Professor John ZietlowMBA 621

Professor John ZietlowMBA 621

Capital BudgetingProcesses And Techniques

Capital BudgetingProcesses And Techniques

Chapter 7Chapter 7

Chapter 7: OverviewChapter 7: Overview

• 7.1 Capital Budgeting Decision Process• 7.2 A Capital Budgeting Problem• 7.3 Payback Analysis

– The payback method– Pros and cons of payback– Discounted payback– Pros and cons of discounted payback

• 7.4 Accounting-Based Methods– Accounting rate of return– Pros and cons of accounting rates of return

• 7.5 Net Present Value– Net present value calculations– Pros and cons of NPV

Chapter 7: Overview (Continued)Chapter 7: Overview (Continued)

• 7.6 Internal Rate of Return– Finding a project’s IRR– Advantages of the IRR method– Problems with the IRR method• Lending vs. borrowing• Multiple IRRs• No real solution• The scale problem• The timing problem

• 7.7 Profitability Index– Calculating the profitability index– The profitability index and capital rationing

• 7.8 Summary

The Capital Budgeting Decision ProcessThe Capital Budgeting Decision Process

• The Capital Budgeting Process involves three basic steps:– Generating long-term investment proposals– Reviewing, analyzing, and selecting from the proposals that

have been granted– Implementing & following up on (monitoring) the proposals that

have been selected• Firms typically make many long-term investments, but the

most common for most firms are to acquire fixed assets – Includes land, plant and equipment– Also computers, telecom equipment

• Managers should separate investment & financing decisions– Use a single required return (discount rate) to evaluate

investment projects & accept those which have positive NPV

Capital Expenditure DefinedCapital Expenditure Defined

• A capital expenditure is an outlay of funds expected to produce benefits for more than one year. – Fixed-asset outlays are capital expenditures, but not all

capital expenditures are classified as fixed assets. – A $150,000 outlay for a long-term advertising program is also

a capital expenditure, but not a fixed asset.• An operating expenditure is an outlay resulting in benefits

received within one year. – Most software is treated as an expense, though long-term

• The basic motives for capital expenditures are to expand, replace, or renew fixed assets. Critical for firms & nations– Capital spending: 13% of GDP in 1991; over 19% today– Tech firms often spend >20% of revenues on cap investment

Key Motives for Capital ExpendituresKey Motives for Capital Expenditures

Key Motives for Making Capital Expenditures

Motive Description

Expansion

Replacement

Renewal

Other purposes

The most common motive for a capital expenditure is to expand the level of operations – usually through acquisition of fixed assets. A growing firm often needs to acquire new fixed assets rapidly, such as the purchase of property and plant facilities.

As a firm’s growth slows and it reaches maturity, most capital expenditures will be made to replace or renew obsolete or worn-out assets. Each time a machine requires a major repair, the outlay for the repair should be compared to the outlay to replace the machine and the benefits of replacement

Renewal, an alternative to replacement, may involve rebuilding, overhauling, or retrofitting an existing fixed asset. For, example, an existing drill press could be renewed by replacing its motor and adding a numeric control system, or a physical facility could be renewed by rewiring and adding air conditioning. To improve efficiency, both replacement and renewal of existing machinery may be suitable solutions

Some capital expenditures do not result in the acquisition or transformation of tangible fixed assets. Instead, they involve a long-term commitment of funds in expectation of a future return. These expenditures include outlays for advertising, research and development, management consulting, and new products. Other capital expenditures proposals – such as the installation of pollution-control and safety devices mandated by the government – are difficult to evaluate because they provide intangible returns rather than clearly measurable cash flows.

Capital Budgeting TerminologyCapital Budgeting Terminology

• Independent projects are those whose cash flows are unrelated or independent of one another – The acceptance of one does not eliminate the others from

further consideration. – If a firm has unlimited funds to invest, all independent projects

with positive-NPVs can be implemented. • Mutually exclusive projects are those that have the same

function and therefore compete with one another. – The acceptance of one eliminates from further consideration all

other similar-function projects. • Example: A firm needing increased production capacity could:

– (1) expand its plant, (2) acquire another company, or (3) contract another company for production.

