ch 12 capital budgeting

7/31/2019 Ch 12 Capital Budgeting

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Should we

build thisplant?

CHAPTER 12The Basics of Capital Budgeting


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What is capital budgeting?

Analysis of potential additions tofixed assets.

Long-term decisions; involve largeexpenditures.

Very importantto firms future.


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Capital Budgeting Decision Rules

5 keys methods to rank project

Payback

Discounted Payback

Accounting Rate of Return

Net Present Value (NPV)

Internal Rate of Return (IRR)

Modified Internal Rate of Return (MIRR)


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Steps

1. Estimate CFs (inflows & outflows).

2. Assess riskiness of CFs.3. Determine k = WACC (adj.).

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 cash flowsof one can be adversely impactedby 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 to

recover a projects cost,- or how long does it take to get our

money back?

Payback = Year before full recovery +the last unrecovered costCash flow during year


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Example: Allied Components CompanyProjects net cash flows ($000), Allied

Projects WACC = 10%

Year Project L Project S

0 (100) (100)

1 10 70

2 60 50

3 80 20


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Payback for Project L

(Long: Large CFs in later years)

10 60

0 1 2 3

-100

=

CFtCumulative -100 -90 -30 50

PaybackL 2 + 30/80 = 2.375 years

0

100

2.4

80


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Project S (Short: CFs come quickly)

70 2050

0 1 2 3

-100CFt

Cumulative -100 -30 20 40

Paybacks 1 + 30/50 = 1.6 years

100

0

1.6

=


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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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Discounted Payback: Uses discounted

for project L rather than raw CFs.

10 8060

0 1 2 3

CFt

Cumulative -100 -90.91 -41.32 18.79

Discountedpayback 2 + 41.32/60.11 = 2.7 years

PVCFt -100

-100

10%

9.09 49.59 60.11

=

Recover invest. + cap. costs in 2.7 years.


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Accounting Rate of Return (ARR)

ARR = Average Annual Income

Average Annual Income =

Average Cash Flow Average depreciation

Average Investment =(Cost + Salvage Value)/2

Average Investment


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Accounting Rate of Return (ARR)

Average Annual Income (AAI) L:

Average cash flow L: 150/3 = 50

Average depreciation: 100/3 = 33.3

AAI L: 50 33.3 = 16.7

Average Investment L:

(Cost + Salvage Value)/2: (100+0)/2 = 50ARR L = 16.7/50 33.4%

ARR S = 13.4/50 26.8%


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.k1

CFNPV

t

t

n

0t

NPV: Sum of the PVs of inflows andoutflows.


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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


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Calculator Solution

Enter in CF for L:

-100

10

60

80

10

CF0

CF1

RCL NPV

CF2

CF3

i% = 18.78 = NPVL

NPVS

= $19.98.


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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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.NPVk1

CFt

t

n

0t

.0IRR1

CFt

tn

0t

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 = NPVEnter CFj in CF, 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 CF, enter CFj and pressIRR = 9.70%.

3 -100 40 0

9.70%

INPUTS

OUTPUT

N COMP i% PV PMT FV


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90 109090

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.

-1134.2

IRR = 7.08%

...


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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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Decisions on Projects S and L per IRR

If S and L are independent, accept

both. IRRs > k = 10%.

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 NPVL andNPVS at different discount rates:

k0

5

1015

20

NPVL50

33

197

(4

NPVS40

29

2012

5(4)


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-10

0

10

20

30

40

50

60

5 10 15 20 23.6

NPV ($)

Discount Rate (%)

IRRL = 18.1%

IRRS = 23.6%

CrossoverPoint = 8.7%

k

0

5

10

15

20

NPVL50

33

19

7

(4)

NPVS40

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 > IRRL

NO CONFLICT


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To Find the Crossover Rate

1. Find cash flow differences betweenthe projects. See data at beginningof the case.

2. Enter these differences in CFLOregister, then press IRR. Crossoverrate = 8.68%, rounded to 8.7%.

3. Can subtract S from L or vice versa,but better to have first CF negative.

4. If profiles dont cross, one projectdominates the other.

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YearProject

LProject

SL-S

Cross

over

0 (100) (100) 0

1 10 70 -60

2 60 50 10

3 80 20 60 8.68%

To Find the Crossover Rate

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Two Reasons NPV Profiles Cross

1. Size (scale) differences. Smallerproject frees up funds at t = 0 for

investment. The higher the opportunitycost, the more valuable these funds, sohigh k favors small projects.

2. Timing differences. Project with fasterpayback provides more CF in earlyyears for reinvestment. If k is high,early CF especially good, NPVS > NPVL.

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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 NPVcomparisons. Can we give them a

better IRR?

Yes, MIRR is the discount rate that

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)

30

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To find TV with Casio, enter in CFLO:

i% = 10

RCL NPV = 118.78 = PV of inflows.Enter PV = -118.78, n = 3, i% = 10, PMT = 0.Press COMP FV = 158.10 = FV of inflows.

Enter FV = 158.10, PV = -100, PMT = 0,n = 3.Press COMP i% = 16.50% = MIRR.

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

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Why use MIRR versus IRR?

MIRR correctly assumes reinvestment

at opportunity cost = WACC. MIRRalso avoids the problem of multipleIRRs.

Managers like rate of returncomparisons, and MIRR is better forthis than IRR.

ch 12 capital budgeting

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