Question

An investment offers $562 per year for 21 years, with the first payment occurring 9 years from now. If the required return is 4 percent, what is the value of the investment? (HINT: Remember that when you calculate the PV of the annuity, the claculator gives you the present value of the annuity 1 period before the annuity starts. So if the annuity starts in year 7, that calculator will to give you the persent value of annuity in year 6. Now you have to bring this number to period 0 by inputting: N=6 (1 period before the annuity starts, in your case it would be a different number depending when your annuity starts) R=4 FV=Present value of annuity you found in step 1. And you solve for PV)

Answer 1

An Investment offers $562 per year for 21 years starting from 1st payment occurring 9 years from now

Firstly, Calculating the Present value of withdrawals at (t = 9 years from now) using Present Value of annuity due formula rather than using Present Value of ordinary annuity which gives present value at time 8 years from now:-

Where, C= Periodic withdrawals = $562

r = Periodic Interest rate =4%

n= no of periods = 9

Present value = $4345.80

Present Value (t = 9 years from now) is $4,345.80

Now, Calculating its Present Value today:-

Present Value = PV_9/(1+r)^9

Present Value = $4345.80/(1+0.04)^9

Present Value = $4345.80/1.42331181242

Present Value = $3,053.30

So, Value of Investment is $3053.30