5/21/2019 Net Present Value (NPV)
INVESTOPEDIA SMALL BUSINESS
Net Present Value (NPV)
REVIEWED BY WILL KENTON | Updated Apr 24, 2019
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.
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The following formula is used to calculate NPV:
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n
Rt
NPV = ∑
t=1
(1 + i)t
where:
Rt = net cash inflow-outflows during a single period t
i = discount rate or return that could be earned in alternative investments
t = number of timer periods
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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
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,
calculators, or Investopedia’s own NPV calculator.
00:22 / 00:22
Understanding Net Present Value
Breaking Down Net Present Value
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
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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%.
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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
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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%.
1
Periodic Rate = ((1 + 0.08) 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.
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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.
60 25,00060
N P V = −$1, 000, 000 + ∑t=1 (1+0.0064)60
That formula can be simplified to the following calculation:
N P V = −$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
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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 thatAdvertisement
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.
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Related Terms
Net Present Value Rule
The net present value rule (NPV) states that an investment should be accepted if the NPV is greater than
zero, and it should be rejected otherwise. more
What the Internal Rate of Return – IRR Measures
The internal rate of return (IRR) is a metric used in capital budgeting to estimate the profitability of
potential investments. more
How the Modified Internal Rate of Return Works
While the internal rate of return (IRR) assumes that the cash flows from a project are reinvested at the IRR,
the modified internal rate of return (MIRR) assumes that positive cash flows are reinvested at the firm's
cost of capital, and the initial outlays are financed at the firm's financing cost. more
How to Include the Benefit of Interest in Present Value Calculations
The adjusted present value is the net present value (NPV) of a project or company, if financed solely by
equity, plus the present value (PV) of any financing benefits, which are the additional effects of debt.
more
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The Hurdle Rate Explained
A hurdle rate is the minimum rate of return on a project or investment required by a manager or investor.
Hurdle rates allow companies to make important decisions on whether to pursue a specific project. more
How to Calculate Present Value, and Why Investors Need to Know It
Present value is the concept that states an amount of money today is worth more than that same amount
in the future. In other words, money received in the future is not worth as much as an equal amount
received today. more
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