– The acceptance of one of these projects eliminates the need for either of the others.

Unlimited Funds Versus Capital RationingUnlimited Funds Versus Capital Rationing

• The availability of funds for capital expenditures affects the firm's decisions.

• If a firm has unlimited funds for investment, making capital budgeting decisions is quite simple: – Accept all independent projects with returns greater than the

firm’s cost of capital– Implies firms should use an accept-reject decision rule

• Firms often operate as though they face capital rationing.– They have a fixed amount of money available for capital

spending and numerous projects will compete for this money– Implicitly assumes firms cannot access capital markets– Such firms should use a ranking approach to cap budgeting– Though frequently observed in practice, this assumption is

usually wrong & firms are constraining capex unnecessarily

Capital Budgeting Decision TechniquesCapital Budgeting Decision Techniques

• At least five capital budgeting decision techniques are commonly used by businesses– Payback period: most commonly used– Accounting rate of return (ARR): least appropriate– Net present value (NPV): best technique theoretically– Profitability index (PI): related to NPV– Internal rate of return (IRR): one businesspeople like most

• Payback and ARR are unsophisticated and ignore the time value of money– Payback slowly dying out in industry, but still popular

• NPV, PI, IRR all are tied to shareholder wealth maximization and all account for time value of money– IRR popular because expressed as rate of return– Unlike IRR, NPV always yields correct answer

U.S. Wireless InvestmentU.S. Wireless Investment

• U.S. Wireless is a nationwide provider of wireless telephony

– Business growing rapidly, but expansion is costly

• USW evaluating two investment proposals

– Major expansion of service in Northeast U.S. base

– Toehold investment establishing service in Atlanta

• Projects have cash flow patterns below (in $ millions):

$850Year 5 inflow

$740Year 4 inflow

$400Year 3 inflow

$250Year 2 inflow

$100Year 1 inflow

-$1.2 billionInitial outlay

$48Year 5 inflow

$47Year 4 inflow

$41Year 3 inflow

$30Year 2 inflow

$22Year 1 inflow

-$75Initial outlay

Northeast Atlanta

U.S. Wireless Investment ProposalsU.S. Wireless Investment Proposals

Northeast expansion ($ millions)

Year

Atlanta toehold ($ millions)

Year

-$1.2 billions

-$75

$100 $250 $400 $740 $850

$22 $30 $41 $47 $48

Payback PeriodPayback Period

• The payback period is the exact amount of time required for the firm to recover its initial investment. – In the case of an annuity, the payback period can be found

by dividing the initial investment by the annual cash inflow. – For a mixed stream of cash inflows, the yearly cash inflows

must be accumulated until the initial investment is recovered.

• When the payback period is used to make accept-reject decisions, the decision criterion is:– If the payback period is less than the maximum acceptable

payback period, accept the project.– If the payback period is greater than the maximum

acceptable payback period, reject the project.• The length of the maximum acceptable payback period is

determined by management.

Calculating Payback Periods For USW’s Northeast And Atlanta Projects

Calculating Payback Periods For USW’s Northeast And Atlanta Projects

• Assume USW managers select a 3-year payback period– Only accept projects that recover costs by end-of-year 3

• The northeast project has initial outflow of -$1.2 billions– But cash inflows over first 3 years only $750 mn– USW would reject northeast project based on payback

• The Atlanta project has initial outflow of -$75 mn– Cash inflows over first 3 years cumulate to $93 mn– Project recovers initial outflow middle of year 3– USW would accept Atlanta project based on payback

• Payback: USW would reject Northeast, accept Atlanta – Will see this is incorrect if mutually exclusive projects

