What Is the Formula for Calculating Net Present Value (NPV)?

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 NPV varies depending on the number and consistency of future cash flows. If there’s one cash flow from a project that will be paid one year from now, the calculation for the net present value is as follows.

Key Takeaways

  • Net present value, or NPV, is used to calculate today’s value of a future stream of payments.
  • 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. 
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The Formula for NPV

 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 flowinitial investmentwhere:i=Required return or discount ratet=Number of time periods

If analyzing a longer-term project with multiple cash flows, the formula for the net present value of a project is:

 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=0n(1+i)tRtwhere: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:

 N P V = Today’s value of the expected cash flows Today’s value of invested cash NPV = \text{Today’s value of the expected cash flows} - \text{Today’s value of invested cash} NPV=Today’s value of the expected cash flowsToday’s value of invested cash

Examples Using NPV

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 there is no salvage value at the end of the project and the required rate of return is 8%. The NPV of the project is calculated as follows:

 N P V = $ 5 0 0 ( 1 + 0 . 0 8 ) 1 + $ 3 0 0 ( 1 + 0 . 0 8 ) 2 + $ 8 0 0 ( 1 + 0 . 0 8 ) 3 $ 1 0 0 0 = $ 3 5 5 . 2 3 \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 = $ 1 0 , 0 0 0 ( 1 + 0 . 1 2 ) 1 + $ 2 7 , 0 0 0 ( 1 + 0 . 1 2 ) 2 + $ 1 9 , 0 0 0 ( 1 + 0 . 1 2 ) 3 $ 3 5 , 0 0 0 = $ 8 , 9 7 7 \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 projectX=(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 = $ 2 7 , 0 0 0 ( 1 + 0 . 1 2 ) 1 + $ 2 7 , 0 0 0 ( 1 + 0 . 1 2 ) 2 $ 3 5 , 0 0 0 = $ 1 0 , 6 3 1 \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 projectY=(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 the discount rate has a smaller effect).

What is NPV used for?

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.

What is the main advantage of NPV over an alternative method like the payback period?

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.

What are the main drawbacks of NPV?

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.

What does a negative NPV number mean?

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

The Bottom Line

Net present value 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 when compared to alternative uses of capital or other projects.