Ch. 10: Capital Budgeting Techniques and Practice

Ch. 10: Capital Budgeting

Techniques andPractice

2000, Prentice Hall, Inc.

Capital Budgeting: the process of planning for purchases of long-term assets.

exampleexample: :

Suppose our firm must decide whether to Suppose our firm must decide whether to purchase a new plastic molding machine purchase a new plastic molding machine for $125,000. How do we decide?for $125,000. How do 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 in 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 The Ideal Evaluation Method should: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,,

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

Decision-making Criteria in Capital Budgeting

Payback 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


00 11 22 33 44 55 8866 77

(500) 150 150 150 150 150 150 150 150 (500) 150 150 150 150 150 150 150 150

Payback Period


00 11 22 33 44 55 8866 77

(500) 150 150 150 150 150 150 150 150 (500) 150 150 150 150 150 150 150 150

Payback period = Payback period = 3.33 years3.33 years..

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 Period

Drawbacks 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!

00 11 22 33 44 55 8866 77

(500) 150 150 150 150 150 (300) 0 0 (500) 150 150 150 150 150 (300) 0 0


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

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

00 11 22 33 44 55 8866 77

(500) 150 150 150 150 150 (300) 0 0 (500) 150 150 150 150 150 (300) 0 0

Other 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)

Each of these decision-making criteria:Each of these decision-making criteria: Examines all net cash flows,Examines all net cash flows, Considers the time value of money, andConsiders the time value of money, and Considers the required rate of return.Considers the required rate of return.

Net Present ValueNet Present Value

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

NPVNPV = - IO = - IO ACFACFtt

(1 + k)(1 + k) tt

nn

t=1t=1

Net 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 Value (NPV)

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.

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:

-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:

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:

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 IndexProfitability Index



(1 + k)(1 + k) tt

nn

t=1t=1


PI = IO ACFt

(1 + k)

n

t=1 t


(1 + k)(1 + k) tt

nn

t=1t=1


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

If PI is less than 1, If PI is less than 1, rejectreject..


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)

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.




(1 + k)(1 + k) tt

nn

t=1t=1



(1 + k)(1 + k) tt

nn

t=1t=1

n

t=1IRR: = IO

ACFt

(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

ACFt

(1 + IRR) t

Calculating 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 Calculator

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

IRR


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 50 1 2 3 4 5

(500) 200 100 (200) 400 300(500) 200 100 (200) 400 300



0 1 2 3 4 50 1 2 3 4 5

(500) 200 100 (200) 400 300(500) 200 100 (200) 400 300

1 1



0 1 2 3 4 50 1 2 3 4 5

(500) 200 100 (200) 400 300(500) 200 100 (200) 400 300

1 2 1 2



0 1 2 3 4 50 1 2 3 4 5

(500) 200 100 (200) 400 300(500) 200 100 (200) 400 300

1 2 31 2 3

Summary 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 50 1 2 3 4 5

(900) 300 400 400 500 600(900) 300 400 400 500 600

Summary 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 50 1 2 3 4 5

(900) 300 400 400 500 600(900) 300 400 400 500 600

Capital RationingCapital Rationing

Suppose that you have evaluated Suppose that you have evaluated 5 capital investment projects5 capital investment projects for for your company.your company.

Suppose that the VP of Finance Suppose that the VP of Finance has given you a has given you a limited capital limited capital budgetbudget..

How do you decide which How do you decide which projects to select?projects to select?


You could rank the projects by IRR:You could rank the projects by IRR:


IRRIRR

5%5%

10%10%

15%15%

20%20%

25%25%

$$

11

You could rank the projects by IRR:You could rank the projects by IRR:


You could rank the projects by IRR:You could rank the projects by IRR:IRRIRR

5%5%

10%10%

15%15%

20%20%

25%25%

$$

11 22



5%5%

10%10%

15%15%

20%20%

25%25%

$$

11 22 33



5%5%

10%10%

15%15%

20%20%

25%25%

$$

11 22 33 44



5%5%

10%10%

15%15%

20%20%

25%25%

$$

11 22 33 44 55



5%5%

10%10%

15%15%

20%20%

25%25%

$$

11 22 33 44 55

$X

Our budget is limitedOur budget is limitedso we accept only so we accept only projects 1, 2, and 3.projects 1, 2, and 3.



