Chapter 9 - Capital Budgeting Decision Criteria

Chapter 9 - Chapter 9 - Capital Budgeting Capital Budgeting Decision CriteriaDecision Criteria

Capital BudgetingCapital Budgeting:: The process The process of planning for purchases of long-of planning for purchases of long-

term assets.term assets.

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

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

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 standard set by the firm.standard 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

Drawbacks of Payback PeriodDrawbacks of Payback Period

Projects A BProjects A B

Cash outlay -10,000 -10,000Cash outlay -10,000 -10,000

Annual CF Annual CF

Year 1 6,000 5,000Year 1 6,000 5,000

Year 2 4,000 5,000Year 2 4,000 5,000

Year 3 3,000 0 Year 3 3,000 0

Year 4 2,000 0Year 4 2,000 0

Year 5 1,000 0Year 5 1,000 0

Drawbacks of Payback PeriodDrawbacks of Payback Period

Firm cutoffs are subjective.Firm cutoffs are subjective. Does not consider time value of Does not consider time value of

money.money. Does not consider any required Does not consider any required

rate of return.rate of return. Does not consider all of the Does not consider all of the

project’s cash flows.project’s cash flows.

Discounted PaybackDiscounted Payback

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 Payback period is calculated using these discounted net cash flows.these discounted net cash flows.

ProblemsProblems:: Cutoffs are still subjective.Cutoffs are still subjective. Still does not examine all cash flows.Still does not examine all cash flows.


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


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

Advantages of PaybackAdvantages of Payback

Use free cash flow, not accounting Use free cash flow, not accounting profitsprofits

Easy understood and calculateEasy understood and calculate Often used as a rough screening deviceOften used as a rough screening device

Other MethodsOther 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


Decision RuleDecision Rule::

If NPV is >=0, If NPV is >=0, acceptaccept.. If NPV is negative, If NPV is negative, rejectreject..

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%..


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.

N = 5 I = 15 N = 5 I = 15

PMT = 100,000PMT = 100,000

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

NPV with the TI BAII Plus:NPV with the TI BAII Plus:

Select CF mode.Select CF mode. CFo=? CFo=? -250,000 -250,000 ENTERENTER C01=? C01=? 100,000 100,000 ENTERENTER F01= 1 F01= 1 5 5 ENTERENTER NPV NPV I= I= 15 15 ENTERENTER

CPTCPT You should get You should get NPV = 85,215.51NPV = 85,215.51


Free Cash FlowFree Cash Flow

Initial outlay -40,000Initial outlay -40,000

Year 1 15,000Year 1 15,000

Year 2 14,000Year 2 14,000

Year 3 13,000Year 3 13,000

Year 4 12,000Year 4 12,000

Year 5 11,000Year 5 11,000

12% required rate of return, what is NPV?12% required rate of return, what is NPV?


Free Cash Flow Discount Factor PVFree Cash Flow Discount Factor PV

Year 1 $15,000 .893 $13,395 Year 1 $15,000 .893 $13,395

Year 2 14,000 .797 11,158Year 2 14,000 .797 11,158

Year 3 13,000 .712 9,256Year 3 13,000 .712 9,256

Year 4 12,000 .636 7,632Year 4 12,000 .636 7,632

Year 5 11,000 .567 Year 5 11,000 .567 6,2376,237

Present Value of free cash flow $47,678Present Value of free cash flow $47,678

Initial outlay Initial outlay -40,000-40,000

Net present value $7,678Net present value $7,678


Financial calculator: select CF modeFinancial calculator: select CF mode

Enter CF0 – CF5 one by oneEnter CF0 – CF5 one by one

Fre = 1Fre = 1

I = 12I = 12

NPV = $7,678NPV = $7,678

Features of NPVFeatures of NPV

Deals with free cash flowDeals with free cash flow

Consider the time value of moneyConsider the time value of money

Acceptance of a project using this Acceptance of a project using this

criterion increases the value of firmcriterion increases the value of firm

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

PI ExamplePI Example

Free Cash FlowFree Cash Flow


Year 1 15,000Year 1 15,000

Year 2 14,000Year 2 14,000

Year 3 13,000Year 3 13,000

Year 4 12,000Year 4 12,000

Year 5 11,000Year 5 11,000

12% required rate of return, what is PI?12% required rate of return, what is PI?

