Chapter 13

13.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Chapter 13Chapter 13

Capital Budgeting Capital Budgeting TechniquesTechniques

Capital Budgeting Capital Budgeting TechniquesTechniques


After Studying Chapter 13, After Studying Chapter 13, you should be able to:you should be able to:

1. Understand the payback period (PBP) method of project evaluation and selection, including its: (a) calculation; (b) acceptance criterion; (c) advantages and disadvantages; and (d) focus on liquidity rather than profitability.

2. Understand the three major discounted cash flow (DCF) methods of project evaluation and selection – internal rate of return (IRR), net present value (NPV), and profitability index (PI).

3. Explain the calculation, acceptance criterion, and advantages (over the PBP method) for each of the three major DCF methods.

4. Define, construct, and interpret a graph called an “NPV profile.”

5. Understand why ranking project proposals on the basis of IRR, NPV, and PI methods “may” lead to conflicts in rankings.

6. Describe the situations where ranking projects may be necessary and justify when to use either IRR, NPV, or PI rankings.

7. Understand how “sensitivity analysis” allows us to challenge the single-point input estimates used in traditional capital budgeting analysis.

8. Explain the role and process of project monitoring, including “progress reviews” and “post-completion audits.”


Capital Budgeting Capital Budgeting TechniquesTechniquesCapital Budgeting Capital Budgeting TechniquesTechniques

• 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


Overview Of Capital Budgeting Techniques

Capital budgeting techniques are used to assess and rank proposed projects.

Preferred techniques should include: Time value considerations Risk and return considerations Valuation considerations

Are used to ensure projects selected are consistent with the firm’s goal of maximising shareholder wealth.


Project Evaluation: Project Evaluation: Alternative MethodsAlternative MethodsProject Evaluation: Project Evaluation: Alternative MethodsAlternative Methods

• Payback Period (PBP)

• Internal Rate of Return (IRR)

• Net Present Value (NPV)

• Profitability Index (PI)

• Refer to the additional PowerPoint slides and the Excel spreadsheet “VW13E-13b.xlsx” for computer-based solutions.

• Payback Period (PBP)

• Internal Rate of Return (IRR)

• Net Present Value (NPV)

• Profitability Index (PI)

• Refer to the additional PowerPoint slides and the Excel spreadsheet “VW13E-13b.xlsx” for computer-based solutions.


Proposed Project DataProposed Project DataProposed Project DataProposed Project Data

Julie Miller is evaluating a new project for her firm, Basket Wonders (BW).

She has determined that the after-tax cash flows for the project will be

$10,000; $12,000; $15,000; $10,000; and $7,000, respectively, for each of

the Years 1 through 5. The initial cash outlay will be $40,000.

Julie Miller is evaluating a new project for her firm, Basket Wonders (BW).

She has determined that the after-tax cash flows for the project will be

$10,000; $12,000; $15,000; $10,000; and $7,000, respectively, for each of

the Years 1 through 5. The initial cash outlay will be $40,000.


Independent ProjectIndependent Project

• IndependentIndependent – A project whose acceptance (or rejection) does not prevent the acceptance of other projects under consideration.

• For this project, assume that it is independent of any other potential projects that Basket Wonders may undertake.


Payback Period (PBP)Payback Period (PBP)Payback Period (PBP)Payback Period (PBP)

PBPPBP is the period of time required for the cumulative

expected cash flows from an investment project to equal the

initial cash outflow.

PBPPBP is the period of time required for the cumulative

expected cash flows from an investment project to equal the

initial cash outflow.

0 1 2 3 4 5

–40 K 10 K 12 K 15 K 10 K 7 K


(c)10 K 22 K 37 K 47 K 54 K

Payback Solution (#1)Payback Solution (#1)Payback Solution (#1)Payback Solution (#1)

PBPPBP = a + ( b – c ) / d= 3 + (40 – 37) /

10 = 3 + (3) / 10= 3.3 Years3.3 Years

PBPPBP = a + ( b – c ) / d= 3 + (40 – 37) /

10 = 3 + (3) / 10= 3.3 Years3.3 Years

0 1 2 3 4 5

–40 K 10 K 12 K 15 K 10 K 7 K

CumulativeInflows

(a)

(-b) (d)


Payback Solution (#2)Payback Solution (#2)Payback Solution (#2)Payback Solution (#2)

PBPPBP = 3 + ( 3K ) / 10K= 3.3 Years3.3 Years

Note: Take absolute value of last negative cumulative cash flow value.

