Question

1. An investment opportunity has just paid a cash flow of $2460. The cash flow from this investment is expected to grow at a constant growth rate of 6% for its expected life of 35 years. What is the fair value of this opportunity today if its required rate of return is 9%?

Answer 1

Given about an investment opportunity,

Last cash flow paid is C0 = $2460

cash flow will grow at g = 6%

Expected life = 35 years.

So, a total of 35 payments are remaining

required rate of return r = 9%

So, value of this opportunity today is

PV = C0*(1+g)/(1+r) + C0*(1+g)^2/(1+r)^2 + C0*(1+g)^3/(1+r)^3...... + C0*(1+g)^35/(1+r)^35

So, this is an GP with

a = C0*(1+g)/(1+r) = 2460*1.06/1.09 = 2392.2936

r = (1+g)/(1+r) = 0.9725

and n = 35

So, sum of a GP is S = a*(r^n - 1)/(r-1) = 2392.2936*(0.9725^35 - 1)/(0.9725-1) = 54193.65

So, fair value of investment is $54193.65