Question

5. Determine the capitalized equivalence of an infinite series of 5-year period payments. Use a 12% nominal interest rate. In each 5-year period, $100 will be paid at the end of years one and five, $200 at the end of years two and four, and $300 at the end of year three. The series repeats forever.

A. $179

B.$1,494

C. $645

D. $1,137

Answer 1

This is an example of continous infinite cash flow series with payment amount increasing constantly by $100/year.

Here A= Annual cash flow increment = $100

i = rate of interest=12%= 0.12

n= number of period= 5 years

The formula for present value of cash flow series

Present Value = $100(P/A, 12%, Infinity) = $100 *(1/0.12)= $833

Future Value of infinite cash flow series = Present Value * (1+.12)⁵ = 833*(1+.12)⁵ = $1468 which is nearest value to $1,494. Therefore, correct answer is B. $1,494