2005, Pearson Prentice Hall

CHAPTER 11CHAPTER 11Capital Budgeting Capital Budgeting

Decision CriteriaDecision Criteria

CHAPTER 11CHAPTER 11The Basics of Capital BudgetingThe Basics of Capital Budgeting

Should we build this

plant?

What is capital budgeting?What is capital budgeting?

The process of planning for purchases of The process of planning for purchases of long-term assets. long-term assets.

Analysis of potential additions to fixed Analysis of potential additions to fixed assets.assets.

Long-term decisions; involve large Long-term decisions; involve large expenditures, therefore irreversible once expenditures, therefore irreversible once made.made.

Very important to firm’s future.Very important to firm’s future.

Capital BudgetingCapital Budgeting

For exampleFor example: : Suppose our firm must Suppose our firm must decide whether to purchase a new plastic decide whether to purchase a new plastic molding machine for $125,000. How do molding machine for $125,000. How do we decide?we decide?

Will the machine be Will the machine be profitableprofitable?? Will our firm earn a Will our firm earn a high rate of returnhigh rate of return

on the investment?on the investment?

Decision-making Criteria Decision-making Criteria in Capital Budgetingin Capital Budgeting

How do we decide How do we decide if a capital if a capital investment investment

project should project should be accepted or be accepted or

rejected?rejected?

The ideal evaluation method should:The ideal evaluation method should:

a) include a) include all cash flowsall cash flows that occur that occur during the life of the project,during the life of the project,

b) consider the b) consider the time value of moneytime value of money, and, and

c) incorporate the c) incorporate the required rate of required rate of returnreturn on the project. on the project.

Decision-making Criteria in Decision-making Criteria in Capital BudgetingCapital Budgeting

Steps to capital budgetingSteps to capital budgeting

1.1. Estimate CFs (inflows & outflows).Estimate CFs (inflows & outflows).

2.2. Assess riskiness of CFs.Assess riskiness of CFs.

3.3. Determine the appropriate cost of capital.Determine the appropriate cost of capital.

4.4. Find NPV and/or IRR.Find NPV and/or IRR.

5.5. Accept if NPV > 0 and/or IRR > WACC.Accept if NPV > 0 and/or IRR > WACC.

What is the difference between independent What is the difference between independent and mutually exclusive projects?and mutually exclusive projects?

Independent projects – if the cash flows of one Independent projects – if the cash flows of one project are unaffected by the acceptance of the project are unaffected by the acceptance of the other projects.other projects.

Mutually exclusive projects – if the cash flows Mutually exclusive projects – if the cash flows of one project can be adversely impacted by the of one project can be adversely impacted by the acceptance of the other project. These are a set acceptance of the other project. These are a set of projects that perform essentially the same of projects that perform essentially the same task, so that acceptance of one will necessarily task, so that acceptance of one will necessarily mean rejection of the others.mean rejection of the others.

What is the difference between normal and What is the difference between normal and nonnormal cash flow streams?nonnormal cash flow streams?

Normal cash flow stream – Cost (negative CF) followed by a series of Normal cash flow stream – Cost (negative CF) followed by a series of positive cash inflows. One change of signs. positive cash inflows. One change of signs.

(- + + + + +)(- + + + + +)

CF($) (500) 150 150 150 150 150 Year 0 1 2 3 4 5

Non-normal cash flow stream – Two or more changes of signs. Most Non-normal cash flow stream – Two or more changes of signs. Most common: Cost (negative CF), then string of positive CFs, then cost to common: Cost (negative CF), then string of positive CFs, then cost to close project. .close project. .(- + + - + +). Examples: (- + + - + +). Examples: Nuclear power plant, strip Nuclear power plant, strip mine, etc.mine, etc.

CF ($) (500) 200 100 (200) 400 300Year 0 1 2 3 4 5

Payback PeriodPayback Period

How long will it take for the project How long will it take for the project to generate enough cash to pay for to generate enough cash to pay for itself?itself?

0 1 2 3 4 5 86 7

(500) 150 150 150 150 150 150 150 150

Payback PeriodPayback Period

How long will it take for the project How long will it take for the project to generate enough cash to pay for to generate enough cash to pay for itself?itself?

Payback period = 3.33 years (50/150 =0.33)

0 1 2 3 4 5 86 7

(500) 150 150 150 150 150 150 150 150

Is a Is a 3.33 year3.33 year payback period good? payback period good? Is it acceptable?Is it acceptable? Firms that use this method will compare Firms that use this method will compare

the payback calculation to some the payback calculation to some standardstandard set by the firm. set by the firm.

