What is the formula for calculating net present value (NPV)?

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A:

Net present value (NPV) is a method of determining the current value of all future cash flows generated by a project after accounting for the initial capital investment. It is widely used in capital budgeting to establish which projects are likely to turn the greatest profit.

The formula for NPV varies slightly depending on the consistency with which returns are generated. If each period generates returns in equal amounts, the formula for the net present value of a project is:

NPV = C x {(1 - (1 + R)-T) / R} − Initial Investment

where C is the expected cash flow per period, R is the required rate of return, and T is the number of periods over which the project is expected to generate income.

However, many projects generate revenue at varying rates over time. In this case, the formula for NPV is:

NPV = (C for Period 1 / (1 + R)1) + (C for Period 2 / (1 + R)2) ... (C for Period x / (1 + R)x) - Initial Investment

In both scenarios, the required rate of return is used as the discount rate for future cash flows to account for the time value of money. In corporate finance, the general consensus is that a dollar today is worth more than a dollar tomorrow. Therefore, when calculating the present value of future income, sums that will be earned down the road must be reduced to account for the delay. If the specific target rate is not known, 10% is often used as the baseline rate.

NPV is used in capital budgeting to compare projects based on their expected rates of return, required investment, and anticipated revenue over time. Typically, projects with the highest NPV are pursued.

For example, consider two potential projects for company ABC:

Project X requires an initial investment of $35,000 but is expected to generate revenues of $10,000, $27,000 and $19,000 for the first, second and third years, respectively. The target rate of return is 12%. Since the cash inflows are uneven, the second formula listed above is used.

NPV = {$10,000 / (1 + 0.12)1} + {$27,000 / (1 + 0.12)2} + {$19,000 / (1 + 0.12)3} - $35,000
NPV = $8,929 + $21,524 + $13,524 - $35,000
NPV = $8,977

Project Y also requires a $35,000 initial investment and will generate $27,000 per year for two years. The target rate remains 12%. Because each period produces equal revenues, the first formula above can be used.

NPV = $27,000 x {(1 - (1 + 0.12)-2) / 0.12} - $35,000
NPV = $45,631 - $35,000
NPV = $10,631

Despite the fact that both projects require the same initial investment and Project X actually generates more total income than Project Y, the latter project has a higher NPV because income is generated faster, meaning the discount rate has a smaller effect.

To learn how to calculate NPV with Excel, read What is the Formula for Calculating NPV in Excel?


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