Question

Assume the spot rate of the ? is $1.7000. The British interest rate is 10%, and the U.S. interest rate is 11% over the 360?day (1 year) period. The British inflation rate is 4% and the U.S. inflation rate is 3.5% over the 360-day (1 year) period. The 180-day forward price is $1.7200/?. The 180-day European call option on the $ with the exercise price of ?0.5800 is selling at 3% premium, while the 180-day European put option on the $ with the exercise price of ?0.5900 is selling at 2% premium. Your U.S. based firm has an account payable of ?200,000 due in 180 days.

A) What should be the 180-day forward rate based on Interest Rate Parity (IRP)?

What is the dollar cost of using a forward hedge? Make sure you state your position in the forward contract.   

B) Assume the firm has no excess cash. Use the above to calculate the dollar cost of using a money market hedge to hedge ?200,000 of payable due in 180 days?

C) Calculate the cost of an option hedge at the time the payment is due assuming you exercise the option when the payment is due.

D) Based on the answers in (a), (b), and (c), which hedging methods should your firm choose?

Answer 1

Account Payable = 200000 Pound

(a)

British Interest Rate = 10 % for 360 days or 5 % for 180 days, US Interest Rate = 11 % for 360 days or 5.5 % for 180 days, Current Spot Rate = $ 1.7/Pound

180 days Forward Rate as per IRP = [1.055/1.05] x 1.7 = $ 1.71/Pound

Dollar Value of Account Payable at IRP determined Forward Rate = D1 = 1.71 x 200000 = $ 342000

Actual Forward Rate = $ 1.72/Pound

Dollar Value of Account Payable at Actual Forward Rate = 1.72 x 200000 = D2 = $ 344000

Dollar Cost of Hedging = D1 - D2 = 344000 - 342000 = $ 2000

As the US Firm has an account payable, the firm needs to purchase 200000 pounds after 180 days, thereby being short on the underlying asset (which is the pound). Hence, a suitable forward hedge would involve purchasing a forward contract, followed by purchasing pound after 180 days under the obligation of the same. Therefore, the forward contract position will have to be long.

(b) A money market hedge would involve the following steps:

- Account Payables in 180 days = 200000 Pound

- Present Value of Payable = 200000 / 1.05 = 190476.19 approximately.

- $ Value of PV of Payable = 190476.19 x 1.7 = $ 323809.52

- Borrow an Amount Equal to the $ PV of the Payable for a 180 day period (borrow $ 323809.52)

- The borrowing will result in a $ liability of 323809.52 x 1.055 = $ 341619.0436 after 180 days.

- The borrowing can be converted into pounds at the current spot rate of $ 1.7/Pound to yield (323809.52/1.7) = 190.476.19 pounds and invested for 180 days at the British rate of 10% per annum.

- Investment Proceeds Value after 180 days = 190476.19 x 1.05 = 199999.999 or 200000 pounds approximately which is used to pay off the accounts payable.

- The $ loan is paid off by the company, thereby exchanging $ 341619.0436 ($ loan proceeds) for 200000 pounds (investment proceeds).

- Money Market Exchange Rate = 341619.0436 / 200000 = $ 1.71/Pound approximately.

- Dollar Cost of Using a Money Market Hedge can be the interest paid on the $ borrowings to execute the hedge. Interest Paid on $ Borrowing = 341619.0436 - 323809.52 = $ 17809.5236

(c) As the option is on the $ instead of the pound, the former becomes the underlying asset. At maturity (after 180 days), the underlying asset has to be sold in exchange for pounds as the account payables are in pounds. Further, selling an underlying asset at a pre-fixed price under an option (pre-fixed price is option strike price) is the characteristic of a put option. Hence, an option hedge would involve buying a put option on the $.

Option Strike Price = 0.59 Pound/$ and Option Premium = 2 % of strike price = 0.02 x 0.59 = 0.0118 Pound/$

Total Effective Exchange Rate = 0.59 + 0.0118 = 0.6018 Pound/$ or $ 1.66/Pound

Cost of Option Hedge = 0.0118 pound per $ or (200000 / 0.59) x 0.0118 = $ 4000

(d) As the exchange rate for the option seems to be the lowest the same should be selected.