NPV Formula

Net Present Value Formula

NPV formula is used mainly for making investment decisions. How would one understand whether an investment is good enough? NPV will help you decide.

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

NPV_{t=1 to T}  = ∑  Xt/(1 + R)^t – Xo

Where,

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

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

NPV = [C_i1/ (1+r)¹ + C_i2/(1+r)² + C_i3/(1+r)³ + …] – X_o

Where,

• R is the specified return rate per period;
• C_i1 is the consolidated cash arrival during the first period;
• C_i2 is the consolidated cash arrival during the second period;
• C_i3 is the consolidated cash arrival during the third period, etc…

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Example of Net Present Value Formula

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 Formula 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 Cash Flows.

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

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.

Uses and Relevance of NPV Formula

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

If the difference is positive, it’s a great project. If the difference is negative, it’s not worthy of the investors.

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

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.

You can easily calculate the NPV in the Excel template provided.

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 NPV Formula. Here we learn to calculate net present value using its formula with some practical examples along with NPV calculator and excel template. You may also have a look at these articles below to learn more about Financial Analysis –

• Value Formula in Excel – Examples
• Examples of Discounted Payback Period Formula
• NPV Function in Excel
• IRR vs NPV
• NPV vs XNPV | Top Differences
• Capital Gains Yield Formula
• Dividend Discount Model
• Discounted Payback Period