Key Concepts and Skills
Chapter 8 • Understand the payback rule and its
shortcomings
• Understand accounting rates of return and
their problems
Net Present Value • Understand the internal rate of return and
and Other its strengths and weaknesses
Investment Criteria
• Understand the net present value rule and
why it is the best decision criteria
Chapter Outline Good Decision Criteria
• Net Present Value • We need to ask ourselves the following
• The Payback Rule questions when evaluating decision
• The Average Accounting Return criteria
– Does the decision rule adjust for the time
• The Internal Rate of Return value of money?
• The Profitability Index – Does the decision rule adjust for risk?
• The Practice of Capital Budgeting – Does the decision rule provide information on
whether we are creating value for the firm?
Project Example Information Net Present Value
• You are looking at a new project and • The difference between the market
you have estimated the following cash value of a project and its cost
flows: • How much value is created from
– Year 0: CF = -165,000 undertaking an investment?
– Year 1: CF = 63,120; NI = 13,620 – The first step is to estimate the expected
– Year 2: CF = 70,800; NI = 3,300 future cash flows.
– Year 3: CF = 91,080; NI = 29,100 – The second step is to estimate the required
– Average Book Value = 72,000 return for projects of this risk level.
• Your required return for assets of this – The third step is to find the present value of
the cash flows and subtract the initial
risk is 12%. investment.
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NPV Decision Rule Computing NPV for the Project
• If the NPV is positive, accept the • Using the formulas:
project – NPV = 63,120/(1.12) + 70,800/(1.12)2 +
• A positive NPV means that the project is 91,080/(1.12)3 – 165,000 = $12,627.41
expected to add value to the firm and will • Using the calculator:
therefore increase the wealth of the – CF0 = -165,000; C01 = 63,120; F01 = 1; C02
owners. = 70,800; F02 = 1; C03 = 91,080; F03 = 1;
NPV; I = 12; CPT NPV = 12,627.41
• Since our goal is to increase owner
wealth, NPV is a direct measure of how • Do we accept or reject the project?
well this project will meet our goal.
Decision Criteria Test - NPV Payback Period
• Does the NPV rule account for the time • How long does it take to get the initial cost
value of money? back in a nominal sense?
• Does the NPV rule account for the risk of • Computation
the cash flows? – Estimate the cash flows
• Does the NPV rule provide an indication – Subtract the future cash flows from the initial
about the increase in value? cost until the initial investment has been
recovered
• Should we consider the NPV rule for our
primary decision criteria? • Decision Rule – Accept if the payback
period is less than some preset limit
Computing Payback For the
Decision Criteria Test - Payback
Project
• Assume we will accept the project if it pays • Does the payback rule account for the
back within two years. time value of money?
– Year 1: 165,000 – 63,120 = 101,880 still to recover
• Does the payback rule account for the risk
– Year 2: 101,880 – 70,800 = 31,080 still to recover
of the cash flows?
– Year 3: 31,080 – 91,080 = -60,000 project pays back
during year 3 • Does the payback rule provide an
– Payback = 2 years + 31,080/91,080 = 2.34 years indication about the increase in value?
• Do we accept or reject the project? • Should we consider the payback rule for
our primary decision criteria?
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Advantages and Disadvantages
Average Accounting Return
of Payback
• Advantages • Disadvantages • There are many different definitions for
– Easy to understand – Ignores the time value average accounting return
– Adjusts for uncertainty of money • The one used in the book is:
of later cash flows – Requires an arbitrary
cutoff point – Average net income / average book value
– Biased towards
liquidity – Ignores cash flows – Note that the average book value depends on
beyond the cutoff date how the asset is depreciated.
– Biased against long- • Need to have a target cutoff rate
term projects, such as
research and • Decision Rule: Accept the project if the
development, and new AAR is greater than a preset rate.
projects
Computing AAR For the Project Decision Criteria Test - AAR
• Assume we require an average accounting • Does the AAR rule account for the time
return of 25% value of money?
• Average Net Income: • Does the AAR rule account for the risk of
($13,620 + 3,300 + 29,100) / 3 = $15,340 the cash flows?
• AAR = $15,340 / 72,000 = .213 = 21.3% • Does the AAR rule provide an indication
• Do we accept or reject the project? about the increase in value?
• Should we consider the AAR rule for our
primary decision criteria?
Advantages and Disadvantages
Internal Rate of Return
of AAR
• Disadvantages
• Advantages • This is the most important alternative to
– Not a true rate of
– Easy to calculate return; time value of NPV
– Needed information money is ignored
will usually be • It is often used in practice and is intuitively
– Uses an arbitrary
available benchmark cutoff appealing
rate • It is based entirely on the estimated cash
– Based on accounting flows and is independent of interest rates
net income and book
values, not cash found elsewhere
flows and market
values
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IRR – Definition and Decision
Computing IRR For the Project
Rule
• Definition: IRR is the return that makes the • If you do not have a financial calculator,
NPV = 0 then this becomes a trial-and-error
• Decision Rule: Accept the project if the process
IRR is greater than the required return • Calculator
Enter the cash flows as you did with NPV
Press IRR and then CPT
IRR = 16.13% > 12% required return
• Do we accept or reject the project?
NPV Profile For the Project Decision Criteria Test - IRR
IRR = 16.13%
70,000 • Does the IRR rule account for the time
60,000
50,000
value of money?
