Capital Budgeting, Risk Considerations and Other Special Issues Capital Budgeting, Risk...

Capital Budgeting, Risk Considerations and Other

Special Issues

13 - 2

Lecture Agenda

• Learning Objectives• Important Terms• The Nature of Capital Expenditure Decisions• The Appropriate Discount Rate• Evaluation of Investment Alternatives using NPV, IRR,

PI and Payback Approaches• Capital Rationing• Independent and Interdependent Projects• Comparing Mutually Exclusive Projects with Unequal

Lives• International Considerations• Summary and Conclusions

– Concept Review Questions

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Learning Objectives

1. The similarities between corporate investment techniques and the techniques used to value shares

2. The basic capital budgeting process3. The most important approaches used to determine the

value of a firm’s capital expenditures (capex)4. The reasons that firms sometimes use techniques that

may seem inconsistent with value maximization.

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Important Chapter Terms

• Bottom-up analysis• Capital budgeting• Capital expenditures• Capital rationing• Chain replication approach• Contingent projects• Crossover rate• Discounted cash flow

(DCF) methodologies• Discounted payback period• Equivalent annual NPV

approach• Five Forces

• Independent projects• Internal rate of return (IRR)• Investment opportunity

schedule (IOS)• Mutually exclusive projects• Net present value (NPV)• Payback period• Profitability index• Pure play approach• Risk-adjusted discount

rates (RADRs)• Top-down analysis

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Capital Expenditures (capex)

Capital expenditures are a firm’s investments in long-lived assets.

Long-lived assets may be:– Tangible (property, plant and equipment)– Intangible (research and development, patents,

copyrights, trademarks, brand names, and franchise agreements)

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Capital ExpendituresImportance

Capex decisions determine the future direction of the company.

• CAPEX decisions are among the most important that the firm can make because:

– Often involve very significant outlay of money and managerial time

– Often take many years to demonstrate their returns– Are often irrevocable– Because of their size and long-term nature, they can

significantly alter the risk of the entire firm.

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Capital Expenditure DecisionsCapital Budgeting

Capital budgeting is the process through which a firm makes capital expenditure decisions by:

1. Identifying investment alternatives2. Evaluating these alternatives3. Implementing the chosen investment decisions,

and4. Monitoring and evaluating the implemented

decisions.

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Capital Expenditure DecisionsFive Forces

Michael Porter’s Five Forces model identified five critical factors that determine the attractiveness of an industry:

1. Entry barriers2. Threat of substitutes3. Bargaining power of buyers4. Bargaining power of suppliers5. Rivalry among existing competitors

Companies do exert control over how they strive to create a competitive advantage within their industry.

They can strive for:6. Cost leadership: strive to be a low-cost producer7. Differentiation: offer “differentiated” products

Once attained, competitive advantage is difficult to sustain, and this requires on-going planning and investment.

CAPEX must be made with a strategic focus and be subject to and pass rigorous financial analysis.

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Capital Expenditure DecisionsBottom-up and Top-Down Analysis

Bottom-up Analysis is an investment strategy in which capex decisions are considered in isolation, without regard for whether the firm should continue in this business or for general industry and economic trends.

Top-down Analysis is an investment strategy that focuses on strategic decisions, such as which industries or products the firm should be involved in, looking at the overall economic picture.

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Capital Expenditure DecisionsDCF Methodolgies

Capex decisions, like security valuation, must take into account the timing, magnitude and riskiness of the net incremental, after-tax cash flow benefits that an initial investment is forecast to produce.

Unlike security valuation decisions, analysts can change the underlying cash flows by changing the structure of the project.

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Capital Expenditure DecisionsDCF Methodologies

The ability to restructure capex proposals means that capex analysis can be iterative and circular as illustrated below:

Project Proposal

Project Analysis

Forecast Outcome Positive (+ NPV)

Forecast Outcome Not Viable (- NPV)

Restructure Proposal

Proceed with Implementation Planning

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Capital Expenditure DecisionsDCF Methodologies

All discounted cash flow approaches require:– Estimate of the initial cost of the CAPEX – Estimate of the net incremental after-tax cash

flow benefits the investment is forecast to produce (we need to know when these cash flows will occur and how large they will be)

– Estimate of the required rate of return on the project (relevant discount rate k)

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Where CFt = estimated future after-tax incremental cash flow at time tCF0 = the initial after-tax incremental cash outlay

Evaluating Investment AlternativesThe Cash Flow Pattern for a Traditional Capital Expenditure

0 1 2 3 … n

CF1 CF2 CF3 … CFn

CF0

13-1 FIGURE

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Firm’s Cost of Capital (WACC = k)

• The firm’s cost of capital determines the minimum rate of return that would be acceptable for a capital project.

