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Copyright 2002 Harcourt, Inc. All rights reserved.

Should we

build thisplant?

CHAPTER 13The Basics of Capital Budgeting:

Evaluating Cash Flows

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Steps

1. Estimate CFs (inflows & outflows).

2. Assess riskiness of CFs.

3. Determine k = WACC for project.

4. Find NPV and/or IRR.5. Accept if NPV > 0 and/or IRR >

WACC.

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What is the difference between

independent and mutually exclusiveprojects?

Projects are:

independent, if the cash flows ofone are unaffected by theacceptance of the other.

mutually exclusive, if the cashflows of one can be adverselyimpacted by the acceptance of the

other.

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An Example of Mutually Exclusive

Projects

BRIDGE vs. BOAT to getproducts across a river.

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Normal Cash Flow Project:

Cost (negative CF) followed by aseries of positive cash inflows.One change of signs.

Nonnormal Cash Flow Project:

Two or more changes of signs.Most common: Cost (negativeCF), then string of positive CFs,then cost to close project.Nuclear power plant, strip mine.

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Inflow (+) or Outflow (-) in Year

0 1 2 3 4 5 N NN

- + + + + + N- + + + + - NN

- - - + + + N

+ + + - - - N

- + + - + - NN

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What is the payback period?

The number of years required torecover a projects cost,

or how long does it take to get the

businesss money back?

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Payback for Project L

(Long: Most CFs in out years)

10 8060

0 1 2 3

-100

=

CFtCumulative -100 -90 -30 50

PaybackL 2 + 30/80 = 2.375 years

0

100

2.4

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Strengths of Payback:

1. Provides an indication of aprojects risk and liquidity.

2. Easy to calculate and understand.

Weaknesses of Payback:

1. Ignores the TVM.2. Ignores CFs occurring after the

payback period.

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10 8060

0 1 2 3

CFt

Cumulative -100 -90.91 -41.32 18.79

Discountedpayback 2 + 41.32/60.11 = 2.7 yrs

Discounted Payback: Uses discounted

rather than raw CFs.

PVCFt -100

-100

10%

9.09 49.59 60.11

=

Recover invest. + cap. costs in 2.7 yrs.

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( )NPVCF

kt

nt

t +0 1 .

NPV: Sum of the PVs of inflows and

outflows.

Cost often is CF0 and is negative.

( ) .CFk1CFNPV 0ttn

1t

+==

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Whats Project Ls NPV?

10 8060

0 1 2 310%

Project L:

-100.00

9.09

49.59

60.11

18.79 = NPVL NPVS = $19.98.

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Calculator Solution

Enter in CFLO for L:

-100

10

60

80

10

CF0

CF1

NPV

CF2

CF3

I = 18.78 = NPVL

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Rationale for the NPV Method

NPV = PV inflows - Cost= Net gain in wealth.

Accept project if NPV > 0.

Choose between mutuallyexclusive projects on basis ofhigher NPV. Adds most value.

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Using NPV method, which project(s)

should be accepted?

If Projects S and L are mutuallyexclusive, accept S becauseNPVs > NPVL .

If S & L are independent,accept both; NPV > 0.

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Internal Rate of Return: IRR

0 1 2 3

CF0 CF1 CF2 CF3Cost Inflows

IRR is the discount rate that forcesPV inflows = cost. This is the sameas forcing NPV = 0.

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( )tn

t

t

CF

kNPV

= + =0 1 .

( )tn

tt

CFIRR

+ =0 1 0.

NPV: Enter k, solve for NPV.

IRR: Enter NPV = 0, solve for IRR.

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Whats Project Ls IRR?

10 8060

0 1 2 3IRR = ?

-100.00

PV3

PV2PV1

0 = NPV

Enter CFs in CFLO, then press IRR:

IRRL = 18.13%. IRRS = 23.56%.

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40 4040

0 1 2 3IRR = ?

Find IRR if CFs are constant:

-100

Or, with CFLO, enter CFs and pressIRR = 9.70%.