PBPPBP = 3 + ( 3K ) / 10K= 3.3 Years3.3 Years

Note: Take absolute value of last negative cumulative cash flow value.

CumulativeCash Flows

–40 K 10 K 12 K 15 K 10 K 7 K

0 1 2 3 4 5

–40 K –30 K –18 K –3 K 7 K 14 K


PBP Acceptance CriterionPBP Acceptance CriterionPBP Acceptance CriterionPBP Acceptance Criterion

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

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

The management of Basket Wonders has set a maximum PBP of 3.5 years for projects of this type.

Should this project be accepted?


Payback Period Peng Xi is currently contemplating two projects: project

A, requiring an initial investment of $42,000; and project B, requiring an initial investment of $45,000. The projected incremental (relevant) operating net cash inflows for the two projects are shown below:


Payback Period

Project A: $42,000 $14,000 = 3 years

Project B: $28,000 (Year 1) + $12,000 (Year 2) $40,000 + $5,000/$10,000 (Year 3)

= 3.5 years


PBP Strengths PBP Strengths and Weaknessesand WeaknessesPBP Strengths PBP Strengths and Weaknessesand Weaknesses

StrengthsStrengths::

• Easy to use and understand

• Can be used as a measure of liquidity

• Easier to forecast ST than LT flows


• Easy to use and understand

• Can be used as a measure of liquidity

• Easier to forecast ST than LT flows

WeaknessesWeaknesses::

• Does not accountfor TVM

• Does not consider cash flows beyond the PBP

• Cutoff period is subjective


Internal Rate of Return (IRR)Internal Rate of Return (IRR)Internal Rate of Return (IRR)Internal Rate of Return (IRR)

IRR is the discount rate that equates the present value of the future net cash flows from an investment project with the project’s initial cash outflow.

We equate the NPV of the investment opportunity with $0.

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

+ . . . ++ICO =


Internal Rate of Return (IRR)Internal Rate of Return (IRR)

Calculated by:

[Equation 13.1]

Where: CF0 = Project’s initial investment CFt = Net cash inflows for year t t = Year t

01 )1(

0$ CFIRR

CFNPV

n

tt

t


Internal Rate of Return (IRR)Internal Rate of Return (IRR)

Requires a trial and error approach, substituting different discount rates until the equation balances.

Get 2 NPVs – one positive, the other negative, then interpolate.

Decision criteria:

Accept if IRR > Hurdle rate (Cost Of Capital)

Reject if IRR < Hurdle rate (Cost Of Capital)


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

IRR SolutionIRR Solution IRR SolutionIRR Solution

$10,000 $12,000

(1+IRR)1 (1+IRR)2

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

+ +

++$40,000 =

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


IRR Solution (Try 10%)IRR Solution (Try 10%)IRR Solution (Try 10%)IRR Solution (Try 10%)

$40,000$40,000 = $10,000(PVIF10%,1) + $12,000(PVIF10%,2) + $15,000(PVIF10%,3) + $10,000(PVIF10%,4) + $ 7,000(PVIF10%,5)

$40,000$40,000 = $10,000(0.909) + $12,000(0.826) + $15,000(0.751) + $10,000(0.683)

+ $ 7,000(0.621)

$40,000$40,000 = $9,090 + $9,912 + $11,265 + $6,830 + $4,347

= $41,444$41,444 [[Rate is too Rate is too low!!low!!]]


IRR Solution (Try 15%)IRR Solution (Try 15%)IRR Solution (Try 15%)IRR Solution (Try 15%)

$40,000$40,000 = $10,000(PVIF15%,1) + $12,000(PVIF15%,2) + $15,000(PVIF15%,3) + $10,000(PVIF15%,4) + $ 7,000(PVIF15%,5)

$40,000$40,000 = $10,000(0.870) + $12,000(0.756) + $15,000(0.658) + $10,000(0.572) + $ 7,000(0.497)

$40,000$40,000 = $8,700 + $9,072 + $9,870 + $5,720 + $3,479

= $36,841$36,841 [[Rate is too high!!Rate is too high!!]]


