Question

What discount rate would make you indifferent between receiving $3,561.00 per year forever and $5,157.00 per year for 25.00 years? Assume the first payment of both cash flow streams occurs in one year.

Answer 1

Given,

Perpetuity = $3561

Annual payment (A) = $5157

No. of years (n) = 25 years

Solution :-

Let discount rate be 'r'

To make indifferent, the equation is,

Perpetuity/r = A/r x [1 - (1 + r)^-n]

$3561/r = $5157/r x [1 - (1 + r)^-25]

$3561/r x r/$5157 = 1 - (1 + r)^-25

0.69051774287 = 1 - (1 + r)^-25

0.69051774287 - 1 = -(1 + r)^-25

-0.30948225713 = -(1 + r)^-25

0.30948225713 = (1 + r)^-25

(0.30948225713)^-1/25 = 1 + r

1.0480 = 1 + r

1.0480 - 1 = r

0.0480 = r

So, discount rate = 0.0480 or 4.80%