NPV Formula - Learn How Net Present Value Really Works, Examples

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 flowCash FlowCash Flow (CF) is the increase or decrease in the amount of money a business, institution, or individual has. In finance, the term is used to describe the amount of cash (currency) that is generated or consumed in a given time period. There are many types of CF.

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 flowsForecasting Cash FlowThis article on forecasting cash flow is the last part of the four-step financial forecasting model in Excel., 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:

Source: 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.

Video Explanation of the NPV Formula

Below is a short video explanation of how the formula works, including a detailed example with an illustration of how future cash flows become discounted back to the present.

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. The model is simply a forecast of a company’s unlevered free cash flow 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 into the future and calculate the company’s Free Cash Flow to the FirmValuationFree valuation guides to learn the most important concepts at your own pace. These articles will teach you business valuation best practices and how to value a company using comparable company analysis, discounted cash flow (DCF) modeling, and precedent transactions, as used in investment banking, equity research, (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, which is also known as minimum acceptable rate of return (MARR), is the minimum required rate of return or target rate that investors are expecting to receive on an investment. The rate is determined by assessing the cost of capital, risks involved, current opportunities in business expansion, rates of return for similar investments, and other factors 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 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
DCF modeling guideDCF Model Training Free GuideA DCF model is a specific type of financial model used to value a business. The model is simply a forecast of a company’s unlevered free cash flow