The present value of a perpetuity, with the first cash flow paid in 4 years time,...

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?

Solutions

Expert Solution

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

jeff jeffy answered 1 year ago

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