Question

An investment offers $3,939 per year for 14 years, with the first payment occurring 5 years from now. If the required return is 9 percent, what is the value of the investment? (HINT: Remember that when you calculate the PV of the annuity, the calculator 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 present 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=9 FV=Present value of annuity you found in step 1. And you solve for PV)

Answer 1

PV of Annuity:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the end of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Present Value after 4 Years:

Particulars	Amount
Cash Flow	$            3,939.00
Int Rate	9.0000%
Periods	14

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 3939 * [ 1 - [(1+0.09)^-14]] /0.09
= $ 3939 * [ 1 - [(1.09)^-14]] /0.09
= $ 3939 * [ 1 - [0.2992]] /0.09
= $ 3939 * [0.7008]] /0.09
= $ 30669.65

PV today:

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Future Value	$            30,669.65
Int Rate	9.0000%
Periods	4

Present Value = Future Value / ( 1 + r )^n
= $ 30669.65 / ( 1 + 0.09 ) ^ 4
= $ 30669.65 / ( 1.09 ) ^ 4
= $ 30669.65 / 1.4116
= $ 21727.15