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Capital Budgeting > Net Present Value
Net Present Value
• Defining NPV
• Calculating the NPV
• Interpreting the NPV
• Advantages of the NPV method
• Disadvantages of the NPV method
• NPV Profiles
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Capital Budgeting > Net Present Value
Defining NPV
• Because of the time value of money, cash inflows and outflows only can be
compared at the same point in time.
• NPV discounts each inflow and outflow to the present, and then sums them to see
how the value of the inflows compares to the other.
• A positive NPV means the investment is worthwhile, an NPV of 0 means the
inflows equal the outflows, and a negative NPV means the investment is not good
for the investor.
Airplane
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Capital Budgeting > Net Present Value
Calculating the NPV
• Cash inflows have a positive sign, while cash outflows are negative.
• To find the NPV accurately, the investor must know the exact size and time of
occurrence of each cash flow. This is easy to find for some investments (like
bonds), but more difficult for others (like industrial machinery).
• Investors use different rates for their discount rate such as using the weighted
average cost of capital, variable rates, and reinvestment rate.
Net Present Value (NPV) Formula
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Capital Budgeting > Net Present Value
Interpreting the NPV
• When inflows exceed outflows and they are discounted to the present, the NPV is
positive. The investment adds value for the investor. The opposite is true when
NPV is negative.
• A NPV of 0 means there is no change in value from the investment.
• In theory, investors should invest when the NPV is positive and it has the highest
NPV of all available investment options.
• In practice, determining NPV depends on being able to accurately determine the
inputs, which is difficult.
Machinery
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Capital Budgeting > Net Present Value
Advantages of the NPV method
• When NPV is positive, it adds value to the firm. When it is negative, it subtracts
value. An investor should never undertake a negative NPV project.
• As long as all options are discounted to the same point in time, NPV allows for
easy comparison between investment options. The investor should undertake the
investment with the highest NPV, provided it is possible.
• An advantage of NPV is that the discount rate can be customized to reflect a
number of factors, such as risk in the market.
NPV Decision Table
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Capital Budgeting > Net Present Value
Disadvantages of the NPV method
• NPV is based on future cash flows and the discount rate, both of which are hard
to estimate with 100% accuracy.
• There is an opportunity cost to making an investment which is not built into the
NPV calculation.
• Other metrics, such as internal rate of return, are needed to fully determine the
gain or loss of an investment.
Medicine
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Capital Budgeting > Net Present Value
NPV Profiles
• The NPV Profile is a graph with the discount rate on the x-axis and the NPV of the
investment on the y-axis.
• Higher discount rates mean cash flows that occur sooner are more influential to
NPV. Since the earlier payments tend to be the outflows, the NPV profile
generally shows an inverse relationship between the discount rate and NPV.
• The discount rate at which the NPV equals 0 is called the internal rate of return
(IRR).
NPV Profile
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Appendix
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Capital Budgeting
Key terms
• cash flow The sum of cash revenues and expenditures over a period of time.
• cash flow The sum of cash revenues and expenditures over a period of time.
• cash inflow Cash that is received by the investor. For example, dividends paid on a stock owned by the investor is a cash
inflow.
• cash outflow Any cash that is spent or invested by the investor.
• discount rate The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to
decrease the amounts of future cash flow to yield their present value.
• discount rate The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to
decrease the amounts of future cash flow to yield their present value.
• gain (or loss) If an investment earns more value than it costs, the difference is the gain. If it costs more than it earns, the
difference is a loss.
• internal rate of return IRR. The rate of return on an investment which causes the net present value of all future cash flows to be
zero.
• Opportunity cost The cost of an opportunity forgone (and the loss of the benefits that could be received from that opportunity);
the most valuable forgone alternative.
• variable something whose value may be dictated or discovered.
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Capital Budgeting
NPV Profile
The NPV Profile graphs how NPV changes as the discount rate used changes.
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Wikipedia. "Internal rate of return." Public domain http://en.wikipedia.org/wiki/Internal_rate_of_return View on Boundless.com
Capital Budgeting
Net Present Value (NPV) Formula
NPV is the sum of of the present values of all cash flows associated with a project. The business will receive regular payments, represented by variable
R, for a period of time. This period of time is expressed in variable t. The payments are discounted using a selected interest rate, signified by the i
variable.