If our senior management had set a cut-If our senior management had set a cut-off of off of 5 years5 years for projects like ours, for projects like ours, what would be our decision?what would be our decision?

Accept the projectAccept the project..

Payback PeriodPayback Period

Further Example:Further Example:Calculating paybackCalculating payback

PaybackL = 2 + / = 2.375 years

CFt -100 10 60 100Cumulative -100 -90 0 50

0 1 2 3

=

2.4

30 80

80

-30

Project L

PaybackS = 1 + / = 1.6 years

CFt -100 70 100 20Cumulative -100 0 20 40

0 1 2 3

=

1.6

30 50

50-30

Project S

Strengths of paybackStrengths of payback

Provides an indication of a project’s risk and Provides an indication of a project’s risk and liquidity.liquidity.

Easy to calculate and understand.Easy to calculate and understand.

Drawbacks of Payback PeriodDrawbacks of Payback Period

Firm cutoffs are Firm cutoffs are subjectivesubjective.. Does not consider Does not consider time value of moneytime value of money.. Does not consider any Does not consider any required rate of required rate of

returnreturn.. Ignores cash flows occurring after the Ignores cash flows occurring after the

payback period.payback period.

Drawbacks of Payback PeriodDrawbacks of Payback Period

Does not consider all of the Does not consider all of the project’s cash flows.project’s cash flows.

Consider this cash flow stream!Consider this cash flow stream!

0 1 2 3 4 5 86 7

(500) 150 150 150 150 150 150 150 150

Drawbacks of Payback PeriodDrawbacks of Payback Period

Does not consider all of the project’s Does not consider all of the project’s cash flows.cash flows.

This project is clearly unprofitable, but we This project is clearly unprofitable, but we would would acceptaccept it based on a 4-year payback it based on a 4-year payback criterion!criterion!

0 1 2 3 4 5 86 7

(500) 150 150 150 150 150 150 150 150

Discounted PaybackDiscounted Payback Uses discounted cash flows rather than Uses discounted cash flows rather than

raw cash flows.raw cash flows. Discounts the cash flows at the firm’s Discounts the cash flows at the firm’s

required rate of return.required rate of return. Payback period is calculated using these Payback period is calculated using these

discounted net cash flows.discounted net cash flows.

ProblemsProblems:: Cutoffs are still subjective.Cutoffs are still subjective.

Still does not examine all cashStill does not examine all cash flows. flows.

Discounted PaybackDiscounted Payback

0 1 2 3 4 5

(500) 250 250 250 250 250

DiscountedDiscounted

YearYear Cash FlowCash Flow CF (14%)CF (14%)

00 -500-500 -500.00-500.00

11 250 250 219.30219.30 1 year1 year

280.70280.70

22 250 250 192.37192.37 2 years2 years

88.3388.33

33 250 250 168.74 168.74

Discounted PaybackDiscounted Payback

0 1 2 3 4 5

(500) 250 250 250 250 250

DiscountedDiscounted

YearYear Cash FlowCash Flow CF (14%)CF (14%) 00 -500-500 -500.00-500.00

11 250 250 219.30219.30 1 year1 year 280.70280.70 22 250 250 192.37192.37 2 years2 years 88.33 88.33 (88.33/168.74)=(88.33/168.74)=

33 250 250 168.74 168.74 .52 years.52 years

Discounted PaybackDiscounted Payback

0 1 2 3 4 5

(500) 250 250 250 250 250

DiscountedDiscounted

YearYear Cash FlowCash Flow CF (14%)CF (14%)

00 -500-500 -500.00-500.00

11 250 250 219.30219.30 1 year1 year

280.70280.70

22 250 250 192.37192.37 2 years2 years

88.3388.33

33 250 250 168.74 168.74 .52 years.52 years

The Discounted Payback

is 2.52 years

Further Example:Further Example:Discounted payback periodDiscounted payback period

Disc PaybackL = 2 + / = 2.7 years

CFt -100 10 60 80

Cumulative -100 -90.91 18.79

0 1 2 3

=

2.7

60.11

-41.32

PV of CFt -100 9.09 49.59

41.32 60.11

10%

Other MethodsOther Methods(Discounted Cash Flow Methods)(Discounted Cash Flow Methods)

1) 1) Net Present ValueNet Present Value (NPV) (NPV)2) 2) Profitability IndexProfitability Index (PI) (PI)3) 3) Internal Rate of ReturnInternal Rate of Return (IRR) (IRR)

Consider each of these decision-making Consider each of these decision-making criteria:criteria:

All net cash flows.All net cash flows. The time value of money.The time value of money. The required rate of return.The required rate of return.

