Capital Budgeting - Joan

Prepared by: Joan C. Basay

Capital Budgeting Techniques

Discounted Cash Discounted Cash Flow TechniquesFlow Techniques

Proposed 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 P10,000; P12,000;

P15,000; P10,000; and P7,000, respectively, for each of the Years 1 through 5. The initial

cash outlay will be P40,000.

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 P10,000; P12,000;

P15,000; P10,000; and P7,000, respectively, for each of the Years 1 through 5. The initial

cash outlay will be P40,000.

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.

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

+ . . . ++ICO =

P15,000 P10,000 P7,000

IRR Solution IRR Solution

P10,000 P12,000

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

Find the interest rate (IRR) that causes the discounted cash flows to equal P40,000.

+ +

++P40,000 =

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

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

P40,000P40,000 = P10,000(PVIF10%,1) + P12,000(PVIF10%,2) + P15,000(PVIF10%,3) + P10,000(PVIF10%,4) + P 7,000(PVIF10%,5)

P40,000P40,000 = P10,000(.909) + P12,000(.826) + P15,000(.751) + P10,000(.683) + P 7,000(.621)

P40,000P40,000 = P9,090 + P9,912 + P11,265 + P6,830 + P4,347

= P41,444P41,444 [[Rate is too low!!Rate is too low!!]]

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

P40,000P40,000 = P10,000(PVIF15%,1) + P12,000(PVIF15%,2) + P15,000(PVIF15%,3) + P10,000(PVIF15%,4) + P 7,000(PVIF15%,5)

P40,000P40,000 = P10,000(.870) + P12,000(.756) + P15,000(.658) + P10,000(.572) + P 7,000(.497)

P40,000P40,000 = P8,700 + P9,072 + P9,870 + P5,720 + P3,479

= P36,841P36,841 [[Rate is too high!!Rate is too high!!]]

.10 P41,444

.05 IRR P40,000 P4,603

.15 P36,841

X P1,444.05 P4,603

IRR Solution (Interpolate)IRR Solution (Interpolate)

P1,444X

=

.10 P41,444

.05 IRR P40,000 P4,603

.15 P36,841

(P1,444)(0.05) P4,603

IRR Solution (Interpolate)IRR Solution (Interpolate)

P1,444X

X = X = .0157

IRR = .10 + .0157 = .1157 or 11.57%

IRR 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.

Should this project be accepted?

IRRs on the Calculator

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

and accurately!

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

Steps in the ProcessStep 1: Press CF keyStep 2: Press 2nd CLR Work keysStep 3: For CF0 Press -40000 Enter keysStep 4: For C01 Press 10000 Enter keysStep 5: For F01 Press 1 Enter keysStep 6: For C02 Press 12000 Enter keysStep 7: For F02 Press 1 Enter keysStep 8: For C03 Press 15000 Enter keysStep 9: For F03 Press 1 Enter keys

Actual IRR Solution Using Your Financial CalculatorActual IRR Solution Using Your 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 keysStep 14: Press keysStep 15: Press IRR keyStep 16: Press CPT key

Result: Internal Rate of Return = 11.47%

IRR Strengths and Weaknesses

IRR Strengths and Weaknesses

StrengthsStrengths: : – Accounts for

TVM– Considers all

cash flows– Less

subjectivity

StrengthsStrengths: : – 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)

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 =

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

13%.

P10,000 P7,000

NPV Solution NPV Solution

P10,000 P12,000 P15,000 (1.13)1 (1.13)2 (1.13)3

+ +

+ - P40,000P40,000(1.13)4 (1.13)5

NPVNPV = +

NPV SolutionNPV Solution

NPVNPV = P10,000(PVIF13%,1) + P12,000(PVIF13%,2) + P15,000(PVIF13%,3) + P10,000(PVIF13%,4) + P 7,000(PVIF13%,5) - P40,000P40,000

NPVNPV = P10,000(.885) + P12,000(.783) + P15,000(.693) + P10,000(.613) + P 7,000(.543) - P40,000P40,000

NPVNPV = P8,850 + P9,396 + P10,395 + P6,130 + P3,801 - P40,000P40,000

= - P1,428P1,428

NPV 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 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 Your Financial Calculator


Steps in the ProcessStep 1: Press CF keyStep 2: Press 2nd CLR Work keysStep 3: For CF0 Press -40000 Enter keysStep 4: For C01 Press 10000 Enter keysStep 5: For F01 Press 1 Enter keysStep 6: For C02 Press 12000 Enter keysStep 7: For F02 Press 1 Enter keysStep 8: For C03 Press 15000 Enter keysStep 9: For F03 Press 1 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 keysStep 14: Press keysStep 15: Press NPV keyStep 16: For I=, Enter 13 Enter keysStep 17: Press CPT keyResult: Net Present Value = -P1,424.42



NPV Strengths and Weaknesses

NPV Strengths and Weaknesses

StrengthsStrengths::– Cash flows

assumed to be reinvested at the hurdle rate.

