Lecture 6,7 & 8Capital Budgeting TechniquesCapital Budgeting Techniques

Presented byMuhammad Khalid Sohail

6-2

Lecture 5Review: Present Value Present Value is the current value of a future amount of

money, or a series of payments (single, un-even, same,infinite), evaluated at a given interest rate.

1. General Present Value Formula(single):

PV0 = C/Fn / (1+i)n

or PV0 = C/Fn (PVIFi,n) -- See Table2. Present Value (un-even C/F):

DF = PVIFi,n = 1 / (1+i)n

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3. a. Present Value (Annuity):PVAn = C/F (PVIFAi%,n)

Or PVAn = C/F * [(1-1/(1+i)^n) / i ]b. PVADn = C/F (PVIFAi%,n)(1+i)

4. Present Value (infinite series):PVp = CF / i = (1 / i) * CF = DFp * CF

5. Present Value (Mixed series):solve according to above fourformulas.

6-4

1. PV of Single Value.

What will be the PV of $10,000 in 5 yearsat a discount rate of 10%.

0 1 2 3 4 5

$10,000PV0

10%

6-5

Calculation based on general formula:PV0 = C/Fn / (1+i)n

PV0 = $10,000 / (1+ 0.10)5= $6,209.21

Calculation based on Table:PV0 = $10,000 (PVIF10%, 5)

= $10,000 (.621) = $6,210.00 [Rounding]

Year CF-AT DF@10% PV0 0 1 0

1 0 0.9091 0

2 0 0.8264 0

3 0 0.7513 0

4 0 0.683 0

5 10000 0.6209 62096209

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2. a. PV of Un-even C/F

What will be thePV of $100, 200,300 occurring in 3years at a discountrate of 10%.

100 200 300

0 1 2 3

Year C/F DF@10 PV0 0 1 01 100 0.9091 912 200 0.8264 1653 300 0.7513 225

481

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2. b. Un-even C/F when interestrate is in fraction

What will be thePV of $100, 200,300 occurring in 3years at a discountrate of 10.5%.

100 200 300

0 1 2 3

Year CF DF@10.5% PV0 0 1 01 100 0.905 912 200 0.819 1643 300 0.7412 222

477

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3. a. What is PV of thisannuity at interest rate 10%3. a. What is PV of thisannuity at interest rate 10%

0 1 2 3

$1000 1000 1000

(Ordinary Annuity)End of

Period 1End of

Period 2

Today Equal Cash FlowsEach 1 Period Apart

End ofPeriod 3

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PVAn = C/F (PVIFAi%,n)PVA3 = $1,000 (PVIFA10%,3)

= $1,000 (2.4869)= $2,487

i n DFA0.10 3 2.624316

Year CF-AT DF@10% PV0 0 1 0

1-3 1000 2.486852 24872487

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3. b. What is PV of this annuity atinterest rate 10.5%

PVAn = C/F (PVIFAi%,n)PVA3 = $1,000 (PVIFA10.5%,3)

= $1,000 (2.2465)= $2,465

Year CF-AT DF@10.5% PV0 0 1 0

1-3 1000 2.465123 24652465

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4.Present Value of Infiniteseries

What will be the PVof $70 occurring ininfinite years at adiscount rate of10%.

PV = CF * DFpPV = 70 * (1/.10)

= 70 * (10)= 700

70 70 70 .

0 1 2 3 .

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Find PV of this C/F

100 200 300 1000 1000 1000 70 70 ..

0 1 2 3 4 5 6 7 8 .

6-13

100 200 300 1000 1000 1000 70 70 ..0 1 2 3 4 5 6 7 8 .

100 200 300 1000 1000 1000 70 70

0 1 2 3 4 5 6 7 8 .

481 2487 700

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481 2487 700

0 1 2 3 4 5 6 7

Year CF-AT DF@10% PV

0 481 1 481

3 2487 0.7513 1868

6 700 0.5645 395

2744

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100 200 300 1000 1000 1000 70 70

0 1 2 3 4 5 6 7 8 .