• WACC is the discount rate (k) we use in NPV analysis and the hurdle rate when using IRR

• The weighted average cost of capital (WACC) is the relevant discount rate for NPV analysis. (assuming the risk of the project being evaluated is similar to the risk of the overall firm)

• If the risk of the project differs from the risk of the overall firm a risk-adjusted discount rate (RADR) should be used.

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Risk-Adjusted Discount Rates (RADRs = k)

• RADRs can be estimated using a number of alternative techniques:1. Use the CAPM formula after determining the project beta and using

the current risk-free rate (RF) and an estimate of the market risk premium• This approach involves forecast ROA that must be regressed against the

ROA of the market index. Estimation errors can be significant.2. Pure play approach where you find the cost of capital of a firm in the

industry associated with the project. • The key to this approach is that the firm must not be diversified across

industries but truly represent an investment solely in that industry.

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Evaluation of Investment AlternativesDCF Methodologies

• Net Present Value (NPV)• Internal Rate of Return (IRR)• Payback Period and Discounted Payback

Period• Profitability Index (PI)

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Project Evaluation TechniquesNet Present Value (NPV) Formula

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Evaluating Investment AlternativesNet Present Value (NPV) Analysis

NPV = the sum of the present value of all benefits minus the present value of costs

If benefits > cost, NPV will be positive and the project is acceptable.

If benefits < cost, NPV will be negative and the project is unacceptable because it destroys firm value.

11

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i stInitial Cok)(BenefitsCash Flow NPV

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Evaluating Investment AlternativesNet Present Value Interpreted

Example:If NPV is forecast to be + $250,000, then the PV of incremental benefits exceeds the present value of costs today by $250,000. Remember the PV is determined by discounting the forecast cash flows by the investor’s required return. A positive NPV indicates that returns are greater than what investors require. This means a positive NPV adds value to the firm.

In this case, if there were 1,000,000 shares outstanding, acceptance of a $250,000 NPV project in an efficient market means that the market price of each share should rise by:

25.0$000,000,1000,250$

gOutstandin Shares ofNumber NPV Price Sharein Increase

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Evaluating Investment AlternativesNet Present Value Interpreted

NPV is an absolute measure (expressed in present dollars) of the net incremental benefits the project is forecast to bring to the shareholders.

In a perfectly efficient market, the total value of the firm should rise by the value of the NPV if the project is undertaken.

Remember – it is the manager’s responsibility to maximize shareholder wealth

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NPV ExampleThe Formula-based Approach

Problem:• Initial outlay = $12,000• After-tax cash flow benefits:

– Year 1 = $5,000– Year 2 = $5,000– Year 3 = $8,000

• Discount rate (k) = 15%

389,1$000,12$260,6$781,3$348,4$

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NPV ExampleThe Spreadsheet Approach


– Year 1 = $5,000– Year 2 = $5,000– Year 3 = $8,000


Initial cost = $12,000Cost of Capital = 15.0%

Year CashflowAfter-tax

incremental CF PV FactorPresent Value

0 Initial cost -$12,000 1 -$12,0001 ATCF operating benefit 5,000 0.869565 $4,3482 ATCF operating benefit 5,000 0.756144 $3,7813 ATCF operating benefit 8,000 0.657516 $5,260

NPV = $1,389

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NPV ExampleThe Financial Calculator Approach


– Year 1 = $5,000– Year 2 = $5,000– Year 3 = $8,000


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NPV ExampleSolution Using a Financial Calculator (TI BA II Plus)

CF 2ND CLR WORK

-12000500050008000

15

gives $1,388.67

ENTER

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NPV

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NPV Profile

• Is a set of NPVs for a project that are created by varying the discount rate used to find the present value of the cash flows.

