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CHAPTER
6Some AlternativeInvestment Rules
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Chapter Outline
6.1 Why Use Net Present Value?6.2 The Payback Period Rule6.3 The Discounted Payback Period Rule6.4 The Average Accounting Return6.5 The Internal Rate of Return6.6 Problems with the IRR Approach6.7 The Profitability Index6.8 The Practice of Capital Budgeting6.9 Summary and Conclusions
6.1 Why Use Net Present Value?6.2 The Payback Period Rule6.3 The Discounted Payback Period Rule6.4 The Average Accounting Return6.5 The Internal Rate of Return6.6 Problems with the IRR Approach6.7 The Profitability Index6.8 The Practice of Capital Budgeting6.9 Summary and Conclusions
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6.1 Why Use Net Present Value?
Accepting positive NPV projects benefits shareholders.
NPV uses cash flowsNPV uses all the cash flows of the projectNPV discounts the cash flows properly
Accepting positive NPV projects benefits shareholders.
NPV uses cash flowsNPV uses all the cash flows of the projectNPV discounts the cash flows properly
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The Net Present Value (NPV) Rule
Net Present Value (NPV) = Total PV of future CF’s + Initial Investment
Estimating NPV:1. Estimate future cash flows: how much? and when?2. Estimate discount rate3. Estimate initial costs
Minimum Acceptance Criteria: Accept if NPV > 0Ranking Criteria: Choose the highest NPV
Net Present Value (NPV) = Total PV of future CF’s + Initial Investment
Estimating NPV:1. Estimate future cash flows: how much? and when?2. Estimate discount rate3. Estimate initial costs
Minimum Acceptance Criteria: Accept if NPV > 0Ranking Criteria: Choose the highest NPV
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Good Attributes of the NPV Rule
1. Uses cash flows
2. Uses ALL cash flows of the project
3. Discounts ALL cash flows properly
Reinvestment assumption: the NPV rule assumes that all cash flows can be reinvested at the discount rate.
1. Uses cash flows
2. Uses ALL cash flows of the project
3. Discounts ALL cash flows properly
Reinvestment assumption: the NPV rule assumes that all cash flows can be reinvested at the discount rate.
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6.2 The Payback Period Rule
How long does it take the project to “pay back” its initial investment?
Payback Period = number of years to recover initial costs
Minimum Acceptance Criteria: set by management
Ranking Criteria: set by management
How long does it take the project to “pay back” its initial investment?
Payback Period = number of years to recover initial costs
Minimum Acceptance Criteria: set by management
Ranking Criteria: set by management
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The Payback Period Rule (continued)
Disadvantages:Ignores the time value of moneyIgnores cash flows after the payback periodBiased against long-term projectsRequires an arbitrary acceptance criteriaA project accepted based on the payback criteria may not have a positive NPV
Advantages:Easy to understandBiased toward liquidity
Disadvantages:Ignores the time value of moneyIgnores cash flows after the payback periodBiased against long-term projectsRequires an arbitrary acceptance criteriaA project accepted based on the payback criteria may not have a positive NPV
Advantages:Easy to understandBiased toward liquidity
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6.3 The Discounted PaybackPeriod Rule
How long does it take the project to “pay back” its initial investment taking the time value of money into account?
By the time you have discounted the cash flows, you might as well calculate the NPV.
How long does it take the project to “pay back” its initial investment taking the time value of money into account?
By the time you have discounted the cash flows, you might as well calculate the NPV.