0.10 $41,444

0.05 IRR $40,000 $4,603

0.15 $36,841

X $1,4440.05 $4,603

IRR Solution (Interpolate)IRR Solution (Interpolate)IRR Solution (Interpolate)IRR Solution (Interpolate)

$1,444X

=


0.10 $41,444

0.05 IRR $40,000 $4,603

0.15 $36,841

X $1,4440.05 $4,603


$1,444X

=


0.10 $41,444

0.05 IRR $40,000 $4,603

0.15 $36,841

($1,444)(0.05) $4,603


$1,444X

X = X = 0.0157

IRR = 0.10 + 0.0157 = 0.1157 or 11.57%


IRR Interpolation Formula

Interpolate for IRR using this formula [(N1k2) – (N2k1)] / (N1 – N2) Where: N1 = Positive NPV N2 = Negative NPV k1 = discount rate for positive NPV k2 = discount rate for negative NPV


IRR Interpolation Formula

Interpolate for IRR [(N1k2) – (N2k1)] / (N1 – N2) [(1,444 x 0.15) – (- 3,159 x .1)]/(41,444

– 36,841) [(216.6 – -315.9)/4,603 532.5/4,603 11.57%


IRR Acceptance CriterionIRR Acceptance CriterionIRR Acceptance CriterionIRR Acceptance Criterion

No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13%. [ IRR < Hurdle Rate ]

No! The firm will receive 11.57% for each dollar invested in this project at a cost of 13%. [ IRR < Hurdle Rate ]

The management of Basket Wonders has determined that the hurdle rate

is 13% for projects of this type.



IRRs on the CalculatorIRRs on the Calculator

We will use the cash flow registry to solve the IRR for this problem

quickly and accurately!


Actual IRR Solution Using Actual IRR Solution Using Your Financial CalculatorYour Financial CalculatorActual IRR Solution Using Actual IRR Solution Using Your Financial CalculatorYour Financial Calculator

Steps in the ProcessStep 1: Press CF key

Step 2: Press 2nd CLR Work keys

Step 3: For CF0 Press -40000 Enter keys

Step 4: For C01 Press 10000 Enter keys

Step 5: For F01 Press 1 Enter keys






Actual IRR Solution Using Actual IRR Solution Using Your Financial CalculatorYour Financial CalculatorActual IRR Solution Using Actual IRR Solution Using Your Financial CalculatorYour Financial Calculator

Steps in the Process (Part II)Step 10:For C04 Press 10000 Enter keysStep 11:For F04 Press 1 Enter keysStep 12:For C05 Press 7000 Enter keysStep 13:For F05 Press 1 Enter keys

Step 14: Press keys

Step 15: Press IRR key

Step 16: Press CPT key

Result: Internal Rate of Return = 11.47%


IRR Strengths IRR Strengths and Weaknessesand WeaknessesIRR Strengths IRR Strengths and Weaknessesand Weaknesses


• Accounts for TVM

• Considers all cash

flows

• Less subjectivity


• Accounts for TVM

• Considers all cash

flows

• Less subjectivity

WeaknessesWeaknesses: :

• Assumes all cash flows

reinvested at the IRR

• Difficulties with project rankings

and Multiple IRRs


Net Present Value (NPV)Net Present Value (NPV)Net Present Value (NPV)Net Present Value (NPV)

NPV is the present value of an investment project’s net cash

flows minus the project’s initial cash outflow.

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

+ . . . ++ - ICOICONPV =


Net Present Value (NPV)Net Present Value (NPV)

Decision criteria: Accept if NPV > $0 Reject if NPV < $0

If the NPV is greater than $0, the firm will earn a return greater than its hurdle rate (cost of capital).


Basket Wonders has determined that the appropriate discount rate (k) for this

project is 13%.

