8/3/2019 2006111512164611635642060

1/60

Capital Budgeting

Technigue

Chapter 9

8/3/2019 2006111512164611635642060

2/60

1

KEY TERMSBenefit-Cost Ratio (see Profitability Index)

Capital Budgeting

Capital RationingEquivalent Annual Annuity (EAA)

Internal Rate of Return (IRR)

Mutually Exclusive Projects

Net Present Value (NPV)

Payback period

Profitability Index (PI or Benefit-Cost Ratio)

8/3/2019 2006111512164611635642060

3/60

2

Key Concepts and SkillsUnderstand the payback rule and itsshortcomings

Understand accounting rates of return andtheir problems

Understand the internal rate of return and itsstrengths and weaknesses

Understand the net present value rule andwhy it is the best decision criteria

8/3/2019 2006111512164611635642060

4/60

3

Capital budgetingPersonal capital budgeting;

Companys capital budgeting;

National fiscal budgeting.

8/3/2019 2006111512164611635642060

5/60

4

capital budgeting, FINDING PROFITABLE PROJECTS

to evaluate profitable projects orinvestments in fixed assets, a processreferred to as capital budgeting,

Axiom 5: The Curse of CompetitiveMarketsWhy Its Hard to FindExceptionally Profitable Projects.

8/3/2019 2006111512164611635642060

6/60

5

8Good Decision CriteriaWe need to ask ourselves the following

questions when evaluating decision criteria

Does the decision rule adjust for the time valueof money?

Does the decision rule adjust for risk?

Does the decision rule provide information on

whether we are creating value for the firm?

8/3/2019 2006111512164611635642060

7/60

6

Net Present Value

The netpresentvalue (NPV) of an

investment proposal is equal to thepresent

value of its annual net cash flows after taxes

less the investments initial outlay.

8/3/2019 2006111512164611635642060

8/60

7

!

n

t 1

t

t

k)(1

ACF NPV = - IO

8/3/2019 2006111512164611635642060

9/60

8

NPV Illustration of Investment in New

Machinery

AFTER-TAX

CASH FLOW

Inflow year1 15,000

2 14,000

3 13,000

4 12,000

5 11,000

Initial outlay $40,000

8/3/2019 2006111512164611635642060

10/60

9

alculationfor NPV IllustrationofInvestmentinNew Machinery

PRESENT VALUE

AFTER-TAX FACTOR AT PRESENT

CASH FLOW 12 PERCENT VALUE

2 14,000 .797 11,1583 13,000 .712 9,256

4 12,000 .636 7,632

5 11,000 .567 6,237

itial outlay 40,000

year1 15,000 .893 $13,395

value of cash flows $ 47,678

sent value $ 7,678

8/3/2019 2006111512164611635642060

11/60

10

8.1.2 Net Present Value

(NPV,

)NPV is the difference between the marketvalue of a project and its cost

How much value is created fromundertaking an investment?

The first step is to estimate the expected futurecash flows.

The second step is to estimate the requiredreturn for projects of this risk level.

The third step is to find the present value of thecash flows and subtract the initial investment.

8/3/2019 2006111512164611635642060

12/60

11

8

.1

.3 NPV Decision RuleIf the NPV is positive, accept the project

A positive NPV means that the project is

expected to add value to the firm and willtherefore increase the wealth of the owners.

Since our goal is to increase owner wealth,

NPV is a direct measure of how well thisproject will meet our goal.

8/3/2019 2006111512164611635642060

13/60

12

8.1

.1

Project Example InformationYou are looking at a new project and you

have estimated the following cash flows:

Year0:CF = -165,000Year1:CF = 63,120;

Year2: CF = 70,800;

Year3: CF = 91

,08

0;Your required return for assets of this risk is

12%.