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6.4 The Average Accounting Return Rule
Another attractive but fatally flawed approach.Ranking Criteria and Minimum Acceptance Criteria set by managementDisadvantages:
Ignores the time value of moneyUses an arbitrary benchmark cutoff rateBased on book values, not cash flows and market values
Advantages:The accounting information is usually availableEasy to calculate
Another attractive but fatally flawed approach.Ranking Criteria and Minimum Acceptance Criteria set by managementDisadvantages:
Ignores the time value of moneyUses an arbitrary benchmark cutoff rateBased on book values, not cash flows and market values
Advantages:The accounting information is usually availableEasy to calculate
Investent of ValueBook Average
IncomeNet AverageAAR
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6.5 The Internal Rate of Return (IRR) Rule
IRR: the discount that sets NPV to zero Minimum Acceptance Criteria:
Accept if the IRR exceeds the required return.Ranking Criteria:
Select alternative with the highest IRRReinvestment assumption:
All future cash flows assumed reinvested at the IRR.Disadvantages:
Does not distinguish between investing and borrowing.IRR may not exist or there may be multiple IRR Problems with mutually exclusive investments
Advantages:Easy to understand and communicate
IRR: the discount that sets NPV to zero Minimum Acceptance Criteria:
Accept if the IRR exceeds the required return.Ranking Criteria:
Select alternative with the highest IRRReinvestment assumption:
All future cash flows assumed reinvested at the IRR.Disadvantages:
Does not distinguish between investing and borrowing.IRR may not exist or there may be multiple IRR Problems with mutually exclusive investments
Advantages:Easy to understand and communicate
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The Internal Rate of Return: Example
Consider the following project:Consider the following project:
0 1 2 3
$50 $100 $150
-$200
The internal rate of return for this project is 19.44%
32 )1(
150$
)1(
100$
)1(
50$0
IRRIRRIRRNPV
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The NPV Payoff Profile for This Example
Discount Rate NPV
0% $100.004% $71.048% $47.3212% $27.7916% $11.6520% ($1.74)24% ($12.88)28% ($22.17)32% ($29.93)36% ($36.43)40% ($41.86)
If we graph NPV versus discount rate, we can see the IRR as the x-axis intercept.
IRR = 19.44%
($60.00)
($40.00)
($20.00)
$0.00
$20.00
$40.00
$60.00
$80.00
$100.00
$120.00
-1% 9% 19% 29% 39%
Discount rate
NPV
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6.6 Problems with the IRR Approach
Multiple IRRs.
Are We Borrowing or Lending?
The Scale Problem
The Timing Problem
Multiple IRRs.
Are We Borrowing or Lending?
The Scale Problem
The Timing Problem
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Multiple IRRsThere are two IRRs for this project: There are two IRRs for this project:
0 1 2 3
$200 $800
-$200
- $800
($150.00)
($100.00)
($50.00)
$0.00
$50.00
$100.00
-50% 0% 50% 100% 150% 200%
Discount rate
NP
V
100% = IRR2
0% = IRR1
Which one should we use?
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The Scale Problem
Would you rather make 100% or 50% on your investments?
What if the 100% return is on a $1 investment while the 50% return is on a $1,000 investment?
Would you rather make 100% or 50% on your investments?
What if the 100% return is on a $1 investment while the 50% return is on a $1,000 investment?
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The Timing Problem
0 1 2 3
$10,000 $1,000$1,000
-$10,000
Project A
0 1 2 3
$1,000 $1,000 $12,000
-$10,000
Project B
The preferred project in this case depends on the discount rate, not the IRR.
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The Timing Problem
($4,000.00)
($3,000.00)
($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
$4,000.00
$5,000.00
0% 10% 20% 30% 40%
Discount rate
NP
VProject A
Project B10.55% = crossover rate
16.04% = IRRA12.94% = IRRB
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Calculating the Crossover RateCompute the IRR for either project “A-B” or “B-A”
Year Project A Project B Project A-B Project B-A 0 ($10,000) ($10,000) $0 $01 $10,000 $1,000 $9,000 ($9,000)2 $1,000 $1,000 $0 $03 $1,000 $12,000 ($11,000) $11,000
($3,000.00)
($2,000.00)
($1,000.00)
$0.00
$1,000.00
$2,000.00
$3,000.00
0% 5% 10% 15% 20%
Discount rate
NP
V A-B
B-A
10.55% = IRR
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Mutually Exclusive vs.Independent Project
Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system.
RANK all alternatives and select the best one.
Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.
Must exceed a MINIMUM acceptance criteria.
Mutually Exclusive Projects: only ONE of several potential projects can be chosen, e.g. acquiring an accounting system.
RANK all alternatives and select the best one.
Independent Projects: accepting or rejecting one project does not affect the decision of the other projects.
Must exceed a MINIMUM acceptance criteria.
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6.7 The Profitability Index (PI) Rule
Minimum Acceptance Criteria: Accept if PI > 1
Ranking Criteria: Select alternative with highest PI
Disadvantages:Problems with mutually exclusive investments
Advantages:May be useful when available investment funds are limited
Easy to understand and communicate
Correct decision when evaluating independent projects
Minimum Acceptance Criteria: Accept if PI > 1
Ranking Criteria: Select alternative with highest PI
Disadvantages:Problems with mutually exclusive investments
Advantages:May be useful when available investment funds are limited
Easy to understand and communicate
Correct decision when evaluating independent projects
Investent Initial
FlowsCash Future of PV TotalPI
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6.8 The Practice of Capital Budgeting
Varies by industry:Some firms use payback, others use accounting rate of return.
The most frequently used technique for large corporations is IRR or NPV.
Varies by industry:Some firms use payback, others use accounting rate of return.
The most frequently used technique for large corporations is IRR or NPV.
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Example of Investment Rules
Compute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 10%.
Year Project A Project B
0 -$200 -$150
1 $200 $50
2 $800 $100
3 -$800 $150
Compute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 10%.
Year Project A Project B
0 -$200 -$150
1 $200 $50
2 $800 $100
3 -$800 $150
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Example of Investment Rules
Project A Project B
CF0 -$200.00 -$150.00
PV0 of CF1-3 $241.92 $240.80
NPV = $41.92 $90.80
IRR = 0%, 100% 36.19%
PI = 1.2096 1.6053
Project A Project B
CF0 -$200.00 -$150.00
PV0 of CF1-3 $241.92 $240.80
NPV = $41.92 $90.80
IRR = 0%, 100% 36.19%
PI = 1.2096 1.6053
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Example of Investment Rules
Payback Period:Project A Project B
Time CF Cum. CF CF Cum. CF0 -200 -200 -150 -1501 200 0 50 -1002 800 800 100 03 -800 0 150 150
Payback period for project B = 2 years.Payback period for project A = 1 or 3 years?
Payback Period:Project A Project B
Time CF Cum. CF CF Cum. CF0 -200 -200 -150 -1501 200 0 50 -1002 800 800 100 03 -800 0 150 150
Payback period for project B = 2 years.Payback period for project A = 1 or 3 years?
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Relationship Between NPV and IRR
Discount rate NPV for A NPV for B-10% -87.52 234.77
0% 0.00 150.0020% 59.26 47.9240% 59.48 -8.6060% 42.19 -43.0780% 20.85 -65.64
100% 0.00 -81.25120% -18.93 -92.52
Discount rate NPV for A NPV for B-10% -87.52 234.77
0% 0.00 150.0020% 59.26 47.9240% 59.48 -8.6060% 42.19 -43.0780% 20.85 -65.64
100% 0.00 -81.25120% -18.93 -92.52
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Project AProject B
($200)
($100)
$0
$100
$200
$300
$400
-15% 0% 15% 30% 45% 70% 100% 130% 160% 190%
Discount rates
NP
V
IRR 1(A) IRR (B)
NPV Profiles
Cross-over Rate
IRR 2(A)
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6.9 Summary and Conclusions
This chapter evaluates the most popular alternatives to NPV:
Payback periodAccounting rate of returnInternal rate of returnProfitability index
When it is all said and done, they are not the NPV rule; for those of us in finance, it makes them decidedly second-rate.
This chapter evaluates the most popular alternatives to NPV:
Payback periodAccounting rate of returnInternal rate of returnProfitability index
When it is all said and done, they are not the NPV rule; for those of us in finance, it makes them decidedly second-rate.