# What is Net Present Value (NPV)?

Businesses around the globe use NPV to evaluate whether they should invest in a new capital project. It tells the management how much money an investment will potentially bring back to the company, considering the capital the firm has spent to realize it.

## What is Net Present Value (NPV)?

Before all else, it is extremely important for you to understand the components of NPV as individual entities. So, we better break it down into NET and PRESENT VALUE.

First, “present value” refers to today’s value of a future amount of money.

Second, “net” means that investors include any cash inflows and outflows in calculating a project’s NPV.

In large, the Net present value of an investment is the present value of its future cash inflows minus the present value of the investment’s cash outflows. It might sound too complex in theory, but it isn’t. You deal with NPV on a daily basis without realizing it.

## How to calculate Net Present Value (NPV)

Here’s the formula you need to use:

NPV=\displaystyle\sum_{t=0}^N \frac{CF_{t}}{(1+r)^t}

The term CF_t is the expected net cash flow at time t, N is the projected life of the investment, and r is the discount rate (also known as the opportunity cost of capital).

Calculating the NPV of an investment goes through a process, which consists of 4 steps.

1. We need to identify all inflows and outflows related to the investment.
2. We must choose an appropriate discount rate, which in turn allows us to obtain the present value of the cash flows.
3. We need to use the discount rate to find the present value of each cash flow. Inflows are positive and increase NPV, while outflows are negative and decrease NPV.
4. We sum all discounted cash flows and find the net present value of the investment.

## Example of Net Present Value (NPV)

Imagine the following scenario. Alpha is a large company operating in the shipbuilding sector. Its R&D department has made a scientific breakthrough. They have developed a new ship prototype which will travel 20% faster than existing ship models, and on top, it will be 10% more efficient in terms of fuel consumption. However, this innovation requires the construction of a new shipbuilding plant. The project consists of an initial investment of $150 million and will generate after-tax cash inflows of$70 million per year for the next 3 years, as shown in the following timeline:

The company’s finance department has assessed that the project’s cost of capital is 9%. And the firm’s CEO wants to know whether the investment would make economic sense.

Do you think it will be a profitable endeavor?

To do that, you need to determine the Net Present Value of the project. By substituting the known parameters, we obtain the following:

NPV= -\$150,000,000 + \frac{\$70,000,000{_1}}{(1+0.09)^1} + \frac{\$70,000,000{_2}}{(1+0.09)^2} + \frac{\$70,000,000{_3}}{(1+0.09)^3} = -\$150,000,000 + \$64,220,183 + \$58,917,600 + \$54,052,844 = \$27,190,627 The initial cost of the new plant is$150 million, which is denoted with a negative sign because this is a cash outlay. You might notice that the initial investment is not discounted at the opportunity cost of capital because it happens at time 0, which is another way to say it occurs in the present moment. Then, we start with the first cash inflow of $70 million which is discounted by (1+9%) raised to the power of 1. Similarly, we apply the same procedure to the rest of the cash flows. In the end, we obtain a positive value of$27,190,627.

Having a positive outcome draws a bright picture on that project. Alpha Corporation can go ahead with the project because it creates value. Alpha had the opportunity to invest in a new plant by paying $150 million dollars for an investment worth$177.19 million dollars. Therefore, Alpha’ shareholders increased their wealth by \$27.19 million dollars.

Calculating NPV is easier when the number of cash flows is small. However, when we consider bigger investment projects, it is a bit more difficult to estimate the net present value. That’s why people started using financial calculators and spreadsheet software.

## The Bottom Line

For investors, there is a clear-cut rule as to how they interpret NPV. An investment should be accepted, if the net present value is positive, and rejected when it is negative.

In other words:

If NPV is higher than 0, we invest in the project;
If NPV is lower than 0, we do not invest in the project.

When we calculate the NPV of a project, we use the opportunity cost of capital as the discount rate. As we saw earlier, the opportunity cost is the alternative return investors forgo when they undertake an investment. When NPV is positive, the investment adds value because it compensates for more than the opportunity cost of capital. That’s why a company undertaking a positive NPV project creates value. The opposite is also valid- accepting investments that have a negative NPV destroys wealth.

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Find out how to calculate NPV in Excel, or take a look at our NPV Excel template.