Question

1. The Pinea Corporation obtains a bank loan that is disbursed as follows: Shs 320 million, Shs 240 million, Shs 160 million and Shs 80 million at the beginning of years one, two, three, and four respectively. The loan is repaid in five equal annual installments of Shs 300 million at the end of years four to eight, and a final amount at the beginning of year 12. Given a rate of inflation of 3.0% per annum during the period, and if Pinea’s real cost of the loan is 14% per annum, what should the final repayment be?

Answer 1

Nominal rate = Inflation rate + Real rate = 3% + 14% = 17%

Future value of loan at end of year 4 = (320 * (1+17%)^4) + (240 * (1+17%)^3) + (160 * (1+17%)^2) + (80 * (1+17%)^1)

= 599.6439 + 384.3871 + 219.024 + 93.6

= 1,296.655 million

Present value of future payment = (Annual annuity payment * PVIFA(17%,5 years)) + (Final payment * PVIF(17%, 8 Years))

1,296.655 = (300 * 3.199346) + (Final payment * 0.284782)

1,296.655 = 959.8038 + (Final payment * 0.284782)

Final payment * 0.284782 = 1,296.655 - 959.8038

Final payment * 0.284782 = 336.8512

Final payment = 336.8512 / 0.284782

Final payment = 1182.84