Question

North Bank has been borrowing in the U.S. markets and lending abroad, thereby incurring foreign exchange risk. In a recent transaction, it issued a one-year $2 million CD at 6 percent and is planning to fund a loan in British pounds at 8 percent for a 2 percent expected spread. The spot rate of U.S. dollars for British pounds is $1.32/£1.

a. However, new information now indicates that the British pound will appreciate such that the spot rate of U.S. dollars for British pounds is $1.30/£1 by year-end. Calculate the loan rate to maintain the 2 percent spread.
b. The bank has an opportunity to hedge using one-year forward contracts at 1.33 U.S. dollars for British pounds. Calculate the net interest margin if the bank hedges its forward foreign exchange exposure.
c. Calculate the loan rate to maintain the 2 percent spread if the bank intends to hedge its exposure using the forward rates.

Answer 1

a.

Amount of loan in £ = $2 million / 1.32 = £1,515,151.51
Interest and principal at year-end = £1,515151.51 x 1.08 = £1,636,363.63*1.30 = $2,127,272.73
Interest and principal of CDs = $2m x 1.06 = $2,120,000
Net interest income = $2,127,272.73 – $2,120,000 = $7,272.73
Net interest margin = $7,272.73/2,000,000 = 0.003636 or 0.36 percent.

In order to maintain a 2 percent spread, the interest and principal earned at $1.30/£1 should be:
£1,515,151.51(1 + x)*1.30 = $2,160,000 (Because ($2.16m. - $2.12m.)/$2.00m. = 0.02, or 2%).

Therefore, (1 + x) = ($2,160,000 / 1.30)/ £1,515,151,51 = 1.0966, and x = 0.0966 or 9.66 percent, or the bank should have charged a rate of 9.66 percent on the loan.

b.

Net interest income if hedged = £1,515,151.51 x 1.08 =£1,636,363.63*1.33 = $2,176,363.63 - $2,120,000 = $56,363.63

Net interest margin = $56,363.63/$2,000,000 = 0.02818, or 2.82 percent

c.

To maintain a 2 percent spread: £1,515,151.51(1 + x)*1.33 = $2,160,000. => x = 7.19 percent