The net present value method assumes that all cash inflows can be immediately reinvested at the

Net present value (NPV) is a method used to determine the current value of all future cash flows generated by a project, including the initial capital investment. It is widely used in capital budgeting to establish which projects are likely to turn the greatest profit.

The formula for net present value varies depending on the number and consistency of future cash flows.

• Net present value (NPV) is used to calculate today’s value of a future stream of payments.
• NPV is used in capital budgeting to compare whether an investment today will generate positive cash flow in the future.
• If the NPV of a project or investment is positive, it means that the discounted present value of all future cash flows related to that project or investment will be positive, and therefore attractive.
• To calculate NPV, you need to estimate future cash flows for each period and determine the correct discount rate.
• NPV is useful in identifying profitable projects, though it falls short when comparing projects of different sizes.

Net present value is a capital budgeting analysis technique used to determine whether a long-term project will be profitable. The premise of the NPV formula is to compare an initial investment to the future cash flows of a project.

An importance aspect of the NPV formula is consideration that $1 today is not worth the same as $1 tomorrow. Because money today can be put to use to generate returns in the future, a quantity of money today is worth more than the same amount of money in the future (assuming positive returns are anticipated).

In general, the NPV formula strives to pull all future cash flow values to what each cash flow is worth today. Then, the NPV formula compares the value of those cash inflows against the initial investment or cash outflow. If the NPV of a project is positive (discounted future cash flow is greater than the initial investment), a project is expected to be profitable. If the NPV is negative, the initial investment is greater than the future cash flows.

If there’s one cash flow from a project that will be paid one year from now, then the calculation for the NPV is as follows:

N P V = Cash flow ( 1 + i ) t − initial investment where: i = Required return or discount rate t = Number of time periods \begin{aligned} &NPV = \frac{\text{Cash flow}}{(1 + i)^t} - \text{initial investment} \\ &\textbf{where:}\\ &i=\text{Required return or discount rate}\\ &t=\text{Number of time periods}\\ \end{aligned} ​NPV=(1+i)tCash flow​−initial investmentwhere:i=Required return or discount ratet=Number of time periods​

If analyzing a longer-term project with multiple cash flows, then the formula for the NPV of a project is as follows:

N P V = ∑ t = 0 n R t ( 1 + i ) t where: R t = net cash inflow-outflows during a single period  t i = discount rate or return that could be earned in alternative investments t = number of time periods \begin{aligned} &NPV = \sum_{t = 0}^n \frac{R_t}{(1 + i)^t}\\ &\textbf{where:}\\ &R_t=\text{net cash inflow-outflows during a single period }t\\ &i=\text{discount rate or return that could be earned in alternative investments}\\ &t=\text{number of time periods}\\ \end{aligned} ​NPV=t=0∑n​(1+i)tRt​​where:Rt​=net cash inflow-outflows during a single period ti=discount rate or return that could be earned in alternative investmentst=number of time periods​

If you are unfamiliar with summation notation, here is an easier way to remember the concept of NPV:

$NPV=\text{Today’s value of the expected cash flows}-\text{Today’s value of invested cash}$

In Excel, there is a NPV function that can be used to easily calculate net present value of a series of cash flow. The NPV function in Excel is simply NPV, and the full formula requirement is:

=NPV(discount rate, future cash flow) + initial investment

In the example above, the formula entered into the grey NPV cell is:

=NPV (green cell, yellow cells) + blue cell

= NPV (C3, C6:C10) + C5

A series of future cash flows can alternate between positive and negative returns. After an initial cash outflow, a company may expect to need to repair equipment, pay property taxes on land, or incur selling costs for a given number of capital projects.

The NPV formula has several important parts to it. Although the formula may be different for different types of cash flow streams, these four components are usually vital in calculating NPV.

When analyzing NPV, it's common for a series of cash flow to start with an initial investment. This cash outflow is represented s a negative cash outflow that will be used to compare the (hopefully) positive cash flow in the future. It is also common to assume that the investment will happen in period 0 (the initial period prior to the investment being implemented).

For example, imagine a $100,000 upfront investment in new machinery that will improve the efficiency of operations in the future and yield more effective manufacturing practices. In this example, the NPV formula will contain a $100,000 cash outflow to represent the initial expenditure.