Year CF-AT DF@10% PV0 0 1 01 100 0.9091 912 200 0.8264 1653 300 0.7513 225

4-6 1000 1.8684 18687-inf 70 5.6447 395

2744Annuity i n DFA

0.1 6 4.3553

0.1 3 2.4869

Ann-diff 1.8684

Annuity i n DFA

0.1 6 4.3553Perp i n DFp

0.1 inf 10Ann-prep-diff 5.6447

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Capital BudgetingTechniquesCapital BudgetingTechniques

Project Evaluation and Selection Potential Difficulties Capital Rationing Project Monitoring Post-Completion Audit

Project Evaluation and Selection Potential Difficulties Capital Rationing Project Monitoring Post-Completion Audit

6-17

Project Evaluation:Alternative MethodsProject Evaluation:Alternative Methods

Average Rate of ReturnPayback Period (PBP) Internal Rate of Return (IRR) Net Present Value (NPV) Profitability Index (PI) Advanced Techniques

Discounted PBP, NTV, MIRR, APV

Average Rate of ReturnPayback Period (PBP) Internal Rate of Return (IRR) Net Present Value (NPV) Profitability Index (PI) Advanced Techniques

Discounted PBP, NTV, MIRR, APV

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Project Types Independent A project whose

acceptance (or rejection) does notprevent the acceptance of otherprojects under consideration. projectdo not compete with each other

Dependent The acceptance of oneproject also depends on theacceptance of other project (s).

Mutually exclusive Compete againsteach other. Best project is selected.

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Proposed Project DataProposed Project Data

JM is evaluating a new project for herfirm, BW. She has determined that

the after-tax cash flows for theproject will be $10,000; $12,000;

$15,000; $10,000; and $7,000,respectively, for each of the Years 1through 5. The initial cash outlay

will be $40,000.

JM is evaluating a new project for herfirm, BW. She has determined that

the after-tax cash flows for theproject will be $10,000; $12,000;

$15,000; $10,000; and $7,000,respectively, for each of the Years 1through 5. The initial cash outlay

will be $40,000.

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Payback Period (PBP)Payback Period (PBP)

No. of year required to recover initialC/F from future C/F

PBP is the period of time required for thecumulative expected cash flows from an

investment project to equal the initial cashoutflow.

No. of year required to recover initialC/F from future C/F

PBP is the period of time required for thecumulative expected cash flows from an

investment project to equal the initial cashoutflow.

0 1 2 3 4 5

-40 10 12 15 10 7

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(c)10 22 37 47 54

PBP = a + ( b - c ) / d= 3 + (40 - 37) / 10= 3 + (3) / 10= 3.3 Years

PBP = a + ( b - c ) / d= 3 + (40 - 37) / 10= 3 + (3) / 10= 3.3 Years

0 1 2 3 4 5

-40 10 12 15 10 7

CumulativeInflows

(a)

(-b) (d)

a: year at which cumulative total does not exceed its ICOb: ICOc: Cumulative total discussed in step-1d: C/F of following years of commutative total in single C/F column

a: year at which cumulative total does not exceed its ICOb: ICOc: Cumulative total discussed in step-1d: C/F of following years of commutative total in single C/F column

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PBP Acceptance CriterionPBP Acceptance Criterion

Yes! The firm will receive back theinitial cash outlay in less than 3.5years. [3.3 Years < 3.5 Year Max.]

Yes! The firm will receive back theinitial cash outlay in less than 3.5years. [3.3 Years < 3.5 Year Max.]

Based upon the management. e.g. Themanagement of BW has set a maximum

PBP of 3.5 years for projects of this type.

Should this project be accepted?

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In case of annuity

PBP = ICO / [CFi (single)] (years)PBP = 600 / 200 = 3 years

-600 200 200 200 200

0 1 2 3 4

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PBP Strengthsand WeaknessesPBP Strengthsand Weaknesses

Strengths: Easy to use and

understand Can be used as a

measure ofliquidity

Easier to forecastST than LT flows

Strengths: Easy to use and

understand Can be used as a

measure ofliquidity

Easier to forecastST than LT flows

Weaknesses: Does not account

for TVM Does not consider

cash flows beyondthe PBP

Cutoff period issubjective

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Lecture 6:Lecture 6:

Net Present Value: NPV is thepresent value of an investment

projects net cash flows minus theprojects initial cash outflow.

