
- To lock in a future foreign-currency payable, compute the present value of the foreign amount using the foreign deposit (lending) rate (the rate at which you can invest the foreign currency).
- Convert that present-value foreign amount into domestic currency at the current spot rate to find the dollar cash needed today.
- Use the euro deposit (lending) rate (3.5% for 6 months) because the euros obtained now will be invested to mature to the payable.

2) Step-by-step reasoning
- Required euro payment in 6 months: 1,250,000 euros.
- Find the euros needed today (PV in euros) so that investing at the euro 6-month deposit rate 3.5% yields 1,250,000 in six months:
  PV_euros = 1,250,000 / (1 + 0.035).

3) Calculations with intermediate steps
- PV_euros = 1,250,000 / 1.035 = 1,207,729.4686 euros (approx).
- Convert these euros to dollars at the spot rate $1.40/euro:
  Dollar amount today = 1,207,729.4686 × 1.40 = $1,690,821.2561.
- Round to nearest dollar: $1,690,822.

4) Why this answer is correct
- Borrowing dollars and converting to euros to deposit ensures you will have exactly 1,250,000 euros at maturity; the dollar outflow required today equals the spot value of the euro deposit required. The correct foreign discount rate is the euro deposit (lending) rate because you will be investing euros, not borrowing them.

5) Why other approaches would differ
- Using the euro borrowing rate (4.5%) or discounting with U.S. rates would be incorrect because they do not reflect the actual cash flows for converting dollars to euros and depositing euros. A forward hedge would cost 1,250,000 × $1.38 = $1,725,000 (more expensive here). The firm’s forecast ($1.43) would imply $1,787,500 (not a hedge).

6) Conclusion
- The dollar cost today to set up the money-market hedge is $1,690,822, which matches the provided answer.

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