$10,000 $7,000

NPV SolutionNPV Solution NPV SolutionNPV Solution

$10,000 $12,000 $15,000 (1.13)1 (1.13)2 (1.13)3

+ +

+ - $40,000$40,000(1.13)4 (1.13)5

NPVNPV = +


NPV SolutionNPV SolutionNPV SolutionNPV Solution

NPVNPV = $10,000(PVIF13%,1) + $12,000(PVIF13%,2) + $15,000(PVIF13%,3) + $10,000(PVIF13%,4) + $ 7,000(PVIF13%,5) – $40,000$40,000

NPVNPV = $10,000(0.885) + $12,000(0.783) + $15,000(0.693) + $10,000(0.613) + $ 7,000(0.543) – $40,000$40,000

NPVNPV = $8,850 + $9,396 + $10,395 + $6,130 + $3,801 – $40,000$40,000

= - $1,428$1,428


NPV SolutionNPV Solution (alternative layout)(alternative layout)

Period CF PVIF13%,5 PV

0 -40,000 1.000 -40,000

1 10,000 0.885 8,850

2 12,000 0.783 9,396

3 15,000 0.693 10,395

4 10,000 0.613 6,130

5 7,000 0.543 3,801

Net present value - 1,428


NPV Acceptance CriterionNPV Acceptance CriterionNPV Acceptance CriterionNPV Acceptance Criterion

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

wealth. [Reject Reject as NPVNPV < 00 ]

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

wealth. [Reject Reject as NPVNPV < 00 ]

The management of Basket Wonders has determined that the required

rate is 13% for projects of this type.



NPV on the CalculatorNPV on the Calculator

We will use the cash flow registry to solve

the NPV for this problem quickly and

accurately!

Hint: If you have not cleared the cash flows from your calculator, then you may skip to Step 15.


Actual NPV Solution Using Actual NPV Solution Using Your Financial CalculatorYour Financial CalculatorActual NPV Solution Using Actual NPV Solution Using Your Financial CalculatorYour Financial Calculator

Steps in the ProcessStep 1: Press CF key

Step 2: Press 2nd CLR Work keys

Step 3: For CF0 Press -40000 Enter keys








Steps in the Process (Part II)Step 10:For C04 Press 10000 Enter keysStep 11:For F04 Press 1 Enter keysStep 12:For C05 Press 7000 Enter keysStep 13:For F05 Press 1 Enter keys

Step 14: Press keys

Step 15: Press NPV key

Step 16: For I=, Enter 13 Enter keys

Step 17: Press CPT key

Result: Net Present Value = -$1,424.42

Actual NPV Solution Using Actual NPV Solution Using Your Financial CalculatorYour Financial CalculatorActual NPV Solution Using Actual NPV Solution Using Your Financial CalculatorYour Financial Calculator


NPV Strengths NPV Strengths and Weaknessesand WeaknessesNPV Strengths NPV Strengths and Weaknessesand Weaknesses


• Cash flows assumed to be

reinvested at the hurdle rate.

• Accounts for TVM.

• Considers all cash flows.


• Cash flows assumed to be

reinvested at the hurdle rate.

• Accounts for TVM.

• Considers all cash flows.


• May not include managerial

options embedded in the project. See Chapter 14.


Ranking & Conflicting Rankings

Ranking is necessary when: Projects are mutually exclusive Capital rationing is necessary

Conflicting rankings arise due to differences in cash flow: Timing Magnitude

Which are a result of differences in the underlying assumptions concerning the reinvestment of intermediate net cash flows.


Ranking & Conflicting Rankings

NPV assumes minimum opportunity cost – the opportunity cost of the current project would be the return on a hypothetical alternative project that just covers the cost of capital.

IRR assumes maximum opportunity cost – the maximum cost of capital a project could sustain and still be acceptable or the opportunity cost on a hypothetical alternative project offering a return equal to the IRR.


Which Is Better – NPV Or IRR? On a theoretical basis NPV is preferred as:

it assumes intermediate flows are reinvested at the firm’s cost of capital.

avoids possibility of time consuming multiple IRR’s. it directly reflects the actual project return.

On a practical basis, many financial managers prefer IRR because: it works with rates of return not dollars. NPV does not measure benefits relative to the amount

invested Most organisations use both.


Net Present Value ProfileNet Present Value ProfileNet Present Value ProfileNet Present Value Profile

Discount Rate (%)0 3 6 9 12 15

IRRNPV@13%

Sum of CF’s Plot NPV for eachdiscount rate.Three of these points are easy now!

Net

Pre

sen

t V

alu

e

$000s15

10

5

0

-4


Creating NPV Profiles Creating NPV Profiles Using the CalculatorUsing the Calculator

Hint: As long as you do not “clear” the

cash flows from the registry, simply start at Step 15 and enter a different discount rate. Each resulting NPV will provide a

“point” for your NPV Profile!