PI ExamplePI Example

Free Cash Flow Discount Factor PVFree Cash Flow Discount Factor PV

Year 1 $15,000 .893 $13,395 Year 1 $15,000 .893 $13,395

Year 2 14,000 .797 11,158Year 2 14,000 .797 11,158

Year 3 13,000 .712 9,256Year 3 13,000 .712 9,256

Year 4 12,000 .636 7,632Year 4 12,000 .636 7,632

Year 5 11,000 .567 Year 5 11,000 .567 6,2376,237

Present Value of free cash flow $47,678Present Value of free cash flow $47,678


PI = 47,678 / 40,000 = 1.19PI = 47,678 / 40,000 = 1.19

• Yield the same accept-reject decision

• NPV: absolute dollar

• PI: relative measure

Compare NPV and PI

• Example:

• Project A: NPV = $10

• Project B: NPV = $20

• Which one is relatively better from the

perspective of profitability?

Compare NPV and PI

• Example:

• It depends on your initial outlay.

• Suppose initial outlay of A = $50

• Suppose initial outlay of B = $150

• PI of A = (10 + 50) / 50 = 1.2

• PI of B = (20 + 150) / 150 = 1.13

• A’s profitability is higher

Compare NPV and PI

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.


NPV = - IO FCFt

(1 + k) t

n

t=1

n

t=1IRR: = IO

FCFt

(1 + IRR) t


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..

ExampleExample

A B CA B C

Initial outlay -10,000 -10,000 -10,000Initial outlay -10,000 -10,000 -10,000

FCF year 1 3,362 0 1,000FCF year 1 3,362 0 1,000

FCF year 2 3,362 0 3,000FCF year 2 3,362 0 3,000

FCF year 3 3,362 0 6,000FCF year 3 3,362 0 6,000

FCF year 4 3,362 13,605 7,000FCF year 4 3,362 13,605 7,000

Required rate of return = 10%Required rate of return = 10%

Will we accept these projects?Will we accept these projects?

ExampleExample

IRR for A = 13% >10% acceptIRR for A = 13% >10% accept

IRR for B = 8% < 10% rejectIRR for B = 8% < 10% reject

IRR for C = 19.04% > 10% acceptIRR for C = 19.04% > 10% accept

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

Relationships of MethodsRelationships of Methods

If NPV is “+”, IRR must be greater than the If NPV is “+”, IRR must be greater than the

required rate of return. Also, PI is >1.required rate of return. Also, PI is >1.

All three discounted cash flow criteria are All three discounted cash flow criteria are

consistent and give similar accept-reject consistent and give similar accept-reject

decision.decision.

Relationships of MethodsRelationships of Methods

NPV: assumes cash flow can be reinvested NPV: assumes cash flow can be reinvested at the project’s required rate of returnat the project’s required rate of return

IRR: assumes cash flow can be reinvested at IRR: assumes cash flow can be reinvested at the project’s IRRthe project’s IRR

NPV is superior to IRRNPV is superior to IRR As discount rate increases, PNV dropsAs discount rate increases, PNV drops

One Drawback of IRROne Drawback of IRR

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

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

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

Modified Internal Rate of ReturnModified Internal Rate of Return(MIRR)(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 provides a rate of return measure that assumes cash flows are measure that assumes cash flows are reinvested at the reinvested at the required rate of required rate of returnreturn..

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

Decision rule:Decision rule:

If MIRR is greater than or equal to the If MIRR is greater than or equal to the

required rate of return, required rate of return, acceptaccept..

If MIRR is less than the required rate of If MIRR is less than the required rate of

return, return, rejectreject..

MIRRMIRR

Find profitable projects, and make Find profitable projects, and make

accurate cash flow forecastingaccurate cash flow forecasting

Correctly evaluate themCorrectly evaluate them

Choose one as main criterionChoose one as main criterion

Use others as robustness check Use others as robustness check

How to Use Evaluating How to Use Evaluating CriteriaCriteria

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Chapter 9 - Capital Budgeting Decision Criteria