The premise of NPV is centered around what the future cash flow will be. It's assumed that after an initial investment, the investment will yield positive cash flow in the future. This cash flow may occur one time in the future, multiple times in the future for different amounts, or multiple times in the future for a consistent cashflow.

In the example above, the $100,000 investment may be expected to yield $25,000 of cost savings per year for the next five years. In this example, the NPV formula will contain a positive $25,000 of cash flow between periods 1 through 5.

The interest rate in the NPV formula is also referred to as the discount rate. This rate is used to determine what a dollar amount in the future is worth today. A company internally sets this rate, and companies often use the cost of capital to set this rate. For example, if it costs 4% to issue additional debt or shareholders expect a 6% dividend, a company may choose to use either of those rates.

With our machinery example, a company may expect its cost of capital to be 5%. Therefore, every cash flow will be discounted using a rate of 5%, though different discounts will be applied to each varying year of cash flow.

Though already touched on early, it is implied that the time period must be considered for an investment. A company may make a one-time upfront investment; however, it may expect cash flow benefits for decades in the future. If the company expects a one-time cash flow in the future, it must identify the time period when they expect the return.

For example, imagine a company buys land for $1,000,000. It can choose to either use the land for operations or it expects to sell it for $1,500,000 five years from now. Once the discount rate is selected, the $1.5 million should be discounted using five years as the period to better understand the difference between the initial investment and discounted future cash flow.

NPV's counterpart is called the internal rate of return (IRR). While NPV returns a dollar value of net discounted cash flow from a project, IRR returns an expected rate of return that can used to compared across projects.

Many projects generate revenue at varying rates over time. In this case, the formula for NPV can be broken out for each cash flow individually. For example, imagine a project that costs $1,000 and will provide three cash flows of $500, $300, and $800 over the next three years. Assume that there is no salvage value at the end of the project and that the required rate of return is 8%. The NPV of the project is calculated as follows:

N P V = $ 500 ( 1 + 0.08 ) 1 + $ 300 ( 1 + 0.08 ) 2 + $ 800 ( 1 + 0.08 ) 3 − $ 1000 = $ 355.23 \begin{aligned} NPV &= \frac{\$500}{(1 + 0.08)^1} + \frac{\$300}{(1 + 0.08)^2} + \frac{\$800}{(1+0.08)^3} - \$1000 \\ &= \$355.23\\ \end{aligned} NPV​=(1+0.08)1$500​+(1+0.08)2$300​+(1+0.08)3$800​−$1000=$355.23​

The required rate of return is used as the discount rate for future cash flows to account for the time value of money. A dollar today is worth more than a dollar tomorrow because a dollar can be put to use earning a return. Therefore, when calculating the present value of future income, cash flows that will be earned in the future must be reduced to account for the delay.

NPV is used in capital budgeting to compare projects based on their expected rates of return, required investment, and anticipated revenue over time. Typically, projects with the highest NPV are pursued.

For example, consider two potential projects for company ABC.

Project X requires an initial investment of $35,000 but is expected to generate revenues of $10,000, $27,000, and $19,000 for the first, second, and third years, respectively. The target rate of return is 12%. Since the cash inflows are uneven, the NPV formula is broken out by individual cash flows.

N P V  of project − X = $ 10 , 000 ( 1 + 0.12 ) 1 + $ 27 , 000 ( 1 + 0.12 ) 2 + $ 19 , 000 ( 1 + 0.12 ) 3 − $ 35 , 000 = $ 8 , 977 \begin{aligned} NPV \text{ of project} - X &= \frac{\$10,000}{(1 + 0.12)^1} + \frac{\$27,000}{(1 + 0.12)^2} + \frac{\$19,000}{(1+0.12)^3} - \$35,000 \\ &= \$8,977\\ \end{aligned} NPV of project−X​=(1+0.12)1$10,000​+(1+0.12)2$27,000​+(1+0.12)3$19,000​−$35,000=$8,977​

Project Y also requires a $35,000 initial investment and will generate $27,000 per year for two years. The target rate remains 12%. Because each period produces equal revenues, the first formula above can be used:

N P V  of project − Y = $ 27 , 000 ( 1 + 0.12 ) 1 + $ 27 , 000 ( 1 + 0.12 ) 2 − $ 35 , 000 = $ 10 , 631 \begin{aligned} NPV \text{ of project} - Y &= \frac{\$27,000}{(1 + 0.12)^1} + \frac{\$27,000}{(1+0.12)^2} - \$35,000 \\ &= \$10,631\\ \end{aligned} NPV of project−Y​=(1+0.12)1$27,000​+(1+0.12)2$27,000​−$35,000=$10,631​

Both projects require the same initial investment, but Project X generates more total income than Project Y. However, Project Y has a higher NPV because income is generated faster (meaning that the discount rate has a smaller effect).

The NPV formula leverages the time value of money; compared to other capital budgeting analysis tools, the NPV formula discounts cash flow and analyzes profitability based on the timing of when cash flow occurs. The NPV formula also factors in the company's specific cost of capital via the discount rate.

By discounting cash flow, the NPV formula naturally builds in long-term exposure to risk. The furthest estimates in the future are discounted most heavily, appropriately factoring in that these cash flows often have the most uncertainty.

The NPV formula often produces a calculation that is easily interpretable. If the finding is positive, the project is profitable. If the finding is negative, the project is not profitable. As opposed to the IRR formula which produces a percentage that has to be compared against a benchmark, NPV yields value on its own.

Like other financial formulas used for strategic planning, the NPV formula is only as valuable as the inputs. The NPV formula relies heavily on the quality of information provided, even though estimates may range decades into the future.

The NPV formula yields a dollar result which, though easy to interpret, may not tell the entire story. Consider the following two investment options: Option A with an NPV of $100,000 or Option B with an NPV of $1,000.

The formula for NPV doesn't distinguish a project's size or give favorability for higher ROI. Option A might require an initial investment of $1 million, while Option B may require an initial investment of $10. Though the NPV formula tells you which project you may earn more for, it doesn't tell you which investment is most efficient regarding starting capital.

Pros

• Considers the time value of money

• Incorporates discounted cash flow using a company's cost of capital

• Returns a single dollar value that is relatively easy to interpret

• May be easy to calculate when leveraging spreadsheets or financial calculators

Cons

• Relies heavily in inputs, estimates, and long-term projections

• Doesn't distinguish between project sizes or ROI

• May be found as complex and difficult to manually calculate, especially for projects with many years of cash flow

• Is driven by quantitative inputs and does not consider non-financial metrics

NPV is calculated by taking the present value of all cash flows over the life of a project. Then, the present value of cash flows is subtracted from the investment's initial investment. If the difference is positive (greater than 0), the project will be profitable.

Net present value (NPV) is used in capital budgeting to determine whether a project will be profitable, or to evaluate different projects and determine which one will be the most profitable.

The main advantage of the NPV method is that it takes into consideration the time value of money, by discounting future cash flows at an appropriate discount rate that is based on the company’s cost of capital and the project’s risk. The payback period estimates how long it will take for a project to generate sufficient cash flows to pay back its initial startup costs, but it does not consider the time value of money and overall project profitability like NPV does.

NPV needs accurate assumptions for a number of variables like initial costs and future cash flows—and, most importantly, the discount rate or cost of capital. As small changes in the discount rate can lead to significant swings in the discounted value of future cash flows, inaccurate discount rates may lead to incorrect NPV and hence an erroneous decision on the project’s profitability and viability.

Another drawback of NPV is that it cannot be used to compare projects of different sizes, since the result of the NPV method is expressed in dollars. Thus, a $10 million project may likely have a higher NPV than a $1 million project in dollar terms, but the latter may be much more profitable on a percentage basis, apart from only needing one-tenth of the capital. The two projects therefore cannot be compared using NPV because they are of very different sizes.

A negative NPV number means that a project will be unprofitable as the initial startup costs exceed the discounted value of net future cash flows.

Net present value (NPV) discounts all the future cash flows from a project and subtracts its required investment. The analysis is used in capital budgeting to determine if a project should be undertaken compared to alternative uses of capital or other projects.