Profitability Index (PI)Profitability Index (PI)Profitability Index (PI)Profitability Index (PI)

PI is the ratio of the present value of a project’s future net cash flows to the project’s initial cash outflow.

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

+ . . . ++ ICOICOPI =

PI = 1 + [ NPVNPV / ICOICO ]

<< OR >>

Method #2:

Method #1:


PI Acceptance CriterionPI Acceptance Criterion PI Acceptance CriterionPI Acceptance Criterion

No! The PIPI is less than 1.00. This means that the project is not profitable.

[Reject Reject as PIPI < 1.001.00 ]

No! The PIPI is less than 1.00. This means that the project is not profitable.

[Reject Reject as PIPI < 1.001.00 ]

PIPI = $38,572 / $40,000

= .9643 (Method #1, previous slide)



PI Strengths PI Strengths and Weaknessesand WeaknessesPI Strengths PI Strengths and Weaknessesand Weaknesses


• Same as NPV

• Allows comparison

of different scale projects


• Same as NPV

• Allows comparison

of different scale projects


• Same as NPV

• Provides only relative

profitability

• Potential Ranking Problems


Evaluation SummaryEvaluation Summary

Method Project Comparison Decision

PBP 3.3 3.5 Accept

IRR 11.47% 13% Reject

NPV -$1,424 $0 Reject

PI .96 1.00 Reject

Basket Wonders Independent Project


Project Evaluation: Remember Project Evaluation: Remember Chapter 12 ‘New Asset’ project?Chapter 12 ‘New Asset’ project?Project Evaluation: Remember Project Evaluation: Remember Chapter 12 ‘New Asset’ project?Chapter 12 ‘New Asset’ project?

Discount rate: 16%PBP: 2.19IRR: 28.40%

NPV: 19,328.69$ PI: 1.26

Accept: Exceeds discount rate

Accept: Increase shareholder wealthAccept: Greater than 1.00

Accept: Assume want payback within 3 yrs

0 (75,000)$ (75,000)$

1 33,332$ (41,668)$ 2 36,446$ (5,222)$

3 28,147$ 22,925$ 4 37,075$ 60,000$

Cumulative CFYear Cash FlowWe will start with the cash

flows of the project and also calculate the cumulative

cash flow values.

We can use Excel functions / approaches to calculate each of the following methods from the above cash flows.


Other Project Other Project RelationshipsRelationships

• Mutually Exclusive Mutually Exclusive – A project whose acceptance precludes the acceptance of one or more alternative projects.

• DependentDependent – A project whose acceptance depends on the acceptance of one or more other projects.


Potential Problems Potential Problems Under Mutual ExclusivityUnder Mutual ExclusivityPotential Problems Potential Problems Under Mutual ExclusivityUnder Mutual Exclusivity

A. Scale of InvestmentA. Scale of Investment

B. Cash-flow PatternB. Cash-flow Pattern

C. Project LifeC. Project Life

A. Scale of InvestmentA. Scale of Investment

B. Cash-flow PatternB. Cash-flow Pattern

C. Project LifeC. Project Life

Ranking of project proposals may create contradictory results.


A. Scale DifferencesA. Scale DifferencesA. Scale DifferencesA. Scale Differences

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

NET CASH FLOWSProject S Project LEND OF YEAR

0 -$100 -$100,000

1 0 0

2 $400 $156,250


A. Scale DifferencesA. Scale DifferencesA. Scale DifferencesA. Scale Differences

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

Which project is preferred? Why?

Project IRR NPV PI

S 100% $ 231 3.31

L 25% $29,132 1.29

S 100% $ 231 3.31

L 25% $29,132 1.29


A. Scale DifferencesA. Scale DifferencesA. Scale DifferencesA. Scale Differences0 (100)$ (100,000)$ 1 -$ -$ 2 400$ 156,250$

Discount rate: 10%IRR: 100.00% 25.00%

NPV: 230.58$ 29,132.23$ PI: 3.31 1.29

BEST!!

