A Japanese electronics firm purchases capital equipment from a U. S. firm for US

Question

A Japanese electronics firm purchases capital equipment from a U. S. firm for USD 5,000. Payment is due in 120 days. Spot USDJPY equals 105. The Japanese firm fears that the USD will strengthen in the near future and wishes to insure against this by purchasing USD call options with a strike price of JPY 105. The premium is JPY 3. Analysts’ forecasts of USD calls for a USDJPY rate of either 100 or 120 in 120 days. Assume equal probability. Use a JPY TIBOR rate of 2.4 percent (actual/ 360) to factor in the financing cost of options in your calculations. What is the cost in JPY if the USDJPY is 120?

Explanation / Answer

Calculation of $1 of purchases

Spot USDJPY = 105

Call option a strike 105 = 3JPY

Financing cost of call option = 2.4*(120/360) = 0.8%

Thus cost of single option = 3*1.008 = 3.024 JPY

If the USD JPY price I 120 after 3 months

Pay offs from underlying = 105-120 = -15 JPY

Pay offs from call option = 120-105-3.024 = 11.976 JPY

Thus net loss = 3.024 JPY

Losses have been reduced due to option hedging

Thus net loss for $5000 = 15120 JPY with option hedging

Without option hedging loss = 5000*15 = 75000 JPY

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