Payment method-Buy pound or investing amount in U.K.

Question

When you have visited the London, you have purchased a Jaguar for £35,000, which is payable within the three months. Enough cash is there at your bank in the New York City that pays 0.35% of interest per month, compounding monthly, to pay for car. Presently, spot exchange rate is $1.45/£ and three-month forward exchange rate is $1.40/£. In London, interest rate of money market is 2.0% for the three-month investment. There exist two optional ways of paying for your Jaguar.

(a) Keep the funds in your bank within the U.S. and buy £35,000 forward.

(b) Buy some pound amount spot today and then invest the amount in U.K. for three months in order that maturity value becomes equal to £35,000. Estimate each payment method. Which of the method you would prefer and why? 

Answer 1

This problem situation can be summarized as:

A/P = £35,000 is payable within three months

iNY = 0.35%/month, compounding monthly

iLD = 2.0% for three months

S = $1.45/£;    F = $1.40/£.

Option a:

  When you will buy £35,000 forward, you require $49,000 within three months in order to fulfill forward contract. Present value of $49,000 is calculated as:

     $49,000/(1.0035)3 = $48,489.

Therefore, cost of the Jaguar as of today is $48,489.

Option b:

   The current value of the £35,000 is £34,314 = £35,000/(1.02). In order to buy £34,314 today, it can cost $49,755 = 34,314x1.45. Therefore, the cost of the Jaguar as of today is $49,755.

Definitely “option a” should be used, and save $1,266, that is the main difference between $49,755 and $48489.