• The slope of the NPV line that is created when you graph these results, depends on the useful life of the project and on the timing of the receipt of the net incremental benefits.– The longer the life of the project, the steeper the slope of the

NPV profile line because more distant cash flows are affected more by the discounting process.

(The following slide demonstrates what an NPV Profile looks like)

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NPV Profile

NPV ($)

Discount Rate (k) (%)

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NPV ExampleA Spreadsheet Modeling Approach

Initial cost = $100,000AT cash flow benefits = $60,000Useful life(years) = 6Cost of Capital = 12%

Year Cashflow After-tax incremental CF PV Factor Present Value0 Initial cost -$100,000 1 -$100,0001 ATCF operating benefit 60,000 0.892857 $53,5712 ATCF operating benefit 60,000 0.797194 $47,8323 ATCF operating benefit 60,000 0.71178 $42,7074 ATCF operating benefit 60,000 0.635518 $38,1315 ATCF operating benefit 60,000 0.567427 $34,0466 ATCF operating benefit 60,000 0.506631 $30,398

NPV = $146,684

Here is a spreadsheet model used to calculate a $100,000 project that has a 6 year life, offers equal annual after-tax cash flow benefits over that life of $60,000 per annum when the relevant cost of capital is 12%.

The NPV result is positive and the project is acceptable because the project looks like it will increase the value of the firm with these assumptions.

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NPV ExampleStress Testing the Project

Now, let us stress – test the model. We can start by setting the discount rate to 0%. (ie. No time value to money)


Year Cashflow After-tax incremental CF PV Factor Present Value0 Initial cost -$100,000 1 -$100,0001 ATCF operating benefit 60,000 1 $60,0002 ATCF operating benefit 60,000 1 $60,0003 ATCF operating benefit 60,000 1 $60,0004 ATCF operating benefit 60,000 1 $60,0005 ATCF operating benefit 60,000 1 $60,0006 ATCF operating benefit 60,000 1 $60,000

NPV = $260,000

Notice that at a 0% discount rate, all of the present value factors become 1. And we work with absolute dollar values. NPV is forecast to be it’s greatest at a 0% discount rate.

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Increasing the discount rate to 5%, we discount the more distant cash flows more heavily and the NPV of the project falls from $260,000 to $204,542.



NPV = $204,542

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Increasing the discount rate to 10%, the NPV of the project falls from $204,542 (at 5%) to $161,316.



NPV = $161,316

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Increasing the discount rate to 20%, the NPV of the project falls to $99,531.



NPV = $99,531

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Increasing the discount rate to 50%, the NPV of the project falls to $9,465.

It is hard to imagine a project having risk that requires a return of more than 50%. Even at a discount rate of 50%, the project has a positive NPV!



NPV = $9,465

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Increasing the discount rate to 60%, the NPV of the project falls to -$5,960. At that discount rate, the project would decrease the value of the firm if accepted.



NPV = -$5,960

Somewhere between 50% and 60%, the NPV turned to $0. Remember, the IRR of the project is that discount rate that causes the NPV to be equal to $0.00

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Initial cost = $100,000AT cash flow benefits = $60,000Useful life(years) = 6Cost of Capital = 55.8055%


NPV = $0

A discount rate of 55.8055% causes the NPV to be equal to $0. This is the project’s IRR. Now we can graph the results of the stress test. NPV is on the vertical axis because it is the dependent variable and discount rate is on the horizontal.

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Project NPV Profile

NPV$

$260,000

Discount Rate (%)IRR = 55.8%

0 0% 5% 10% 20% 40% 50% 60%

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Project NPV Profile

NPV$

$260,000

$146,684


0 0% 5% 10% 20% 40% 50% 60%

IF the appropriate discount rate (k) is 12%, then the NPV is forecast to be positive.

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Project NPV Profile

NPV$

$260,000

$146,684


0 0% 5% 10% 20% 40% 50% 60%

Even if your estimate of the project’s required return (RADR) is wrong, the project’s NPV remains positive over a wide range of values for k (from 0% to 55%)

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NPV Profiles

• The slope of the NPV profile depends on the timing and magnitude of cash flows.

• Projects with cash flows that occur late in the project’s life will have an NPV that is more sensitive to discount rate changes.

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IRR

• The internal rate of return (IRR) is that discount rate that causes the NPV of the project to equal zero.

