Hanson Corp. frequently uses a forward hedge to hedge its British pound (£) payables. For the next quarter, Hanson has identified its net exposure to the pound as being £1,000,000. The 90-day forward rate is $1.50. Furthermore, Hanson's financial center has indicated that the possible values of the British pound at the end of next quarter are $1.57 and $1.59, with probabilities of .50 and .50, respectively. Based on this information, what is the expected real cost of hedging payables?

Question

Quizplus · Accepted Answer

To calculate the expected real cost of hedging payables, we need to first calculate the cost of hedging at each possible exchange rate:
- At $1.57: £1,000,000 x $1.57 = $1,570,000. Hedging at the 90-day forward rate of $1.50 would cost: £1,000,000 x $1.50 = $1,500,000. The cost of hedging at this rate is therefore $70,000 ($1,570,000 - $1,500,000).
- At $1.59: £1,000,000 x $1.59 = $1,590,000. Hedging at the 90-day forward rate of $1.50 would cost: £1,000,000 x $1.50 = $1,500,000. The cost of hedging at this rate is therefore $90,000 ($1,590,000 - $1,500,000).
Next, we need to calculate the weighted average of these two costs, based on the probabilities given:
- Expected cost of hedging = (.50 x $70,000) + (.50 x $90,000) = $80,000
Therefore, the expected real cost of hedging payables is $80,000.