40,000 • Does the IRR rule account for the risk of
30,000
NPV
20,000
the cash flows?
10,000 • Does the IRR rule provide an indication
0
-10,000 about the increase in value?
-20,000
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
• Should we consider the IRR rule for our
Discount Rate primary decision criteria?
Summary of Decisions For the
Advantages of IRR
Project
• Knowing a return is intuitively appealing Summary
• It is a simple way to communicate the
value of a project to someone who doesn’t Net Present Value Accept
know all the estimation details
Payback Period Reject
• If the IRR is high enough, you may not
need to estimate a required return, which Average Accounting Return Reject
is often a difficult task
Internal Rate of Return Accept
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IRR and Nonconventional Cash
NPV vs. IRR
Flows
• NPV and IRR will generally give us the • When the cash flows change signs more
same decision than once, there is more than one IRR
• Exceptions • When you solve for IRR, you are solving
– Nonconventional cash flows – cash flow signs for the root of an equation and when you
change more than once cross the x-axis more than once, there will
– Mutually exclusive projects be more than one return that solves the
• Initial investments are substantially different equation
• Timing of cash flows is substantially different
• If you have more than one IRR, which one
do you use to make your decision?
Another Example –
NPV Profile
Nonconventional Cash Flows
IRR = 10.11% and 42.66%
• Suppose an investment will cost $90,000 $4,000.00
initially and will generate the following $2,000.00
cash flows: $0.00
($2,000.00)
NPV
– Year 1: $132,000
($4,000.00)
– Year 2: $100,000 ($6,000.00)
– Year 3: -$150,000 ($8,000.00)
• The required return is 15%. ($10,000.00)
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55
• Should we accept or reject the project? Discount Rate
IRR and Mutually Exclusive
Summary of Decision Rules
Projects
• The NPV is positive at a required return of • Mutually exclusive projects
15%, so you should Accept – If you choose one, you can’t choose the other
• If you use the financial calculator, you – Example: You can choose to attend graduate
school next year at either Harvard or Stanford,
would get an IRR of 10.11% which would
but not both
tell you to Reject
• Intuitively, you would use the following
• You need to recognize that there are decision rules:
nonconventional cash flows, and that you – NPV – choose the project with the higher NPV
need to look at the NPV profile – IRR – choose the project with the higher IRR
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Example With Mutually
NPV Profiles
Exclusive Projects
IRR for A = 19.43%
Period Project Project The required $160.00
$140.00
IRR for B = 22.17%
A B return for both $120.00 Crossover Point = 11.8%
0 -500 -400 projects is 10%. $100.00
$80.00
NPV
A
$60.00
1 325 325 $40.00
B
$20.00
2 325 200 Which project $0.00
should you ($20.00)
IRR 19.43% 22.17% accept and why? ($40.00)
0 0.05 0.1 0.15 0.2 0.25 0.3
NPV 64.05 60.74 Discount Rate
Modified Internal Rate of Return
Conflicts Between NPV and IRR (MIRR)
• NPV directly measures the increase in
value to the firm • Compute IRR of modified cash flows
• Controls for some problems with IRR
• Whenever there is a conflict between • Discounting Approach – Discount future
NPV and another decision rule, you outflows to present and add to CF0
should always use NPV • Reinvestment Approach - Compound all CFs
except the first one forward to end
• IRR is unreliable in the following • Combination Approach – Discount outflows to
situations present; compound inflows to end
– Non-conventional cash flows • MIRR will be a unique number for each
method, but is difficult to interpret;
– Mutually exclusive projects discount/compound rate is externally supplied
Example: MIRR Profitability Index
• Project cash flows: • Measures the benefit per unit cost, based
• Time 0: -$500 today; Time 1: + $1,000; on the time value of money
Time 2: -$100 • A profitability index of 1.1 implies that for
• Use combined method and RRR = 11% every $1 of investment, we receive $1.10
• PV (outflows) = -$500 + -$100/(1.11)2 = worth of benefits, so we create an
-$581.16 additional $0.10 in value
• FV (inflow) = $1,000 x 1.11 = $1,110 • This measure can be very useful in
• MIRR: N=2; PV=-581.16; FV=1,110; CPT situations in which we have limited capital
I/Y = MIRR = 38.2%
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Advantages and Disadvantages
Capital Budgeting In Practice
of Profitability Index
• Advantages • Disadvantages • We should consider several investment
– Closely related to – May lead to incorrect criteria when making decisions
NPV, generally leading decisions in
to identical decisions comparisons of • NPV and IRR are the most commonly
– Easy to understand mutually exclusive used primary investment criteria
and communicate investments
• Payback is a commonly used secondary
– May be useful when
available investment investment criteria
funds are limited
Quick Quiz Comprehensive Problem
• Consider an investment that costs $100,000 and
has a cash inflow of $25,000 every year for 5 • An investment project has the following cash
years. The required return is 9% and the required
flows: CF0 = -1,000,000; C01 – C08 = 200,000
payback is 4 years.
each
– What is the payback period?
– What is the NPV? • If the required rate of return is 12%, what
– What is the IRR?
decision should be made using NPV?
– Should we accept the project? • How would the IRR decision rule be used for this
• What should be the primary decision method? project, and what decision would be reached?
• When is the IRR rule unreliable? • How are the above two decisions related?
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