8/3/2019 2006111512164611635642060

14/60

13

8.1.4 Computing NPV for the

ProjectUsing the formulas:

NPV = 63,120/(1.12) + 70,800/(1.12)2 +

91,080/(1.12)3

165,000 = 12,627.42Using the calculator:

CF0 = -165,000; C01 = 63,120; F01 = 1; C02 =

70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV;

I = 12; CPT NPV = 12,627.42

Do we accept or reject the project?

8/3/2019 2006111512164611635642060

15/60

14

8.1.5 Decision Criteria Test -

NPVDoes the NPV rule account for the timevalue of money?-Y

Does the NPV rule account for the risk ofthe cash flows?-N

Does the NPV rule provide an indicationabout the increase in value?-Y

Should we consider the NPV rule for ourprimary decision criteria?-Y

8/3/2019 2006111512164611635642060

16/60

15

8.1.6 Calculating NPVs with a

SpreadsheetSpreadsheets are an excellent way tocompute NPVs, especially when you have

to compute the cash flows as well.Using the NPV function

The first component is the required returnentered as a decimal

The second component is the range of cashflows beginning with year 1

Subtract the initial investment after computingthe NPV

8/3/2019 2006111512164611635642060

17/60

16

8

.2 Payback Period (

)How long does it take to get the initial cost

back in a nominal sense?

ComputationEstimate the cash flows

Subtract the future cash flows from the initialcost until the initial investment has been

recoveredDecision Rule Accept if the payback

period is less than some preset limit

8/3/2019 2006111512164611635642060

18/60

17

8.2.1 Computing PaybackFor The

ProjectAssume we will accept the project if it pays

back within two years.

Year1:

165,000

63,

120 =

10

1,88

0 still torecover

Year2: 101,88070,800 = 31,080 still torecover

Year3: 31

,08

091

,08

0 = -6

0,000project paysback in year 3

Do we accept or reject the project?

8/3/2019 2006111512164611635642060

19/60

18

2 years vs 2 years

A B

Initial cash outlay $10,000 $10,000

Annual net cash inflows Year 1 $ 6,000 $ 5,000

2 4,000 5,000

3 3,000 0

4 2,000 0

5 1,000 0

8/3/2019 2006111512164611635642060

20/60

19

2 years and4years

Initial cash outlay $10,000 $10,000

Annual net cash inflows

Year 1 $ 6,000 $ 1,000

2 4,000 2,000

3 3,000 3000

4 2,000 4000 5 1,000 5000

8/3/2019 2006111512164611635642060

21/60

20

8.2.3 Decision Criteria Test -

PaybackDoes the payback rule account for the timevalue of money?-N

Does the payback rule account for the riskof the cash flows?-N

Does the payback rule provide an indicationabout the increase in value?-Y

Should we consider the payback rule for ourprimary decision criteria?-Y

8/3/2019 2006111512164611635642060

22/60

21

8.2.4 Advantages and Disadvantages

of PaybackAdvantages

Easy to understand

Adjusts for

uncertainty of later

cash flows

Biased towardsliquidity(

)

DisadvantagesIgnores the time value ofmoney

Requires an arbitrary () cutoff point

Ignores cash flows beyondthe cutoff date

Biased against long-termprojects, such as research anddevelopment, and new

projects

8/3/2019 2006111512164611635642060

23/60

22

8.3 Average Accounting Return

(

)There are many different definitions foraverage accounting return

The one used in the book is:Average net income / average book value

Note that the average book value depends onhow the asset is depreciated.

Need to have a target cutoff rateDecision Rule: Accept the project if theAAR is greater than a preset rate.

8/3/2019 2006111512164611635642060

24/60

23

8.3.1 Computing AARFor The

ProjectYou are looking at a new project and you have estimated thefollowing cash flows:

Year0: CF = -165,000

Year1

: CF

=63,120

; NI =13,620

Year2: CF = 70,800; NI = 3,300

Year3: CF = 91,080; NI = 29,100

Average Book Value = 59,660

Assume we require an average accounting return of25%

Average Net Income:(13,620 + 3,300 + 29,100) /3 = 15,340

AAR = 15,340/59,660 = .257 = 25.7%

Do we accept or reject the project?