• If IRR > WACC, then the project is acceptable because it will return a rate of return on invested capital that is likely to be greater than the cost of funds used to invest in the project.

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Project Evaluation TechniquesInternal Rate of Return (IRR)

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13 - 41

IRR ExampleThis Example Will Be Used To Demonstrate Alternative Approaches to

Solve for IRR


– Year 1 = $5,000– Year 2 = $5,000– Year 3 = $8,000

• Cost of Capital = 15%

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IRR ExampleFormula-based Approach to the Solution

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13 - 43


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13 - 45

IRR ExampleFormula-based Approach to the Solution – Linear Interpolation

Summarizing our results:Discount Rate Present Value of Benefits

20% $12,268.52IRR $12,00025% $11,296

We can now estimate the IRR assuming a linear relationship between PV of benefits (which isn’t exactly true because compound interest is a curvilinear relationship)

IRR is between 20% and

25%

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IRR ExampleSolution Using a Financial Calculator (TI BA II Plus)

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IRR ExampleSpreadsheet Model-based Approach to the Solution

A B C D E1 Time Type of Cash Flow ATCF2 0 Initial Project cost = -$12,0003 1 Incremental ATCF Benefit= $5,0004 2 Incremental ATCF Benefit= $5,0005 3 Incremental ATCF Benefit= $8,00067 IRR = 21.31282726%Simply place the cash flows into their own individual cells on the spreadsheet, remembering that the cost of the project is a negative cash flow representing funds leaving the firm.

Next, insert the built-in IRR function (fx) into a cell and provide the function values in the format of: =IRR(value 0, value 1, value 2,…, guess)

=IRR(D2:D5,0.10)

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IRR versus NPV

• Both methods use the same basic decision inputs.

• The only difference is the assumed discount rate.

• The IRR assumes intermediate cashflows are reinvested at IRR…NPV assumes they are reinvested at WACC– This difference, however, can produce conflicting

decision results under specific conditions

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Evaluating Investment AlternativesComparing NPV and IRR

Issue NPV IRR1. Future cash flows

change signIt still works the same for both accept/reject and ranking decisions.

Multiple IRRs may result - in this case, the IRR cannot be used for either accept/reject or ranking decisions.

2. Ranking projects Higher NPV implies greater contribution to firm wealth - it is an absolute measure of wealth.

The higher IRR project may have a lower NPV, and vice versa, depending on the appropriate discount rate, and the size of the

3. Reinvestment rate assumed for future cash flows received

Assumes all future cash flows are reinvested at the discount rate. This is appropriate because it treats the reinvestment of all future cash flows consistently, and k is the investor's opportunity cost.

Assumes cash flows from each project are reinvested at that project's IRR. This is inappropriate, particularly when the IRR is high.

Table 13 - 1 NPV versus IRR

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IRR versus NPVConditions Where NPV and IRR Will Give Conflicting Decision Results

1. Evaluating two or more mutually exclusive investment proposals

2. NPV profiles of the projects have different slopes and cross at a positive NPV

3. The cost of capital (relevant discount rate k) is lower than the crossover discount rate.

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Evaluating Investment AlternativesTwo NPV Profiles

13 - 2 FIGURE

A

NPV ($)

700

500

0


Crossover Rate = 9%

12 15

B

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Evaluating Investment AlternativesTwo NPV Profiles

13 - 2 FIGURE

A

NPV ($)

700

500

0


Crossover Rate = 9%

12 15

B

If k is less than 9%, then project A will

have a higher NPV than B and A should

be chosen to maximize the value

of the firm.

IRRB>IRRA

The IRR approach would lead us to

believe the Project B is best!

However, NPVA is greater when

k<9%

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Evaluating Investment AlternativesComparing NPV and IRR

• Both techniques use the same inputs• NPV measures in absolute terms, the estimated

increase in the value of the firm today the project is expected to produce.– NPV assumes cash flows are reinvested at WACC

• IRR estimates the rate of return on the project– IRR assumes cash flows produced by the project are

reinvested by the firm at the project’s IRR.

The reason for the different accept/reject decisions is the different reinvestment rate assumptions

used by the two techniques.

