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 the current value of a future stream of payments.

Key Takeaways

  • Net present value, or NPV, is used to calculate the current value of a future stream of payments from a company, project, or investment.
  • To calculate NPV, you need to estimate the timing and amount of future cash flows and pick a discount rate equal to the minimum acceptable rate of return.
  • The discount rate may reflect your cost of capital or the returns available on alternative investments of comparable risk.
  • If the NPV of a project or investment is positive, it means its rate of return will be above the discount rate.
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Understanding Net Present Value

Net Present Value (NPV) Formula

If there’s one cash flow from a project that will be paid one year from now, then the calculation for the NPV is as follows:

N P V = Cash flow ( 1 + i ) t initial investment where: i = Required return or discount rate t = Number of time 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 flowinitial investmentwhere:i=Required return or discount ratet=Number of time periods

If analyzing a longer-term project with multiple cash flows, then the formula for the NPV of a project is as follows:

N P V = t = 0 n R t ( 1 + i ) t where: R t = net cash inflow-outflows during a single period  t i = discount rate or return that could be earned in alternative investments t = number of time 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 cash inflow-outflows during a single period ti=discount rate or return that could be earned in alternative investmentst=number of time periods

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

N P V = Today’s value of the expected cash flows Today’s value of invested cash NPV = \text{Today’s value of the expected cash flows} - \text{Today’s value of invested cash} NPV=Today’s value of the expected cash flowsToday’s value of invested cash

What Net Present Value Can Tell You

NPV accounts for the time value of money and can be used to compare the rates of return of different projects, or to compare a projected rate of return with the hurdle rate required to approve an investment. The time value of money is represented in the NPV formula by the discount rate, which might be a hurdle rate for a project based on a company's cost of capital. No matter how the discount rate is determined, a negative NPV shows the expected rate of return will fall short of it, meaning the project will not create value.

In the context of evaluating corporate securities, the net present value calculation is often called discounted cash flow (DCF) analysis. It's the method Warren Buffett uses to compare the net present value of a company's discounted future cash flows with its current price.

The discount rate is central to the formula. It accounts for the fact that, so long as interest rates are positive, a dollar today is worth more than a dollar in the future. Inflation erodes the value of money over time. Meanwhile, today's dollar can be invested in a safe asset like government bonds; investments riskier than Treasuries must offer a higher rate of return. However it's determined, the discount rate is simply the baseline rate of return that a project must exceed to be 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 might be worthwhile if comparable investments of equal risk offered less over the same period.

If, on the other hand, an investor could earn 8% with no risk over the next year, the offer of $105 in a year would not suffice. 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—discounted for their present value—exceed the anticipated costs, also in today's 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 says only investments with a positive NPV should be considered.

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

How To Calculate NPV Using Excel

In Excel, there is a NPV function that can be used to easily calculate the net present value of a series of cash flows. The NPV function in Excel is simply NPV, and the full formula requirement is:

=NPV(discount rate, future cash flow) + initial investment

NPV Example
NPV Example, Excel.

In the example above, the formula entered into the gray NPV cell is:

=NPV(green cell, yellow cells) + blue cell

= NPV(C3, C6:C10) + C5

Example of Calculating Net Present Value

Imagine a company can invest in equipment that would cost $1 million and is expected to generate $25,000 a month in revenue for five years. Alternatively, the company could invest that money in securities with an expected annual return of 8%. Management views the equipment and securities as comparable investment risks.

There are two key steps for calculating the NPV of the investment in equipment:

Step 1: NPV of the initial investment

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 the immediate expenditure of $1 million doesn’t need to be discounted.

Step 2: NPV of future cash flows

  • Identify the number of periods (t): The equipment is expected to generate monthly cash flow for five years, which means there will be 60 periods included in the calculation after multiplying the number of years of cash flows by the number of months in a year.
  • Identify the discount rate (i): The alternative investment is expected to return 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, compound rate. Using the following formula, we find that the periodic monthly compound rate is 0.64%.

