Question

Given the data below, calculate the net present value of an infinite chain of replacement using the equivalent annual value method. Assume the cost of capital is 11% p.a.

Initial Outlay	Year 1	Year 2	Year 3
-$10,000	$10,000	$20,000	$30,000

Can kindly help to explain about this and the solution?

Answer 1

We need to find the NPV of the project. We will find present value of cash flows by discounting it with cost of capital. So, we need to discount cash inflows of year1, year 2 and year 3 and initial outlay will be deducted from the amount to find Net present value-

Present value of cash flows = Amount of cash inflow/outflow/ (1+ cost of capital(%) )^ (no.of years)

Net present value of project = -$10,000 + $10,000/(1+0.11) +   $10,000/(1+0.11)^2 + $10,000/(1+0.11)^3

=-10,000 + 10,000/1.11 + 20,000/1.2321 + 10,000/1.367631

= -10,000 + 9009.009 + 16232.45 + 21935.74

= $37,177