When calculating the net present value, a situation might arise where you are face with a constant series of payments without an end. This is what we refer to as NPV for a perpetuity.
To find the net present value of a perpetuity, we need to first know the future value of the investment.
General syntax of the formula
- FV- is the future value
- i – is the interest rate for the perpetuity
To understand how the NPV of a perpetuity works in excel, we need to consider the example below;
Figure 1: Finding NPV of perpetuity in excel
To better understand the above NPV, we need to consider a real case study;
Imagine you are evaluating a firm based on its future profits. The firm’s expected profit per year is $100 as shown in cell B2, without an end. The cash flow is then discounted at the rate of 4% as shown in cell B3. To get the NPV, we simply divide the Future value, which is $100, by the rate.
What if the cash flow grows at a constant rate?
In a perpetuity case, a scenario might emerge where the cash flow increases at a given constant rate. To find the NPV in such a case, we proceed as follows;
- FV– is the future value of the cash flows
- i – is the discount rate
- g- is the growth rate of the firm
Assume that a firm anticipates a profit of $100 per year without an end. The discounted rate is 4% and the profit is expected to grow at a rate of 2% every year. What is the NPV of the perpetuity?
Figure 2: NPV of perpetuity with growth rate
Notice that when we have the growth rate given, the NPV is higher than that of when we don’t have a growth rate.
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