Net Present Value

Net Present Value is a finance concept that dates back to the early 1800s, finding use by the insurance industry among others. It is somewhat complicated in that there are multiple different formulas for calculating this sum. NPV is a calculation of today’s value of an amount of money in the future. This is a mathmatical expression of an idea called "the time value of money." In a nutshell this means that the purchasing power of money can vary over time. As intuitive as that may be today, this was a radical concept 500 years ago.

It dates back to the beginning of liberal monitarist theory in the writings of Tomas de Mercado and Martin de Azpilcueta. This is why variations of the same formula can used to calculate depreciation, inflation or accrued interest. For example: the value of money at a point in the future can be calculated by accounting for interest accrued and/or an devauluation from inflation. From that point of view, PV and NPV are two seperate formulas but it's all a part of the same process. Since they are used together there will be some references to PV in here.

Net Present Value (NPV) is used here to calculate the total value of all cash flows related to a project. NPV is simply the PV (Present Value) of future cash flows minus costs. In finace this is sometimes represented as Net Present Worth (NPW) rather than NPV. That is because there the formula is used primarily in compound interest calculations. To calculate NPV you must first compute FV (Future Value), estimate the term "n" and an interest rate "i". We apply these in the following formula:
FV ÷ (1 + i)n= PV
The calculation can also be done in reverse of course:
PV = FV ÷ (1+r)n


FV = $999
i = 10% (0.1)
n = 3 years

FV = 999(1 + 0.05)3
Then: PV = $999 ÷ (1 + 0.10)3 = $999 ÷ 1.103 = $751

Or we can write that out this way:
Year 1 = $999 ÷ 1.10 = $908.18
Year 2 = $908.18 ÷ 1.10 = $825.61
year 3 = $825.61 ÷ 1.10 = $750.55

But that formula only produces PV. How do we get from PV to NPV? Simple, subtract the initial costs of the project from the PV. NPV = PV1 + PV2 + PV3 + PVn - Invested amount

Calculating NPV vs. PV is just calculating net vs. gross. It's a completely pedestrian book-keeping calculation. Gross income is the total income and net income is the profit after all cost have been subtracted (costs, shrinkage, overhead, taxes etc.)


Most explanations of NPV simply state that if your project's NPV is positive it is good. Ultimately any project with a positive NPV is better than one which is zero or negative. This is simply a gauge of profitability. In Project management it can be used in project selection.

Of course, uncertainty increases along your time line so a certain amount of hedging is appropriate. While that is true, resources are limited and you (or management) will be choosing multiple projects from a possible portfolio. Projects are never all concurrent or coterminus so in practice this is not a single calculation, but one to be performed at each decision point.


NPV formula calculations assume a lot of things. Your costs could be higher than you've predicted, and interest rates lower. Infation enerally moves only in one direction but that rate too rate is variable. Your project could also take longer to complete or take longer to produce revenue. The formula navigates all these variables as if they were static values. But if any of these figures were dynamic instead of static the formula would be wildly more complicated. NPV is more managable and can be calculated at any number of points during a project.

This is no different than any other gross versus net calculation. Excel, Calc & Co. have built-in NPV and IRR functions.