8/3/2019 2006111512164611635642060

25/60

24

8.3.2 Decision Criteria Test -

AARDoes the AAR rule account for the timevalue of money?-N

Does the AAR rule account for the risk ofthe cash flows?-N

Does the AAR rule provide an indicationabout the increase in value?-Y

Should we consider the AAR rule for ourprimary decision criteria?

8/3/2019 2006111512164611635642060

26/60

25

8.3.3Advantages and Disadvantages

of AARAdvantages

Easy to calculate

Needed information

will usually be

available

Disadvantages

Not a true rate of return;

time value of money is

ignored

Uses an arbitrary

benchmark cutoff rate

Based on accounting

net income and bookvalues, not cash flows

and market values

8/3/2019 2006111512164611635642060

27/60

26

8.4 Internal Rate of Return(

)

This is the most important alternative to

NPV

It is often used in practice and is intuitivelyappealing

It is based entirely on the estimated cash

flows and is independent of interest ratesfound elsewhere

8/3/2019 2006111512164611635642060

28/60

27

8.4.1 IRRDefinition and Decision

RuleDefinition: IRR is the return that makes the

NPV = 0

Decision Rule: Accept the project if theIRR is greater than the required return

8/3/2019 2006111512164611635642060

29/60

28

8.4.2 Computing IRRFor The

ProjectExample: You are looking at a new project and you haveestimated the following cash flows:

Year0: CF = -165,000

Year1: CF = 63,120;

Year2: CF = 70,800;

Year3: CF = 91,080;

Required return 12%

Calculator

Enter the cash flows as you did with NPVPress IRR and then CPT

IRR = 16.13% > 12% required return

Do we accept or reject the project?

8/3/2019 2006111512164611635642060

30/60

29

8.4.3 NPV Profile For The

Project

-20,000

-10,000

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22

Discount Rate

NPV

IRR = 16.13%

8/3/2019 2006111512164611635642060

31/60

30

8.4.4 Decision Criteria Test - IRR

Does the IRR rule account for the time value

of money?-Y

Does the IRR rule account for the risk of thecash flows? -N

Does the IRR rule provide an indication

about the increase in value? -YShould we consider the IRR rule for our

primary decision criteria?

8/3/2019 2006111512164611635642060

32/60

31

PROJECT A PROJECT B

$500 $500 $500 $300 $300 $300 $300 $300 $300

1 2 3 year 1 2 3 4 5 6 year

$1,000 $1,000NPV = $234.50 NPV = $306.50

PI = 1.2435 PI = 1.306

IRR = 23% IRR = 20%

Examining the discounted cash flow criteria, we find that the net present value and

profitability index criteria indicate that project B is the better project, whereas theinternal rate of return criterion favors project A. this ranking inconsistency is caused bythe different life spans of the projects being compared. In this case the decision is adifficult one because the projects are not comparable.