3 -100 40 0

9.70%

N I/YR PV PMT FV

INPUTS

OUTPUT

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90 1,09090

0 1 2 10IRR = ?

Q. How is a projects IRRrelated to a bonds YTM?

A. They are the same thing.A bonds YTM is the IRRif you invest in the bond.

-1,134.2

IRR = 7.08% (use TVM or CFLO).

...

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Rationale for the IRR Method

If IRR > WACC, then the projects

rate of return is greater than itscost-- some return is left over toboost stockholders returns.

Example: WACC = 10%, IRR = 15%.Profitable.

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IRR Acceptance Criteria

If IRR > k, accept project.

If IRR < k, reject project.

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Construct NPV Profiles

Enter CFs in CFLO and find NPVL and

NPVS at different discount rates:

k0

5

1015

20

NPVL

50

33

197

NPVS

40

29

2012

5(4)

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-10

0

10

20

30

40

50

60

0 5 10 15 20 23.6

NPV ($)

Discount Rate (%)

IRRL = 18.1%

IRRS = 23.6%

CrossoverPoint = 8.7%

k

0

5

10

15

20

NPVL

50

33

19

7

(4)

NPVS

40

29

20

12

5

S

L

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NPV and IRR always lead to the sameaccept/reject decision for independent

projects:

k > IRR

and NPV < 0.Reject.

NPV ($)

k (%)IRR

IRR > k

and NPV > 0Accept.

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Mutually Exclusive Projects

k 8.7 k

NPV

%

IRRS

IRRL

L

S

k < 8.7: NPVL> NPVS , IRRS > IRRLCONFLICT

k > 8.7: NPVS> NPVL , IRRS > IRRLNO CONFLICT

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Reinvestment Rate Assumptions

NPV assumes reinvest at k

(opportunity cost of capital).IRR assumes reinvest at IRR.

Reinvest at opportunity cost, k, ismore realistic, so NPV method isbest. NPV should be used to choosebetween mutually exclusive projects.

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Managers like rates--prefer IRR to NPV

comparisons. Can we give them abetter IRR?

Yes, MIRR is the discount rate which

causes the PV of a projects terminalvalue (TV) to equal the PV of costs.TV is found by compounding inflowsat WACC.

Thus, MIRR assumes cash inflows arereinvested at WACC.

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MIRR = 16.5%

10.0 80.060.0

0 1 2 310%

66.012.1

158.1

MIRR for Project L (k = 10%)

-100.0

10%

10%

TV inflows-100.0

PV outflowsMIRRL = 16.5%

$100 = $158.1(1+MIRRL)

3

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To find TV with 10B, enter in CFLO:

I =10NPV = 118.78 = PV of inflows.Enter PV = -118.78, N = 3, I = 10, PMT =0.

Press FV = 158.10 = FV of inflows.Enter FV = 158.10, PV = -100, PMT = 0,N = 3.Press I = 16.50% = MIRR.

CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80

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Why use MIRR versus IRR?

MIRR correctly assumes reinvestmentat opportunity cost = WACC. MIRRalso avoids the problem of multipleIRRs.

Managers like rate of return

comparisons, and MIRR is better forthis than IRR.

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Pavilion Project: NPV and IRR?

5,000 -5,000

0 1 2k = 10%

-800

Enter CFs in CFLO, enter I = 10.

NPV = -386.78

IRR = ERROR. Why?

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We got IRR = ERROR because thereare 2 IRRs. Nonnormal CFs--two sign

changes. Heres a picture:

NPV Profile

450

-800

0 400100

IRR2 = 400%

IRR1 = 25%

k

NPV

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Logic of Multiple IRRs

1. At very low discount rates, the PV ofCF2 is large & negative, so NPV < 0.

2. At very high discount rates, the PV ofboth CF1 and CF2 are low, so CF0

dominates and again NPV < 0.

