chapter 9 capital budgeting © 2000 south-western college publishing

Chapter 9Chapter 9

Capital BudgetingCapital Budgeting

© 2000 South-Western College Publishing

Capital BudgetingCapital BudgetingA major part of the financial management of the firm

Kinds Of Spending In Business

Short term - to support day to day operations

Long term - to support long lived equipment and projects

Long term spending is called Capital

Capital BudgetingCapital BudgetingPlanning and Justifying How Capital Dollars

Are Spent On Long Term ProjectsProvides methods for evaluating whether projects make financial sense

and for choosing among them

TM 9-1 Slide 1 of 2

Project Types and RiskProject Types and Risk

Projects fall into three general categories characterized by increasing risk:

Replacement

Expansion

New Venture

STAND-ALONE AND MUTUALLY EXCLUSIVE PROJECTS

The Stand-Alone DecisionIs the project a good idea if there's no competition

for the resources to do it

The Mutually Exclusive DecisionSelecting either project excludes the other

Choosing among different ways to do something or among

separate projects competing for limited resources

TM 9-1 Slide 2 of 2

PROJECT CASH FLOWSPROJECT CASH FLOWSThe first step in capital budgeting is to represent all projects as a series of

incremental cash flows

Example: A new venture takes an initial investment of $50,000, will lose $10,000 in the first year, and earn $15,000 per year for five years

C0 ($50,000)

C1 ($10,000)

C2 $15,000

C3 $15,000

C4 $15,000

C5 $15,000

C6 $15,000

TM 9-2 Slide 1 of 2

PROJECT CASH FLOWS (cont.)PROJECT CASH FLOWS (cont.)

The typical pattern involves outflows first

and inflows later

C0, the Initial Outlay, is virtually always negative

(A few of the later flows may also be negative)

Estimating cash flows is the most difficult part of capital budgeting (Chapter 10)

For now, we'll take them as given

TM 9-2 Slide 2 of 2

THE COST OF CAPITALTHE COST OF CAPITALThe average rate of return the firm pays to its long term

investors for the use of their money.

Intuitive Purpose:

An investment makes sense only if it earns more than the

cost of funds put into it.

A weighted average concept where the weights are the proportionate amounts invested in each kind of capital

Portion Return

Equity .75 x 10% = 7.5%

Debt .25 x 8% = 2.0%

Weighted Average Cost of Capital 9.5%

TM 9-3

CAPITAL BUDGETING TECHNIQUESCAPITAL BUDGETING TECHNIQUES

Payback periodNet Present Value (NPV)

Internal Rate of Return (IRR)

Profitability Index (PI)

Each involves calculating a number for every project under consideration and applying decision rules to those numbers

to make accept or reject choices

TM 9-4 Slide 1 of 4

PAYBACK PERIODPAYBACK PERIODMeasure the time it takes for the project to "break even"

in terms of undiscounted cash flows

Example:Year 0 1 2 3 4

Cash Flow (Ci)

($200,000) $60,000 $60,000 $60,000 $60,000

Cumulative Cash Flow

($200,000) ($140,000) ($80,000) ($20,000) $40,000

Payback Period = 3.33 years

TM 9-4 Slide 2 of 4

Payback Decision RulesPayback Decision Rules

It's better to recover invested money sooner than later

Stand-alone Projects:

Businesses generally have stated policies as to the maximum time allowable for capital recovery

Payback period < Policy Maximum AcceptAccept Payback Period > Policy Maximum RejectReject

TM 9-4 Slide 3 of 4

Mutually Exclusive ProjectsMutually Exclusive ProjectsShorter Is Better:

P/BA < P/BB Choose Project AA over Project B

Weaknesses of the Payback Method

Ignores the time value of money

Ignores cash flows after the payback period

TM 9-4 Slide 4 of 4

Example 9-1 Choose between mutually exclusive projects A and B:

Project A Project B

C0 ($1,200) ($1,200)

C1 $400 $400

C2 $400 $400

C3 $400 $350

C4 $200 $800

C5 $200 $800

Solution: P/BA = 3 years

P/BB = slightly more than 3 years

Therefore, Payback chooses Project A, but Project B

is better because of years 4 and 5

Why Use the Payback Method?Quick and easy to apply serves as a rough screening device

before more sophisticated methods TM 9-5

NET PRESENT VALUE (NPV)

The present value of future cash flows is what counts

when making decisions based on value.

The Net Present Value of all of a project's cash flows is its expected contribution to the firm's value and shareholder wealth

PVs are taken at k, the cost of capital

Outflows are Ci with negative values and tend to occur first

NPV is the difference between the present values of all the positives and

all the negatives TM 9-6 Slide 1 of 2

NPV = C0

C

k

C

k

C

k

nn

1 221 1 1( ) ( )

...( )

NPV DECISION RULESStand-alone Projects:

NPV > 0 Accept NPV < 0 Reject

Example 9-2:

Should project Alpha be undertaken if the cost of capital is 12%?