8/3/2019 2006111512164611635642060

33/60

32

8.4.5 Advantages of IRR

Knowing a return is intuitively appealing

It is a simple way to communicate the value

of a project to someone who doesnt knowall the estimation details

If the IRR is high enough, you may not

need to estimate a required return, which isoften a difficult task

8/3/2019 2006111512164611635642060

34/60

33

8.5 Summary of Decisions For

The Project

Summary

Net Present Value Accept

Payback Period Reject

Average Accounting Return Reject

Internal Rate of Return Accept

8/3/2019 2006111512164611635642060

35/60

34

8.5.1 Calculating IRRs With A

Spreadsheet

You start with the cash flows the same as

you did for the NPV

You use the IRR functionYou first enter your range of cash flows,

beginning with the initial cash flow

You can enter a guess, but it is not necessary

The default format is a whole percentyou

will normally want to increase the decimal

places to at least two

8/3/2019 2006111512164611635642060

36/60

35

8.5.2 NPV Vs. IRR

NPV and IRR will generally give us the

same decision

ExceptionsNon-conventional cash flows cash flow signs

change more than once

Mutually exclusive projects

Initial investments are substantially different

Timing of cash flows is substantially different

8/3/2019 2006111512164611635642060

37/60

36

8.5.2.1 IRR and Nonconventional

Cash Flows

When the cash flows change sign more thanonce, there is more than one IRR

When you solve for IRR you are solving forthe root of an equation and when you crossthe x-axis more than once, there will bemore than one return that solves the

equation (Figure 8.6 on p238)If you have more than one IRR, which onedo you use to make your decision?

8/3/2019 2006111512164611635642060

38/60

37

8.5.2.2 Another Example

Nonconventional Cash Flows

Suppose an investment will cost $90,000 initiallyand will generate the following cash flows:

Year1: 132,000

Year2: 100,000Year3: -150,000

The required return is 15%.

By calucualting, we got IRR=10.11%

Should we accept or reject the project?

8/3/2019 2006111512164611635642060

39/60

38

8.5.2.2.1 Summary of Decision

Rules

The NPV is positive at a required return of15%, so you should Accept

If you use the financial calculator, youwould get an IRR of10.11% which wouldtell you to Reject

You need to recognize that there are non-

conventional cash flows and look at theNPV profile.

(example 8.4 on p239)

8/3/2019 2006111512164611635642060

40/60

39

8.5.2.3 IRR and Mutually Exclusive

Projects

Mutually exclusive projects

If you choose one, you cant choose the other

Example: You can choose to attend graduateschool next year at either Harvard or Stanford,but not both

Intuitively you would use the following

decision rules:NPV choose the project with the higher NPV

IRRchoose the project with the higher IRR

8/3/2019 2006111512164611635642060

41/60

40

8.5.2.3.1 Example With Mutually

Exclusive Projects

Period Project A Project B

0 -500 -400

1 325 325

2 325 200

IRR 19.43% 22.17%

NPV 64.05 60.74

8/3/2019 2006111512164611635642060

42/60

41

8.5.2.3.2Example With MutuallyExclusive Projects

The required return for both projects is 10%.

Which project should you accept and why?

B has greater total cash flow, but it pays back more slowlythan A. As a result, it has a higher NPV at lower discount

rate

We are ultimately interested in creating value for the

stockholders, so we choose whichever provides biggerNPV.

8/3/2019 2006111512164611635642060

43/60

42

8.5.2.3.2 NPV Profiles

($40.00)

($20.00)

$0.00

$20.00

$40.00

$60.00

$80.00$100.00

$120.00

$140.00

$160.00

0 0.05 0.1 0.15 0.2 0.25 0.3

Discount Rate

NPV A

B

IRR for A = 19.43%

IRR for B = 22.17%

Crossover Point = 11.8%

8/3/2019 2006111512164611635642060

44/60

43

8.5.3 Conflicts Between NPV

and IRR

NPV directly measures the increase in value

to the firm

Whenever there is a conflict between NPVand another decision rule, you should

always use NPV

IRR is unreliable in the following situationsNon-conventional cash flows

Mutually exclusive projects//

8/3/2019 2006111512164611635642060

45/60

44

8.6 Profitability Index (

)

Measures the benefit per unit cost, based on

the time value of moneyp242

A profitability index of1.1 implies that forevery $1 of investment, we create an

additional $0.10 in value

This measure can be very useful insituations where we have limited capital

8/3/2019 2006111512164611635642060

46/60

45

Profitability Index (Benefit-

Cost Ratio)

The profitability index (PI), or benefit-

cost ratio, is the ratio of the present value

of the future net cash flows to the initial

outlay.