3. In between, the discount rate hits CF2harder than CF1, so NPV > 0.

4. Result: 2 IRRs.

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Could find IRR with calculator:

1. Enter CFs as before.2. Enter a guess as to IRR by

storing the guess. Try 10%:

10 STO

IRR = 25% = lower IRR

Now guess large IRR, say, 200:

200 STO

IRR = 400% = upper IRR

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When there are nonnormal CFs and

more than one IRR, use MIRR:

0 1 2

-800,000 5,000,000 -5,000,000

PV outflows @ 10% = -4,932,231.40.TV inflows @ 10% = 5,500,000.00.

MIRR = 5.6%

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Accept Project P?

NO. Reject because MIRR =

5.6% < k = 10%.

Also, if MIRR < k, NPV will be

negative: NPV = -$386,777.

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S and L are mutually exclusive and

will be repeated. k = 10%. Which isbetter? (000s)

0 1 2 3 4

Project S:(100)

Project L:(100)

60

33.5

60

33.5 33.5 33.5

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S L

CF0 -100,000 -100,000CF1 60,000 33,500

Nj 2 4

I 10 10

NPV 4,132 6,190

NPVL > NPVS. But is L better?

Cant say yet. Need to performcommon life analysis.

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Note that Project S could berepeated after 2 years to generateadditional profits.

Can use either replacement chainor equivalent annual annuityanalysis to make decision.

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Project S with Replication:

NPV = $7,547.

Replacement Chain Approach (000s)

0 1 2 3 4

Project S:(100)

(100)

60

60

60

(100)(40) 6060 6060

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Compare to Project L NPV = $6,190.

Or, use NPVs:

0 1 2 3 4

4,1323,4157,547

4,13210%

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If the cost to repeat S in two years

rises to $105,000, which is best? (000s)

NPVS = $3,415 < NPVL = $6,190.

Now choose L.

0 1 2 3 4

Project S:(100)

60 60(105)

(45)

60 60

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Year0123

CF($5,000)

2,1002,0001,750

Salvage Value$5,0003,1002,000

0

Consider another project with a 3-year

life. If terminated prior to Year 3, themachinery will have positive salvagevalue.

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1.751. No termination

2. Terminate 2 years

3. Terminate 1 year

(5)

(5)

(5)

2.1

2.1

5.2

2

4

0 1 2 3

CFs Under Each Alternative (000s)

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NPV(no) = -$123.

NPV(2) = $215.

NPV(1) = -$273.

Assuming a 10% cost of capital, what is

the projects optimal, or economic life?

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The project is acceptable only ifoperated for 2 years.

A projects engineering life does notalways equal its economic life.

Conclusions

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Choosing the Optimal Capital Budget

Finance theory says to accept allpositive NPV projects.

Two problems can occur when thereis not enough internally generatedcash to fund all positive NPV projects:

An increasing marginal cost ofcapital.

Capital rationing

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Increasing Marginal Cost of Capital

Externally raised capital can have

large flotation costs, which increasethe cost of capital.

Investors often perceive large capital

budgets as being risky, which drivesup the cost of capital.

(More...)

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If external funds will be raised, thenthe NPV of all projects should beestimated using this higher marginal

cost of capital.

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Capital Rationing

Capital rationing occurs when acompany chooses not to fund all

positive NPV projects.The company typically sets an

upper limit on the total amount

of capital expenditures that it willmake in the upcoming year.

(More...)

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Reason: Companies want to avoid thedirect costs (i.e., flotation costs) andthe indirect costs of issuing newcapital.

Solution: Increase the cost of capitalby enough to reflect all of these costs,and then accept all projects that still

have a positive NPV with the highercost of capital.

(More...)

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Reason: Companies dont haveenough managerial, marketing, orengineering staff to implement allpositive NPV projects.

Solution: Use linear programming to

maximize NPV subject to notexceeding the constraints on staffing.

(More...)

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Reason: Companies believe that theprojects managers forecastunreasonably high cash flow estimates,so companies filter out the worst

projects by limiting the total amount ofprojects that can be accepted.

Solution: Implement a post-audit

process and tie the managerscompensation to the subsequentperformance of the project.

Ch 13 Show

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