CF1 CF2 CFn(1+k)1 (1+k)2 (1+k)n

+ . . . ++ - ICONPV =

NPV = PV of CFi PV of CFo

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More consistent with the goal i.e. Maximization ofwealth of owners.

NPV is $ amount of change in the value of firm asa result of undertaking the project.

NPV positive means, the project will add value tothe firm, as a result MPS will also increase.

NPV0, Firm value will not change, remainsame expected rate of return.

NPV+, Firm value will , return exceeds thefirm RRR.

NPV-, Firm value will , return will be less thanthe firm RRR.

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NPV SolutionNPV SolutionBW has determined that the appropriatediscount rate (k) for this project is 13%.

-40000 10000 12000 15000 10000 7000

0 1 2 3 4 5

PV of C/Fo ? PV of C/Fi ?

Year CF-AT DF@13% PV0 -40000 1 -400001 10000 0.885 88502 12000 0.7831 93973 15000 0.6931 103974 10000 0.6133 61335 7000 0.5428 3800

NPV -1423

3857740000

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NPV Acceptance CriterionNPV Acceptance Criterion

No! The NPV is negative. This meansthat the project is reducing shareholder

wealth. [Reject as NPV < 0 ]

No! The NPV is negative. This meansthat the project is reducing shareholder

wealth. [Reject as NPV < 0 ]

The management of BW hasdetermined that the required rate is

13% for projects of this type.Should this project be accepted?

* For Ind. Project: accept NPV>=0.

* For M.E projects: rank according to higher NPV

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NPV Strengthsand WeaknessesNPV Strengthsand Weaknesses

Strengths: Cash flows

assumed to bereinvested at thehurdle rate.

Accounts for TVM. Considers all

cash flows.

Strengths: Cash flows

assumed to bereinvested at thehurdle rate.

Accounts for TVM. Considers all

cash flows.

Weaknesses: May not include

managerialoptions embeddedin the project.

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Net Present Value ProfileNet Present Value Profile

Discount Rate (%)0 3 6 9 12 15

IRRNPV@13%

Sum of CFs Plot NPV for eachdiscount rate.

Net

Pre

sent

Val

ue

$000s15

10

5

0

-4

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Profitability Index (PI)Profitability Index (PI)PI is the ratio of the present value of aprojects future net cash flows to the

projects initial cash outflow. OR BCR :Benefit Cost Ratio.

PI = Benefits / Cost = PV of CFi / PV of CFo

CF1 CF2 CFn(1+k)1 (1+k)2 (1+k)n

+ . . . ++ ICOPI =

PI = 1 + [ NPV / ICO ]>

Method #2:

Method #1:

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PI Acceptance CriterionPI Acceptance Criterion

No! The PI is less than 1.00. Thismeans that the project is not profitable.

[Reject as PI < 1.00 ]

No! The PI is less than 1.00. Thismeans that the project is not profitable.

[Reject as PI < 1.00 ]

PI = $38,577 / $40,000 = .9644 (Method #1)PI = 1 + (-1423)/ 40,000 = .9644 (Method #2)

Should this project be accepted?

6-33

PI Strengthsand WeaknessesPI Strengthsand Weaknesses

Strengths: Same as NPV Allows

comparison ofdifferent scaleprojects

Strengths: Same as NPV Allows

comparison ofdifferent scaleprojects

Weaknesses: Same as NPV Provides only

relative profitability Potential Ranking

Problems

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Internal Rate of Return (IRR):IRR is the discount rate that equates

the present value of the future net cashflows from an investment project withthe projects initial cash outflow. OR

The rate at which NPV becomes zero

CF1 CF2 CFn(1+IRR)1 (1+IRR)2 (1+IRR)n

+ . . . ++ICO =

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$15,000 $10,000 $7,000

IRR SolutionIRR Solution

$10,000 $12,000(1+IRR)1 (1+IRR)2

Find the interest rate (IRR) that causes thediscounted cash flows to equal $40,000.

