# How does one calculate the net present value (NPV) of a sum of money?

Jul 5, 2015

Net Present Value (NPV) is an important concept, used extensively in Finance and Economics. The calculation in symbols is simply this: NPV = PV of Benefits - PV of Costs.

#### Explanation:

Let's focus on the word net. it suggests the difference between two things. In this case it is the difference between the present value of benefits and the present value of costs.

Here is an example from Managerial Finance. A furniture store is considering setting up another store in a near-by city. Is it a good idea? There are qualitative factors to consider like the ability of management to look after two stores. And then there are quantitative factors. NPV analysis focuses on quantitative factors - numbers.

Quantitative data will be a combination of benefits and cost - spread out over time. Benefits would include such things as added revenues from the new store and lower prices from buying larger quantities of inventory. Cost would include the outlay required to build the new store and additional labour costs. In practice, depreciation and tax implications make the analysis "messier."

The first step is to identify the negative cash flows (costs) and the positive cash flows (benefits) and to assign them to a time period.
The next step is to bring all of these cash flows back to the present, so they can then be compared. The NPV is the difference between the present value of benefits minus the present value of costs. If it is positive (more benefits than costs) then this is taken by management as a strong signal to proceed.

At the heart of NPV analysis is the ability to perform time value of money calculations, especially present value calculations. In our example, the present value of yearly inventory savings and additional revenues would have to be calculated as present values of annuities. The cost of building the store would already be in the present, but the additional labour costs that would occur every year would have to be "present valued."

NPV = PV of Benefits - PV of Costs.