Question

Princess Cruise Company (PCC) purchased a ship from Mitsubishi Heavy Industry. PCC owes Mitsubishi Heavy Industry ¥500 million payable in one year. The current spot rate is ¥124/$ and the one-year forward rate is ¥110/$. Interest rate is 5% per annum in Japan and 8% per annum in the U.S. The 1-year call option on ¥ at the strike price of $.0081/¥ currently sells for a premium of .014 cents per Yen.

(1) Construct forward hedge for PCC and calculate the future dollar cost of meeting its ¥ obligation using this hedge.

(2) Construct money market hedge (MMH) for PCC and calculate the future dollar cost of meeting its ¥ obligation using MMH.

(3) How to hedge PCC’s foreign currency exposure in option market? Conduct cash flow analysis to examine the result of option hedge.

(4) At what future spot rate will PCC be indifferent between option hedge and forward hedge? Explain.

Answer 1

1) In the forward hedge, PCC buys the forward contract for 500 million Yen today by fixing a price of 110Yen/$.

After one year, PCC get 500 million Yen from the forward contract by paying $ 500 million/110 =$4.5455 million and pays the same to Mitsubishi

Future Dollar cost of meeting the obligation is $4.5454 million or $4,545,455 (rounded to nearest dollar)

2) In money market Hedge, PCC borrows $3,840,246 (500million Yen / 1.05 * 1/124) today at 8% , converts them to Yen at 124Yen/$ (spot rate today) to get 476,190,476 Yen and invests the same in Japan at 5% for one year.

After one year, the deposit in Yen matures to 47190476*1.05 = 500 million Yen and is paid to Mitsubishi

The Dollar loan matures to become 3840246*1.08 = $4,147,465 which is the future cost of meeting the obligation

3) One year call options to purchase 500 million Yen at a strike price of $0.0081/Yen or 123.4568 Yen/$ can be bought by paying a premium of 0.014 cents/ Yen . So for the total contract of 500 million Yen, premium paid = 0.014 * 500 million cents = 7 million cents = $70,000

After one year, if exchange rate >123.4568 Yen/$ say $125 Yen/$ , the option becomes worthless and the Yen can be purchased at the then rate to pay the obligation, the maximum amount to be paid in dollars is

$ 500 million/ 123.4568 = $4.05 million = $4,050,000

Else

After one year, if exchange rate <123.4568 Yen/$ say $120 Yen/$ , the option can be exercised and the Yen can be purchased using the Option to pay the obligation, the amount to be paid in dollars is

$ 500 million/ 123.4568 = $4.05 million = $4,050,000

So, using options , the amount to be paid is $4050000 + $70000 (ignoring time value)

= $4,120,000

4) In forward hedge, PCC will always pay $4,545,455 to meet the future obligation irrespective of the exchange rate. In options hedge, the maximum amount PCC will have to pay is $4,120,000 as explained above.

Hence there is no rate at which the future obligation in Dollars is the same for Forward and options hedge.

There is no point of indifference.