A Japanese company purchased currency options to hedge AUD 1 million payable. The exercise price of the option is JPY100/AUD with a premium of JPY5/AUD. The spot rate became JPY110/AUD at the time of maturity. Which of the following statements is true?

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Question restatement: A Japanese company purchased currency options to hedge a payable of AUD 1 million. The option has an exercise price of JPY 100 per AUD, with a premium of JPY 5 per AUD. At maturity, the spot rate is JPY 110 per AUD. Which statement is true?

Option a: 'The company will not exercise the option ending up with JPY 100 million.' If the company does not exercise, the payable would be settled at the spot rate, which is 110 JPY per AUD, giving 1,000,000 × 110 = 110,000,000 JPY. The premium paid reduces this benefit, but the option gives a floor and a cap in different ways. Since the spot rate (110) is above the strike (100), exercising would be advantageous relative to paying 110 per AUD directly if considering the hedge structure; however, this option would typically still incur the premium. This option’s assertion of 100 million is inconsistent with the actual economics (the premium and the spot-rate outcome would not result in exactly 100 million). Therefore, this statement is incorrect.

Option b: 'The company will end up with JPY 105 million by exercising the option.' Exercising the option lets the company buy 1,000,000 AUD at 100 JPY per AUD, totaling 100,000,000 JPY. The premium paid is 5 JPY per AUD, amounting to 5,000,000 JPY. The net cash outlay is 100,000,000 + 5,000,000 = 105,000,000 JPY, which is 105 million JPY. In terms of hedging, this is the correct accounting of the net cost when the option is exercised and the premium is included. Thus, this statement correctly reflects the outcome.

Option c: 'The company will end up with JPY 100 million by exercising the option.' If the company exercises, they pay 100 JPY per AUD for 1,000,000 AUD, which is 100,000,000 JPY, but they have paid a premium of 5 JPY per AUD (5,000,000 JPY) earlier. The total cash effect equals 100,000,000 + 5,000,000 = 105,000,000 JPY, not 100,000,000 JPY. Therefore, this statement is incorrect because it ignores the premium.

Option d: 'The company will not exercise the option ending up with 110 million JPY.' If the option is not exercised, the company would settle the payable at the spot rate of 110 JPY per AUD, yielding 1,000,000 × 110 = 110,000,000 JPY. The premium paid is sunk relative to that decision, but the raw outcome of not exercising is 110 million JPY, so this statement misstates the inclusion of the premium and the hedge mechanics. Hence, this statement is incorrect.

A Japanese company purchased currency options to hedge AUD 1 million payable. The exercise price of the option is JPY100/AUD with a premium of JPY5/AUD. The spot rate became JPY110/AUD at the time of maturity. Which of the following statements is true?

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