# Net Present Value (NPV): Definition & Formula

Updated: Dec. 13, 2022Written By: Kent ThuneReviewed By:

Net present value is a calculation used to determine the current value of a business, an investment, a capital project, or another finance activity based on the future value of assets. Read to learn more about NPV, including the advantages and disadvantages, how investors use it, and how to calculate it.

## What Is Net Present Value?

Net present value (NPV) is a calculation used by businesses and investors that estimate the current value of future cash flows. The NPV calculation accounts for the revenue, expense, and capital cost associated with a project's projected free cash flow (FCF).

To estimate the current value of future cash flows, a business or investor can use discounted cash flow analysis (DCF) which applies a discount rate to those future cash values . Because the output of a DCF analysis is the present value of future cash flow, it is also a common way analysts and investors measure the value of a company.

### Positive vs. Negative NPV

If the NPV of a project or investment is positive, it means that the project is expected to deliver returns in excess of the discount rate. A project that returns less than its discount rate will have a negative NPV expectation, and therefore is not a worthwhile investment.

## How NPV Is Calculated

NPV is calculated by determining the difference between the present value of cash inflows and the present value of cash outflows, over a period of time. The formula for calculating NPV can be relatively straightforward but will vary depending on the amount of cash flow needed for the calculation.

Tip: In most cases, investors won't manually calculate NPV. Many financial calculators include an NPV function, while spreadsheet models also calculate NPV. There is also an NPV function in Excel that can simplify the NPV calculation once the inputs, such as the cash flows and discount rate, are known.

### NPV Formula

A simple way to break down the NPV formula calculation is to subtract the current value of invested cash from the current value of expected cash flow.

The Present Value formula for a single cash flow is:

Present Value = Future Cash Flow Amount / (1 + discount Rate)t

where t = the time period in # of years

This same calculation is essentially performed for every expected future cashflow (inflows and outflows). The sum of all these Present Values is called the Net Present Value.

For a constant stream of cashflows, the NPV formula is:

• Rt = cash flow amount
• i = discount rate, or desired rate of return
• t = the time periods in # of years
• C = initial cash investment

### How to Calculate Net Present Value

Although it's not common to manually calculate net present value, it's important to know the inputs that go into the formula, as well as the math behind it.

#### Step 1: Identify the Initial Investment (C)

The initial investment is the first cash flow and is set at the present time, so there is no need to discount it. If a financial calculator is used, this number will be negative.

#### Step 2: Identify Number of Periods (t)

An investor may use a simplified NPV calculation that includes years for cash flow periods, but a business may use months. For example, if the elapsed time will be 5 years, a business may choose a number of months, which would be 60 (5 x 12).

#### Step 3: Identify the Discount Rate (i)

The discount rate is the expected return, which is usually annualized. If the time periods are measured by months, the discount rate would need to be adjusted to a monthly rate.

#### Step 4: Calculate PV of Each Cash Flow

Calculate the present value of each period's projected returns by dividing the projected cash flow for each year (FV) by (1 + discount rate)t:

Present value of cash flow = FV / (1 + discount rate)t

#### Step 5: Calculate NPV of All Cash Flows

After calculating the figure for each of the cash flow periods in Step 4, add them together. This will represent the value of all projected returns. Subtract the initial investment from this number to get the NPV.

## How Investors Use & Analyze NPV

Investors may use NPV to decide if an investment is worth pursuing. For example, if an investor wanted to outperform the average stock market return, they may use the expected S&P 500 index return as a discount rate. If the net present value is positive, the investment may be worth pursuing.

As is the case with many other valuation metrics, it's important to understand the pros and cons of NPV before using it to make investment decisions.

### Pros

• Cashflows can be a better indicator than net income: Using cash flow numbers is often preferred by analysts since net income is subject to management decisions about accounting methods and assumptions. (see cash flow vs. net income)
• NPV accounts for time value of money: It's best to measure the future profitability of an investment or project in today's dollars.

### Cons

• Potential for errors: NPV relies on estimates, such as discount rate and projected returns, which may prove to be inaccurate or inappropriate.
• Limited comparisons: NPV is not a good tool for comparing projects of different sizes because, in dollar terms, larger projects will always appear to have a higher NPV than smaller projects.

## Net Present Value Example

For a simple net present value example, let's say someone buys 1000 shares of stock at \$10, for a cost of \$10,000. The stock pays a 50c dividend annually, or a \$500 total dividend each year on the 1000 shares held. The investor plans to hold the stock for five years and expects to be able to sell it for \$13,000 after 5 years. The investor seeks a minimum return of 10% on individual stocks (discount rate = 10%).

To calculate the present value of the first dividend cash flow, divide the year one dividend of \$500 by 1+ the discount rate (1 + 0.10), which will look like this:

Rt/(1 + i)t = \$500 / (1+1.10)1 = \$454.55

This means that the present value of \$500 dividend received by the investor in year one is worth \$454.55 in today's dollars.

For the full five year period, calculations would look like this:

Year 1 PV = \$500 / (1 + 0.10)1 = \$454.55

Year 2 PV = \$500 / (1 + 0.10)2 = \$413.22

Year 3 PV = \$500 / (1 + 0.10)3 = \$375.65

Year 4 PV = \$500 / (1 + 0.10)4 = \$341.51

Year 5 PV = \$500 / (1 + 0.10)5 = \$310.46

If the investor is correct and can sell the stock for \$13,000 after 5 years, the present value of the sales proceeds would be:

Sales value = \$13,000 / (1 + 0.10)5 = \$8,071.98

What is the Net Present Value of this investment? Add the present value of each expected cashflow:

\$454.55 + \$413.22 + \$375.65 + \$341.51 + \$310.46 + \$8,071.98 = \$9,967.37

....and subtract the initial investment from the sum, like this:

\$9,967.37 - \$10,000 = -\$32.63

The expected NPV is negative -\$32.63. This means that, if the investor's \$10,000 of stock pays \$500 in annual dividends for 5 years, and the investor sells the shares for \$13,000 after 5 years, the investment delivers a negative return on a net present value basis using a discount rate (required rate of return) of 10%.

The NPV in this example is only slightly negative. Had the investor's required rate of return been 9.5%, the expected NPV would be positive.

## NPV & Discount Rate

The discount rate is an percentage rate used in discounted cash flow (DCF) analysis to calculate the present value of future cash flows. For example, this can be the rate of return that the investors expect or it can be a company's cost of capital.

Future cash flows are reduced by the discount rate, which means that a higher discount rate will translate to lower future cash flows. Thus, lower discount rates translate to a higher present value. In different words, a higher discount rate means that the future value of money is worth less in today's dollars. This concept is true regarding inflation, which reduces the purchasing power of a dollar.

## NPV & Payback Period

The payback period, or payback method, is a different methodology that calculates the time required to recoup the money invested in a project or investment, or to reach the break-even point. However, unlike the NPV calculation, the payback method does not account for the time value of money.

Some businesses use a combination of the payback method and NPV for comparing capital projects or making investment decisions. For example, when comparing multiple projects, the business may narrow down the choices with the payback method and compare the top two or three projects using the NPV method.

## Bottom Line

Net present value, or NPV, is a method of determining the profitability of a business, project, or investment, in today's dollars. Therefore, NPV is a metric that is very useful to businesses and investors. A major advantage of NPV is that it accounts for the time value of money. However, a key disadvantage of NPV is that it relies on estimates, which can be inaccurate.