+ +

++$40,000 =

(1+IRR)3 (1+IRR)4 (1+IRR)5

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IRR : Single Value For single value in CFi. IRR = (CFi / CFo)^(1/n) - 1

P:6.4n= 4CFi 30000CFo 10000IRR 0.316074

-10000 30000

0 1 2 3 4

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For Annuity

i. Calculate DF = CFo / Annuityii. Locate two DFs close to DF in

PVIFA table under year niii. Interpolate IRR as:LDR + (DRs) (LDF DF) / (LDF HDF)orHDR - (DRs) (DF HDF) / (LDF HDF)

6-38

IRR: Annuity Case: Problem 6.4

-10000 5000 5000 5000 5000

0 1 2 3 4

PVIFA RateLDF 2.166 0.3 LDR

(i) DF 2.000 IRRHDF 1.849 0.4 HDR

IRR = 0.30 + (0.10) (0.5237) = 0.3524 = 35.24%

Or IRR = 0.40 (0.10) (0.4763) = 0.3524 = 35.24%

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Now we Check,whether NPVbecomes 0, at35.24%.

Now, with thehelp of computerprogram, IRR is34.90%, again wecheck, whetherNPV becomes 0,at this rate.

Yes it is near to0.

Annuityi n DFA

0.3524 4 1.9894

Year CF-AT DF@35.24% PV0 -10000 1 -10000

1-4 5000 1.9894 9947NPV -53

Annuity

i n DFA

0.349 4 2.0001

Year CF-AT DF@35.24% PV

0 -10000 1 -10000

1-4 5000 2.0001 10001

NPV 1

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Lecture 7

IRR : Mixed Stream of C/F, with the help ofNPV

Calculate Two NPVs, one + & other - Interpolate IRR as:LDR + (DRs) (|NPVLDR|) / (|NPVLDR|+ |NPVHDR|)OrHDR - (DRs) (|NPVHDR|) /(|NPVLDR|+ |NPVHDR|)

6-41

Annuityi n DFA

0.3 4 2.1662

Year CF-AT DF@30% PV0 -10000 1 -10000

1-4 5000 2.1662 10831NPV 831

Annuityi n DFA

0.35 4 1.9969

Year CF-AT DF@35% PV0 -10000 1 -10000

1-4 5000 1.9969 9985NPV -15

LDR Diff Fraction IRR0.3 0.05 0.98227 0.3491

ORHDR Diff Fraction IRR

0.35 0.05 0.01773 0.3491Check

Annuityi n DFA0.3491 4 1.9998

Year CF-AT DF@35.91% PV0 -10000 1 -10000

1-4 5000 1.9998 9999NPV -1

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IRR : Mixed Stream of C/Fi. Get Fake Annuity : FA = CFi / nii. Calculate DF = CFo / FAiii. Find DF in PVIFA table under year n, this will

give rough IRR = k.iv. Adjustment in k=Rough IRR [if required]

If CFi >FA in earlier years: k=Rough IRR+1If CFi

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IRR: solution with the help of 7-steps

-40000 10000 12000 15000 10000 7000

0 1 2 3 4 5

step 1 FA 10800step 2 DF 3.7037step 3 in PVIFA 3.696 Rate=k= 0.11step 4 Adjustment in k= 0step 5 Find NPV at k= 0.11

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step 5 step 6 CheckYear CF-AT 0.11 PV 0.16 PV 0.1151 PV

0 -40000 1 -40000 1 -40000 1 -400001 10000 0.9009 9009 0.8621 8621 0.8968 89682 12000 0.8116 9739 0.7432 8918 0.8042 96503 15000 0.7312 10968 0.6407 9611 0.7212 108184 10000 0.6587 6587 0.5523 5523 0.6468 64685 7000 0.5935 4155 0.4761 3333 0.58 4060

NPV 458 NPV -3994 NPV -36

step 6 Now NPV, + Find NPV at k= 0.16step 7 LDR 0.11 NPV 458

HDR 0.16 NPV -3994

LDR Diff Fraction IRR0.11 0.05 0.102875 0.1151

6-45

IRR Acceptance CriterionIRR Acceptance Criterion

No! The firm will receive 11.51% foreach dollar invested in this project ata cost of 13%. [ IRR < Hurdle Rate ]

No! The firm will receive 11.51% foreach dollar invested in this project ata cost of 13%. [ IRR < Hurdle Rate ]

The management of BW hasdetermined that the hurdle rate is

13% for projects of this type.Should this project be accepted?