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Evaluating Investment AlternativesNPV and IRR Compared

Which method should be relied upon?– It depends on which reinvestment assumption is

most realistic.– Most often, the NPV assumption of reinvestment at

WACC is the most realistic because no rational manager would reinvest cash flows at rates lower than the firm’s cost of capital.

– Projects with high IRRs are not common – to assume that future cash flows will be reinvested at the inflated IRR rate is probably wrong.

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Evaluation TechniquesCFO Preferences

Despite the inherent superiority of the NPV approach, CFOs continue to use other approaches and do not favour NPV over IRR.

Perhaps, the reason for this is that it is difficult for people to understand what a positive NPV really means.

(See Figure 13 – 3 on the following slide.)

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CFO PreferencesEvaluation Technique

13 - 3 FIGURE

0% 10% 20% 30% 40% 50% 60% 70% 80%

IRRNPV

Hurdle RatePayback

Sensitivity AnalysisP/E multiples

Discounted paybackReal options

Book rate of returnSimulation analysis

Profitability IndexAPV

Evaluation Technique

Source: Data from Graham, John R. and Harvey, Campbell R. “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics 60 (2001), p. 187-243.

Payback and Discounted Payback

Capital Budgeting, Risk Considerations and Other Special

Issues

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Payback Method

• This is a simple approach to capital budgeting that is designed to tell you how many years it will take to recover the initial investment.

• It is often used by financial managers as one of a set of investment screens, because it gives the manager an intuitive sense of the project’s risk.

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Simple Payback Example

Initial cost = $100,000AT cash flow benefits = $60,000Useful life(years) = 5Cost of Capital = N/A

Year CashflowAfter-tax incremental

Cash Flows PV FactorCumulative Cash Flows

0 Initial cost -$100,000 -$100,0001 ATCF operating benefit $60,000 -$40,0002 ATCF operating benefit $60,000 $20,0003 ATCF operating benefit $60,000 4 ATCF operating benefit $60,000 5 ATCF operating benefit $60,000 6 ATCF operating benefit $60,000

Payback period = 1.7 years

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Discounted Payback Example

Initial cost = $100,000AT cash flow benefits = $60,000Useful life(years) = 5Cost of Capital = 10.0%

Year CashflowAfter-tax incremental

Cash Flows PV Factor

Present Value of ATCFs

Cumulative Cash Flows

0 Initial cost -$100,000 1 -$100,000 -$100,0001 ATCF operating benefit $60,000 0.90909091 $54,545 -$45,4552 ATCF operating benefit $60,000 0.82644628 $49,587 $4,1323 ATCF operating benefit $60,000 0.7513148 $45,079 $49,2114 ATCF operating benefit $60,000 0.68301346 $40,981 $90,1925 ATCF operating benefit $60,000 0.62092132 $37,255 $127,4476 ATCF operating benefit $60,000 0.56447393 $33,868 $161,316

Payback period = 1.9 years

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Discounted Payback Graphed

NPV$

Years

Discounted PaybackPoint

13 - 62

Discounted Payback

• Overcomes the lack of consideration of the time value of money…

• Graphing the cumulative PV of cash flows can help us see the pattern of cash flows beyond the payback point.

• If carried to the end of the project’s useful life…will tell us the project’s NPV (if you are using the firm’s WACC)

13 - 63

Profitability Index

• Uses exactly the same decision inputs as NPV • simply expresses the relative profitability of the projects

incremental after-tax cashflow benefits as a ratio to the project’s initial cost.

PI = PV of incremental ATCF benefitsPV of initial cost of project

If PI>1, then we accept; because the PV of benefits exceeds the PV of costs.

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Project Evaluation TechniquesProfitability Index (PI)

• PI is a ratio of the present value of benefits to costs.• As a pure coefficient, as long as it exceeds 1.00 the

project will increase the value of the firm if accepted.• A PI of more than 1.0 indicates that the project is

expected to earn a return greater than the required return.

outflows)(cash PVinflows)PV(cash

PI[ 13-3]

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Independent and Interdependent Projects

Independent Projects– Are projects that have no relationship with one another– Accepting one project has no impact on the decision to

accept another projectContingent Projects

– Are projects for which the acceptance of one requires the acceptance of another, either before-hand or simultaneously.

