The Difference Between Present Value (PV) and Net Present Value (NPV)

Present value (PV) is the current value of a future sum of money or stream of cash flow given a specified rate of return. Meanwhile, net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

While both PV and NPV use a form of discounted cash flows to estimate the current value of future income, these calculations differ in one important way. The NPV formula accounts for the initial capital outlay required to fund a project, making it a net figure, while the PV calculation only accounts for cash inflows.

Though understanding the concept behind the PV calculation is important, the NPV formula is a much more comprehensive indicator of a given project's potential profitability.

Since the value of revenue earned today is higher than that of revenue earned down the road, businesses discount future income by the investment's expected rate of return. This rate, called the hurdle rate, is the minimum rate of return a project must generate for the business to consider investing in it.

The PV calculation indicates the discounted value of all revenue generated by the project, while the NPV indicates how profitable the project will be after accounting for the initial investment required to fund it.

The formula to calculate NPV is as follows:

$\begin{aligned} &\text{NPV}=\text{cash flow} \div (1 + i)*t - \text{initial investment} \\ &\textbf{where:}\\ &i=\text{required rate or discount rate}\\ &t=\text{number of time periods}\\ \end{aligned}$​NPV=cash flow÷(1+i)∗t−initial investmentwhere:i=required rate or discount ratet=number of time periods​

For example, assume a given project requires an initial capital investment of $15,000. The project is anticipated to generate revenues of $3,500, $9,400 and $15,100 in the next three years, respectively, and the company's hurdle rate is 7%.

The present value of the anticipated income is:

$\frac{\$3,500}{(1+0.07)^1} + \frac{\$9,400}{(1+0.07)^2} + \frac{\$15,100}{(1+0.07)^3} = \$23,807$(1+0.07)1$3,500​+(1+0.07)2$9,400​+(1+0.07)3$15,100​=$23,807
The NPV of this project can be determined by simply subtracting the initial capital investment from the discounted revenue:

$\$23,807 - \$15,000 = \$8,807$$23,807−$15,000=$8,807

While the PV value is useful, the NPV calculation is invaluable to capital budgeting. A project with a high PV figure may actually have a much less impressive NPV if a large amount of capital is required to fund it. As a business expands, it looks to finance only those projects or investments that yield the greatest returns, which in turn enables additional growth. Given a number of potential options, the project or investment with the highest NPV is generally pursued.