Question

Assume that you are attempting to find the present value of a 50-period, $100 annuity, where the first payment takes place at Period 1, and the last payment takes place at Period 50 (some people would describe this as a regular annuity). However, these annuity payments are growing at a constant rate of 10 percent, so you will actually receive $110.00 at Period 1, $121.00 at Period 2, $133.10 at Period 3, etc.Finally assume that your required rate of return is 8 percent. Determine the present value, at Period 0, of this annuity.

Answer 1

The cash flows are compounded by using compounding formula, which is as under:

Future Value = Present Value * (1+r)^n

In the question we are given following Future values at 10% required return:

Y1 $110

Y2 $121

Y3 $133

All we have to do is to find Present value at required return 8%, which can be found from following formula:

Present Value For year n= Future Value / (1+r)^n

PV for Y1 = $110 / (1.08)^1 = $ 101.85 - 100 Investment = NPV $1.85 at Y1

PV for Y2 = $121 / (1.08)^2 = $ 103.74 - 100 Investment = NPV $3.74 at Y2

PV for Y3 = $133 / (1.08)^3 = $ 105.58 - 100 Investment = NPV $5.58 at Y3