Periodic Rate = ( ( 1 + 0.08 ) 1 12 ) 1 = 0.64 % \text{Periodic Rate} = (( 1 + 0.08)^{\frac{1}{12}}) - 1 = 0.64\% Periodic Rate=((1+0.08)121)1=0.64%

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

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.

N P V = $ 1 , 000 , 000 + t = 1 60 25 , 00 0 60 ( 1 + 0.0064 ) 60 NPV = -\$1,000,000 + \sum_{t = 1}^{60} \frac{25,000_{60}}{(1 + 0.0064)^{60}} NPV=$1,000,000+t=160(1+0.0064)6025,00060

That formula can be simplified to the following calculation:

N P V = $ 1 , 000 , 000 + $ 1 , 242 , 322.82 = $ 242 , 322.82 NPV = -\$1,000,000 + \$1,242,322.82 = \$242,322.82 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 would not have made sense.

Limitations of Net Present Value

A notable limitation of NPV analysis is that it makes assumptions about future events that may not prove correct. The discount rate value used is a judgment call, while the cost of an investment and its projected returns are necessarily estimates. The net present value calculation is only as reliable as its underlying assumptions.

The NPV formula yields a dollar result which, though easy to interpret, may not tell the entire story. Consider the following two investment options: Option A with an NPV of $100,000 or Option B with an NPV of $1,000.

NPV Formula

Pros
  • Considers the time value of money

  • Incorporates discounted cash flow using a company's cost of capital

  • Returns a single dollar value that is relatively easy to interpret

  • May be easy to calculate when leveraging spreadsheets or financial calculators

Cons
  • Relies heavily on inputs, estimates, and long-term projections

  • Doesn't consider project size or ROI

  • May be hard to calculate manually, especially for projects with many years of cash flow

  • Is driven by quantitative inputs and does not consider non-financial metrics

Net Present Value vs. Payback Period

Easy call, right? How about if Option A requires an initial investment of $1 million, while Option B will only cost $10? The extreme numbers in the example make a point. The NPV formula doesn't evaluate a project's return on investment (ROI), a key consideration for anyone with finite capital. Though the NPV formula estimates how much value a project will produce, it doesn't tell you whether it is an efficient use of your investment dollars.

The payback period, or payback method, is a simpler alternative to NPV. The payback method calculates how long it will take to recoup an investment. One drawback of this method is that it fails to account for the time value of money. For this reason, payback periods calculated for longer-term investments have a greater potential for inaccuracy.

Moreover, the payback period calculation does not concern itself with what happens once the investment costs are nominally recouped. An investment’s rate of return can change significantly over time. Comparisons using payback periods assume otherwise.

NPV vs. Internal Rate of Return (IRR)

The internal rate of return (IRR) is calculated by solving the NPV formula for the discount rate required to make NPV equal zero. This method can be used to compare projects of different time spans on the basis of their projected return rates.

For example, IRR could be used to compare the anticipated profitability of a three-year project with that of a 10-year one. Although the IRR is useful for comparing rates of return, it may obscure the fact that the rate of return on the three-year project is only available for three years, and may not be matched once capital is reinvested.

What Does the Net Present Value Mean?

Net present value (NPV) is a financial metric that seeks to capture the total value of an 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,” indicating the project is worthwhile. In practice, since estimates used in the calculation are subject to error many planners will set a higher bar for NPV to give themselves an additional margin of safety.

Why Are Future Cash Flows Discounted?

NPV uses discounted cash flows to account for the time value of money. So long as interest rates are positive, a dollar today is worth more than a dollar tomorrow because a dollar today can earn an extra day's worth of interest. Even if future returns can be projected with certainty they must be discounted for the fact time must pass before they're realized, time during which a comparable sum could earn interest.

Article Sources
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  1. Harvard Business Review. "A Refresher on Net Present Value."

  2. YouTube. "Warren Buffett, Chairman, Berkshire Hathaway Investment Group. Terry Leadership Speaker Series."

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