Pros And Cons Of Payback PeriodPros And Cons Of Payback Period

• Payback period is popular because of its computational simplicity and intuitive appeal. – Also considers cash flows rather than accounting profits. – It also gives some implicit consideration to the timing of cash

flows; can thus be viewed as a measure of risk exposure. – Frequently used as the primary decision technique for risky

foreign investments and for high-risk domestic investments.• Major weakness: “appropriate” payback period is arbitrarily

determined & is not based on discounting cash flows. – Often yields bizarrely short payback periods

• Two other serious weaknesses of payback period:– Fails to fully account for time value of money. – Zero discount rate years 1-3, infinite after years 3

Discounted Payback PeriodDiscounted Payback Period

• Using discounted payback can account for TV problem– Apply discount rate to CFs during payback period– Still ignores CFs after payback period

• Table below assumes USW uses an 18% discount rate

RejectReject--Accept / reject

$67.531$528.29--Cumulative PV

$26.2687$256.280.6407PV Year 1 inflow

$22.296$185.80.7432PV Year 1 inflow

$18.9662$86.210.8621PV Year 1 inflow

DCFs Atlanta project ($mn)

DCFs Northeast project ($mn)

PV Factors

(16%)Item

Accounting Rate Of Return (ARR)Accounting Rate Of Return (ARR)

• Accounting rate of return (ARR) is popular because it can be computed from available accounting data – Need only profits after taxes and depreciation.

• The most common definition of the accounting rate of return (ARR) for a given project is:

– Accounting ROR = Avg Profits after taxes Avg Investment • Average profits after taxes can be estimated by subtracting

average annual depreciation from the average annual operating cash inflows.

Average profits after taxes

Average annual operating cash inflows

Average annual depreciation

= -

• ARR uses accounting numbers, not CFs; no TV of money

Net Present ValueNet Present Value

• Net present value (NPV) found by subtracting the PV of cash outflows from the PV of cash inflows – Both discounted at the firm’s cost of capital (r).

• Cost of capital (discount rate): minimum return firm must earn on a project to satisfy investors– Adjusts cash flows for risk and TV of money

NT

r

CF

r

CF

r

CF

r

CFCFNPV

)1(...

)1()1()1( 33

221

0

(Eq 7.1)

• Decision rule: Accept positive, reject negative NPV projects – Positive NPV occurs when:

TT

r

CF

r

CF

r

CF

r

CFCF

)1(...

)1()1()1( 33

221

0

Calculating NPVs For US Wireless’ ProjectsCalculating NPVs For US Wireless’ Projects

• Assuming US Wireless uses 16% discount rate, NPVs are:

5432 )16.1(

850

)16.1(

740

)16.1(

400

)16.1(

250

)16.1(

100bn 2.165.141 northeastNPV

5432 )16.1(

48

)16.1(

47

)16.1(

41

)16.1(

30

)16.1(

227534.41 AtlantaNPV

Northeast project: NPV = $141.65 mn

Atlanta project: NPV = $41.43 mn

• Both projects have positive NPVs, so both acceptable– If mutually exclusive, select Northeast since higher NPV

Pros & Cons Of Using NPV As Decision RulePros & Cons Of Using NPV As Decision Rule

• NPV is the “gold standard” of investment decision rules– Almost always yields correct answer

• Key benefits of using NPV as decision rule– Focuses on cash flows, not Accounting earnings– Makes appropriate adjustment for TV of money– Decision rule based on market values (reqd return)– Can properly account for risk differences between projects– Incorporates all CFs; doesn’t ignore those after payback

• Though best measure, NPV has some drawbacks– Answer in $ amounts, not rate of return or years to payback– Doesn’t capture managerial flexibility (option value) well

Internal Rate of ReturnInternal Rate of Return

• Internal rate of return (IRR) is the discount rate that equates the PV of cash inflows, with the PV of cash outflows.

NN

r

CF

r

CF

r

CF

r

CFCFNPV

)1(....

