Question

How much would you pay (today) for a $500,000 growing perpetuity that begins in 1 year. Assume the annual discount rate (I/Y) of 5.5% and a 1.00% annual growth in the perpetuity payment that you will receive.

Answer 1

The amount of cash payable for the growing perpetuity today is $11,111,111.11

What is a growing perpetuity?

A growing perpetuity is an investment opportunity that pays its holder cash flows on periodic basis, such that the subsequent cash flows grow at a constant rate forever.

The present value of the growing perpetuity means the amount that needs to be paid today in order to be entitled to the annual cash flows that grows at the constant rate forever.

The formula for the present value formula of a growing annuity is as below:

PV=D1/(r-g)

D1=first cash flow=$500,000

r=discount rate=5.5%

g=growth rate=1.00%

PV=$500,000/(5.5%-1.00%)

PV=$11,111,111.11

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