Question

Princess Cruise Company (PCC) purchased a ship from Mitsubishi Heavy Industry. PCC owes

Mitsubishi Heavy Industry 500 million yen in one year. The current spot rate is 124 yen per dollar and the one-year forward rate is 110 yen per dollar. The annual interest rate is 5% in Japan and 8% in the U.S.

PCC can also buy a one-year call option on yen at the strike price of $.0081 per yen for a premium of .014 cents per yen.

(c) Assuming that the Options (call option) exchange rate is the best predictor of the future spot rate, compute the expected future dollar cost of meeting this obligation

(d) What is the best alternative?

Answer 1

(c) Options (call option) exchange rate is the best predictor of the future spot rate. Hence, future spot rate = $.0081 per yen.

Expected future dollar cost of meeting this obligation at future spot rate = 500mn yen* $.0081 per yen = $4.05 million

(d) Cost under forward contract : One year forward rate = 110 yen per dollar

Cost in dollar = 500million yen * (1/110) dollar per yen = $4,545,455

Cost under option contract : Call option strike price = $.0081 per yen

Premium = .014 cents per yen

Total contract value = 500 million yen

Cost of purchasing this contract = 500 mn yen * $.0081 per yen = $4.05 million

Premium = 500 million yen * .014 cents per yen = 7 million cents = $70000

Total cost under option contract = $4.05 million + $.07 million = $4.12 million

We can also enter into a money market hedge:

Borrow an amount in $ and invest in yen such that it amounts to 500 million yen in one year.

Let us say the amount invested in yen is 'x'.

yen interest rate = 5%.

To get an amount of 500 million yen after one year we have:

x + x*5% = 500 million

Hence x = 476,190,476 yen

Converting this into dollar at current spot rate of 124 yen per dollar = 476190476*(1/124) = $3,840,246

We have to borrow this amount today. At the end of one year the amount to be paid back will be :

=$3840246 + 3840246*8% = $4,147,466

Out of these four alternatives if future spot rate prediction stands out to be true than that will be the cheapest and the best alternative.

However, if we cannot estimate the future spot rate than option contract would be the best alternative.