How Net Present Value (NPV) is Calculated

In capital budgeting, the net present value is one of the most common decision methods to decide if a project should be undertaken or not. Net Present Value (NPV) is defined as "the difference between the present value of cash inflows and the present value of cash outflows." Because payback and discounted payback decision methods both disregard cash flows that are paid or received after the payback period, NPV is introduced to define the profitability of a project.

NPV is based on discounted cash flow (DCF) valuation method. In DCF, the value of an asset is the present value of the expected cash flows discounted by the cost of risk incurred by the cash flows and the life of the asset.

The steps for the calculation of the net present value (NPV) of a project are the following:

1. Estimate the cash flows (inflows and outflows) discounted at the project's cost of capital.
2. Sum the discounted cash flows to determine the project's NPV.
3. Determine if the project is worth undertaking based on whether NPV is positive or negative and if the two projects into consideration are independent or mutually exclusive.

Example

To better understand how the Net Present Value (NPV) is calculated and which are the criteria for choosing a project over another, we assume that a Project Manager needs to choose between two mutually exclusive expansion projects, Project A and Project B. The cost of capital (WACC) is 10% and the expected cash flows for each project for a period of 4 years are as follows:

Project A

Year 0: 1,200

Year 1: 600

Year 2: 500

Year 3: 400

Year 4: 200

Project B:

Year 0: 1,200

Year 1: 200

Year 2: 300

Year 3: 400

Year 4: 500

Step 1: Estimate the cash flows (inflows and outflows) discounted at the project's cost of capital.

Project A:

Year 1: 600 / (1+10%) = 545.46

Year 2: 500 / (1+10%)^2 = 413.22

Year 3: 400 / (1+10%)^3 = 300.75

Year 4: 200 / (1+10%)^4 = 136.60

Project B:

Year 1: 200 / (1+10%) = 181.82

Year 2: 300 / (1+10%)^2 = 247.94

Year 3: 400 / (1+10%)^3 = 300.75

Year 4: 500 / (1+10%)^4 = 341.51

Step 2: Sum the discounted cash flows to determine the project's NPV.

NPV (A) = -1,200 + 545.46+ 413.22 + 300.75 + 136.60= $196.03

NPV (B) = -1,200 + 181.82 + 247.94 + 300.75 + 341.51 = $127.98

Step 3: Determine if the project is worth undertaking based on whether NPV is positive or negative and if the two projects into consideration are independent or mutually exclusive.

Two projects are independent when the cash flows of one are unaffected by the undertaking of the other. Two projects are mutually exclusive when the cash flows of one are adversely affected by the undertaking of the other. If two projects are independent, we undertake the project with the positive NPV. If two projects are mutually exclusive, we undertake the one with the higher NPV between the two.

On this basis, project A should be chosen over B because they are mutually exclusive and A has the higher NPV.

The rationale behind the net present value is pretty straightforward:

• A positive NPV implies that the cash flows generated are sufficient to pay back the invested capital and to provide the required return to shareholders.
• A negative MPV implies that the cash flows generated are not sufficient to service the debt and to provide the required return to shareholders.
• A NPV of zero implies that the project's cash flows are exactly sufficient to service the debt and to provide the required return to shareholders.

In the above example, if Project A is undertaken, the shareholder's value will be increased by $196.03, while if Project B is undertaken, the shareholder's value will be increased by only $127.98. Therefore, NPV is used to determine the profitability of a project taking into account the cash flows (both inflows and outflows) after the payback period.

Sources:

http://www.investopedia.com/terms/n/npv.asp

Brigham E.F., Ehrhardt, M.C., (2005), Financial Management: Theory and Practice, 11^th edition.