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Wikipedia. "Net present value." GNU FDL http://en.wikipedia.org/wiki/Net_present_value View on Boundless.com
Capital Budgeting
Airplane
Before purchasing a new airplane, airlines evaluate the NPV of the plan by calculating the PV of the revenue it can earn from it and the PV of its cost
(e.g., purchase cost, maintenance, fuel, etc. ).
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Viewology. "Pictures: AirAsia 9M-AFY Airbus A320-216 Airplane Arriving/Departing at Penang Airport – Viewology.Net." CC BY-SA http://viewology.net/picturesairasia-9m-afy-airbus-a320-216-airplane-arrivingdeparting-at-penang-airport/768/ View on Boundless.com
Capital Budgeting
Medicine
Drug developers must try to calculate the future revenues of a drug in order to find the NPV to determine if it is worth the cost of development.
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Flickr. "Pills.| Flickr - Photo Sharing!." CC BY http://www.flickr.com/photos/59334544@N00/2322167178/ View on Boundless.com
Capital Budgeting
Machinery
Being able to accurately find the NPV of a piece of machinery means having a good idea when all costs are going to occur (when it will need fixing) and
when it will generate revenue (when it will be used on a job).
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Fotopedia. "Liebherr R 317 by Alexandre Prévot in Heavy equipment, Hydraulic machinery, Liebherr Group on Fotopedia - Images for Humanity." CC BY-SA
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Capital Budgeting
NPV Decision Table
NPV simply and clearly shows whether a project adds value to the firm or not. It's easy of use in decision making is one of its advantages.
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Wikipedia. "Net present value." GNU FDL http://en.wikipedia.org/wiki/Net_present_value View on Boundless.com
Capital Budgeting
Which of the following is a correct definition of Net Present Value.
A) The sum of the present values of all a project's revenues and
expenses.
B) All of these answers.
C) NPV = PVinflows + PVoutflows
D) A means of evaluating a project's profitability.
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Capital Budgeting
Which of the following is a correct definition of Net Present Value.
A) The sum of the present values of all a project's revenues and
expenses.
B) All of these answers.
C) NPV = PVinflows + PVoutflows
D) A means of evaluating a project's profitability.
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Capital Budgeting
When evaluating the cash flows from a project, a financial
manager needs to analyze the:
A) costs, benefits, and opportunity costs of the project.
B) The costs of the project
C) The benefits of the project
D) The costs and benefits of the project
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Capital Budgeting
When evaluating the cash flows from a project, a financial
manager needs to analyze the:
A) costs, benefits, and opportunity costs of the project.
B) The costs of the project
C) The benefits of the project
D) The costs and benefits of the project
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Saylor OER. "Business Administration « Saylor.org – Free Online Courses Built by Professors." CC BY 3.0
http://www.saylor.org/majors/Business/
Capital Budgeting
The net present value can be:
A) Positive, Zero, or Negative
B) Positive
C) Negative
D) Zero
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Capital Budgeting
The net present value can be:
A) Positive, Zero, or Negative
B) Positive
C) Negative
D) Zero
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Saylor OER. "Business Administration « Saylor.org – Free Online Courses Built by Professors." CC BY 3.0
http://www.saylor.org/majors/Business/
Capital Budgeting
A company is considering a project that has a discount rate of 5%.
In the first year, it will have -$100,000 in cash flows. In year 2, it
will have cash flows of $100,000, and in year 3 the project will
generate $200,000. What is the project's NPV?
A) $358,708
B) $190,476
C) $193,204
D) $168,232
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Capital Budgeting
A company is considering a project that has a discount rate of 5%.
In the first year, it will have -$100,000 in cash flows. In year 2, it
will have cash flows of $100,000, and in year 3 the project will
generate $200,000. What is the project's NPV?
A) $358,708
B) $190,476
C) $193,204
D) $168,232
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Capital Budgeting
The sum of cash revenues and expenditures over a period of
time.