5%5%

10%10%

15%15%

20%20%

25%25%

$$

11 22 33

$X

Our budget is limitedOur budget is limitedso we accept only so we accept only projects 1, 2, and 3.projects 1, 2, and 3.

Problems with Project RankingProblems with Project Ranking

1) Mutually exclusive projects of 1) Mutually exclusive projects of unequal unequal sizesize (the (the size disparitysize disparity problem) problem)

The NPV decision may not agree with The NPV decision may not agree with IRR or PI.IRR or PI.

Solution:Solution: select the project with the select the project with the largest largest NPVNPV..

Size Disparity exampleSize Disparity example

Project AProject A

yearyear cash flowcash flow

00 (135,000)(135,000)

11 60,000 60,000

22 60,000 60,000

33 60,000 60,000

required return = 12%required return = 12%

IRR = 15.89%IRR = 15.89%

NPV = $9,110NPV = $9,110

PI = 1.07PI = 1.07


Project BProject B


00 (30,000) (30,000)

11 15,000 15,000

22 15,000 15,000

33 15,000 15,000


IRR = 23.38%IRR = 23.38%

NPV = $6,027NPV = $6,027

PI = 1.20PI = 1.20

Project AProject A


00 (135,000)(135,000)

11 60,000 60,000

22 60,000 60,000

33 60,000 60,000


IRR = 15.89%IRR = 15.89%

NPV = $9,110NPV = $9,110

PI = 1.07PI = 1.07


Project BProject B


00 (30,000) (30,000)

11 15,000 15,000

22 15,000 15,000

33 15,000 15,000


IRR = 23.38%IRR = 23.38%

NPV = $6,027NPV = $6,027

PI = 1.20PI = 1.20

Project AProject A


00 (135,000)(135,000)

11 60,000 60,000

22 60,000 60,000

33 60,000 60,000


IRR = 15.89%IRR = 15.89%

NPV = $9,110NPV = $9,110

PI = 1.07PI = 1.07

Problems with Project RankingProblems with Project Ranking

2) The 2) The time disparitytime disparity problem with mutually problem with mutually exclusive projects.exclusive projects.

NPV and PI assume cash flows are NPV and PI assume cash flows are reinvested at the required rate of returnreinvested at the required rate of return for for the project.the project.

IRR assumes cash flows are IRR assumes cash flows are reinvested at reinvested at the IRR.the IRR.

The NPV or PI decision may not agree with The NPV or PI decision may not agree with the IRR. the IRR.

Solution:Solution: select the largest select the largest NPVNPV..

Time Disparity exampleTime Disparity example

Project AProject A yearyear cash flowcash flow

00 (48,000) (48,000)

11 1,200 1,200

22 2,400 2,400

33 39,000 39,000

44 42,000 42,000


IRR = 18.10%IRR = 18.10%

NPV = $9,436NPV = $9,436

PI = 1.20PI = 1.20


Project BProject B yearyear cash flowcash flow

00 (46,500) (46,500)

11 36,500 36,500

22 24,000 24,000

33 2,400 2,400

44 2,400 2,400


IRR = 25.51%IRR = 25.51%

NPV = $8,455NPV = $8,455

PI = 1.18PI = 1.18


00 (48,000) (48,000)

11 1,200 1,200

22 2,400 2,400

33 39,000 39,000

44 42,000 42,000


IRR = 18.10%IRR = 18.10%

NPV = $9,436NPV = $9,436

PI = 1.20PI = 1.20


Project BProject B yearyear cash flowcash flow

00 (46,500) (46,500)

11 36,500 36,500

22 24,000 24,000

33 2,400 2,400

44 2,400 2,400


IRR = 25.51%IRR = 25.51%

NPV = $8,455NPV = $8,455

PI = 1.18PI = 1.18


00 (48,000) (48,000)

11 1,200 1,200

22 2,400 2,400

33 39,000 39,000

44 42,000 42,000


IRR = 18.10%IRR = 18.10%

NPV = $9,436NPV = $9,436

PI = 1.20PI = 1.20

Mutually Exclusive Investments Mutually Exclusive Investments with with Unequal LivesUnequal Lives

Suppose our firm is planning to expand Suppose our firm is planning to expand and we have to select 1 of 2 machines. and we have to select 1 of 2 machines.

