capital budgeting decisions criteria

2005, Pearson Prentice Hall

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, andc) 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?



0 1 2 3 4 5 86 7

(500) 150 150 150 150 150 150 150 150



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, what for projects like ours, what would be our decision?would be our decision?

Accept the projectAccept the project..


Drawbacks of Payback PeriodDrawbacks of Payback Period

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

moneymoney.. Does not consider any Does not consider any required required

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

project’s project’s cash flowscash flows..


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


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

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


0 1 2 3 4 5

(500) 250 250 250 250 250


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


0 1 2 3 4 5

(500) 250 250 250 250 250


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


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


0 1 2 3 4 5

(500) 250 250 250 250 250


0 1 2 3 4 5

(500) 250 250 250 250 250


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


0 1 2 3 4 5

(500) 250 250 250 250 250


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


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

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

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 ValueNPV 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.Using TVM:Using TVM:

P/Y = 1 N = 5 I = 15 P/Y = 1 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 HP10B:NPV with the HP10B:

-250,000 -250,000 CFjCFj 100,000 100,000 CFjCFj 5 5 shift Nj shift Nj 15 15 I/YR I/YR shift NPVshift NPV You should get NPV = You should get NPV = 85,215.5185,215.51..

NPV with the HP17BII:NPV with the HP17BII:

Select Select CFLOCFLO mode. mode. FLOW(0)=? FLOW(0)=? -250,000 INPUT-250,000 INPUT FLOW(1)=? FLOW(1)=? 100,000 INPUT100,000 INPUT #TIMES(1)=1 #TIMES(1)=1 5 INPUT 5 INPUT

EXITEXIT CALC 15 I% NPVCALC 15 I% NPV You should get NPV = You should get NPV = 85,215.5185,215.51

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

Select CF mode.Select CF mode.


Select CF mode.Select CF mode. CFo=? CFo=? -250,000 -250,000 ENTERENTER


Select CF mode.Select CF mode. CFo=? CFo=? -250,000 -250,000 ENTERENTER C01=? C01=? 100,000 100,000 ENTERENTER


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


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



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

Profitability Index

Profitability Index

NPV = - IO FCFt(1 + k) t

n

t=1

Profitability Index

PI = IO FCFt(1 + k)

n

t=1 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 with the HP10B:PI with the HP10B:

-250,000-250,000 CFjCFj 100,000 100,000 CFjCFj 5 5 shift Nj shift Nj 15 15 I/YR I/YR shift NPVshift NPV Add back IO:Add back IO: + 250,000+ 250,000 Divide by IO:Divide by IO: / 250,000 =/ 250,000 = You should get You should get PI = 1.34PI = 1.34

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.




n

t=1



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..

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



0 1 2 3 4 5

(500) 200 100 (200) 400 300

1 1



0 1 2 3 4 5

(500) 200 100 (200) 400 300

1 2



0 1 2 3 4 5

(500) 200 100 (200) 400 300

1 2 3

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

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%.

MIRRMIRR

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

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capital budgeting decisions criteria