NPV Calculation Into Perpetuity

by Kaushalya
(Sri Lanka)

A company is evaluating a new project which requires an initial investment of Rs 1,000,000 and would generate Rs125,000 p.a in perpetiuty starting one year from now. Assume cost of capital as 10%. what is the NPV of the project?

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Oct 26, 2022
Net Present Value Calculation Into Perpetuity
by: Dee

The net present value in perpetuity is the future value of investments that are discounted to their current value or present value.

The NPV in perpetuity formula simplifies to

NPV = -Investment + Annual Payment/r

where r is the discount rate, t is the time period, and n is the number of periods. This of course assumes that the Annual Payment remains constant.

If on the other hand the Annual Payments are changing each year then the traditional method of calculating net present value must be used.

Another special case is if the Annual Payments are increasing by a fixed percentage (i) each year. The formula is then

NPV = -Investment + Annual Payment/(r - i)

Investing into perpetuity is a long-term investment with a payoff that may not be seen for decades. Investments in perpetuity are generally made in the hope that they will provide some sort of return to investors.

Investments into perpetuity are possible, but they have a very different payoff profile than traditional investments.

So to answer the original question by plugging the numbers

NPV = -1,000,000 + 125,000 / .1 = 250,000

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