Corporate Finance Ross Westerfield Jaffe

6-1

McGraw-Hill Ryerson © 2003 McGraw–Hill Ryerson Limited

Corporate Finance Ross Westerfield Jaffe Sixth Edition

6Chapter Six

Some Alternative Investment Rules

Prepared by

Gady JacobyUniversity of Manitoba

and

Sebouh AintablianAmerican University of Beirut

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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

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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

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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 rate

– 3. Estimate initial costs

• Minimum Acceptance Criteria: Accept if NPV > 0• Ranking 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.

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The NPV Rule : Example

• Assume you have the following information on Project X:

– Initial outlay -$1,100

– Required return = 10%

• Annual cash revenues and expenses are as follows:

Year Revenues Expenses

1 $1,000 $500

2 2,000 1,300

3 2,200 2,700

4 2,600 1,400

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The NPV Rule : Example (continued)

Initial outlay

($1,100)

Revenues $1,000Expenses 500

Cash flow $500

Revenues $2,000Expenses 1,300

Cash flow $700

= NPV

+$377.02

+819.62


Cash flow (500)


Cash flow $1,200

0 1 2 3 4

1$500 x 1.10

1$700 x 1.10

2

1- $500 x 1.10

3

1$1,200 x 1.10

4

– $1,100.00

+454.54

+578.51

-375.66

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NPV = -C0 + PV0(Future CFs)

= -C0 + C1/(1+r) + C2/(1+r)2 + C3/(1+r)3 + C4/(1+r)4

= -1,100 + 500/1.1 + 700/1.12 + (-500)/1.13 + 1,200/1.14

= $377.02 > 0

The NPV Rule : Example (continued)

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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

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The Payback Period Rule (continued)

• Disadvantages:– Ignores the time value of money– Ignores cash flows after the payback period– Biased against long-term projects– Requires an arbitrary acceptance criteria– A project accepted based on the payback

criteria may not have a positive NPV

• Advantages:– Easy to understand– Biased toward liquidity

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6.3 The Discounted Payback Period 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.

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• Assume you have the following information on Project X:– Initial outlay -$1,000

– Required return = 10%

• Annual that cash flows and their PVs are as follows:

Year Cash flow PV of Cash flow 1 $ 200 $ 182 2 400 331 3 700 526 4 300 205

The Discounted Payback Period Rule: Example

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Year Accumulated discounted CF 1 $ 182 2 513 3 1,039 4 1,244

The Discounted Payback Period Rule: Example (continued)

• Discounted payback period is just under 3 years

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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 management• Disadvantages:

– Ignores the time value of money– Uses an arbitrary benchmark cutoff rate– Based on book values, not cash flows and market values

• Advantages:– The accounting information is usually available– Easy to calculate

Investent of ValueBook Average

IncomeNet AverageAAR

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6.4 The Average Accounting Return Rule: Example• You want to invest in a machine that produces

squash balls• The machine costs $90,000• The machine will ‘die’ after 3 years • Assuming straight line depreciation, the annual

depreciation is $30,000• The estimate cash flows for the life of the project:

Year 1 Year 2 Year 3

Sales 140 160 200

Expenses 120 100 90

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6.4 The Average Accounting Return Rule: Example (continued)• Projected Net Income from the project:

Year 1 Year 2 Year 3

Sales 140 160 200

Expenses 120 100 90

E.B.D. 20 60 110

Depreciation 30 30 30

E.B.T. -10 30 80

Taxes (40%) -4 12 32

NI: -6 18 48

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6.4 The Average Accounting Return Rule: Example (continued)We calculate:

(i) 2020

48186NI Average

454

0306090 BVAverage

(ii) Average book value (BV) of the investment (machine):

time-0 time-1 time-2 time-3

BV of investment: 90 60 30 0

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• Conclusion

If target AAR < 44.44% => accept

If target AAR > 44.44% => reject

6.4 The Average Accounting Return Rule: Example (continued)

(iii) The Average Accounting Return:

4444.45

20AAR

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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 IRR• Reinvestment 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:

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

NP

V

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6.6 Problems with the IRR Approach

• Multiple IRRs.

• Are We Borrowing or Lending?

• The Scale Problem.

• The Timing Problem.

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Multiple IRRs

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?

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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

V

Project A

Project B10.55% = crossover rate

12.94% = IRRB 16.04% = IRRA

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Calculating the Crossover Rate

Compute 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.

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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

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.

• Discounted cash flow techniques (such as IRR or NPV ) are the most frequently used by large industrial corporations in Canada.

• Payback is most commonly used by small firms and by CEOs without an MBA.

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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

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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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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

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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

IRR 2(A)

Cross-over Rate

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6.9 Summary and Conclusions

• This chapter evaluates the most popular alternatives to NPV:– Payback period– Accounting rate of return– Internal rate of return– Profitability 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.

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