Net present value聽(NPV) is a method used to determine the current value of all future聽cash flows聽generated by a project, including the initial capital investment. It is widely used in聽capital budgeting聽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鈥檚 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鈥檚 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.聽

The Formula for NPV

NPV=Cash聽flow(1+i)tinitial聽investmentwhere:i=Required聽return聽or聽discount聽ratet=Number聽of聽time聽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聽flowinitial聽investmentwhere:i=Required聽return聽or聽discount聽ratet=Number聽of聽time聽periods

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

NPV=t=0nRt(1+i)twhere:Rt=net聽cash聽inflow-outflows聽during聽a聽single聽period聽ti=discount聽rate聽or聽return聽that聽could聽be聽earned聽in聽alternative聽investmentst=number聽of聽time聽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聽cash聽inflow-outflows聽during聽a聽single聽period聽ti=discount聽rate聽or聽return聽that聽could聽be聽earned聽in聽alternative聽investmentst=number聽of聽time聽periods

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

NPV=Today鈥檚聽value聽of聽the聽expected聽cash聽flowsToday鈥檚聽value聽of聽invested聽cashNPV = \text{Today鈥檚 value of the expected cash flows} - \text{Today鈥檚 value of invested cash}NPV=Today鈥檚聽value聽of聽the聽expected聽cash聽flowsToday鈥檚聽value聽of聽invested聽cash

Examples nba腾讯体育直播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:

NPV=$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聽discount rate聽for future cash flows to account for the聽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聽present value聽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,聽projects with the highest NPV聽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聽target rate of return聽is 12%. Since the cash inflows are uneven, the NPV formula is broken out by individual cash flows.

NPV聽of聽projectX=$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聽of聽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.

NPV聽of聽projectY=$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聽of聽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).

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.