Question

11. Assume that a bank has assets located in London worth £150 million on which it earns an average of 8 percent per year. The bank has £100 million in liabilities on which it pays an average of 6 percent per year. The current spot exchange rate is £2/$.


a. Given new exchange rate is £1.80/$ what is the effect in dollars on the net interest income from the foreign assets and liabilities? Note: The net interest income is interest income minus interest expense

b.What is the effect of the exchange rate change on the value of assets and liabilities in dollars?

Answer 1

a) First compute the pound value of Interest and then convert it into dollars.

Interest Income in dollars (old exchange rate) = 150,000,000 x 8% / £2/$ = $6,000,000

Interest Income in dollars (New exchange rate) = 150,000,000 x 8% /£1.80/$ = 6,666,666.67

Interest expense in dollars (old exchange rate) = 100,000,000 x 6% / £2/$ = 3,000,000

Interest expense in dollars (New exchange rate) = 100,000,000 x 6% / £1.80/$ = 3,333,333.33

Net Interest income (new) = 6,666,666.67 - 3,333,333.33 = 3,333,333.34

Net Interest income (old) = 6,000,000 - 3,000,000 = 3,000,000

Net effect = 3,333,333.34 - 3,000,000 = 333,333.34

b) Value of Assets in dollars (old) = £150,000,000 / £2/$ = $75,000,000

Value of liabilities in dollars (old) = £100,000,000 / £2/$ = $50,000,000

Value Assets in dollars (new) = £150,000,000 / £1.80/$ = $83,333,333.33

Value of liabilities in dollars (New) = £100,000,000/ £1.80/$ = $55,555,555.56

Effect on assets = 83,333,333.33 - 75,000,000 = $8,333,333.33

Effect on liabilities = 55,555,555.56 - 50,000,000 = 5,555,555.56