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 $2.20 million CD at 5 percent and is planning to fund a loan in British pounds at 9 percent for a 4 percent expected spread. The spot rate of U.S. dollars for British pounds is $1.4500/£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 $1.4300/£1 by year-end. Calculate the loan rate to maintain the 4 percent spread? (Do not round intermediate calculations. Round your answer to 2 decimal places.(e.g., 32.16))

Loan rate

%

b.	The bank has an opportunity to hedge using one-year forward contracts at 1.4600 U.S. dollars for British pounds. Calculate the net interest margin if the bank hedges its forward foreign exchange exposure? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Net interest margin

%

c.	Calculate the loan rate to maintain the 4 percent spread if the bank intends to hedge its exposure using the forward rates? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Loan rate

%

Answer 1

Step 1 : Determine the amount of Loan denominated in British Pounds

Value in US $ of 1 year CD at 5 %= $ 2,200,000

Exchange rate : 1 GBP (British Pound) = $ 1.45

So, if $ 1.45 = $ 2,200,000

Then $ 1 = 2,200,000/1.45 = GBP 1,517,241.38 ( Principal amount)

Step 2 : Value of Principal and Interest at 9% p.a

Interest = $ 1517,241.38 * 9% *1 = GBP 136,551.72

Therefore, Principal + Interest in British Pounds (GBP) = GBP 1517241.38 + 136,551.72 = GBP 1,653,793.10

Q a)

Step3 : Convert GBP back into US $ using exchange rate of 1 GBP - $ 1.43

1   GBP = $ 1.43

Therefore, GBP 1,653,793.10 = 1.43 * GBP 1,653,793.10 = $ 2,364,924.13

Step 4 : Value of Principal and Interest on $ 2.2 Million CD at 5% for 1 year

Principal = $ 2,200,000

Interest at 5% for 1 year = 2,200,000* 5% * 1 = $ 110,000

Therefore, Principal + Interest = $ 2,200,000 + $ 110,000 = $ 2,310,000

Step 5 :Calculate Net Income (Step 3 - Step 4)

$ 2,364,924.13 - $ 2,310,000

Therefore, Net Income = $ 54,924.13

Step 6 : Calculate the Spread

Spread = Net Income / Value of CD

=> $ 54,924.13 / $ 2,200,000

=> 2.29655% or 2.30 %

Step 7 : In order to maintain a 4% spread, the interest and principal earned at 1 GBP = $ 1.43, we need to calculate the value of "x" in :

(x - 2,310,000) / 2,200,000 = 4%

x - 2,310,000 = 4% * 2,200,000

x = 88,000 + 2,310,000

x = $ 2,398,000

Step 8 : To calculate the Loan rate to maintain the 4% spread

The value of the loan rate"x" can be calculated by using the following formula:

x = ($ 2,398,000/1.43) / GBP1,517,241.38 (see Step 1)

$ 2398,000/1.43 = GBP 1,676,923.08

so, X = GBP 1,676,923.08 / GBP 1,517,241.38

X = 1.105244755 or 10.52 %

Answer to Q (a) = 10.52%. That is a Loan Rate of 10.52 % will produce a spread of 4%

Q (b)

Step 1

If hedged, th net interest income will be = GBP 1,517,241.38 + 9% of GBP 1,517,241.38 = GBP 1,653,793.10 ((Step2 of Q (a))

One year forward contract rate = $ 1.46/ 1 GBP (Given)

Step 2

Therefore, the value of principal & interest at the contract rate = 1,653,793.10 * 1.46 = $ 2,414,537.926

Step 3

Value of interest (at 5%)and principal of CD in $ = 2,200,000 * 1.05 = $ 2,310,000 ((Refer step 4 of Q (a))

Step 4

Net Interest Margin = ((Step 2- Step 3) / 2,200,000) *100

=> $ 104,537.10/ 2,200,000 * 100

Answer (b) => Net Interest Margin = 4.75 %

Q (c)

To maintain a 4% sprwead on contract rate of $ 1.46/ 1 GBP, we need to solve for value of "x" in the equation:

GBP 1,517,241.38 (1+x)*1.46 = $ 2,398,000 ((Refer step 7 in Q (a))

Therefore x = ($2,398,000/1.46)/ GBP 1,517,241.38 (Refer step1 of Q (a))

=> x = 1.082534 or 8.25%

Answer (c) :Therefore, North Bank should increase the rate of the loan to 8.25% p.a and hedge with the sale of forward Dollars in order to maintain a spread of 4%