A) Cash
B) Assets
C) Account Receivables
D) Cash Flow
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Capital Budgeting
The sum of cash revenues and expenditures over a period of
time.
A) Cash
B) Assets
C) Account Receivables
D) Cash Flow
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Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com/
Capital Budgeting
Under the present value concept, a lottery winner would rather
receive:
A) $10,000 per year for the next 5 years than receive $50,000 today.
B) $10,000 per year for the next 5 years than receive $40,000 today.
C) None of these, as the best answer depends on the interest rate that
the lottery winner faces.
D) $10,000 per year for the next 5 years than receive $30,000 today.
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Capital Budgeting
Under the present value concept, a lottery winner would rather
receive:
A) $10,000 per year for the next 5 years than receive $50,000 today.
B) $10,000 per year for the next 5 years than receive $40,000 today.
C) None of these, as the best answer depends on the interest rate that
the lottery winner faces.
D) $10,000 per year for the next 5 years than receive $30,000 today.
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Saylor OER. "Business Administration « Saylor.org – Free Online Courses Built by Professors." CC BY 3.0 http://www.saylor.org/majors/Business/
Capital Budgeting
Each choice listed below represents a net present value of a
potential project. If you were a CFO of a company which project
would you choose?
A) NPV = $500,000
B) NPV = $200,000
C) NPV = $0
D) NPV = -$100,000
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Capital Budgeting
Each choice listed below represents a net present value of a
potential project. If you were a CFO of a company which project
would you choose?
A) NPV = $500,000
B) NPV = $200,000
C) NPV = $0
D) NPV = -$100,000
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Capital Budgeting
Which of the following is an advantage of using the NPV method
to evaluate different projects?
A) All of these answers.
B) It allows for easy comparisons of potential investments.
C) NPV can be customized to reflect the financial concerns and demands
of the company.
D) NPV converts future revenue to current dollars, allowing the company
to quantify a project's value.
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Capital Budgeting
Which of the following is an advantage of using the NPV method
to evaluate different projects?
A) All of these answers.
B) It allows for easy comparisons of potential investments.
C) NPV can be customized to reflect the financial concerns and demands
of the company.
D) NPV converts future revenue to current dollars, allowing the company
to quantify a project's value.
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Capital Budgeting
Which of the following is NOT included in calculating a project's
NPV?
A) All of these answers.
B) The project's opportunity cost.
C) The exact discount rate.
D) The exact amounts of cash flow related to the project.
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Capital Budgeting
Which of the following is NOT included in calculating a project's
NPV?
A) All of these answers.
B) The project's opportunity cost.
C) The exact discount rate.
D) The exact amounts of cash flow related to the project.
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Capital Budgeting
Which of the following reasons is a reason why a higher discount
rate generally means a lower NPV?
A) Most projects do not pay off until years later, and those cash flows are
highly discounted.
B) A higher discount rate emphasizes earlier cash flows, which is when
the expenses are incurred.
C) All of these answers.
D) When the discount rate is large, there are larger differences between
PV and FV for each cash flow.
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Capital Budgeting
Which of the following reasons is a reason why a higher discount
rate generally means a lower NPV?
A) Most projects do not pay off until years later, and those cash flows are
highly discounted.
B) A higher discount rate emphasizes earlier cash flows, which is when
the expenses are incurred.
C) All of these answers.
D) When the discount rate is large, there are larger differences between
PV and FV for each cash flow.
