Question

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 X that makes you indifferent between these options. r = 5%.

SHOW WORK

Answer 1

first we have to calculate present value of future receipts under option.

Here present value discount factor is r=5%

Present Value of total receipts under option A is

= 25/(1+0.05)⁵+25/(1+0.05)6+...........+25/(1+0.05)25

=$263.75

Value under option B is,

under this option we receives the amount $x forever, so we can compute the present value of cashflows by using perpetuity  formula i.e, =c/r c=Cash flows receipts , r= rate of interest

The indifference means there will be no difference between the outcome of the two options.

so at the indifference $263.75=X/0.05

X=263.75*0.05

X=$13.1875

therefore present value of perpetuity = 13.1875/0.05

=263.75

so, there is no difference in choosing either of the option based on the above calculations