C0 C1 C2 C3

($5,000) $1,000 $2,000 $3,000

Solution: Year Cash Flow PV Factor PV of Cash Flow

0 ($5,000) - ($5,000.00)

1 $1,000 .8929 $892.90

2 $2,000 .7972 $1,594.40

3 $3,000 .7118 $2,135.40

NPV = ($377.30)

Project Alpha's negative NPV REJECT

TM 9-6 Slide 2 of 2

Mutually Exclusive Projects:A bigger NPV is better

NPVA > NPVB Choose Project A over B

The idea is straightforward, but a number of practical questions arise

Example 9-3: Xavier makes outdoor power equipment and is considering two projects:

1) making larger tractors and 2) making snowblowers (snowblowers use similar

technology, but are a new product for Xavier). Management wants to base

the decision on only 5 years of estimated cash flow as follows ($000):

Year Tractor Snowblower

0 ($3,000) ($3,500)

1 ($250) ($700)

2 $500 $800

3 $1,000 $1,200

4 $1,500 $2,000

5 $1,500 $2,000

Evaluate each project as a stand alone and if only $5M in capital is available TM 9-7 Slide 1 of 2

Solution:

Cash Flows PV of Cash FlowsYear Factor Tractor Snowblower Tractor Snowblower

0 ($3,000) ($3,500) ($3,000) ($3,500)

1 .9174 ($250) ($700) ($229) ($642)

2 .8417 $500 $800 $421 $673

3 .7722 $1,000 $1,200 $772 $927

4 .7084 $1,500 $2,000 $1,063 $1,417

5 .6499 $1,500 $2,000 $975 $1,300

NPV's $2 $175

Stand-alone: Both are marginally acceptable

Mutually Exclusive: Snowblower is marginally better

(Both NPVs are small relative to C0s)

TM 9-7 Slide 2 of 2

Reevaluate if management considers two more years of cash flow at the level of 5th year

Cash Flows PV of Cash Flows Year Factor Tractor Snowblower Tractor Snowblower

6 .5963 $1,500 $2,000 $894 $1,193

7 .5470 $1,500 $2,000 $821 $1,094

Addition to NPVs $1,715 $2,287

Previous NPV s $2 $175

New NPVs $1,717 $2,462

Notice the change in the complexion of the problem.

Stand-alone: Both projects clearly favorable

Mutually exclusive: Snowblower seems the obvious choice

However, cash flows become less certain as they are further into the future

TM 9-8 Slide 1 of 2

Are Other Risk Considerations Relevant?Are Other Risk Considerations Relevant?

Yes!!!Yes!!!

Tractors are an expansion - Snowblowers are a new venture

Risks are unlikely to be the same

Is a straight comparison of NPVs appropriate???

Probably not - Stay tuned until Chapter 10

TM 9-8 Slide 2 of 2

INTERNAL RATE OF RETURN (IRR)INTERNAL RATE OF RETURN (IRR)Define IRR in two ways:

The return a project earns on invested funds or

In terms of the NPV equation

The Project as an InvestmentView a project as an investment similar to the purchase of

a financial asset

The initial outlay is the "price" of receiving the future inflows

IRR is the return on the investment (equates the PV of future

cash flows to the price today)

Finding a project's IRR is analogous to finding a bond's yield

at a given price

TM 9-9 Slide 1 of 2

Defining IRR Through the NPV Equation

At the IRR the PVs of project inflows and

outflows are equal, so

NPV = 0

A project's IRR is the solution to this equation for a given set of Ci

TM 9-9 Slide 2 of 2

0 = C0

C

IRR

C

IRR

C

IRR

nn

1 221 1 1( ) ( )

...( )

IRR Decision RulesFollow from thinking in terms of a return on investment

Stand-alone Projects: Invest only if IRR exceeds k, the cost of capital

IRR > k Accept

IRR < k Reject

Mutually Exclusive Projects: a bigger IRR is better

IRRA > IRRB Choose Project A over Project B

Calculating IRRsIRR equation is an nth order polynomial in the unknown IRR

Can't generally be solved algebraically

Use an iterative approach in the NPV equation starting with a guess at k

Calculate NPV, if not zero guess again moving closer to solution

TM 9-10

Example 9-4

Find IRR for cash flows of Example 9-2:

C0 C1 C2 C3

($5,000) $1,000 $2,000 $3,000

Is the project acceptable if k = 8%, 10%?