8/3/2019 2006111512164611635642060

47/60

46

IO

k

ACFn

t

tt

! 1 )1(PI =

8/3/2019 2006111512164611635642060

48/60

47

PRESENT VALUE

AFTER-TAX FACTOR AT PRESENT

CASH FLOW 10 PERCENT VALUE

Inflow year1 15,000 0.909 13,635

2 8,000 0.826 6,608

3 10,000 0.751 7,5104 12,000 0.683 8,196

5 14,000 0.621 8,694

6 16,000 0.564 9,024

Initial outlay $50,000 1.000 $50,000

8/3/2019 2006111512164611635642060

49/60

48

IO

k

ACFn

t

t

t

! 1 )

1(

000,50$024,9$694,8196,8$510,7$608,6$635,13$

000,50$

667,53$

= 1.0733

8/3/2019 2006111512164611635642060

50/60

49

8.6.1 Advantages and Disadvantages

of Profitability Index

Advantages

Closely related to NPV,

generally leading to

identical decisions

Easy to understand and

communicate

May be useful when

available investmentfunds are limited

Disadvantages

May lead to incorrect

decisions in

comparisons ofmutually exclusive

investments

8/3/2019 2006111512164611635642060

51/60

50

500 000 700 000

600 000

0.70

0.30

1 //%

500 000300 000

0.400.60

21/

2

/

/%

300 000 300 000

200 000

100 000

0.40

0.50

0.10

8/3/2019 2006111512164611635642060

52/60

51

8/3/2019 2006111512164611635642060

53/60

52

Objective 4

PROBLEMS IN PROJECT RANKING-CAPITAL

RATIONING, MUTUALLY EXCLUSIVE PROJECTS,

AND PROBLEMS WITH THE IRR.

1 Size disparity

2 Time disparity

3 Unequallive

8/3/2019 2006111512164611635642060

54/60

53

Capital-Rationing Example ofFive Indivisible Projects

Project Initial Outlay Profitability Index Net Present Value

A $200,000 2.4 $280,000

B 200,000 2.3 260,000

C 800,000 1.7 560,000

D 300,000 1.3 90,000

E 300,000 1.2 60,000

8/3/2019 2006111512164611635642060

55/60

54

Investment Evaluation A Primary A Secondary Total Using

Methods Used: Method Method This Method

Payback period 24% 59% 83%

Internal rate of return 88% 11% 99%

Net present value 63% 22% 85%

Profitability index 15% 18% 33%

8/3/2019 2006111512164611635642060

56/60

55

Project Size and Decision-Making Authority

Project Size Typical Boundaries Primary Decision Site

Very small Up to $100,000 Plant

Small $100,000 to $1 million Division

Medium $1 million to $10 million Corporate

investment committee

Large Over $10 million CEO & board

8/3/2019 2006111512164611635642060

57/60

56

8.7 Capital Budgeting In Practice

p243

We should consider several investment

criteria when making decisionsNPV and IRR are the most commonly used

primary investment criteria

Payback is a commonly used secondaryinvestment criteria

8/3/2019 2006111512164611635642060

58/60

57

QuickQuiz

Consider an investment that costs $100,000 andhas a cash inflow of $25,000 every year for5years. The required return is 9% and required

payback is 4 years.What is the payback period?

What is the NPV?

What is the IRR?

Should we accept the project?What decision rule should be the primary decisionmethod?

When is the IRR rule unreliable?

8/3/2019 2006111512164611635642060

59/60

58

12%

k*=20%

/

/

/

1

2

3

4

5

30 000

20 000

40 000

40 000

30 000

0.8929

0.7972

0.7118

0.6355

0.5674

26 787

15 944

28 472

25 420

17 022

0.8333

0.6944

0.5787

0.4823

0.4019

24 999

13 888

23 148

19 292

12 057

=

113 645=

100 000

=13 645

=

9 3384

=

100 000

=

6 616

8/3/2019 2006111512164611635642060

60/60

!

!n

t tf

ttI

R

CF

1 )1(

)(

E