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Chapter 11

The Basics of CapitalBudgeting:

Evaluating Cash Flows

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Topics! Overview and vocabulary! Methods

! NPV! IRR, MIRR! Profitability Index! Payback, discounted payback

! Unequal lives! Economic life

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What is capital budgeting?!Analysis of potential projects.! Long-term decisions; involve large

expenditures.!Very important to firms future.

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Steps in Capital Budgeting! Estimate cash flows (inflows &

outflows).

!Assess risk of cash flows.! Determine r = WACC for project.! Evaluate cash flows.

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Independent versus Mutually

Exclusive Projects! Projects are:

! independent, if the cash flows of one are

unaffected by the acceptance of the other.! mutually exclusive, if the cash flows of one

can be adversely impacted by theacceptance of the other.

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Cash Flows for Franchise L

and Franchise S

10 8060

0 1 2 310%

Ls CFs:

-100.00

70 2050

0 1 2 310%

Ss CFs:

-100.00

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NPV: Sum of the PVs of all

cash flows.

Cost often is CF0and is negative.

NPV =!n

t = 0

CFt(1 + r)t

.

NPV =!nt = 1

CFt(1 + r)t

. - CF0.

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Whats Franchise Ls NPV?

10 8060

0 1 2 310%

Ls CFs:

-100.00

9.09

49.59

60.11

18.79 = NPVL NPVS= $19.98.

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Calculator Solution: Enter

values in CFLO register for L.

-100

10

60

8010

CF0

CF1

NPV

CF2

CF3

I = 18.78 = NPVL

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Rationale for the NPV Method! NPV = PV inflows Cost

! This is net gain in wealth, so acceptproject if NPV > 0.

! Choose between mutually exclusiveprojects on basis of higher NPV. Addsmost value.

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Using NPV method, which franchise

(s) should be accepted?! If Franchise S and L are mutually

exclusive, accept S because NPVs>

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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Whats Franchise Ls IRR?

10 8060

0 1 2 3IRR = ?

-100.00

PV3

PV2

PV1

0 = NPV Enter CFs in CFLO, then pressIRR: IRRL= 18.13%. IRRS=23.56%.

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40 4040

0 1 2 3

-100

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

3 -100 40 0

9.70%

N I/YR PV PMT FV

INPUTS

OUTPUT

Find IRR if CFs are constant:

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Rationale for the IRR Method! If IRR > WACC, then the projects rate

of return is greater than its cost-- somereturn is left over to boost stockholdersreturns.

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

! So this project adds extra return toshareholders.

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Decisions on Projects S and L

per IRR! If S and L are independent, accept

both: IRRS> r and IRRL> r.

! If S and L are mutually exclusive,accept S because IRRS> IRRL.

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Construct NPV Profiles! Enter CFs in CFLO and find NPVLand

NPVSat different discount rates:

r NPVL NPVS

0 50 40

5 33 29

10 19 20

15 7 12

20 (4) 5

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NPV Profile

IRRL= 18.1%

IRRS= 23.6%

CrossoverPoint = 8.7%

S

L

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r > IRRand NPV < 0.

Reject.

NPV ($)

r (%)IRR

IRR > rand NPV > 0

Accept.

NPV and IRR: No conflict for

independent projects.

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Mutually Exclusive Projects

8.7

NPV

%

IRRS

IRRL

L

S

r < 8.7: NPVL> NPVS , IRRS > IRRLCONFLICT

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

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To Find the Crossover Rate

! Find cash flow differences between theprojects. See data at beginning of the case.

! Enter these differences in CFLO register, thenpress IRR. Crossover rate = 8.68%, roundedto 8.7%.

! Can subtract S from L or vice versa, buteasier to have first CF negative.

! If profiles dont cross, one project dominatesthe other.

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Two Reasons NPV ProfilesCross

! Size (scale) differences. Smaller project freesup funds at t = 0 for investment. The higherthe opportunity cost, the more valuable these

funds, so high r favors small projects.

! Timing differences. Project with fasterpayback provides more CF in early years forreinvestment. If r is high, early CF especially

good, NPVS> NPVL.

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Reinvestment RateAssumptions

! NPV assumes reinvest at r (opportunitycost of capital).

