Question

Problem 9-8 (LG 9-5) 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 $2.00 million CD at 4 percent and is planning to fund a loan in British pounds at 6 percent for a 2 percent expected spread. The spot rate of U.S. dollars for British pounds is $1.450/£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 $1.43/81 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 1.46 US 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. (For all requirements, do not round intermediate calculations. Round your answers to 2 decimal places. (e.g., 32.16)) a. Loan rate b. Net interest margin c. Loan rate

Answer 1

a) Let the loan rate be x%

Loan given in pounds = 2 million/ 1.45 = 1379310.34 pounds

After one year , the loan repayment including interest that North bank receives = 1379310.34 *(1+x) pounds

The amount in dollar to be repaid = 2 million * 1.04 = $2080000

Spread of 2% = 2 million *2% = $40000

Total amount required in Dollars = = $2080000 +$40000 =$2120000

So, amount required in pounds after one year = 2120000/1.43= 1482517.48 pounds

So, 1379310.34 *(1+x) = 1482517.48

=> x =0.0748 or 7.48%

So, the loan rate at which North bank lends in pound must be 7.48%

b) If hedge is done at 1.46 Dollars per Pound

then,

After one year , the loan repayment including interest that North bank receives = 1379310.34 *(1+0.06) pounds

= 1462068.97 pounds

This amount is converted to US dollars at the rate of 1.46$/pound to get 1462068.97*1.46 Dollars = $2134620.69

The amount in dollar to be repaid = 2 million * 1.04 = $2080000

So, net interest profit = $2134620.69 -$2080000 = $54620

So, Net interest margin = 54620/2000000 = 0.02731 or 2.73%

c)  

Let the loan rate be x%

Loan given in pounds = 2 million/ 1.45 = 1379310.34 pounds

After one year , the loan repayment including interest that North bank receives = 1379310.34 *(1+x) pounds

The amount in dollar to be repaid = 2 million * 1.04 = $2080000

Spread of 2% = 2 million *2% = $40000

Total amount required in Dollars = = $2080000 +$40000 =$2120000

So, amount required in pounds after one year (in case of hedging) = 2120000/1.46= 1452054.79 pounds

So, 1379310.34 *(1+x) = 1452054.79

=> x =0.052739 or 5.27%

So, the loan rate at which North bank lends in pound must be 5.27%