Question

The spot exchange rate is currently $1.85 US per 1 British pound. One year interest rate is 4% in the US and 3% in the UK. A US bank is long a futures contract to buy 1,000,000 pounds for $1.8 million in one year. What is the current present value of the futures contract to the bank in US$?

Answer 1

Spot rate = $1.85 per pound

Interest rate in US = 4%

Interest rate in UK = 3%

Future spot rate = Spot rate * (1+US rate ) / (1+ UK rate)

Future spot rate = 1.85 * 1.04 / 1.03

Future rate = $1.87 per pound

So for long futures contract to buy 1000,000 pounds, bank ideally needs to pay $1.87 million or $1.87 per pound

But bank has a future contract in which they are buying 100,000 for $1.8 million

So after 1 year, bank can buy 1000,000 pounds and can pay $1.8 million and can convert that in USD and can get $1.87 million

So profit after 1 year = 1.87 - 1.8 = $0.07 million = $70,000

So present value = 70,000 / ( 1+ us rate )

present value = 70,000 / ( 1.04) = $67,307