Negotiating the Rate.A sovereign borrower is considering a $100 million loan for
ID: 2786448 • Letter: N
Question
Negotiating the Rate.A sovereign borrower is considering a $100 million loan for a 4-year
maturity. It will be an amortizing loan, meaning that the interest and principal payments will total, annually, to a constant amount over the maturity of the loan. There is, however, a debate over the appropriate interest rate. The borrower believes the appropriate rate for its current credit standing in the market today is 9%, but a number of international banks with which it is negotiating are arguing that is most likely 13%, at the minimum 9%.
What impact do these different interest rates have on the prospective annual payments?
The annual payment, if the interest was at 9%, $__________ (30,866,866.00)
The annuyal payment, if the interest was at 13%, $__________ (33,619,420.000
The difference in annual payment? $__________ (680,214.00)
Explanation / Answer
Calculation of annual payment if interest rate was 9% Using Present value of annuity formula, we can calculate the annual payments. PV of annuity = P*{[1 - (1+r)^-n]/r} PV of annuity = present value of annuity = $100 million P = Periodic payment i.e. annual payment = ? r = rate of interest per annum = 9% n = number of years = 4 100 = P*{[1 - (1+0.09)^-4]/0.09} 100 = P*3.23972 P = 30.86687 million Annual payment if the interest rate was 9% = $3,08,66,866 Calculation of annual payment if interest rate was 13% Using Present value of annuity formula, we can calculate the annual payments. PV of annuity = P*{[1 - (1+r)^-n]/r} PV of annuity = present value of annuity = $100 million P = Periodic payment i.e. annual payment = ? r = rate of interest per annum = 13% n = number of years = 4 100 = P*{[1 - (1+0.13)^-4]/0.13} 100 = P*2.974471 P = 33.61942 million Annual payment if the interest rate was 13% = $3,36,19,420 The difference in annual payment = $3,36,19,420 - $3,08,66,866 = $27,52,554
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