Question

6. Hedging with forwards, options and money market. Princess Cruise Company (PCC) purchased a ship from Mitsubishi Heavy Industry for 500 million yen payable in one year. The current spot rate is ¥124/$ and the one year forward rate is ¥110/$. The annual interest rate is 5 percent in Japan and 8 percent in the U.S. PCC can also buy a oneyear call option on yen at the strike price of $0.0081 per yen for a premium of 0.014 cents per yen.

a) Compute the US dollar cash flows associated with 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 US dollar cash flows associated with meeting this obligation when the option hedge is used.

c) At what future spot rate, do you think PCC may be indifferent between the forward and the option hedge?

Answer 1

а. Calculate the US dollar cash flows in the case of forward hedge as follows: Cost of ship One year forward rate Dollar cost ¥500,000,000 110/S $4,545,454.55 Calculate the US dollar cash flows in the case of market hedge as follows Cost of ship x(1+Annual rate in U.S.) Dollar cost = Current spot rate x (1+Annual rate in Japan ¥500,000,000x (1+8%) 124/Sx(15%) X X ¥540,000, 000 ¥130.20/S S4,147,465.44

Calculate the Total expected cost as follows Future value of option permium + Total expected cost =| Excersice price 0.014 x500,000, 000 x1.08 100 (500,000,000 x 0.0081) -[S75,600+ $4,050, 000] S4,125, 000 C. When the option hedge is used, PCC will spend "at most" $4,125,000. when the forward hedging is used, PCC will have to spend $4,545,455 regardless of the future spot rate This means that the options hedge dominates the forward hedge. At no future spot rate, PCC will be indifferent between forward and options hedges