NPV = the total PV of the annual net cash flows - the initial outlay.

NPVNPV = - IO = - IO FCFFCFtt

(1 + k)(1 + k) tt

nn

t=1t=1

Net Present ValueNet Present Value

Net Present ValueNet Present Value

Decision RuleDecision Rule::

If NPV is positive, If NPV is positive, acceptaccept.. If NPV is negative, If NPV is negative, rejectreject..

NPV ExampleNPV Example

Suppose we are considering a capital Suppose we are considering a capital investment that costs investment that costs $250,000$250,000 and and provides annual net cash flows of provides annual net cash flows of $100,000$100,000 for five years. The firm’s for five years. The firm’s required rate of return is required rate of return is 15%15%..

NPV ExampleNPV Example

0 1 2 3 4 5

(250,000) 100,000 100,000 100,000 100,000 100,000

Suppose we are considering a capital Suppose we are considering a capital investment that costs investment that costs $250,000$250,000 and and provides annual net cash flows of provides annual net cash flows of $100,000$100,000 for five years. The firm’s for five years. The firm’s required rate of return is required rate of return is 15%15%..

Net Present ValueNet Present Value

NPV is just the PV of the annual cash NPV is just the PV of the annual cash flows minus the initial outflow.flows minus the initial outflow.

Mathematical Solution:Mathematical Solution:

PV of cash flows = $100,000(PVIFA15%,5)PV of cash flows = $100,000(PVIFA15%,5)

= $100,000(3.352)= $100,000(3.352)

PV of cash flows =PV of cash flows = $335,216$335,216

- Initial outflow- Initial outflow ($250,000)($250,000)

= Net PV= Net PV $85,216$85,216

EXAMPLE:EXAMPLE:What is What is ProjectProject S’s and L’s NPVs? S’s and L’s NPVs?

YearYear CFs CFs PVs PVs CFCFLL PV PV LL

00 -100-100 -100-100 -$100.00 -$100.00

11 70 70 10 10 9.09 9.09

22 50 50 60 60 49.59 49.59

33 20 20 80 80 60.11 60.11

NPVs = $19.98NPVs = $19.98 NPVNPVLL= $ 18.79= $ 18.79

(k = 10%)(k = 10%)

RationaleRationale for the NPV method for the NPV method

NPVNPV = PV of inflows – Cost= PV of inflows – Cost= Net gain in wealth= Net gain in wealth

If projects are independent, accept if the If projects are independent, accept if the project NPV > 0.project NPV > 0.

If projects are mutually exclusive, accept If projects are mutually exclusive, accept projects with the highest positive NPV, projects with the highest positive NPV, those that add the most value.those that add the most value.

In this example, we would accept S if the 2 In this example, we would accept S if the 2 projects are mutually exclusive (NPVprojects are mutually exclusive (NPVss > > NPVNPVLL), and would accept both if they are ), and would accept both if they are independent projects.independent projects.

Profitability Index

NPV = - IO FCFt

(1 + k) t

n

t=1

Profitability Index

PI = IO FCFt

(1 + k)

n

t=1 t

NPV = - IO FCFt

(1 + k) t

n

t=1

Decision Rule:

If PI is greater than or equal to 1, accept.

If PI is less than 1, reject.

Profitability Index

Mathematical SolutionMathematical Solution

PI = $335,216/$250,000PI = $335,216/$250,000 = 1.34= 1.34

PI = IO FCFt

(1 + k)

n

t=1 t

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

IRRIRR:: The return on the firm’s The return on the firm’s invested capital. IRR is simply the invested capital. IRR is simply the rate of returnrate of return that the firm earns on that the firm earns on its capital budgeting projects.its capital budgeting projects.

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

NPV = - IO FCFt

(1 + k) t

n

t=1

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

NPV = - IO FCFt

(1 + k) t

n

t=1

n

t=1IRR: = IO

FCFt

(1 + IRR) t

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

IRR is the IRR is the rate of returnrate of return that makes the that makes the PV PV of the cash flowsof the cash flows equalequal to the to the initial outlayinitial outlay..