)1()1()1(0

33

221

0

• IRR found by computer/calculator or manually by trial & error– Actually computed by trial and error—even by computer

• The decision criterion when IRR is used to make accept-reject decisions is:– If IRR is greater than the cost of capital, accept the project.– If IRR is less than the cost of capital, reject the project– Guarantees that the firm earns at least its required return

Calculating IRRs For US Wireless’ ProjectsCalculating IRRs For US Wireless’ Projects

• US Wireless will accept all projects with at least 16% IRR:

Northeast project: IRR (rNE) = 19.63%

Atlanta project: IRR (rA) = 36.53%

• Both projects have positive IRRs, so both acceptable– If mutually exclusive, pick Atlanta: higher IRR (wrong answer)

5432 )1(

850

)1(

740

)1(

400

)1(

250

)1(

100bn 2.10

NENENENENE rrrrr

5432 )1(

48

)1(

47

)1(

41

)1(

30

)1(

22750

AAAAA rrrrr

Comparing NPV and IRR TechniquesComparing NPV and IRR Techniques

• IRR has many good features; almost as good as NPV. – Properly adjusts for TV of money; uses CFs rather than

earnings; accounts for all CFs; uses market values – IRR also yields intuitive rate of return (%) answer

• NPV and IRR are found by specifying either the discount rate or NPV and solving Eq 7.1 for the other value. – NPV calculated with known discount rate (the cost of capital) – IRR is calculated using a known NPV (i.e., $0).

• NPV and IRR usually give the same accept-reject decision– but differences in their underlying assumptions can cause

them to rank projects differently. • Three key problems encountered in using IRR:

– (1) Lending versus borrowing? – (2) Multiple IRRs– (3) No real solutions

Problems With IRR(1) Lending Versus Borrowing

Problems With IRR(1) Lending Versus Borrowing

• IRR can give incorrect answers for projects with non-standard cashflows. Consider two mirror image projects: – Project 1: Invest $120 today, receive $170 in one year.– Project 2: Receive $120 today, pay back $170 in one year.– Project 1 amounts to lending; project 2 to borrowing (Fig 7.4)

Project CF today CF in one yr IRR NPV (20%) #1 -$120 +$170 41.67% +$21.67 #2 +$120 -$170 41.67% -$21.67

• Both projects have same IRR, but #1 obviously superior – When borrowing, a low IRR is preferred on the loan.

Lending Versus BorrowingLending Versus Borrowing

Project #1: Lending

Discount rate

IRR

41.67%

     

      

NPV

Lending Versus BorrowingLending Versus Borrowing

Project #2: Borrowing

Discount rate

IRR

41.67%

     

NPV

Problems With IRR(2) Multiple IRRS

Problems With IRR(2) Multiple IRRS

• If a project has more than one change in the sign of cash flows, there may be multiple IRRs. – Can have as many IRRs as sign changes.– Consider project with following CFs:

Year CF ($ Mns)

0 +100

1 -460

2 +791

3 -602.6

4 +171.6

• Though odd pattern, can be observed in high-tech and other industries.• Four changes in sign of CFs, and have four different IRRs.• Next figure plots project’s NPV at various discount rates.• NPV is the only decision rule that works for this project type.

Multiple IRRsMultiple IRRs

NPV ($)

NPV<0

10% NPV>0 20% 30%

NPV>0

0

$10,000

$5,000

-$5,000

-$10,000

Discount rateNPV<0

Multiple IRRs: Example 2Multiple IRRs: Example 2

• Project doesn’t have to have bizarre CF patterns. Consider the following project: Initial investment of $10,000– Followed by a $50,000 cash inflow at end-of-year 1 and a

$60,000 cash outflow at EOY 2.• This project has two sign changes in its cash flows, and

has two IRRs: – 100% and 200%, as shown in its NPV profile next page.

• This project would be acceptable using NPV only when the firm’s COC is between IRR1 of 100% and IRR2 of 200%.

– At discount rates below 100% and above 200% the project would have a negative NPV and would be rejected.

