Trying to understand how to calculate Arbitrage questions.

Question

The following are quotes for Japanese (JPY) against the dollar (USD) for spot, 1 month forward, 3 months forward, 6 months forward and one year forward. All the rates are quoted as the number of JPY per USD.

Spot exchange rate:

Bid rate 128.02 JPY per USD

Ask rate 128.06 JPY per USD 

Forward points: 

1 month forward 12 - 09

3 month forward 46 - 41

6 month forward 102 - 92 

1 year forward 204 - 184

Q 1 & Q 2 combined: A customer TBI International inc calls you and ask you for the exchange rate at which they can sell to you 500 mio JPY for delivery 3 months forward. 

Q 1: What exchange rate do you quote? Give your answer to 2 decimal places.

Q 2: How many USD will the customer TBI International inc receive in 3 months time in exchange for the 500 mio JPY. Give your answer to the nearest USD. 

Answer 1

Q1: To determine the exchange rate at which TBI International Inc can sell 500 million JPY for delivery 3 months forward, we need to use the 3 month forward rate.

The 3 month forward rate is quoted as 46 - 41. This means that the bid rate for the 3 month forward contract is 46 JPY per USD, and the ask rate is 41 JPY per USD.

To calculate the exchange rate at which TBI International Inc can sell 500 million JPY for delivery 3 months forward, we take the ask rate (41 JPY per USD) and divide it into the amount of JPY being sold (500,000,000 JPY).

Exchange rate = 500,000,000 JPY / 41 JPY per USD = 12,195,122.00 USD

Therefore, the exchange rate at which TBI International Inc can sell 500 million JPY for delivery 3 months forward is 12,195,122.00 USD / 500,000,000 JPY = 0.02439 USD per JPY, rounded to 2 decimal places.

Answer to Q1: 0.02 USD per JPY

Q2: To calculate how many USD TBI International Inc will receive in 3 months time in exchange for the 500 million JPY, we use the exchange rate calculated in Q1 (0.02439 USD per JPY) and multiply it by the amount of JPY being sold (500,000,000 JPY).

USD received = 0.02439 USD per JPY x 500,000,000 JPY = 12,195,122 USD

Therefore, TBI International Inc will receive approximately 12,195,122 USD in 3 months time in exchange for 500 million JPY.

Answer to Q2: 12,195,122 USD.