Question

On July 1, an American auto dealer enters into a contract to purchase 25 British sports cars with payment to be made in pounds on November 1. Each car costs 40,000 pounds. The dealer is concerned that the pound will strengthen over the next few months. The dealer plans to trade in December pound futures contracts. The December pound futures price is $1.300 per pound. Each contract is for delivery of 62,500 pounds.

The spot rate on November 1 is $1.2500 per pound and the December pound futures price is $1.2700. What is the effective dollar price that the auto dealer pays per sports car after taking into account the gain or loss in the futures market? Assume the dealer trades in the correct number of futures contracts.

Answer 1

Solution:

The trading currency as per the given question is £, therefore, the American auto dealer that is the trader is required take the position in £ currency in the futures market. The trader, therefore, takes a long position in the futures market in £.

The calculation for the total amount of the contract to be payable by the American auto dealer can be made as follows:

Total contract amount = Number of British sports car * price per car

                                    = 25 * £40,000

                                    = £1,000,000

Hence, the total amount of the contract is £1,000,000.

  

The formula to calculate the total number of the lots to make long by the trader in the futures market is as follows:

Number of lots = Total amount of contract / lot size

                        = £1,000,000 / £62,500

                        = 16 contracts

Hence, the trader has to make a total of 16 contracts long in £ in the futures market.

The formula to calculate the total amount of $ to pay as on expiry is as follows:

Total amount of $ to pay = Total contracts * lot size * future contract rate

                                         = 16 * £62,500 * $1.300

                                         = $1,300,000

Hence, the total amount of the $ to be paid as on expiry in futures market is $1,300,000.

The formula to calculate the total amount of $ to square-off the position as on expiry is as follows:

Total amount of $ to square-off position = Total contracts * lot size * future market rate on expiry

                                         = 16 * £62,500 * $1.27

                                         = $1,270,000

Hence, the total amount of the $ used to square-off the position as on expiry in the futures market is $1,270,000.

The calculation for the gain or loss in the futures market as on expiry can be made as follows:

Long position taken by the trader to pay $                                         = $1,300,000

Short position taken by the trader to square-off the position for $    = $1,270,000

Net loss as on expiry in futures market                                               = $30,000

Hence, the total loss in the futures market as on expiry is $30,000.

In the futures market the trader cannot take the delivery of the currency but the trader requires £ to pay, therefore trader exchange the total $ in order to receive the £ from the bank.

The formula to calculate the total amount of $ to be payable by the trader to the bank as on expiry in order to receive the £ to pay for the British sports car is as follows:

Amount of $ required to pay = Total amount of £ under contract * bank exchange rate as on expiry

                                               = £1,000,000 * $1.25

                                               = $1,250,000

Hence, the trader requires $1,250,000 to be payable to the bank as on expiry in order to receive total amount of £ required.

The calculation of the total amount to be payable in $ after considering the loss incurred in the futures market can be made as follows:

Total amount of $ = Amount of $ payable to the bank + loss in the futures market

                              = $1,250,000 + $30,000

                              = $1,280,000

Hence, the total amount of the $ required is $1,280,000.