Lecture 5 (Chapter 9)
Investment Criteria
•
•
•
Up to now, we have analyzed how to finance a firm (capital
structure)
Today we switch to analyzing what to do with the money once
we’ve got it (capital budgeting / investment decisions)
– Focus on real assets rather than financial assets
– Continue to use discounted cash flow as primary tool
Tasks for today:
1. Calculate the net present value of an investment and apply the
NPV decision rule
2. Learn about some “rules of thumb”, such as the payback rule,
accounting return, and the profitability index
3. Calculate the Internal rate of return (IRR) and relate it to the
NPV
Lecture 5: Investement Criteria
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Some Problems
• Consider the following three possible investments, each
with a discount rate of 10%:
– Movie: $1 million to build a mega-movie-theater. You plan to
operate this theater for three years, earning $200,000 each year,
and you believe that you can sell the theater for $500,000 at the
end of the third year.
– Restaurant: A fast-food restaurant for $500,000, which will earn
you profits of $75,000 for each of the next 30 years.
– Mine: A gold mine that will cost $4 million to construct and will
yield profits of $3 million a year for four years. At the end of the
fifth year, a $9 million charge for environmental cleanup is
expected
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Net Present Value (NPV)
• Definition: Present value of future cash flows discounted at
the opportunity cost of capital minus (net of) the initial
investment.
• Intuitive definitions of NPV:
– Change in the firm’s value from investing in the project
– Change in shareholders wealth from investing in the project
– Amount that an outside investor would be willing to pay for the
opportunity to carry-out the project
• Since our job as a manager is to increase the wealth of
shareholders, the NPV shows us exactly how well we are
doing.
• It is also a simple application of what we learned about
present value, so it is easy to calculate.
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NPV Examples
• NPV of the movie theater project
• NPV of the restaurant project
• NPV of the mine
• Which projects should we take?
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Four Steps in Using NPV
1.
Forecast the project cash flows.
2.
Estimate the opportunity cost of capital (the discount rate).
3.
Use the opportunity cost of capital to discount the future cash
flows.
4.
Apply the NPV decision rule: subtract the initial outlay from the
present value of the forecasted cash flows from step 3. If NPV
> 0, accept the project.
Rationale: if the project’s NPV at the opportunity cost of capital is
positive, the project adds value to the firm.
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Payback Rule
• Payback period
Length of time before the initial investment in the project is
recovered.
• Payback rule
A project should be accepted if its payback period is less
than a specified cutoff period.
• What is the payback period for
– Movie theater
– Restaurant
– Mine
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3
Payback Period Rule
Advantages
Disadvantages
– Easy to understand;
– Ignores time value of
money;
– Adjusts for uncertainty of
later cash flows;
– Requires an arbitrary cutoff
point;
– Biased towards liquidity.
– Ignores cash flows beyond
the cut-off date;
– Biased against long-term
project, such as research
and development, and new
projects.
– Works only for
“conventional” projects
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Discounted Payback Rule
• The discounted payback period: The amount of time (i.e.
number of years) until discounted net cash flows to exceed the initial
investment.
• Decision rule: An investment is acceptable if its discounted
payback is less than some prespecified number of years
• Example: What is the discounted payback period for the
restaurant?
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Discounted Payback Period Rule
Advantages
– Includes time value of money;
– Easy to understand;
– Does not accept negative
estimated NPV;
– Biased towards liquidity.
Disadvantages
– May reject positive NPV
investments;
– Requires an arbitrary cut-off
point;
– Ignores cash flows beyond the
cut-off date;
– Biased against long-term
project, such as research and
development, and new
projects.
– Works only for “conventional”
projects
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Average Accounting Return Rule
• Average accounting return (AAR): An investment’s average
net income divided by it’s average book value
• Decision rule: An investment is acceptable if its average
accounting return exceeds a target average accounting return
• Example
•
What is the AAR for a project that requires an initial investment in
machinery of $15 million? The machinery will be fully depreciated
over the project’s life of 5 years. The new machinery will generate
additional net income of $2 million the first year, $5 million the
second and third and $3 million in each of the following years.
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Average Accounting Return Rule
Advantages
Disadvantages
– Easy to calculate;
– Needed information usually
available.