! IRR assumes reinvest at IRR.! Reinvest at opportunity cost, r, is more

realistic, so NPV method is best. NPVshould be used to choose betweenmutually exclusive projects.

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Modified Internal Rate ofReturn (MIRR)

! MIRR is the discount rate which causes the PV of a projects

terminal value (TV) to equal the PV ofcosts.

! TV is found by compounding inflows atWACC.

! Thus, MIRR assumes cash inflows arereinvested at WACC.

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10.0 80.060.0

0 1 2 310%

66.012.1

158.1

-100.010%

10%

TV inflows

-100.0

PV outflows

MIRR for Franchise L: First,find PV and TV (r = 10%)

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Second, find discount rate thatequates PV and TV

MIRR = 16.5% 158.1

0 1 2 3

-100.0

TV inflowsPV outflows

MIRRL= 16.5%

$100 = $158.1(1+MIRRL)

3

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To find TV with 10B: Step 1,find PV of Inflows

! First, enter cash inflows in CFLO register:! CF0= 0, CF1= 10, CF2= 60, CF3= 80

! Second, enter I = 10.

! Third, find PV of inflows:! Press NPV = 118.78

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Step 2, find TV of inflows.

! Enter PV = -118.78, N = 3, I = 10, PMT= 0.

! Press FV = 158.10 = FV of inflows.

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Step 3, find PV of outflows.

! For this problem, there is only oneoutflow, CF0= -100, so the PV of

outflows is -100.! For other problems there may be

negative cash flows for several years,and you must find the present value for

all negative cash flows.

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Step 4, find IRR of TV ofinflows and PV of outflows.

! Enter FV = 158.10, PV = -100, PMT =0, N = 3.

! Press I = 16.50% = MIRR.

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Why use MIRR versus IRR?

! MIRR correctly assumes reinvestment atopportunity cost = WACC. MIRR also

avoids the problem of multiple IRRs.! Managers like rate of return

comparisons, and MIRR is better for thisthan IRR.

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Normal vs. Nonnormal CashFlows

! Normal Cash Flow Project:! Cost (negative CF) followed by a series of positive

cash inflows.

! One change of signs.! Nonnormal Cash Flow Project:

! Two or more changes of signs.! Most common: Cost (negative CF), then string of

positive CFs, then cost to close project.! For example, nuclear power plant or strip mine.

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Inflow (+) or Outflow (-) inYear

0 1 2 3 4 5 N NN

- + + + + + N

- + + + + - NN

- - - + + + N

+ + + - - - N

- + + - + - NN

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Pavilion Project: NPV and IRR?

5,000 -5,000

0 1 2r = 10%

-800

Enter CFs in CFLO, enter I = 10.

NPV = -386.78IRR = ERROR. Why?

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NPV Profile

450

-800

0

400100

IRR2= 400%

IRR1= 25%

r

NPV

Nonnormal CFs--two signchanges, two IRRs.

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Logic of Multiple IRRs

!At very low discount rates, the PV ofCF2is large & negative, so NPV < 0.

!At very high discount rates, the PV ofboth CF1and CF2are low, so CF0dominates and again NPV < 0.

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

! Result: 2 IRRs.

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

storing the guess. Try 10%:

10 STOIRR = 25% = lower IRR

(See next slide for upper IRR)

Finding Multiple IRRs withCalculator

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Now guess large IRR, say, 200:200 STO

IRR = 400% = upper IRR

Finding Upper IRR withCalculator

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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%

When there are nonnormal CFs andmore than one IRR, use MIRR:

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Accept Project P?

! NO. Reject because MIRR = 5.6% < r= 10%.

!Also, if MIRR < r, NPV will be negative:NPV = -$386,777.

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Profitability Index

! The profitability index (PI) is thepresent value of future cash flows

divided by the initial cost.! It measures the bang for the buck.

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Franchise Ls PV of FutureCash Flows

10 8060

0 1 2 3

10%

Project L:

9.09

49.59

60.11

118.79

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Franchise Ls Profitability Index

PIL=PV future CF

Initial Cost

$118.79=

PIL= 1.1879

$100

PIS= 1.1998

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Payback for Franchise S

70 2050

0 1 2 3

-100CFt

Cumulative -100 -30 20 40

PaybackS 1 + 30/50 = 1.6 years

0

1.6

=

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Strengths and Weaknesses ofPayback

! Strengths:! Provides an indication of a projects risk

and liquidity.

