Question

13. Investment A is an annuity that pays $1,230 at the end of each year for 10 years.

Investment B is a perpetuity that pays $315 at the end of each year forever.

Given that the interest rate is 3% per year, which investment has the higher present value as of today?

1. Investment A
2. Investment B

Answer 1

PV of Investment A:

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

Particulars	Amount
Cash Flow	$            1,230.00
Int Rate	3.0000%
Periods	10

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 1230 * [ 1 - [(1+0.03)^-10]] /0.03
= $ 1230 * [ 1 - [(1.03)^-10]] /0.03
= $ 1230 * [ 1 - [0.7441]] /0.03
= $ 1230 * [0.2559]] /0.03
= $ 10492.15

PV of Investment B:

= CF / Int rate

= $ 315 / 3%

= $ 10500

Investment in B is having higher present Value.