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# Net Present Value (NPV)

## 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. NPV is the result of calculations used to find today’s value of a future stream of payments.

### Key Takeaways

• Net present value, or NPV, is used to calculate the current total 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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## Net Present Value (NPV) Formula

\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}

## What Net Present Value Can Tell You

NPV accounts for the time value of money and can be used to compare similar investment alternatives. The NPV relies on a discount rate that may be derived from the cost of the capital required to invest, and any project or investment with a negative NPV should be avoided. One important drawback of NPV analysis is that it makes assumptions about future events that may not be reliable.

NPV looks to assess the profitability of a given investment on the basis that a dollar in the future is not worth the same as a dollar today. Money loses value over time due to inflation. However, a dollar today can be invested and earn a return, making its future value possibly higher than a dollar received at the same point in the future.

NPV seeks to determine the present value of an investment's future cash flows above the investment's initial cost. The discount rate element of the NPV formula discounts the future cash flows to the present-day value. If subtracting the initial cost of the investment from the sum of the cash flows in the present day is positive, then the investment is worthwhile.

For example, an investor could receive $100 today or a year from now. Most investors would not be willing to postpone receiving$100 today. However, what if an investor could choose to receive $100 today or$105 in one year? The 5% rate of return (RoR) for waiting one year might be worthwhile for an investor unless another investment could yield a rate greater than 5% over the same period.

If an investor knew they could earn 8% from a relatively safe investment over the next year, they would choose to receive $100 today and not the$105 in a year, with the 5% rate of return. In this case, 8% would be the discount rate.

### Positive vs. Negative NPV

A positive NPV 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.

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.

## Calculating Net Present Value

Money in the present is worth more than the same amount in the future due to inflation and possible 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 the 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.

NPV can be calculated using tables, spreadsheets (for example, Excel), or financial calculators.

## Steps for Net Present Value

There are two key steps for calculating NPV:

Because the equipment is paid for upfront, this is the first cash flow included in the calculation. No elapsed time 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 2: 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. Image by Sabrina Jiang © Investopedia 2020 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.

## Limitations of Net Present Value

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.

## Net Present Value vs. Payback Period

The 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.

## NPV vs. Internal Rate of Return (IRR)

The 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 amounts 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.

## What Does the Net Present Value Mean?

Net present value (NPV) is a financial metric that seeks to capture the total value of a potential investment opportunity. The idea behind NPV is to project all of the future cash inflows and outflows associated with an investment, discount all those future cash flows to the present day, and then add them together. The resulting number after adding all the positive and negative cash flows together is the investment’s NPV. A positive NPV means that, after accounting for the time value of money, you will make money if you proceed with the investment.

## What Is the Difference Between NPV and IRR?

NPV and IRR are closely related concepts, in that the IRR of an investment is the discount rate that would cause that investment to have an NPV of zero. Another way of thinking about this is that NPV and IRR are trying to answer two separate but related questions. For NPV, the question is, “What is the total amount of money I will make if I proceed with this investment, after taking into account the time value of money?” For IRR, the question is, “If I proceed with this investment, what would be the equivalent annual rate of return that I would receive?”

## What Is a Good NPV?

In theory, an NPV is “good” if it is greater than zero. After all, the NPV calculation already takes into account factors such as the investor’s cost of capital, opportunity cost, and risk tolerance through the discount rate. And the future cash flows of the project, together with the time value of money, are also captured. Therefore, even an NPV of $1 should theoretically qualify as “good.” In practice, however, many investors will insist on certain NPV thresholds, such as$10,000 or greater, to provide themselves with an additional margin of safety.

## Why Are Future Cash Flows Discounted?

NPV uses discounted cash flows due to the time value of money (TMV). The time value of money is the concept that money you have now is worth more than the identical sum in the future due to its potential earning capacity through investment and other factors such as inflation expectations. The rate used to account for time, or the discount rate, will depend on the type of analysis undertaken. Individuals should use the opportunity cost of putting their money to work elsewhere as an appropriate discount rate—simply put, it’s the rate of return the investor could earn in the marketplace on an investment of comparable size and risk.

### Article Sources

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1. CFA Institute. "Chapter 8 Quantitative Concepts." Page 242. Accessed Oct. 15, 2021.

2. Harvard Business Review. "A Refresher on Net Present Value." Accessed Oct 25, 2021.