Question

The present value of a perpetuity, with the first cash flow paid in 4 years time, is equivalent to receiving $100,000 in 15 years time. The perpetuity and the lump sum are of equivalent risk and have a required rate of return of 10%. What is the annual cash flow associated with the perpetuity?

Answer 1

We first need to apply basic time value of money functon to calculate the value of the lumpsum amount today: FV = PV * (1 + r)ⁿ

$100,000 = PV * (1 + 10%)¹⁵

PV = $23,939.20

PV of a perpetuity is mathematically represented as:

Now, FV of $23,939.20 at year 3 (one year before the perpetuity begins)

FV = $23,939.20 * (1 + 10%)³ = $31,863.08

Now, applying PV of perpetuity formula,

D = $31,863.08 * 10% = $3,186.31