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Capital Budgeting
Attribution
• Wikibooks. "Principles of Finance/Section 1/Chapter 2/Time Value of Money/PV and NPV." CC BY-SA 3.0
http://en.wikibooks.org/wiki/Principles_of_Finance/Section_1/Chapter_2/Time_Value_of_Money/PV_and_NPV#What_NPV_Me
ans
• Wikipedia. "Net present value." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Net_present_value
• Wikispaces. "SU3FINANCE - Chapter 4 - NPV and the Time Value of Money." CC BY-SA
http://su3finance.wikispaces.com/Chapter+4+-+NPV+and+the+Time+Value+of+Money
• Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//finance/definition/cash-outflow
• Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//finance/definition/cash-inflow
• Wikibooks. "Principles of Finance/Section 1/Chapter 2/Time Value of Money/PV and NPV." CC BY-SA 3.0
http://en.wikibooks.org/wiki/Principles_of_Finance/Section_1/Chapter_2/Time_Value_of_Money/PV_and_NPV#What_NPV_Me
ans
• Wikipedia. "Net present value." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Net_present_value
• Wikispaces. "SU3FINANCE - Chapter 4 - NPV and the Time Value of Money." CC BY-SA
http://su3finance.wikispaces.com/Chapter+4+-+NPV+and+the+Time+Value+of+Money
• Wiktionary. "cash flow." CC BY-SA 3.0 http://en.wiktionary.org/wiki/cash+flow
• Wiktionary. "variable." CC BY-SA 3.0 http://en.wiktionary.org/wiki/variable
• Wiktionary. "discount rate." CC BY-SA 3.0 http://en.wiktionary.org/wiki/discount+rate
• Wikibooks. "Principles of Finance/Section 1/Chapter 2/Time Value of Money/PV and NPV." CC BY-SA 3.0
http://en.wikibooks.org/wiki/Principles_of_Finance/Section_1/Chapter_2/Time_Value_of_Money/PV_and_NPV#What_NPV_Me
ans
• Wikipedia. "Net present value." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Net_present_value
• Wikispaces. "BUS304-PrinciplesofFinance - Chapter 7." CC BY-SA http://bus304principlesoffinance.wikispaces.com/Chapter+7
Free to share, print, make copies and changes. Get yours at www.boundless.com
• Wikispaces. "SU3FINANCE - Chapter 4 - NPV and the Time Value of Money." CC BY-SA
Capital Budgeting
• Wiktionary. "discount rate." CC BY-SA 3.0 http://en.wiktionary.org/wiki/discount+rate
• Wikibooks. "Principles of Finance/Section 1/Chapter 2/Time Value of Money/PV and NPV." CC BY-SA 3.0
http://en.wikibooks.org/wiki/Principles_of_Finance/Section_1/Chapter_2/Time_Value_of_Money/PV_and_NPV#What_NPV_Me
ans
• Wikipedia. "Net present value." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Net_present_value
• Wikispaces. "SU3FINANCE - Chapter 4 - NPV and the Time Value of Money." CC BY-SA
http://su3finance.wikispaces.com/Chapter+4+-+NPV+and+the+Time+Value+of+Money
• Boundless Learning. "Boundless." CC BY-SA 3.0 http://www.boundless.com//finance/definition/gain-or-loss
• Wikibooks. "Principles of Finance/Section 1/Chapter 2/Time Value of Money/PV and NPV." CC BY-SA 3.0
http://en.wikibooks.org/wiki/Principles_of_Finance/Section_1/Chapter_2/Time_Value_of_Money/PV_and_NPV#What_NPV_Me
ans
• Wikipedia. "Net present value." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Net_present_value
• Wikispaces. "SU3FINANCE - Chapter 4 - NPV and the Time Value of Money." CC BY-SA
http://su3finance.wikispaces.com/Chapter+4+-+NPV+and+the+Time+Value+of+Money
• Wiktionary. "Opportunity cost." CC BY-SA 3.0 http://en.wiktionary.org/wiki/Opportunity+cost
• Wikispaces. "SU3FINANCE - Chapter 4 - NPV and the Time Value of Money." CC BY-SA
http://su3finance.wikispaces.com/Chapter+4+-+NPV+and+the+Time+Value+of+Money
• Wikipedia. "Net present value." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Net_present_value
• Wikibooks. "Principles of Finance/Section 1/Chapter 2/Time Value of Money/PV and NPV." CC BY-SA 3.0
http://en.wikibooks.org/wiki/Principles_of_Finance/Section_1/Chapter_2/Time_Value_of_Money/PV_and_NPV#What_NPV_Me
ans
• Wiktionary. "cash flow." CC BY-SA 3.0 http://en.wiktionary.org/wiki/cash+flow
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