6-46

P:6.3Year Net C/F - Depr. = CF_BT - Tax Inc. C/F

1 8000 5600 2400 816 71842 8000 8960 -960 -326 83263 8000 5376 2624 892 71084 8000 3226 4774 1623 63775 8000 3226 4774 1623 63776 8000 1612 6388 2172 58287 8000 0 8000 2720 5280

step 1 FA 6640

step 2 DF 4.2169step 3 in PVIFA 4.288 rate = k = 0.14

step 4 Adjustment in k 0

step 5 Find NPV at k= 0.14

6-47

step 5 step 6 CheckYear CF-AT .14 PV 0.19 PV 0.1581 PV

0 -28000 1 -28000 1 -28000 1 -280001 7184 0.8772 6302 0.8403 6037 0.8635 62032 8326 0.7695 6407 0.7062 5880 0.7456 62083 7108 0.675 4798 0.5934 4218 0.6438 45764 6377 0.5921 3776 0.4987 3180 0.5559 35455 6377 0.5194 3312 0.419 2672 0.48 30616 5828 0.4556 2655 0.3521 2052 0.4145 24167 5280 0.3996 2110 0.2959 1562 0.3579 1890

NPV 1360 NPV -2399 NPV -101

step 6 Now NPV, + Find NPV at k= 0.19step 7 LDR 0.14 NPV 1360

HDR 0.19 NPV -2399

LDR Diff Fraction IRR

0.14 0.05 0.361798 0.1581

6-48

IRR Strengthsand WeaknessesIRR Strengthsand Weaknesses

Strengths: Accounts for

TVM Considers all

cash flows Less

subjectivity

Strengths: Accounts for

TVM Considers all

cash flows Less

subjectivity

Weaknesses: Assumes all cash

flows reinvested atthe IRR

smaller project mayhave higher IRR, butoverall do not changefirm value.

Difficulties withproject rankings andMultiple IRRs

6-49

Evaluation Summary

Method Project Comparison DecisionPBP 3.3 3.5 AcceptIRR 11.51% 13% RejectNPV -$1,423 $0 Reject

PI .96 1.00 Reject

BW Independent Project

6-50

Potential ProblemsUnder Mutual ExclusivityPotential ProblemsUnder Mutual Exclusivity

A. Scale of InvestmentB. Cash-flow PatternC. Project Life

A. Scale of InvestmentB. Cash-flow PatternC. Project Life

Ranking of project proposals maycreate contradictory results.

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A. Scale DifferencesA. Scale Differences

Compare a small (S) and alarge (L) project.

NET CASH FLOWSProject S Project LEND OF YEAR

0 -$100 -$100,0001 0 02 $400 $156,250

6-52

Scale DifferencesScale Differences

Calculate the PBP, IRR, NPV@10%,and PI@10%.

Which project is preferred? Why?Project IRR NPV PI

S 100% $ 231 3.31L 25% $29,132 1.29S 100% $ 231 3.31L 25% $29,132 1.29

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B. Cash Flow PatternB. Cash Flow Pattern

Let us compare a decreasing cash-flow (D)project and an increasing cash-flow (I) project.

NET CASH FLOWSProject D Project IEND OF YEAR

0 -$1,200 -$1,2001 1,000 1002 500 6003 100 1,080

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D 23% $198 1.17I 17% $198 1.17D 23% $198 1.17I 17% $198 1.17

Cash Flow PatternCash Flow Pattern

Calculate the IRR, NPV@10%,and PI@10%.

Which project is preferred?

Project IRR NPV PI

6-55

C. Project Life DifferencesC. Project Life Differences

Let us compare a long life (X) projectand a short life (Y) project.

NET CASH FLOWSProject X Project YEND OF YEAR

0 -$1,000 -$1,0001 0 2,0002 0 03 3,375 0

6-56

X 50% $1,536 2.54Y 100% $ 818 1.82X 50% $1,536 2.54Y 100% $ 818 1.82

Project Life DifferencesProject Life Differences

Calculate the PBP, IRR, NPV@10%,and PI@10%.

Which project is preferred? Why?

Project IRR NPV PI

6-57

Capital RationingCapital Rationing occurs when a

constraint (or budget ceiling) is placedon the total size of capital expenditures

during a particular period.

