Net present valueÂ (NPV) is a method used to determine the current value of all futureÂ cash flowsÂ generated by a project, including the initial capital investment. It is widely used inÂ capital budgetingÂ 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 thereâ€™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 todayâ€™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.Â

## The Formula for NPV

ï»¿$\begin{aligned} &NPV = \frac{\text{Cash flow}}{(1 + i)^t} - \text{initial investment} \\ &\textbf{where:}\\ &i=\text{Required return or discount rate}\\ &t=\text{Number of time periods}\\ \end{aligned}$ï»¿

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

ï»¿$\begin{aligned} &NPV = \sum_{t = 0}^n \frac{R_t}{(1 + i)^t}\\ &\textbf{where:}\\ &R_t=\text{net cash inflow-outflows during a single period }t\\ &i=\text{discount rate or return that could be earned in alternative investments}\\ &t=\text{number of time periods}\\ \end{aligned}$ï»¿

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

ï»¿$NPV = \text{Todayâ€™s value of the expected cash flows} - \text{Todayâ€™s value of invested cash}$ï»¿

## Examples nbaÌÚÑ¶ÌåÓýÖ±²¥ing 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:

ï»¿$\begin{aligned} NPV &= \frac{\$500}{(1 + 0.08)^1} + \frac{\$300}{(1 + 0.08)^2} + \frac{\$800}{(1+0.08)^3} - \$1000 \\ &= \$355.23\\ \end{aligned}$ï»¿

The required rate of return is used as theÂ discount rateÂ for future cash flows to account for theÂ 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 theÂ present valueÂ 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,Â projects with the highest NPVÂ 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. TheÂ target rate of returnÂ is 12%. Since the cash inflows are uneven, the NPV formula is broken out by individual cash flows.

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

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.

ï»¿$\begin{aligned} NPV \text{ of project} - Y &= \frac{\$27,000}{(1 + 0.12)^1} + \frac{\$27,000}{(1+0.12)^2} - \$35,000 \\ &= \$10,631\\ \end{aligned}$ï»¿

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).

## 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.