# Net Present Value (NPV) ## Net Present Value (NPV) Definition

Net Present Value (NPV), most commonly used to estimate the profitability of a project, is calculated as the difference between the present value of cash inflows and the present value of cash outflows over the project’s time period. If the difference is positive, it’s a profitable project and if its negative, then it’s not worthy.

### The formula of Net Present Value (NPV)

NPVt=1 to T = ∑Xt / [(1+R)t – X0]

For eg:
Source: Net Present Value (NPV) (wallstreetmojo.com)

Here’s the Net Present Value formula (when cash arrivals are even):

NPVt=1 to T  = ∑  Xt/(1 + R)t – Xo

Where,

• X= total cash inflow for period t
• X= net initial investment expenditures
• R = discount rate, finally
• t = total time period count

The Net present value formula (when cash arrivals are uneven):

NPV = [Ci1/ (1+r)1 + Ci2/(1+r)2 + Ci3/(1+r)3 + …] – Xo

Where,

• R is the specified return rate per period;
• Ci1 is the consolidated cash arrival during the first period;
• Ci2 is the consolidated cash arrival during the second period;
• Ci3 is the consolidated cash arrival during the third period, etc

### Explanation of Net Present Value Formula

The NPV formula has two parts.

• The first part talks about cash inflows from investments. When an investor looks at an investment, he is presented with the projected future values of the investments. He then can use the present value method [i.e., PV = FV / (1 + i) ^n, where PV = Present Value, FV = Future Value, I = interest (cost of capital), and n = number of years] to discount the future values and find out the cash inflows from the investments at the present date.
• The second part talks about the cost of investments in the project. It means how much an investor has to pay for the investments at the present date.

If the cost of investments is lesser than the cash inflows from the investments, then the project is quite good for the investor since he is getting more than what he is paying for. Otherwise, if the cost of investments is more than the cash inflows from the investments, then it’s better to drop the project since the investor has to pay more than what he is paying as of now.

### Examples

You can download this Net present Value Excel Template here – Net present Value Excel Template

Hills Ltd. would like to invest in a new project. The company has the following information for this new investment –

• Cost of the new investment as of now – \$265,000
• The project will receive cash inflows as follows –
• Year 1 – \$60,000
• Year 2 – \$70,000
• Year 3 – \$80,000
• Year 4 – \$90,000
• Year 5 – \$100,000

Find out the NPV and conclude whether this is a worthy investment for Hills Ltd. Assume the rate of return as 10%.

By using the above information, we can easily do the NPV Calculation of the new investment.

Cash Inflows from Investments = \$60,000/1.1 + \$70,000/1.1^2 + \$80,000/1.1^3 + \$90,000/1.1^4 + \$100,000/1.1^5

= 54,545.5 + 57,851.2 + 60,105.2 + 61,471.2 + 62,092.1 = 296,065.2

Net Present Value  = Cash Inflows from Investments – Cost of Investments

Or, Net Present Value  = \$296,065.2 – \$265,000 = \$31,065.2

From the above result, we can be sure that this is a worthy investment; because the NPV of this new investment is positive.

### Using NPV for Valuation – Alibaba Case Study

Alibaba will generate \$1.2 billion of free cash flows in March’19. As we note below that Alibaba will generate a predictable positive Free .

• Step 1 here is to apply the net present value formula to calculate the present value of the FCFF explicit period.
• Step 2 is to apply the net present value formula to calculate the PV of the terminal value.

The sum total of the NPV Calculation in steps 1 and 2 gives us the total Enterprise Value of Alibaba.

Below is the table that summarizes Alibaba’s DCF Valuation output.

### Uses and Relevance

By using this formula, the investors find out the difference between the cash inflows from the investments and the cost of investments.

It is used for making prudent business decisions for the following reasons –

• First of all, this is very easy to calculate. Before making any decisions regarding investments, if you know how to calculate NPV, you will be able to make better decisions.
• Secondly, it compares the present value of both cash inflow and cash outflow. As a result, the comparison provides the right perspective for the investors to make the right decision.
• Thirdly, NPV offers you a conclusive decision. After calculating this, you will directly get to know whether to go for the investments or not.

### NPV Calculator

You can use the following NPV Calculator

 Year1 Year2 Year3 Year4 Year5 R (percentage) Cash Inflows from Investments Cost of Investments Net Present Value Formula =

Net Present Value Formula =
 [Year1/(1 + R)1 + Year2/(1 + R)2 + Year3/(1 + R)3 + Year4/(1 + R)4 + Year5/(1 + R)5] − Cost of Investments =
 [0/(1+0)1 + 0/(1+0)2 + 0/(1+0)3 + 0/(1+0)4 + 0/(1+0)5] − 0 = 0

### Net Present Value in Excel (with excel template)

Let us now do the same example above in Excel.

This is very simple. You need to provide the two inputs of Cash Inflows from Investments and Cost of Investments.

Step 1 – Find the present value of the cash inflows.

Step 2 – Find the sum total of the present values.

Step 3 – NPV Calculation = \$296,065.2 – \$265,000 = \$31,065.2

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This has been a guide to Net Present Value (NPV) and its Definition. Here we discuss the formula to calculate Net Present Value along with examples, interpretation and uses. You may also have a look at these articles below to learn more about Financial Analysis –