Question

Question 1 Suppose you can choose one of the following two options: • Option A: Receive $25 per year for 25 years with the first payment in year 5. • Option B: Receive $X per year forever with the first payment this year. Solve for the value of X that makes you indifferent between these options. Assume r = 5%.

use only equations, no pv tables.

Answer 1

Let's calculate first the PV of annuity and then apply that PV to compute the payment of 2nd annuity.
P = PMT x (((1-(1 + r) ^- n)) / r)
Where:
P = the present value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	$                25.00
r = the effective interest rate (also known as the discount rate)	5%
n = the number of periods in which payments will be made	25	Years
PV of annuity at the beginning of 5th year =	25* (((1-(1 + 5%) ^- 25)) / 5%)
PV of annuity at the beginning of 5th year =	$             352.35
PV of annuity today =	352.35/(1+5%)^4
PV of annuity today =	$             289.88
Now for 2nd annuity, the PV of annuity should be equal $ 289.88
PV of annuity forever=	Annual payment/rate
289.88=	Annual payment/rate
289.88=	Annual payment/5%
Annual payment for 2nd annuity=	289.88*5%
Annual payment for 2nd annuity=	$                14.49