Greatest NPV

Rate NPV - Small NPV Large0% $300.00 $56,250.002% $284.47 $50,182.624% $269.82 $44,461.916% $256.00 $39,061.948% $242.94 $33,959.19

10% $230.58 $29,132.2312% $218.88 $24,561.5414% $207.79 $20,229.3016% $197.27 $16,119.2018% $187.27 $12,216.3220% $177.78 $8,506.9422% $168.74 $4,978.5024% $160.15 $1,619.41

Year CF - Small CF - Large

$0.00

$10,000.00

$20,000.00

$30,000.00

$40,000.00

$50,000.00

$60,000.00

$0.00

$50.00

$100.00

$150.00

$200.00

$250.00

$300.00

$350.00

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24%

Axis Title

Graph the NPV Profiles for 'Small' and 'Large' projects

NPV - Small

NPV Large

Refer to VW13E-13b.xlsx on the ‘Scale’ tab.

Remember to refer to Excel spreadsheet ‘VW13E-13b.xlsx’ and the ‘Scale’ tab.


B. Cash Flow PatternB. Cash Flow PatternB. 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 -$1,200 1 1,000 100

2 500 600

3 100 1,080


D 23% $198 1.17$198 1.17

I 17% $198 1.17$198 1.17

D 23% $198 1.17$198 1.17

I 17% $198 1.17$198 1.17

Cash Flow PatternCash Flow PatternCash Flow PatternCash Flow Pattern

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

Which project is preferred?

Project IRR NPV PI


Examine NPV ProfilesExamine NPV ProfilesExamine NPV ProfilesExamine NPV Profiles

Discount Rate (%)0 5 10 15 20 25-2

00

0

200

400

600

IRR

NPV@10%

Plot NPV for eachproject at various

discount rates.

Net

Pre

sen

t V

alu

e ($

)

Project IProject I

Project DProject D


Fisher’s Rate of IntersectionFisher’s Rate of IntersectionFisher’s Rate of IntersectionFisher’s Rate of Intersection

Discount Rate ($)0 5 10 15 20 25-2

00

0

200

400

600

Net

Pre

sen

t V

alu

e ($

)

At k<10%, I is best!At k<10%, I is best! Fisher’s Fisher’s RateRate of ofIntersectionIntersection

At k>10%, D is best!At k>10%, D is best!


B. Cash Flow PatternB. Cash Flow PatternB. Cash Flow PatternB. Cash Flow Pattern

Refer to VW13E-13b.xlsx on the ‘Pattern’ tab.

0 (1,200)$ (1,200)$ 1 1,000$ 100$ 2 500$ 600$ 3 100$ 1,080$


NPV: 197.45$ 198.20$ PI: 1.16 1.17

BEST??

Greatest NPV

Rate NPV - Decrease NPV Increase0% $400.00 $580.002% $355.21 $492.454% $312.72 $411.006% $272.36 $335.138% $233.98 $264.33

10% $197.45 $198.2012% $162.63 $136.3214% $129.42 $78.3716% $97.72 $24.0118% $67.41 ($27.02)20% $38.43 ($75.00)22% $10.67 ($120.15)24% ($15.92) ($162.69)

Year CF - Decrease CF - Increase

($200.00)

($100.00)

$0.00

$100.00

$200.00

$300.00

$400.00

$500.00

$600.00

$700.00

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24%

NPV Profiles for two similar projects

NPV - Decrease

NPV Increase

Remember to refer to Excel spreadsheet ‘VW13E-13b.xlsx’ and the ‘Pattern’ tab.


C. Project Life DifferencesC. Project Life DifferencesC. Project Life DifferencesC. Project Life Differences

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

NET CASH FLOWSProject X Project YEND OF YEAR

0 -$1,000 -$1,000 1 0 2,000

2 0 0

3 3,375 0


X 50% $1,536 2.54

Y 100% $ 818 1.82

X 50% $1,536 2.54

Y 100% $ 818 1.82

Project Life DifferencesProject Life DifferencesProject Life DifferencesProject Life Differences

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

Which project is preferred? Why?

Project IRR NPV PI



Remember to refer to Excel spreadsheet ‘VW13E-13b.xlsx’ and the ‘Life’ tab.

0 (1,000)$ (1,000)$ 1 -$ 2,000$ 2 -$ -$ 3 3,375$ -$


NPV: 1,535.69$ 818.18$ PI: 2.54 1.82

BEST??

