Question

our firm (an Australian firm) makes a sale to a Japanese customer. The sale price is 200 million Japanese Yen payable in exactly three months from today. The current exchange rate is AUD/JPY = 90 (i.e., 1 Australian Dollar (AUD) is worth 90 Japanese Yen (JPY)). The current interest rates in Australia and Japan are 3% p.a. and 0.5% p.a., respectively.

Given this information, please answer the following questions. Please label your answers according to parts.

(a) Given that Australian Dollar is the domestic currency, what is the direct quote of the exchange rate between Australian Dollar and Japanese Yen ? Please round the final answer to five decimal places.

(b) What is the theoretical current forward exchange rate quoted directly in terms of Australian Dollar (i.e. JPY/AUD) for delivery three months from today ? Show your input to the formula to arrive at the final answer. Please round the final answer to five decimal places.

(c) How can the firm take advantage of any decreases in the exchange rate and also ensure that it receives at least Australian $2 million ? (Hint: Which derivative instrument can be used to achieve this objective?)

(d) Ignoring the cost of the derivative instrument to be used in part (c), what would be the outcome from hedging if the spot exchange rate in 3 month’s time is (i) AUD/JPY=150 and (ii) AUD/JPY = 50?

Answer 1

a) Direct quote will give how much AUD one can get in One Japanese Yen

1 Yen = 1/90 = 0.01111 AUD

So, direct quote is 1 Yen = 0.01111 AUD or 0.01111 AUD/Yen

b) Theoretical Forward rate in JPY/AUD for 3 months delivery

= Spot rate*(1+interest rate in japan* time in years) /(1+interest rate in Australia*time in years)

=90*(1+0.005*0.25)/(1+0.03*0.25)

=89.44169 JPY/AUD

c) The Australian firm can sell the Japanese Yen in 3 months forward and fix the above exchange rate for the Yen receivables after 3 months.to receive 200 million/89.44169 = AUD 2.236 million If the forward cover is not available, the Australian firm can borrow 200/(1+0.005*0.25)Yen today = 199.7503 Million yen , convert to AUD today to get AUD 2.219448 million AUD and invest the amount in Australia to get 2.219448*(1+0.03*0.25) = 2.236 million AUD. All the above instruments fix the amount of receivables in AUD

To ensure that the firm receives at least Australian $2 million, the firm can buy JPY put options, in this case the put option bought must have a strike price of JPY 100/AUD. This ensures that the minimum amount received is AUD 2 million.

d)   if the spot exchange rate in 3 month’s time is

(i) AUD/JPY=150 , the put option will be exercised and the amount received would be

JPY 200 million / 100 JPY/AUD = AUD 2 million

(ii) AUD/JPY = 50, the put option will not be exercised and the amount received would be

JPY 200 million / 50 JPY/AUD = AUD 4 million

Thus hedging would fix the minimum receivables at AUD 2 million