Example: JM must determine whatinvestment opportunities to undertakefor BW Co.. She is limited to amaximum expenditure of $32,500 onlyfor this capital budgeting period.

6-58

Available Projects for BW

Project ICO IRR NPV PIA $ 500 18% $ 50 1.10B 5,000 25 6,500 2.30C 5,000 37 5,500 2.10D 7,500 20 5,000 1.67E 12,500 26 500 1.04F 15,000 28 21,000 2.40G 17,500 19 7,500 1.43H 25,000 15 6,000 1.24

6-59

Choosing by IRRs for BW

Project ICO IRR NPV PIC $ 5,000 37% $ 5,500 2.10F 15,000 28 21,000 2.40E 12,500 26 500 1.04B 5,000 25 6,500 2.30

Projects C, F, and E have thethree largest IRRs.

The resulting increase in shareholder wealthis $27,000 with a $32,500 outlay.

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Choosing by NPVs for BW

Project ICO IRR NPV PIF $15,000 28% $21,000 2.40G 17,500 19 7,500 1.43B 5,000 25 6,500 2.30

Projects F and G have thetwo largest NPVs.

The resulting increase in shareholder wealthis $28,500 with a $32,500 outlay.

6-61

Choosing by PIs for BWProject ICO IRR NPV PI

F $15,000 28% $21,000 2.40B 5,000 25 6,500 2.30C 5,000 37 5,500 2.10D 7,500 20 5,000 1.67G 17,500 19 7,500 1.43

Projects F, B, C, and D have the four largest PIs.The resulting increase in shareholder wealth is

$38,000 with a $32,500 outlay.

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Summary of ComparisonMethod Projects Accepted Value Added

PI F, B, C, and D $38,000NPV F and G $28,500IRR C, F, and E $27,000

PI generates the greatest increase inshareholder wealth when a limited capital

budget exists for a single period.

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Post-Completion Audit

Post-completion AuditA formal comparison of the actual costs andbenefits of a project with original estimates.

Identify any project weaknesses Develop a possible set of corrective actions

Provide appropriate feedback

Result: Making better future decisions!

6-64

Multiple IRR Problem*Multiple IRR Problem*

Two!! There are as many potentialIRRs as there are sign changes.

Two!! There are as many potentialIRRs as there are sign changes.

Let us assume the following cash flowpattern for a project for Years 0 to 4:

-$100 +$100 +$900 -$1,000How many potential IRRs could this

project have?

6-65

Multiple IRR exampleP:6-10Year CF-AT DF@25% PV

0 -800 1 -8001 5000 0.8 40002 -5000 0.64 -3200

NPV 0

Year CF-AT DF@400% PV0 -800 1 -8001 5000 0.2 10002 -5000 0.04 -200

NPV 0

Lecture 6,7 & 8Lecture 5Slide63Slide64Slide672. a. PV of Un-even C/FSlide71Slide66Slide653. b. What is PV of this annuity at interest rate 10.5%4.Present Value of Infinite seriesFind PV of this C/FSlide75Slide74Capital Budgeting TechniquesProject Evaluation: Alternative MethodsProject TypesProposed Project DataPayback Period (PBP)Slide7PBP Acceptance CriterionIn case of annuityPBP Strengths and WeaknessesLecture 6: Slide95NPV SolutionNPV Acceptance CriterionNPV Strengths and WeaknessesNet Present Value ProfileProfitability Index (PI) PI Acceptance CriterionPI Strengths and WeaknessesSlide11 IRR SolutionIRR : Single ValueFor AnnuityIRR: Annuity Case: Problem 6.4Slide81Lecture 7Slide88IRR : Mixed Stream of C/FIRR: solution with the help of 7-stepsSlide86IRR Acceptance CriterionSlide104Slide105IRR Strengths and WeaknessesEvaluation SummaryPotential Problems Under Mutual ExclusivityA. Scale DifferencesScale DifferencesB. Cash Flow PatternCash Flow PatternC. Project Life DifferencesProject Life DifferencesCapital RationingAvailable Projects for BWChoosing by IRRs for BWChoosing by NPVs for BWChoosing by PIs for BWSummary of ComparisonPost-Completion AuditMultiple IRR Problem*Multiple IRR example