Solution:

Use NPV equation and find value of k where NPV = 0

TM 9-11 Slide 1 of 3

NPV = C0

C

k

C

k

C

k

nn

1 221 1 1( ) ( )

...( )

Rationale:

Larger interest rates shrink positive Ci in the distant future more than

early negative Ci , especially C0

Hence NPV for normal projects decreases as k increases

NPV

k

IRR

Figure 9-1 NPV Profile


Finding an IRR is equivalent to locating the crossover point

of the NPV Profile by testing points on either side

Set up a two column table and calculate as in Example 9-2

Interest Calculated

Rate Guess NPV

12% ($377)

10% ($184)

9% ($83)

8% $22

7% $130

IRR is between 8% and 9% (where NPV changes sign)

k = 8% project is marginally favorable

k = 9% project is unfavorable(Technique is similar to finding bond yields)

TM 9-11 Slide 3of 3

TECHNICAL PROBLEMS WITH IRRTECHNICAL PROBLEMS WITH IRRMultiple Solutions

IRR equation can have as many as n solutions

(positive, negative, or imaginary)

Only as many positive solutions as sign reversals

Only one is generally reasonable

The Reinvestment AssumptionImplicitly assumes reinvestment of inflows at the IRR

Unlikely to be possible if IRR very high

Overstates calculated IRR somewhat

Rarely affects acceptance or ranking

(Note: NPV's reinvestment assumption is usually easily satisfied)

Technical problems rarely present practical difficulties

TM 9-12

COMPARING IRR AND NPVCOMPARING IRR AND NPV

NPV and IRR May Occasionally Give Conflicting Results

in Mutually Exclusive Decisions

NPV

NPVB k2

NPVA

NPVA k1 A NPVB

B

k2 k1

IRRB IRRA

Figure 9-2 Projects For Which IRR and NPV Can Give Different Solutions


k

In Case of Conflict The NPV Method is Preferred

Reinvestment assumption is more easily satisfied.

Direct link to shareholder wealth

Businesspeople Tend to Prefer IRR Over NPV

More used to working with rates of return

PV'd dollars are a little abstract


PROJECTS WITH A SINGLE PROJECTS WITH A SINGLE OUTFLOW AND REGULAR INFLOWSOUTFLOW AND REGULAR INFLOWS

Many projects are characterized by an initial outflow and equal regular inflows:

PV of annuity formula makes pattern easy to work with

NPV: NPV = C0 + C [PVFAk,n]

IRR: 0 = C0 + C [PVFAIRR,n]

TM 9-14

PROFITABILITY INDEXPROFITABILITY INDEX

A variation on the NPV methodA variation on the NPV method

Compares PV of future cash flows with initial outlay in a ratio

(NPV works with the difference between inflows and outflows)

(Also known as the Benefit/Cost Ratio)

Concept poorly defined if some early Cs after C0 are negative


PI

C

k

C

k

C

kC

nn

1 22

0

1 1 1( ) ( )....

( )

PIPV Inflows

PV Outflows

DECISION RULESDECISION RULES

Stand-alone Projects: PI > 1.0 AcceptAccept

PI < 1.0 RejectReject

Mutually Exclusive Projects:PIA > PIB Choose Project A over Project B


COMPARING PROJECTS WITH UNEQUAL LIVESCOMPARING PROJECTS WITH UNEQUAL LIVES

C0 C1 C2 C3 C4 C5 C6

Short Lived Project

($1,500) $750 $750 $750

IRR = 23.4% NPV = $432.82

Long Lived Project

($2,600) $750 $750 $750 $750 $750 $750

IRR = 18.3% NPV = $867.16

Figure 9-3 Comparing Projects with Different Lives

NPV method adds up six years of benefits for one project and three years for the other. Hence longer lived machine gets a higher NPV.


The Replacement Chain Method

Chain short projects to cover the time span of the longer project.

Two Short-Lived Projects Back-to-Back

($1,500) $750 $750 $750

($1,500) $750 $750 $750 ($750)

NPV = $776.41

Figure 9-4 A Three-Year Project Chained into Six Years

A problem exists if a large number of replacements are necessary.


The Equivalent Annual Annuity (EAA) MethodThe Equivalent Annual Annuity (EAA) Method

Replace each link in the chain by its NPVReplace each link in the chain by its NPV

Then replace each NPV with an annuity of the same length Then replace each NPV with an annuity of the same length

and equal NPV and equal NPV

Example: Shorter project has n = 3 yrs and NPV = $432.82.

PVA = PMT [PVFAk,n]

$432.82 = PMT [PVFA8,3]

$432.82 = PMT (2.5771)

PMT = $167.95

= EAA


First link Second link

0 1 2 3 4 5 6

(1,500) $750 $750 $750

PROJECTS ($1,500) $750 $750 $750

NPVs $432.82 $432.82

EAA $167.95 $167.95 $167.95 $167.95 $167.95 $167.95

Figure 9-5 Replacing a Project with its NPV and EAA


Since the project can be chained forward indefinitely,

it can be represented by an indefinitely long EAA.

Can calculate an EAA for any project

For the longer project:

PVA = PMT [PVFAk,n]

$867.16 = PMT [PVFA8,6]

$867.16 = PMT (4.6229)

PMT = $187.58

= EAA

So choose the longer project since it has the larger EAA


CAPITAL RATIONINGCAPITAL RATIONING

k% Possible $16M Funds Limitation

15%

10% Cost of Capital

5%

$8 $13 $19 $22 $28 $35 $

Cumulative Capital Investment

(for the year in $M)

The Capital BudgetCapital Budget is generally less than the total of projects available

Requires selecting projects to maximize total NPV

TM 9-18

A

B C D

E F

chapter 9 capital budgeting © 2000 south-western college publishing

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