– Not a true rate of return;
time value of money
ignored;
– Uses an arbitrary
benchmark cut-off point;
– Based on accounting
(book) values, not cash
flows and market values.
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Internal Rate of Return
• Internal rate of return (IRR): The discount rate that makes
the NPV of an investment zero
• Decision rule: An investment is acceptable if its IRR exceeds
the required return. It should be rejected otherwise.
•
Intuition is that when IRR > r, our money grows fasters in this
project than in our best alternative (opportunity cost)
•
This looks different from the NPV rule, but it should give the same
decisions.
• IRR > r means that NPV > 0
•
Remember: IRR is specific to the project and should not be
confused with r. r depends on what you have to give up to
undertake the project.
Ø IRR is the r which makes NPV = 0
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IRR Example
•
What is the IRR of the movie theater project?
− 1,000 +
•
200
200
700
+
+
=0
2
(1 + IRR ) (1 + IRR ) (1 + IRR ) 3
As always, when trying to find a rate, we need to either use trial and
error, or we need to use a calculator/computer
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Problems with IRR
• IRR and NPV decision rules will lead to identical
decisions if:
– project cash flows are ‘conventional’;
– project is independent.
• Problems when cash flows are non-conventional:
– The problem is that the NPV graph’s slope may change several
times, causing it to intersect the NPV = 0 axis in several places.
• For this to happen, the cashflow must change sign multiple
times. (e.g. decommissioning costs, multi-stage project.)
• Solution: None. Must use NPV rule.
• Example: Find the IRR of the Mine project.
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Problems with IRR: Mutually Exclusive
Investments
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•
Example:
Choose one of these two riskless investments:
– Invest $1,000 today, get $4,000 in one year (IRR=300%)
– Invest $1,000,000 today, get $1,500,000 in one year (IRR=50%)
•
IRR ranks the first higher than the second, but fails to take account of
size. We’d rather make $500,000 than $3,000 in profit next year.
•
•
•
Example:
Given $1 million to invest and a 7.5% discount rate, which riskless
investment would you prefer?
– one which pays $2 million after 1 year (IRR=100%)
– one which pays $300,000 per year, forever (IRR=30%)
•
We know how to value these two cashflows:
The first is worth $2,000,000 / 1.075 = $1,860,465
The second is worth $300,000 / 0.075 = $4,000,000
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Mutually Exclusive Investments
Net present value
Project A
Project B
0
Discount rate
IRR A
IRR B
• Consider projects A and B.
• for low discount rates, NPVA is higher than NPVB.
• for high discount rates, NPVB is higher than NPVA.
•
Possible solution: Find IRR of incremental cashflows (change
between projects.
•
Better solution: Use NPV
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IRR Rule
Advantages
Disadvantages
– Closely related to NPV,
generally leading to identical
decisions;
– Easy to understand and
communicate.
– May result in multiple answers
or no answer with nonconventional cash flows;
– May lead to incorrect
decisions in comparisons of
mutually exclusive
investments.
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Profitability Index (PI)
• Definition : The PV of an investment’s expected cash flows
divided by its initial cost. Also referred to as the benefit cost ratio.
• Decision rule
– An investment is acceptable if its PI is greater than one. It is
unacceptable if its PI is less than one. Investors are indifferent between
accepting and rejecting the project if its PI is equal to one.
• Example
– PI of Movie theater:
– PI of Restaurant:
– PI of Mine:
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Profitability Index Rule
•Advantages
• Disadvantages
– Closely related to NPV,
generally leading to identical
decisions;
– May lead to incorrect
decisions in comparisons of
mutually exclusive
investments.
– Easy to understand and
communicate;
– May be useful when available
investment funds are limited.
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What we know now
• Net Present Value (NPV)
– Primary investment criteria
– Shows the increase in stockholder wealth from an investment
– Requires cashflows and an opportunity cost of capital
• Other Investment Criteria
– Payback, Discounted Payback, Average Accounting Return,
Profitability Index
• Understand how to use them and their advantages and
disadvantages, but always use NPV when possible
– Internal Rate of Return
• Use sparingly, and only for conventional, non-exclusive projects
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