InvestorQ : How do you calculate the present value of perpetuity?

# How do you calculate the present value of perpetuity?

1 year ago
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The present value of a perpetuity that pays an annual cash flow of Rs. X per period is:

PV = X/r

As an example, suppose that perpetuity pays Rs.100 per year; assume that the appropriate rate of interest is 5% per year. The present value of the perpetuity is Rs.100/0.05 = Rs.2,000.

### This is a constant perpetuity. Let us also look at how the value of a growing perpetuity is calculated in this case.

Suppose that the cash flows provided by perpetuity grow at a fixed rate each year. The present value formula is adjusted as follows:

PV = C/(r – g)

where:

g = annual growth rate of the perpetuity

For simplicity, let us suppose that perpetuity currently pays Rs.50 per year; assume that the appropriate rate of interest is 7% per year, and that the cash flow paid by the perpetuity is estimated to grow at a rate of 3% per year. The present value of the perpetuity is: Rs.50/(0.07 – 0.03) = Rs.1,250.

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