Greatest NPV

Rate NPV - X NPV - Y0% $2,375.00 $1,000.002% $2,180.34 $960.784% $2,000.36 $923.086% $1,833.72 $886.798% $1,679.18 $851.85

10% $1,535.69 $818.1812% $1,402.26 $785.7114% $1,278.03 $754.3916% $1,162.22 $724.1418% $1,054.13 $694.9220% $953.13 $666.6722% $858.64 $639.3424% $770.14 $612.90

Year CF - X CF - Y

$0.00

$500.00

$1,000.00

$1,500.00

$2,000.00

$2,500.00

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24%

NPV Profiles for X and Y - neither repeated

NPV - X

NPV - Y


Comparing Projects With Unequal Lives

Often a financial manager will need to select a project from a group of unequal life project options.

When unequal life projects are mutually exclusive, the impact of differing lives must be considered as the projects will not provide benefits over comparable time periods. This is especially important when continuing service is needed from the project under consideration.


Annualised Net Present Value Approach

Converts the net present value of unequal life projects into an equivalent annual amount (in NPV terms).

Calculated by:

Decision criteria:

Select the project with the highest ANPV

jnr

jj PV IFA

NPVANPV

,



Xi Chen Limited is evaluating two projects, X and Y. The relevant cash flows for each project are given in the table below. The applicable cost of capital for use in evaluating these equally risky projects is 10%.



Table use The NPV of each project at a 10% cost of capital is calculated by finding the present value of each net cash inflow, summing these values and subtracting the initial investment from the sum of the present values.

NPVX = [$28,000 × (0.909)] + [$33,000 × (0.826)] + [$38,000 × (0.751)] – $70,000

= ($25,452 + $27,258 + $28,538) – $70,000 = $11,248

NPVY = [$35,000 × (0.909)] + [$30,000 × (0.826)] + [$25,000 × (0.751)] + [$20,000 × (0.683)] + [$15,000 × (0.621)] + [$10,000 × (0.564)] –

$85 000 = ($31,815 + $24,780 + $18,775 + $13,660 + $9,315 + $5,640) –

$85,000 = $18 985 The NPV for project X is $11,248; that for project Y is $18,985.



Ignoring the differences in project lives, we can see that both projects are acceptable (NPVs greater than zero) and that project Y is preferred to project X.

If the projects are independent and only one could be accepted, project Y, with the larger NPV, would be preferred.

However, if the projects are mutually exclusive, their differing lives must be considered, as project Y provides three more years of service than project X.



Calculate the ANPV for each project. ANPVx = $11,248/PVIFA10%, 3 yrs

= $11,248/2.487 = $4,523

ANPVY = $18,985/PVIFA10%, 6 yrs

= $18,985/4.355 = $4,359



Reviewing the ANPVs calculated above, we can see that project X would be preferred to project Y.

Given that projects X and Y are mutually exclusive, project X would be the recommended project because it provides the higher ANPV.


Another Way to Another Way to Look at ThingsLook at Things

1. Adjust cash flows to a common terminal year if project “Y” will NOTNOT be replaced.

Compound Project Y, Year 1 @10% for 2 years.

Year 0 1 2 3

CF –$1,000 $0 $0 $2,420

Results: IRR* = 34.26% NPV = $818

*Lower IRR from adjusted cash-flow stream. X is still Best.


Replacing Projects Replacing Projects with Identical Projectswith Identical Projects

2. Use Replacement Chain Approach (Appendix B) when project “Y” will be replaced.

0 1 2 3

––$1,000 $2,000$1,000 $2,000 – –1,000 $2,0001,000 $2,000

– –1,000 $2,0001,000 $2,000

––$1,000 $1,000 $1,000 $2,000$1,000 $1,000 $1,000 $2,000

Results: IRR = 100% NPV*NPV* = $2,238.17$2,238.17

*Higher NPV, but the same IRR. Y is BestY is Best.



Remember to refer to Excel spreadsheet ‘VW13E-13b.xlsx’ and the ‘Life2’ tab.

Year 0 Year 1 Year 2 Year 3-1000 2000

0 (1,000)$ (1,000)$ -1000 20001 -$ 1,000$ -1000 20002 -$ 1,000$ -1000 1000 1000 20003 3,375$ 2,000$


NPV: 1,535.69$ 2,238.17$ PI: 2.54 3.24

BEST??

