## What is Net Present Value (NPV)?

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. NPV is used in capital budgeting and investment planning to analyze the profitability of a projected investment or project.

The following formula is used to calculate NPV:

$\begin{aligned} &NPV = \sum_{t = 1}^n \frac { R_t }{ (1 + i)^t } \\ &\textbf{where:} \\ &R_t=\text{Net cash inflow-outflows during a single period }t \\ &i=\text{Discount rate or return that could be earned in} \\ &\text{alternative investments} \\ &t=\text{Number of timer periods} \\ \end{aligned}$

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

$\begin{aligned} &\textit{NPV} = \text{TVECF} - \text{TVIC} \\ &\textbf{where:} \\ &\text{TVECF} = \text{Today's value of the expected cash flows} \\ &\text{TVIC} = \text{Today's value of invested cash} \\ \end{aligned}$

A positive net present value indicates that the projected earnings generated by a project or investment - in present dollars - exceeds the anticipated costs, also in present dollars. It is assumed that an investment with a positive NPV will be profitable, and an investment with a negative NPV will result in a net loss. This concept is the basis for the Net Present Value Rule, which dictates that only investments with positive NPV values should be considered.

Apart from the formula itself, net present value can be calculated using tables, spreadsheets, or calculators.

#### Understanding Net Present Value

## How to Calculate Net Present Value (NPV)

Money in the present is worth more than the same amount in the future due to inflation and to earnings from alternative investments that could be made during the intervening time. In other words, a dollar earned in the future won’t be worth as much as one earned in the present. The discount rate element of the NPV formula is a way to account for this.

For example, assume that an investor could choose a $100 payment today or in a year. A rational investor would not be willing to postpone payment. However, what if an investor could choose to receive $100 today or $105 in a year? If the payer was reliable, that extra 5% may be worth the wait, but only if there wasn’t anything else the investors could do with the $100 that would earn more than 5%.

An investor might be willing to wait a year to earn an extra 5%, but that may not be acceptable for all investors. In this case, the 5% is the discount rate which will vary depending on the investor. If an investor knew they could earn 8% from a relatively safe investment over the next year, they would not be willing to postpone payment for 5%. In this case, the investor’s discount rate is 8%.

A company may determine the discount rate using the expected return of other projects with a similar level of risk or the cost of borrowing money needed to finance the project. For example, a company may avoid a project that is expected to return 10% per year if it costs 12% to finance the project or an alternative project is expected to return 14% per year.

Imagine a company can invest in equipment that will cost $1,000,000 and is expected to generate $25,000 a month in revenue for five years. The company has the capital available for the equipment and could alternatively invest it in the stock market for an expected return of 8% per year. The managers feel that buying the equipment or investing in the stock market are similar risks.

## Step One: NPV of the Initial Investment

Because the equipment is paid for up front, this is the first cash flow included in the calculation. There is no elapsed time that needs to be accounted for so today’s outflow of $1,000,000 doesn’t need to be discounted.

### Identify the number of periods (t)

The equipment is expected to generate monthly cash flow and last for five years, which means there will be 60 cash flows and 60 periods included in the calculation.

### Identify the discount rate (i)

The alternative investment is expected to pay 8% per year. However, because the equipment generates a monthly stream of cash flows, the annual discount rate needs to be turned into a periodic or monthly rate. Using the following formula, we find that the periodic rate is 0.64%.

$\text{Periodic Rate} = (( 1 + 0.08)^{\frac{1}{12}}) - 1 = 0.64\%$

## Step Two: NPV of Future Cash Flows

Assume the monthly cash flows are earned at the end of the month, with the first payment arriving exactly one month after the equipment has been purchased. This is a future payment, so it needs to be adjusted for the time value of money. An investor can perform this calculation easily with a spreadsheet or calculator. To illustrate the concept, the first five payments are displayed in the table below.

The full calculation of the present value is equal to the present value of all 60 future cash flows, minus the $1,000,000 investment. The calculation could be more complicated if the equipment was expected to have any value left at the end of its life, but, in this example, it is assumed to be worthless.

$NPV = -\$1,000,000 + \sum_{t = 1}^{60} \frac{25,000_{60}}{(1 + 0.0064)^{60}}$

That formula can be simplified to the following calculation:

$NPV = -\$1,000,000 + \$1,242,322.82 = \$242,322.82$

In this case, the NPV is positive; the equipment should be purchased. If the present value of these cash flows had been negative because the discount rate was larger, or the net cash flows were smaller, the investment should have been avoided.

## Net Present Value Drawbacks and Alternatives

Gauging an investment’s profitability with NPV relies heavily on assumptions and estimates, so there can be substantial room for error. Estimated factors include investment costs, discount rate, and projected returns. A project may often require unforeseen expenditures to get off the ground or may require additional expenditures at the project’s end.

Payback period, or “payback method,” is a simpler alternative to NPV. The payback method calculates how long it will take for the original investment to be repaid. A drawback is that this method fails to account for the time value of money. For this reason, payback periods calculated for longer investments have a greater potential for inaccuracy.

Moreover, the payback period is strictly limited to the amount of time required to earn back initial investment costs. It is possible that the investment’s rate of return could experience sharp movements. Comparisons using payback periods do not account for the long-term profitability of alternative investments.

## Net Present Value vs. Internal Rate of Return

Internal rate of return (IRR) is very similar to NPV except that the discount rate is the rate that reduces the NPV of an investment to zero. This method is used to compare projects with different lifespans or amount of required capital.

For example, IRR could be used to compare the anticipated profitability of a three-year project that requires a $50,000 investment with that of a 10-year project that requires a $200,000 investment. Although the IRR is useful, it is usually considered inferior to NPV because it makes too many assumptions about reinvestment risk and capital allocation.

## The Bottom Line

Net present value (NPV) is the calculation used to find today’s value of a future stream of payments. It accounts for the time value of money and can be used to compare investment alternatives that are similar. The NPV relies on a discount rate of return that may be derived from the cost of the capital required to make the investment, and any project or investment with a negative NPV should be avoided. An important drawback of using an NPV analysis is that it makes assumptions about future events that may not be reliable.