We started a discussion on the importance and description of cash flow for the operating firm. You can find that post here: cash flow intro.

Moving forward now to the topic of net present value of cash flow (or NPV). An investment project generally should be undertaken if benefits outweigh costs. In order to compare the two categories we must convert them first to the same time period by finding their present value. If the PV of benefits is greater than the PV of costs the project is profitable.

Usually the costs of the project incur in year 0 while benefits incur in years 1 to t. The difference between the PV of benefits and costs is called net present value (NPV). If we denote with Ao the initial cash flow (negative if it is a cost, positive if it is revenue) and with AI, … , At all the future cash flows, the net present value of the project is:

where d = 1/(1 + r) is the discount factor for one year and r is the interest rate for discount purposes.

In order to obtain this result we can calculate the present value of each cash flow separately (with the corresponding sign) and add them up together, you can also the Excel NPV function: **= NPV (Interest rate, Range) **

(For the range select or specify the range of cells containing the undiscounted cash flows. )

The NPV function operates similarly to the PV function, i.e. it calculates the PV of all cash flows for the period before the first cash flow occurs. If the first cash flow occurs in year “0”, then the NPV function discounts everything to period “-1 ”. As we usually want to find the NPV at period 0 we should compound the result of the NPV function for one period, i.e. multiply it by (1 + r). Or we can calculate the NPV at year 0 by adding the first cash flow to the present value of all the subsequent cash flows, as:

**Thus, the NPV rule: An investment project should be accepted if the NPV is positive and rejected if not. **

This post is part of a series of articles on cash flow analysis. Visit our cash flow analysis page to find a summary of each method.