! Easy to calculate and understand.! Weaknesses:

! Ignores the TVM.! 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 = 2.7yrs

PVCFt -100

-100

10%

9.09 49.59 60.11

=

Recover invest. + cap. costs in 2.7 yrs.

Discounted Payback: Usesdiscounted rather than raw CFs.

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S and L are mutually exclusiveand will be repeated. r = 10%.

0 1 2 3 4

Project S:(100)

Project L:(100)

60

33.5

60

33.5 33.5 33.5Note: CFs shown in $ Thousands

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NPVL

> NPVS

. But is L better?

S L

CF0 -100 -100

CF1 60 33

NJ 2 4

I 10 10

NPV 4.132 6.190

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Equivalent Annual AnnuityApproach (EAA)

! Convert the PV into a stream of annuitypayments with the same PV.

!S: N=2, I/YR=10, PV=-4.132, FV = 0.Solve for PMT = EAAS= $2.38.

! L: N=4, I/YR=10, PV=-6.190, FV = 0.Solve for PMT = EAAL= $1.95.

! S has higher EAA, so it is a betterproject.

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Put Projects on Common Basis

! Note that Project S could be repeatedafter 2 years to generate additionalprofits.

! Use replacement chain to put oncommon life.

! Note: equivalent annual annuityanalysis is alternative method, shown inTool Kit and Web Extension.

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Replacement Chain Approach (000s).Franchise S with Replication:

NPV = $7,547.

0 1 2 3 4

Franchise S:(100)

(100)

60

60

60(100)

(40)

60

60

60

60

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NPVS= $3,415 < NPVL= $6,190.Now choose L.

0 1 2 3 4

Franchise S:(100) 60 60

(105)(45)

60 60

Suppose cost to repeat S in twoyears rises to $105,000.

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Economic Life versus PhysicalLife

! Consider another project with a 3-yearlife.

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

! Should you always operate for the fullphysical life?

! See next slide for cash flows.

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Economic Life versus PhysicalLife (Continued)

Year CF Salvage Value

0 ($5000) $5000

1 2,100 3,100

2 2,000 2,000

3 1,750 0

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CFs Under Each Alternative(000s)

0 1 2 3

1. No termination (5) 2.1 2 1.75

2. Terminate 2 years (5) 2.1 4

3. Terminate 1 year (5) 5.2

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NPVs under Alternative Lives (Cost ofcapital = 10%)

! NPV(3) = -$123.! NPV(2) = $215.! NPV(1) = -$273.

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Conclusions

! The project is acceptable only ifoperated for 2 years.

!A projects engineering life does notalways equal its economic life.

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Choosing the Optimal CapitalBudget

! Finance theory says to accept allpositive NPV projects.

! Two problems can occur when there isnot enough internally generated cash tofund all positive NPV projects:

!An increasing marginal cost of capital.! Capital rationing

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Increasing Marginal Cost ofCapital

! Externally raised capital can have largeflotation costs, which increase the costof capital.

! Investors often perceive large capitalbudgets as being risky, which drives upthe cost of capital.

(More...)

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! If external funds will be raised, then theNPV of all projects should be estimatedusing this higher marginal cost ofcapital.

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Capital Rationing

! Capital rationing occurs when acompany chooses not to fund allpositive NPV projects.

! The company typically sets an upperlimit on the total amount of capitalexpenditures that it will make in the

upcoming year.(More...)

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! Reason: Companies want to avoid thedirect costs (i.e., flotation costs) and theindirect costs of issuing new capital.

! Solution: Increase the cost of capital byenough to reflect all of these costs, andthen accept all projects that still have a

positive NPV with the higher cost ofcapital.

(More...)

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! Reason: Companies dont have enoughmanagerial, marketing, or engineeringstaff to implement all positive NPVprojects.

! Solution: Use linear programming tomaximize NPV subject to not exceedingthe constraints on staffing. (More...)

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