Example 2: NPV Profile For A Project With Multiple IRRs

Example 2: NPV Profile For A Project With Multiple IRRs

-500

-400

-300

-200

-100

0

100

200

300

400

500

0 50 100 150 200 250

Discount Rate, %

NPV$000

Problems With IRR(3) No Real SolutionProblems With IRR(3) No Real Solution

• Sometimes projects do not have a real IRR solution. – Modify USW’s Northeast project

to include a large negative outflow (-$1.3 bn) in year 6.

– There is no real number that, used in Eq 7.1, will make NPV=0, so no real IRR.

– Project is a bad idea based on NPV. At r =16%, project has NPV= -$391.92 mn, so reject!

Year CF ($ Mns)

0 -$1.2 billion

1 $100

2 $250

3 $400

4 $740

5 $850

6 -$1.3bn

Sources Of Conflicting NPV And IRR Rankings For Mutually Exclusive Projects

Sources Of Conflicting NPV And IRR Rankings For Mutually Exclusive Projects

• The Scale Problem: High IRRs may have low total payoff. – Northeast project has lower IRR, but increases wealth more.

• The Timing Problem: One project has most of its payoff in early years; other pays more in later years – Assume firm must choose between two $1 billion projects– Project 1: New product development, biggest payoff year 5– Project 2: Marketing blitz, biggest payoffs early years (1-3)

$41.34 mn36.53%Atlanta

$141.65 mn19.63%Northeast

NPV (16%)IRRProject

The Timing Problem With IRRThe Timing Problem With IRR

$122.65 mn$139.81 mnNPV (10%)

16.35%13.24%IRR

$100$1,325Year 5

$120$225Year 4

$285$135Year 3

$375$75Year 2

$500$0Year 1

-$1,000 mn-$1,000 mnInitial Outlay

Marketing blitzProduct developmentCash Flow

Marketing project has higher IRR (16.35% vs 13.24%), while development project has higher NPV ($139.81 mn vs $122.65 mn). Which to take?

The Timing ProblemThe Timing Problem

Discount rate

Marketing CampaignIRR = 16.35%

Product developmentIRR = 13.24%

10.7%10%

NPV

Select project with higher NPV (product development project)

Profitability IndexProfitability Index

• Profitability index (PI) calculated by dividing the PV of a project’s cash inflows by the PV of its outflows– Also called the benefit-cost ratio, calculated as Eq 7.3:

• Decision rule: Accept projects with PI > 1.0, equal to NPV > 0• Calculate PIs for U.S. Wireless’ two projects:

0

221

)1(...

)1()1(

CF

r

CF

r

CF

r

CF

PIT

T

(Eq 7.3)

• Both projects’ PI > 1.0, so both acceptable if independent– If mutually exclusive, Atlanta project looks better (but isn’t)

1.55$75 mn$116.34 mnAtlanta

1.12$1.2 bn$1341.65 mnNortheast

PIInitial OutlayPV of CF (yrs1-5)Project

Net Present Value ProfilesNet Present Value Profiles

• Projects can be compared graphically with net present value profiles depicting their NPVs for various discount rates. – These are useful in evaluating and comparing projects, especially

when conflicting rankings exist. • To prepare NPV profiles, first develop a set of discount-rate/NPV

coordinates. – Three coordinates can easily be obtained for each project;

discount rates of 0%, 16% (the COC, r), and the IRR. – The NPV at a 0% discount rate is found by adding all the cash

inflows and subtracting the initial investment• Compute NPV profiles for two USW projects.

– Northeast, NPV0 = $1.14bn; NPV16% = $141.65mn; NPV19.63% =0

– Atlanta, NPV0 = $113mn; NPV16%= $41.34mn; NPV36. 53% = 0

Net Present Value Profiles (Continued)Net Present Value Profiles (Continued)

• Plotting these data results in the net present value profiles for Northeast and Atlanta projects (next slide). – Note that, graphically, the IRRs occur where each NPV

profile crosses the discount-rate axis due to the definition of IRR as the discount rate that causes NPV = $0.