They differ in terms of They differ in terms of economic lifeeconomic life and and capacitycapacity. .

How do we decide which machine to How do we decide which machine to select?select?

The after-tax cash flows are:The after-tax cash flows are:

YearYear Machine 1Machine 1 Machine 2Machine 2

0 (45,000) (45,000)0 (45,000) (45,000)

1 20,000 12,0001 20,000 12,000

2 20,000 12,0002 20,000 12,000

3 20,000 12,0003 20,000 12,000

4 12,0004 12,000

5 12,0005 12,000

6 12,0006 12,000 Assume a required return of 14%.Assume a required return of 14%.

Step 1: Calculate NPVStep 1: Calculate NPV

NPVNPV11 = = $1,433$1,433 NPVNPV22 = = $1,664$1,664

So, does this mean #2 is better?So, does this mean #2 is better? No! The two NPVs can’t be No! The two NPVs can’t be

compared!compared!

Step 2: Equivalent Annual Annuity (EAA) method

If we assume that each project will be If we assume that each project will be replaced an infinite number of timesreplaced an infinite number of times in the in the future, we can convert each NPV to an future, we can convert each NPV to an annuityannuity..

The projects’ EAAs The projects’ EAAs cancan be compared to be compared to determine which is the best project!determine which is the best project!

EAA:EAA: Simply annualize the NPV over the Simply annualize the NPV over the project’s life.project’s life.

EAA with your calculator:EAA with your calculator:

Simply “spread the NPV over the life Simply “spread the NPV over the life of the project” of the project”

Machine 1Machine 1:: PV = 1433, N = 3, I = 14, PV = 1433, N = 3, I = 14,

solve: solve: PMT = -617.24PMT = -617.24. .

Machine 2Machine 2:: PV = 1664, N = 6, I = 14, PV = 1664, N = 6, I = 14,

solve: solve: PMT = -427.91PMT = -427.91..

EAAEAA11 = $617 = $617 EAAEAA22 = $428 = $428 This tells us that:This tells us that: NPVNPV11 = annuity of = annuity of $617$617 per year. per year. NPVNPV22 = annuity of = annuity of $428$428 per year. per year. So, we’ve reduced a problem with So, we’ve reduced a problem with

different time horizons to a couple of different time horizons to a couple of annuities.annuities.

Decision Rule:Decision Rule: Select the highest Select the highest EAA.EAA. We would choose machine #1. We would choose machine #1.

Step 3: Convert back to NPV


Assuming infinite replacement, the Assuming infinite replacement, the EAAs are actually perpetuities. Get the EAAs are actually perpetuities. Get the PV by dividing the EAA by the required PV by dividing the EAA by the required rate of return.rate of return.



NPV NPV 11 = 617/.14 = $4,407 = 617/.14 = $4,407



NPV NPV 11 = 617/.14 = $4,407 = 617/.14 = $4,407

NPV NPV 22 = 428/.14 = $3,057 = 428/.14 = $3,057


Assuming infinite replacement, the EAAs Assuming infinite replacement, the EAAs are actually perpetuities. Get the PV by are actually perpetuities. Get the PV by dividing the EAA by the required rate of dividing the EAA by the required rate of return.return.

NPV NPV 11 = 617/.14 = $4,407 = 617/.14 = $4,407

NPV NPV 22 = 428/.14 = $3,057 = 428/.14 = $3,057

This doesn’t change the answer, of course; This doesn’t change the answer, of course; it just converts EAA to a NPV that can be it just converts EAA to a NPV that can be compared.compared.

Documents

Ch. 10: Capital Budgeting Techniques and Practice