This looks very similar to our Yield to This looks very similar to our Yield to Maturity formula for bonds. In fact, YTM Maturity formula for bonds. In fact, YTM isis the IRR of a bond. the IRR of a bond.

n

t=1IRR: = IO

FCFt

(1 + IRR) t

Calculating IRRCalculating IRR

Looking again at our problem:Looking again at our problem: The IRR is the discount rate that The IRR is the discount rate that

makes the PV of the projected cash makes the PV of the projected cash flows flows equalequal to the initial outlay. to the initial outlay.

0 1 2 3 4 5

(250,000) 100,000 100,000 100,000 100,000 100,000

IRR with your CalculatorIRR with your Calculator

IRR is easy to find with your financial IRR is easy to find with your financial calculator.calculator.

Just enter the cash flows as you did Just enter the cash flows as you did with the NPV problem and solve for with the NPV problem and solve for IRR.IRR.

You should get You should get IRR = 28.65%!IRR = 28.65%!

IRRIRR

Decision RuleDecision Rule::

If IRR is greater than or equal to If IRR is greater than or equal to the required rate of return, the required rate of return, acceptaccept..

If IRR is less than the required If IRR is less than the required rate of return, rate of return, rejectreject..

IRR Acceptance CriteriaIRR Acceptance Criteria

If IRR > k, accept project.If IRR > k, accept project. If IRR < k, reject project.If IRR < k, reject project.

If projects are independent, accept both If projects are independent, accept both projects, if both projects’ IRR > k.projects, if both projects’ IRR > k.

If projects are mutually exclusive, accept If projects are mutually exclusive, accept the project with the higher IRRthe project with the higher IRR ..

IRR is a good decision-making tool as IRR is a good decision-making tool as long as cash flows are long as cash flows are conventionalconventional. . (- + + + + +)(- + + + + +)

Problem:Problem: If there are multiple sign If there are multiple sign changes in the cash flow stream, we changes in the cash flow stream, we could get multiple IRRs. could get multiple IRRs. (- + + - + +)(- + + - + +)

0 1 2 3 4 5

(500) 200 100 (200) 400 300

1 2 3

Rationale for the IRR methodRationale for the IRR method

If IRR > WACC, the project’s rate of If IRR > WACC, the project’s rate of return is greater than its costs. There is return is greater than its costs. There is some return left over to boost some return left over to boost stockholders’ returns.stockholders’ returns.

Summary ProblemSummary Problem

Enter the cash flows only once.Enter the cash flows only once. Find the Find the IRRIRR.. Using a discount rate of Using a discount rate of 15%,15%, find find NPVNPV.. Add back IO and divide by IO to get Add back IO and divide by IO to get PIPI..

0 1 2 3 4 5

(900) 300 400 400 500 600

Summary ProblemSummary Problem

IRR = 34.37%.IRR = 34.37%. Using a discount rate of 15%, Using a discount rate of 15%,

NPV = $510.52.NPV = $510.52. PI = 1.57PI = 1.57..

0 1 2 3 4 5

(900) 300 400 400 500 600

NPV ProfilesNPV Profiles

A graphical representation of project NPVs at A graphical representation of project NPVs at various different costs of capital.various different costs of capital.

k k NPVNPVLL NPVNPVSS

00 $50$50 $40$40 55 33 33 29291010 19 19 20201515 7 7 12122020 (4) (4) 55

Drawing NPV profilesDrawing NPV profiles

-10

0

10

20

30

40

50

60

5 10 15 20 23.6

NPV ($)

Discount Rate (%)

IRRL = 18.1%

IRRS = 23.6%

Crossover Point = 8.7%

SL

.

.

...

.

..

.

. .

Comparing the NPV and IRR methodsComparing the NPV and IRR methods

If projects are independent, the two If projects are independent, the two methods always lead to the same methods always lead to the same accept/reject decisions.accept/reject decisions.

If projects are mutually exclusive …If projects are mutually exclusive … If k > crossover point, the two methods lead If k > crossover point, the two methods lead

to the same decision and there is no conflict.to the same decision and there is no conflict. If k < crossover point, the two methods lead If k < crossover point, the two methods lead

to different accept/reject decisions.to different accept/reject decisions.

FindingFinding the crossover pointthe crossover point(using financial calculator)(using financial calculator)

1.1. Find cash flow differences between the projects Find cash flow differences between the projects for each year.for each year.

2.2. Enter these differences in CFLO register, then Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68%, rounded to press IRR. Crossover rate = 8.68%, rounded to 8.7%.8.7%.

