Question

Suppose IBM purchased computer chips from NEC, a Japanese electronics concern, and was billed ¥250 million payable in one year. The current spot rate is 99 yen per dollar and the one-year forward rate is 95 yen per dollar. The annual interest rate is 5% in Japan and 8% in the U.S. IBM can also buy a one-year call option on yen at the strike price of $0.01 per yen for a premium of .014 cents per yen.

1.Explain how IBM should do a forward hedge. Compute the future dollar costs of meeting this obligation using the forward hedges.

2.Assuming that the forward exchange rate is the best predictor of the future spot rate, compute the expected future dollar cost of meeting this obligation when the option hedge is used.

3.At what future spot rate do you think IBM may be indifferent between the option and forward hedge?

Answer 1

1. Forward hedge can be done using either futures contract or by entering into an option contract:

A. Forward contracr hedge: Buy a 1-yr forward contract for Yen 250 million @95 yen per $. At expiry, the forward contract will be executed and you will be required to pay $(250million/95) = $2.6316 million.

B. Option contract hedge:

At T=0: Buy a one year call option and pay $(0.014/100 *250) = $0.035 million. The 1-yr future value of this amount is 0.035*(1+0.08) = $0.0378 million

At T=1: Assuming the interest rate partity holds true, the Spot rate will be 96.25 Yen/Dollar (99*1.05/1.08) or $0.0104 per Yen. Since the strike price is lower than spot price on expiry, the call option will be excercised and you will pay $(0.01*250) = $2.5 million.

Total cost of options contract = 2.5+0.0378 = $2.5378 million, which is lower than the forward rate.

So, the call option on yen is better, with total cost of $2.5378 million

2)

Option contract hedge:

At T=0: Buy a one year call option and pay $(0.014/100 *250) = $0.035 million. The 1-yr future value of this amount is 0.035*(1+0.08) = $0.0378 million

At T=1: The future spot rate is 95 yen per dollar or $0.0105 per Yen Since the strike price($0.01 per yen) is lower than spot price on expiry($0.0105 per Yen), the call option will be excercised and you will pay $(0.01*250) = $2.5 million.

Total cost of options contract = 2.5+0.0378 = $2.5378 million

3) To be indifferent, the cost of futures contract ($2.6316 million) should be equal to cost of options contract.

$0.0378 million+payment on option expiry = $2.6316 mn

payment on option expiry = $2.5938 mn = Future $/Yen spot rate * 250mn

Future $/Yen spot rate = 0.0103752

Future Yen/$ spot rate = 96.3837