Boeing imported a Rolls-Royce jet engine for £10 million payable in three months
ID: 2788876 • Letter: B
Question
Boeing imported a Rolls-Royce jet engine for £10 million payable in three months. The current spot rate is $1.36/£ and three-month forward rate is $1.3/£. A three-month put option on pounds with a strike price of $1.32/£ has a premium of $0.015 per pound, while a three-month call option on pounds with the same strike price has a premium of $0.018 per pound . Currently, three-month interest rate is 3.2% per annum in the U.S. and 4.4% per annum in the U.K.
Boeing is considering alternative ways of hedging this foreign currency payable. It tries to minimize the dollar cost of paying off the payable. All questions below refer to cash flows in three months.
1) If Boeing decides to hedge using money market instruments, what would be the U.S. dollar cost of the payable in this case? How risky (certain/uncertain) is this cash flow?
Explanation / Answer
Money market hedges use short term investment instruments such as T-Bills to hedge either foreigh currency payables or recievables.
In this case it is foreign currency (pound) payables due three months from now.
US 3-month Interest Rate = Annual Interest Rate / 4 = 0.8% and UK 3-month Interest Rate = Annual Interest Rate/4 =1.1%
Money Market Hedge for Payables worth £ 10 million would be done as below :
Calculate present value of payables at 3-month UK rate of 1.1% = 10 million / (1.011) = £ 9.8911 million
Convert this pound amount into dollar at the spot rate of $ 1.36/£ = 1.36 x 9.8911 = $ 13.45 million
Purchase 3 -month (because payable is due in 3 months) securities (money market instruments) worth $13.45 million at US inerest rate of 0.8%
Value of 3-month money market instrument after 3-months = 13.45 x 1.008 = $ 13.5576 million
Convert the maturity value of the money market investment into £ the forward rate of $1.3 / £ = 13.5576 / 1.3 = £10.4289 million
The resultant £ value of the money market instrument is enough to cover the pound payable of 10 million.
Also, the investment value is slightly more than the required payable value as the forward rate calculated using the US and UK interest rate and current spot rates (using interest rate parity) is more than the actual spot rate of $1.3/£. Hence, the position is slightly overhedged.
Since $13.5576 million is used to pay £ 10 million the effective forward conversion rate = 13.5576 /10 = $1.33576/ £
Also the effective dollar cost of payment = 1.33576 x 10 = $ 13.5576 million.
The cash flow amount (which overhedges the foreign currency payable) is uncertain owing to the fact that the exchange rate appreciated from $1.36/£ $1.35576/ £ only due to the interest rate in the USA (=3.2%) being less than that in the UK (=4.4%). By the Interest Rate Parity theorem, the country with the lower interest rate sees its currency gaining in value. However, the US interest rates go above those of the UK, then by the same theorem the US dollar would depreciate with respect to the UK pound and the pound payables would become costly in dollar terms.