Greatest NPV

Rate NPV - X NPV - Y0% $2,375.00 $3,000.002% $2,180.34 $2,826.214% $2,000.36 $2,664.096% $1,833.72 $2,512.638% $1,679.18 $2,370.93

10% $1,535.69 $2,238.1712% $1,402.26 $2,113.6114% $1,278.03 $1,996.6016% $1,162.22 $1,886.5518% $1,054.13 $1,782.9020% $953.13 $1,685.1922% $858.64 $1,592.9524% $770.14 $1,505.79

Year CF - X CF - Y

$0.00

$500.00

$1,000.00

$1,500.00

$2,000.00

$2,500.00

$3,000.00

$3,500.00

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24%

NPV Profiles for X and Y-repeated

NPV - X

NPV - Y


Capital RationingCapital Rationing

Capital Rationing occurs when a constraint (or budget ceiling) is placed on the total size of capital expenditures

during a particular period.

Example: Julie Miller must determine what investment opportunities to undertake for Basket Wonders (BW). She is limited to a maximum expenditure of $32,500 only for this capital budgeting period.


Available Projects for BWAvailable Projects for BW

Project ICO IRR NPV PI

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


Choosing by IRRs for BWChoosing by IRRs for BW


C $ 5,000 37% $ 5,500 2.10 F 15,000 28 21,000 2.40 E 12,500 26 500 1.04 B 5,000 25 6,500 2.30

Projects C, F, and E have the three largest IRRs.

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


Choosing by NPVs for BWChoosing by NPVs for BW


F $15,000 28% $21,000 2.40 G 17,500 19 7,500 1.43 B 5,000 25 6,500 2.30

Projects F and G have the two largest NPVs.



Choosing by PIs for BWChoosing by PIs for BW


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

Projects F, B, C, and D have the four largest PIs.



Summary of ComparisonSummary of Comparison

Method Projects Accepted Value Added

PI F, B, C, and D $38,000

NPV F and G $28,500

IRR C, F, and E $27,000

PIPI generates the greatestgreatest increaseincrease in shareholder wealth shareholder wealth when a limited capital

budget exists for a single period.


Single-Point Estimate Single-Point Estimate and Sensitivity Analysisand Sensitivity AnalysisSingle-Point Estimate Single-Point Estimate and Sensitivity Analysisand Sensitivity Analysis

• Allows us to change from “single-point” (i.e., revenue, installation cost, salvage, etc.) estimates to a “what if” analysis

• Utilize a “base-case” to compare the impact of individual variable changes• E.g., Change forecasted sales units to see

impact on the project’s NPV

• Allows us to change from “single-point” (i.e., revenue, installation cost, salvage, etc.) estimates to a “what if” analysis

• Utilize a “base-case” to compare the impact of individual variable changes• E.g., Change forecasted sales units to see

impact on the project’s NPV

Sensitivity AnalysisSensitivity Analysis: A type of “what-if” uncertainty analysis in which variables or assumptions are changed from a base case in order to determine their impact on a project’s measured results (such as NPV or IRR).


Post-Completion AuditPost-Completion Audit

Post-completion Audit

A formal comparison of the actual costs and benefits 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!


Multiple IRR Problem*Multiple IRR Problem*Multiple IRR Problem*Multiple IRR Problem*

Two!! Two!! There are as many potential IRRs as there are sign changes.

Two!! Two!! There are as many potential IRRs as there are sign changes.

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

–$100 +$100 +$900 –$1,000

How many How many potentialpotential IRRs could this IRRs could this project have?project have?

* Refer to Appendix A


NPV Profile – Multiple IRRsNPV Profile – Multiple IRRsNPV Profile – Multiple IRRsNPV Profile – Multiple IRRs

Discount Rate (%)0 40 80 120 160 200

Net

Pre

sen

t V

alu

e($

000s

)

Multiple IRRs atk k = 12.95%12.95% and 191.15%191.15%

75

50

25

0

–100


NPV Profile – Multiple IRRsNPV Profile – Multiple IRRs

Hint: Your calculator will only find ONE IRR – even if there

are multiple IRRs. It will give you the

lowest IRR. In this case, 12.95%.

Chapter 13

Documents

Transcript of Chapter 13