# NPV Calculator – Net Present Value

Created by Bogna Szyk and Tibor Pál, PhD candidate
Reviewed by Steven Wooding
Based on research by
Brigham EF, Ehrhardt MC. Financial Management: Theory and Practice; 2016See 2 more sources
Cipra T. Financial and Insurance Formulas; 2010Zwillinger D. CRC Standard Mathematical Tables and Formulas (Advances in Applied Mathematics), 33rd Edition; 2018
Last updated: Jun 05, 2023

If you are trying to assess whether a particular investment will bring you profit in the long term, this NPV calculator is a tool for you. Based on your initial investment and consecutive cash flows, it will determine the net present value, and hence the profitability, of a planned project.

In this article, we will help you understand the concept of net present value and provide step-by-step instructions on how to calculate NPV. We will also tell you how to interpret the result.

NPV is often used in company valuation – check out the discounted cash flow calculator for more details.

## What is the net present value?

By definition, net present value is the difference between the present value of cash inflows and the present value of cash outflows for a given project.

To understand this definition, you first need to know what is the present value. Imagine that you want to have $2200 in your account next year. You know that the yearly interest rate on that account is 10%. It means that you need to put$2000 on that account today to have $2200 twelve months from now. The present value of "$2200 due in 12 months" is $2000. You can notice that for a positive discount rate, the future value (FV – future value calculator) is always higher or equal to the present value (PV). Following that logic, every project that needs your investment at the beginning and returns some money each year has a present value of each cash flow: the initial investment and every cash inflow. If you sum up all of these present values, you will get a net present value (NPV) of that project. ## How to calculate net present value? Again, the surest way to understand the formula behind NPV is to start with the present value equation: $\small {\rm PV} = \frac{\text{cash flow}}{(1 + r)^n}$ where: • $\rm PV$ – Present value of money; • $\text{cash flow}$ – Amount of money you will get in the future; • $r$ – Discount rate (interest rate used in cash flow analysis); and • $n$ – Number of time periods (typically, years) between now and the moment when you will receive your money. To calculate NPV, you need to sum up the PVs of all cash flows. • The first cash flow $C_0$ – your investment – will happen at a time when $n = 0$. Additionally, as this is your expenditure, it will be negative in value. • Every other cash flow $C_i$ will be either positive (income) or negative (expenses). Each year, you have to increase the $n$ value by 1. If you apply all of these principles, you will get the following net present value formula: $\small {\rm NPV} = -C_0 + \sum_{i\ =\ 1}^n\left[\frac{C_i}{(1 + r)^i}\right]$ Or, if you don't want to use the summation notation: $\small {\rm NPV} = -C_0 + \frac{C_1}{(1 + r)} + \frac{C_2}{(1 + r)^2}\\[1em]\qquad + \frac{C_3}{(1 + r)^3} + \dots + \frac{C_n}{(1 + r)^n}$ You can use our NPV calculator in advanced mode to find the net present value of up to ten cash flows (investment and nine cash inflows). If you want to take into account more cash flows, we recommend you use a spreadsheet instead. ## How to calculate NPV: an example Let's analyze the following example: a company has to choose between two projects that both cost$10,000 to implement. Each of them will last for 5 years, but they have different expected cash inflows. The discount rate is 5% in each case. Which project should the company choose?

Time

Project 1

Project 2

Initial investment

$10,000$10,000

Year 1

$5000$1000

Year 2

-$1000$1000

Year 3

$3000$1000

Year 4

$3000$5000

Year 5

$2000$4000

If you use our NPV calculator to determine the NPV for each of these projects, you will discover that the NPV of project 1 is equal to $481.55, while the NPV of project 2 is equal to –$29.13.

This result means that project 1 is profitable because it has a positive NPV. Project 2 is not profitable for the company, as it has a negative NPV. That is why the company should choose to implement project 1.

## What are the expected cash flows?

You probably noticed that our NPV calculator determines two values as results. The first one is NPV, and the second is called the "expected cash flow".

This is the present value of all of your cash inflows, not taking the initial investment into account.

## Net present value (NPV) and internal rate of return (IRR)

The internal rate of return (IRR calculator) of a project is such a discount rate at which the NPV equals zero. In other words, the company will neither earn nor lose on such a project – the gains are equal to costs.

IRR is typically used to assess the minimum discount rate at which a company will accept the project. It allows you to establish reasonably quickly whether the project should be considered as an option or discarded because of its low profitability.

Bogna Szyk and Tibor Pál, PhD candidate
Discount rate
%
Initial costs
$Annual cash flows Year 1$
Year 2
$Year 3$
Year 4
$Year 5$
NPV
Net present value
$Expected cash flows$
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