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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.