• Figure shows that for any r below about 18.73%, the NPV for Northeast is greater than the NPV for Atlanta. – For any r > 18.73%, NPV for Atlanta > NPV for Northeast.

• Since the NPV profiles cross at a positive NPV, the IRRs cause conflicting rankings whenever they are compared to NPVs calculated at discount rates below 18.73%.– At USW’s r =16%, Northeast’s NPV ($141.65mn) is

preferred– But Atlanta has a higher IRR (36.53% vs 19.63%)

• Basic cause of conflicting rankings: implicit assumptions regarding reinvestment rate for intermediate cash flows

Net Present Value ProfilesNet Present Value Profiles

($700)

($500)

($300)

($100)

$100

$300

$500

$700

$900

$1,100

0% 16% 50%

Mn

IRRNE=19.63%

IRRATL =36.53%

•

Causes Of Conflicting Project Rankings: Differing Reinvestment Rate AssumptionsCauses Of Conflicting Project Rankings:

Differing Reinvestment Rate Assumptions

• The underlying cause of conflicting rankings is the implicit assumption about reinvestment of intermediate cash flows. – An ability to reinvest intermediate cash flows at the stated

discount rate is embedded in time value mathematics.• NPV assumes that intermediate cash flows are reinvested

at the cost of capital. – IRR assumes that intermediate cash flows are reinvested at

a rate equal to the project’s IRR. • Consider a project requiring a $850,000 initial investment

with expected operating cash flows of $200,000, $300,000, and $600,000 at the end of each of the next three years. – The project’s NPV (at the firm’s 10 % cost of capital) is

$30,540.95, and its IRR is 11.7%.

Differing Reinvestment Rate AssumptionsDiffering Reinvestment Rate Assumptions

• The NPV of the project (at the firm’s 10% COC) is $30,540.9, and its IRR is 11.7%. Clearly, the project is acceptable. – NPV = $30,540.9 > $0 and IRR = 11.7% > 10% cost of capital.

• Next slide calculates the project’s FV at the end of year 3, assuming both a 10% and a 11.7% (its IRR) rate of return. – FV of $1,172,000 results from reinvestment at the 10% COC– FV of $1,184,637.8 results from reinvestment at the 11.7% IRR.

• If the FVs in next slide are viewed as the return received in three years from the $850,000 initial investment: – At the 10% reinvestment rate, the NPV remains at $30,540.95– Reinvestment at the 11.7% IRR produces an NPV of $40,035.9

• NPV assumes reinvestment at the cost of capital (10%). • IRR assumes an ability to reinvest intermediate CF at IRR.

– If reinvestment doesn’t occur at this rate, IRR won’t be 11.7%

Reinvestment Rate Comparisons: NPV at 10% versus IRR

Reinvestment Rate Comparisons: NPV at 10% versus IRR

Reinvestment Rate

10% 11.7%

Year

Cash Flow

# Yrs Interest Earned

(1.10)t

Future Value

(1.117)t

Future Value

1

$200,000

2

(1.10)2

$242,000

(1.117)2

$249,537.

8

2

300,000 1

(1.10)1

330,000

(1.117)1

335,100

3

600,000

0

(1.10)0

600,000

(1.117)0

600,000

Future Value end of year 3

$1,172,000

$1,184,637.8

NPV at 10% = $30,540.9 NPV at 11.7% (IRR) = $40,035.9

Reconciling IRR and NPVReconciling IRR and NPV

• Have seen that NPV is theoretically superior to IRR for making accept-reject decisions for projects– But IRR much more popular with managers because it yields

an intuitively pleasing rate of return measure• Generally both IRR and NPV yield the same decision, but

IRR has several problems:– Non-standard cash flows (outflows followed by inflows),

multiple IRRs, imaginary IRRs (not covered)– IRR also incorrectly assumes intermediate CFs can be

reinvested at IRR, not firm’s cost of capital