NPV Formula

What is the NPV formula?

The NPV formula is a way of calculating the Net Present Value (NPV) of a series of cash flows based on a specified discount rate. The NPV formula can be very useful for financial analysis and financial modeling when determining the value of an investment (a company, a project, a cost-saving initiative, etc.).

Below is an illustration of the NPV formula for a single cash flow.

Screenshot of CFI’s Corporate Finance 101 Course.

NPV for a series of cash flows

In most cases, a financial analyst needs to calculate the net present value of a series of cash flows, not just one individual cash flow. The formula works in the same way, however, each cash flow has to be discounted individually, and then all of them are added together.

Here is an illustration of a series of cash flows being discounted:

Souce: CFI’s Free Corporate Finance Course.

What is the math behind the NPV formula?

Here is the mathematical formula for calculating the present value of an individual cash flow.

NPV = F / [ (1 + i)^n ]

Where,

PV = Present Value

F = Future payment (cash flow)

i = Discount rate (or interest rate)

n = the number of periods in the future the cash flow is

How to use the NPV formula in Excel

Most financial analysts never calculate the net present value by hand nor with a calculator, instead, they use Excel.

=NPV(discount rate, series of cash flow)

(See screenshots below)

Example of how to use the NPV function:

Step 1: Set a discount rate in a cell.

Step 2: Establish a series of cash flows (must be in consecutive cells).

Step 3: Type “=NPV(“ and select the discount rate “,” then select the cash flow cells and “)”.

Congratulations, you have now calculated net present value in Excel!

Download the free template.

NPV function in Excel

NPV Excel formula

Source: CFI’s Free Excel Crash Course.

If you need to be very precise in your calculation, it’s highly recommended to use XNPV instead of the regular function.

To find out why, read CFI’s guide to XNPV vs NPV in Excel.

DCF Modeling

The main use of the NPV formula is in Discounted Cash Flow (DCF) modeling in Excel. In DCF modelsDCF Model Training Free GuideA DCF model is a specific type of financial model used to value a business. DCF stands for Discounted Cash Flow, so the model is simply a forecast of a company’s unlevered free cash flow discounted back to today’s value. This free DCF model training guide will teach you the basics, step by step with examples and images an analyst will forecast a company’s three financial statementsThree Financial StatementsThe three financial statements are the income statement, the balance sheet, and the statement of cash flows. These three core statements are intricately linked to each other and this guide will explain how they all fit together. By following the steps below you'll be able to connect the three statements on your own. into the future and calculate the company’s Free Cash Flow to the FirmValuationA guide to the NPV formula in Excel when performing financial analysis. It's important to understand exactly how the NPV formula works in Excel and the math behind it. NPV = F / [ (1 + r)^n ] where, PV = Present Value, F = Future payment (cash flow), r = Discount rate, n = the number of periods in the future (FCFF). Additionally, a terminal valueTerminal ValueThe terminal value is used in valuing a company. The terminal value exists beyond the forecast period and assumes a going concern for the company. is calculated at the end of the forecast period. Each of the cash flows in the forecast and terminal value are then discounted back to the present using a hurdle rateHurdle Rate DefinitionA hurdle rate is the rate of return that must be achieved before accepting and funding an investment project. Hurdle rates are used in financial modeling to calculate NPV. If IRR > Hurdle Rate then the investment creates value. The rate is determined by assessing the cost of capital, risks involved, opportunity cost of the firm’s weighted average cost of capital (WACCWACCWACC is a firm’s Weighted Average Cost of Capital and represents its blended cost of capital including equity and debt. The WACC formula is = (E/V x Re) + ((D/V x Rd) x (1-T)). This guide will provide an overview of what it is, why its used, how to calculate it, and also provides a downloadable WACC calculator).

Below is an example of a DCF model from one of CFI’s financial modeling courses.

Screenshot: CFI financial modeling courses.

More helpful resources

Thank you for reading this guide to calculating net present value. CFI’s mission is to help anyone become a world-class financial analyst. To keep learning and advancing your career, these additional financial resources will be a big help:

XNPV formula in Excel
Walk me through a DCF modelWalk me through a DCFThe question, walk me Through a DCF analysis is common in investment banking interviews. Learn how to ace the question with CFI's detailed answer and guide. Build a 5-year forecast of unlevered free cash flow, calculate a terminal value, and discount all those cash flows to present value using WACC.
Valuation methodsValuation MethodsWhen valuing a company as a going concern there are three main valuation methods used: DCF analysis, comparable companies, and precedent transactions. These methods of valuation are used in investment banking, equity research, private equity, corporate development, mergers & acquisitions, leveraged buyouts and finance
DCF modeling guideDCF Model Training Free GuideA DCF model is a specific type of financial model used to value a business. DCF stands for Discounted Cash Flow, so the model is simply a forecast of a company’s unlevered free cash flow discounted back to today’s value. This free DCF model training guide will teach you the basics, step by step with examples and images