Question

TGG Ltd currently has a bank loan outstanding that requires it to make annual payments of $1,000,000 at the end of each of the next three years. The bank has offered to allow TGG Ltd to skip making the next two payments and instead make one large payment at the end of the loan’s term in three years. If the interest rate on the loan is 6% p.a., compounded quarterly, the final payment that will make TGG Ltd indifferent between the two payment options is closest to?

Answer 1

Frequency of compounding (m = 4) is different from frequency of payment (n = 1) so first effective interest rate is to be calculated for annual payments.

Effective rate (r) = [(1 + APR/m)^(m/n)] -1 where APR = 6%; m = 4; n = 1

= [(1+6%/4)^(4/1)] -1 = 6.14%

Present Value (PV) of annual payments of 1 million: PMT = 1,000,000; FV = 0; N = 3; rate = 6.14%, solve for PV.

PV = 2,666,282.78

The final payment that will make TGG Ltd. indifferent between the two payment options will be

Future Value (FV) = PV*(1+APR/m)^(m*3) = 2,666,282.78*(1+6%/4)^(4*3) = 3,187,856.14 or 3,187,856 (Answer)