Question

What discount rate would make you indifferent between receiving $3,965.00 per year forever and $5,295.00 per year for 26.00 years? Assume the first payment of both cash flow streams occurs in one year.

Answer 1

To be indifferent, the discount rate should be such that the present value of both options is equal.

Present value of perpetual cash flow = perpetual cash flow / discount rate.

Let us say the discount rate is R. Then, present value of receiving $3,965.00 forever = $3,965 / R.

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment

r = interest rate per period

n = number of periods

Here, P = equal annual payment, which is $5,295

r = annual interest rate, which is R

n = number of years, which is 26.

PV of annuity = $5,295 * [1 - (1 + R)^-26] / R

To find R, we equate the present values of both options.

$3,965 / R =  $5,295 * [1 - (1 + R)^-26] / R

($3,965 / R) - ($5,295 * [1 - (1 + R)^-26] / R) = 0

($3,965 - ($5,295 * [1 - (1 + R)^-26]) / R = 0

($3,965 - ($5,295 * [1 - (1 + R)^-26]) = 0

$5,295 * [1 - (1 + R)^-26] = $3,695

[1 - (1 + R)^-26] = ($3,965 / $5,295)

(1 + R)^-26   = 1 - ($3,965 / $5,295)

R = (1 - ($3,965 / $5,295))^1/-26 - 1

R = 0.0546, or 5.46%

The indifference discount rate is 5.46%