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. Required:
a. Compute the future dollar costs of meeting this obligation using the money market and forward hedges.
b. 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.
c. At what future spot rate do you think PCC may be indifferent between the option and forward hedge?

Explanation:

a)

In  the case of forwarding hedge:

The future dollar cost will be = FX receiveable ÷ Foward exchange rate

= 500 million yen ÷ 110 yen/dollar

= $4.55 million

For money market hedge:

Present value of yen payable =

= 476.20 million yen

PCC would convert dollars to yens at the spot market rate and borrow yen such that it would get 500 million yen at maturity(i.e after one year)  for Mitsubishi to receive it.

Dollars needed to get these yen = 476.30 yen  ÷ 124 yen/dollar

= $3.84 million

Future Value of these dollars (for comparison with the foward market hedge) = $3.84 × (1 + 0.08)

= $4.15 million

Hence, the money market hedge is better as the dollar cost is lower than the forward market hedge to meet the obligation.

b)

On the maturity date, the spot rate is 110 yen/dollar  

Ad the strike price = 0.0081 /dollar

It is better for the company to go for the strike price due to the fact that it has a lower rate than the spot rate.

Now;

The premium amount = 500000000 yen × 0.014 dollar / yen

= 70000 dollars

However; the Future dollar-cost payable = 500000000 yen × 0.0081 dollar /yen

= 4050000 dollars

By applying option hedge, the total dollar cost required to meet the obligation = (4050000 + 70000) dollars

= 4120000 dollars

c)

The dollar cost needed from the option hedge required to matching the forward hedge is determined by subtracting it from the premium amount:

Thus;

for option hedge, dollar cost needed = (4550000 - 70000) dollars

= 4480000 dollars

The required future spot rate = 500000000/4480000

= 111.61 yen/dollar

As a result, at the future spot rate of 111.61 yen/dollar, PCC will be unconcerned about and indifferent about the option or forward hedge because the future dollar cost of meeting the obligation will be the same.