Answer to Question #222675 in Financial Math for Collins

Question

You had a chat with the relationship manager of your bank, and they are willing to lend $50 million to you for 1 year at an interest rate of 7.5% which appears to be far better than the current 1-year cedi lending rate of 18.01% on the domestic market. Your intention is to borrow in USD and convert this to Ghana Cedis and use for your expansion program. The current exchange rate is 5.20 per USD and is forecasted to be 5.75per USD in a year’s time.

a) Calculate the effective annual Financing Cost of the USD Loan and advise Yogobozz whether it is prudent to borrow USD at this stage.

b) Assume that Interest rate Parity (IRP) holds and that you intend to hedge the exchange rate risk by entering into a 1 year Forward transaction with your Bank. What will be the effective annual interest rate in this case?

Answer 1

a)let's find the effective bid

$re=(1+\frac{r}{m})^m-1=(1+\frac{0.075}{12})^{12}-1=0.077=7.7$

annuity payment:

$х = S\times(r + (\frac{r}{(1+r)^{n}-1}))= 50 000 000\times(0.077 + (\frac{0.077}{(1+0.077)^{12}-1}))=6 531 989,13$

total loan amount

$F=6 531 989,13\times12=78 383 869,61$

it is necessary to take a loan in dollars at this stage, so the dollar is cheaper in relation to another currency

b)the hedge will be at the exchange rate 5.20 per USD and the effective rate will be 7.7%