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

4.4. If profiles don’t cross, one project dominates the If profiles don’t cross, one project dominates the other.other.

Reasons why NPV profiles crossReasons why NPV profiles cross

Size (scale) differences – the smaller project frees Size (scale) differences – the smaller project frees up funds at t = 0 for investment. The higher the up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, opportunity cost, the more valuable these funds, so high k favors small projects (Project S with so high k favors small projects (Project S with higher NPV).higher NPV).

Timing differences – the project with faster Timing differences – the project with faster payback provides more payback provides more CFs in early years forCFs in early years for reinvestmentreinvestment. If k is high, early CF especially . If k is high, early CF especially good, NPVgood, NPVS S > NPV> NPVLL..

(CF(CFLL=-100, +10, +60, +80; NPV=18.79)=-100, +10, +60, +80; NPV=18.79)

(CFs = -100, +70, +50, +20; NPV = $19.98)(CFs = -100, +70, +50, +20; NPV = $19.98)

Reinvestment rate assumptionsReinvestment rate assumptions

NPV method assumes CFs are reinvested at k, NPV method assumes CFs are reinvested at k, the opportunity cost of capital.the opportunity cost of capital.

IRR method assumes CFs are reinvested at IRR method assumes CFs are reinvested at IRR.IRR.

Assuming CFs are reinvested at the Assuming CFs are reinvested at the opportunity cost of capital is more realistic, so opportunity cost of capital is more realistic, so NPV method is the best. NPV method should NPV method is the best. NPV method should be used to choose between mutually exclusive be used to choose between mutually exclusive projects.projects.

Perhaps a hybrid of the IRR that assumes cost Perhaps a hybrid of the IRR that assumes cost of capital reinvestment is needed.of capital reinvestment is needed.

Since managers prefer the IRR to the NPV Since managers prefer the IRR to the NPV method, is there a better IRR measure?method, is there a better IRR measure?

Yes, Yes, Modified Internal Rate of Return (MIRR)Modified Internal Rate of Return (MIRR).. IRRIRR assumes that all cash flows are assumes that all cash flows are

reinvested at the reinvested at the IRRIRR.. MIRRMIRR provides a rate of return measure provides a rate of return measure

that assumes cash flows are reinvested at that assumes cash flows are reinvested at the the required rate of return (or WACC)required rate of return (or WACC)..

MIRR is the discount rate that causes the MIRR is the discount rate that causes the PV of a project’s terminal value (TV) to PV of a project’s terminal value (TV) to equal the PV of costs. TV is found by equal the PV of costs. TV is found by compounding inflows at WACC.compounding inflows at WACC.

MIRR Steps:MIRR Steps:

Calculate the PV of the cash outflows.Calculate the PV of the cash outflows. Using the required rate of return.Using the required rate of return.

Calculate the FV of the cash inflows at Calculate the FV of the cash inflows at the last year of the project’s time line. the last year of the project’s time line. This is called the terminal value (TV).This is called the terminal value (TV). Using the required rate of return.Using the required rate of return.

MIRR: the discount rate that equates MIRR: the discount rate that equates the PV of the cash outflows with the PV the PV of the cash outflows with the PV of the terminal value, ie, that makes:of the terminal value, ie, that makes:

PVPVoutflowsoutflows = PV = PVinflowsinflows

MIRRMIRRUsing our time line and a 15% rate:Using our time line and a 15% rate: PV outflows = PV outflows = (900).(900). FV inflows (at the end of year 5) = FV inflows (at the end of year 5) = 2,837.2,837. MIRR: FV = 2837, PV = (900), N = 5.MIRR: FV = 2837, PV = (900), N = 5. Solve: I = Solve: I = 25.81%.25.81%.

0 1 2 3 4 5

(900) 300 400 400 500 600

Using our time line and a 15% rate:Using our time line and a 15% rate: PV outflows = PV outflows = (900).(900). FV inflows (at the end of year 5) = FV inflows (at the end of year 5) = 2,837.2,837. MIRR: FV = 2837, PV = (900), N = 5.MIRR: FV = 2837, PV = (900), N = 5. Solve: I = Solve: I = 25.81%.25.81%.

ConclusionConclusion: : The project’s IRR of The project’s IRR of 34.37%34.37% assumes that cash flows are reinvested at assumes that cash flows are reinvested at 34.37%.34.37%.

Assuming a reinvestment rate of Assuming a reinvestment rate of 15%,15%, the project’s MIRR is the project’s MIRR is 25.81%.25.81%.

MIRRMIRR