– Accounts for TVM.– Considers all

cash flows.

StrengthsStrengths::– Cash flows

assumed to be reinvested at the hurdle rate.

– Accounts for TVM.– Considers all

cash flows.

WeaknessesWeaknesses::– May not include managerial options embedded in the project. See Chapter 14.

Net 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

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P000s15

10

5

0

-4

Creating NPV Profiles Using 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)

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 Criterion PI 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 = P38,572 / P40,000= .9643 (Method #1, 13-34)


PI Strengths and Weaknesses

PI Strengths and Weaknesses

StrengthsStrengths::– Same as NPV– Allows comparison of different scale projects

StrengthsStrengths::– Same as NPV– Allows comparison of different scale projects

WeaknessesWeaknesses::– Same as NPV– Provides only relative profitability– Potential Ranking

Problems

Evaluation 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

Other Project Relationships

• Mutually ExclusiveMutually 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 Under Mutual Exclusivity

Potential Problems Under 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 Differences

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

NET CASH FLOWSProject S Project LEND OF YEAR

0 -P100 -P100,000

1 0 0

2 P400 P156,250

Scale DifferencesScale Differences

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

Which project is preferred? Why?Project IRR NPV PI

S 100% P 231 3.31

L 25% P29,132 1.29

S 100% P 231 3.31

L 25% P29,132 1.29

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 -P1,200 -P1,200 1 1,000 100

2 500 600

3 100 1,080

D 23% P198 1.17P198 1.17

I 17% P198 1.17P198 1.17

D 23% P198 1.17P198 1.17

I 17% P198 1.17P198 1.17

Cash Flow PatternCash Flow Pattern

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

Which project is preferred?

Project IRR NPV PI

Examine 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

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)

Project IProject I

Project DProject D

Fisher’s Rate of IntersectionFisher’s Rate of Intersection

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

00

0

200

400

600

Net

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)

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!

C. 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 -P1,000 -P1,000 1 0 2,000

2 0 0

3 3,375 0

X 50% P1,536 2.54

Y 100% P 818 1.82

X 50% P1,536 2.54

Y 100% P 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

Another Way to Look 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 -P1,000 P0 P0 P2,420

Results: IRR* = 34.26% NPV = P818*Lower IRR from adjusted cash-flow stream. X is still Best.

Replacing Projects with Identical Projects

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

0 1 2 3

-P1,000 P2,000-P1,000 P2,000 -1,000 P2,000-1,000 P2,000

-1,000 P2,000-1,000 P2,000

-P1,000 P1,000 P1,000 P2,000-P1,000 P1,000 P1,000 P2,000

Results: IRR = 100% NPV*NPV* = P2,238.17P2,238.17

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

Capital 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 P32,500 only for this capital budgeting period.

Available Projects for BW

Project ICO IRR NPV PIA P 500 18% P 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 E12,500 26 500 1.04 F15,000 28 21,000 2.40 G

17,500 19 7,500 1.43 H25,000 15 6,000 1.24

Choosing by IRRs for BW

Project ICO IRR NPV PIC P 5,000 37% P 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 P27,000 with a P32,500 outlay.

Choosing by NPVs for BW

Project ICO IRR NPV PI F P15,000 28% P21,000 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 BW

Project ICO IRR NPV PI F P15,000 28% P21,000 2.40

B 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 Comparison

Method Projects Accepted Value Added

PI F, B, C, and D P38,000

NPV F and G P28,500

IRR C, F, and E P27,000

PIPI generates the greatestgreatest increaseincrease in shareholder wealth shareholder wealth when a limited capital budget exists for a single period.

Single-Point Estimate and Sensitivity AnalysisSingle-Point Estimate

and 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 Audit

Post-completion AuditA 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*

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:

-P100 +P100 +P900 -P1,000

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

* Refer to Appendix A

NPV Profile -- Multiple IRRsNPV Profile -- Multiple IRRs

Discount Rate (%)0 40 80 120 160 200

Net

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

75

50

25

0

-100

NPV 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%.

Capital Budgeting - Joan

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