Mutually Exclusive Projects– Are projects that are substitutes of one another– Acceptance of one automatically means the other is

rejected.

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Evaluating Mutually Exclusive Projects with Unequal Lives

There are two approaches to adjust for unequal lives among mutually exclusive projects:1. Chain replication approach

• A way to compare projects with unequal lives by finding a time horizon into which all the project lives under consideration divide equally, and then assuming each project repeats until it reaches this horizon.

2. Equivalent Annual NPV (EANPV) approach• A way to compare projects by finding the NPV of the

individual projects, and then determining the amount of an annual annuity that is economically equivalent to the NPV generated by each project over its respective time horizon.

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Evaluating Mutually Exclusive Projects with Unequal Lives

The Chain Replication Approach

Consider two mutually exclusive projects A and B. – Useful life of A is 2 years.– Useful Life of B is 3 years.O 1 2A

O 1 2

O 1 2

O 1 2 3BO 1 2 3

You can now calculate NPV for both alternatives assuming replication over a six year time horizon.

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Project Evaluation TechniquesEquivalent Annual NPV (EANPV) Approach

k)(11-1

NPVProject

n

k

PANPV[ 13-4]

13 - 69

Capital Rationing

• The corporate practice of limiting the amount of funds dedicated to capital investments in any one year.

• Is academically illogical.– Why would a manager not invest in a project that will

offer a greater return than the cost of capital used to finance it?

• In the long-run could threaten a firm’s continuing existence through erosion of its competitive position.

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Capital RationingPractical Reasons for This Practice

• The firm may have owners who do not want to raise additional external equity because it will mean ownership dilution to them

• The firm may have so many great investment projects that they exceed the firm’s short-term managerial capacity to take advantage of them.

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Capital RationingRanking Projects

• Under capital rationing, the cost of capital is no longer the appropriate opportunity cost

• IRR may have more validity because the firm may be able to reinvest its cash flows at rates that are higher than the cost of capital.

• The PI may be a useful starting point because it ranks projects on PV per unit of investment.

• In the absence of capital rationing, NPV, IRR and PI will select value-maximizing projects.

See Figure 13 – 4 on the following slide for Rothman’s unconstrained Investment opportunity schedule.

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Optimal InvestmentRothman’s Inc.’s Investment and Internal Fund Availability, 2006

13 - 4 FIGURE

$11,976 Million

Rate of Return

WACC

Internal Funds Available

OPTIMAL INVESTMENT

IOS

$177,607 Million

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Investment Opportunity Schedule (IOS)

• An Investment opportunity schedule is the prioritized list of capital projects, ranked from highest to lowest.

• At the same time, the cumulative investment required is listed.

Example:Consider a firm that has six different capital investment proposals this year. Each project has it’s own IRR, NPV, PI and capital cost.

(See the next slide)

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Investment Opportunity Schedule (IOS)

Example:Consider a firm that has six different capital investment proposals this year. Each project has it’s own IRR, NPV, PI and capital cost. Each project has the same risk as the firm as a whole.

Firm's Cost of Capital = 10.00%

Capital Project Initial Cost

Annual ATCF

BenefitsUseful

Life NPV IRR PIA $1,500,000 $290,000 7 -$88,159 8.19% 0.94B $3,000,000 $700,000 6 $48,682 10.55% 1.02C $4,000,000 $1,040,000 6 $529,471 14.40% 1.13D $70,000 $20,000 7 $27,368 21.08% 1.39E $1,000,000 $290,000 5 $99,328 13.82% 1.10F $960,000 $200,000 8 $106,985 12.99% 1.11

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Investment Opportunity Schedule (IOS)Projects Ranked by NPV

Example:In the absence of capital rationing the projects as ranked by NPV would be:

Project A would be unacceptable because of a forecast negative NPV



Annual ATCF

BenefitsUseful

Life NPV IRR PIC $4,000,000 $1,040,000 6 $529,471 14.40% 1.13F $960,000 $200,000 8 $106,985 12.99% 1.11E $1,000,000 $290,000 5 $99,328 13.82% 1.10B $3,000,000 $700,000 6 $48,682 10.55% 1.02D $70,000 $20,000 7 $27,368 21.08% 1.39

$9,030,000 $811,835A $1,500,000 $290,000 7 -$88,159 8.19% 0.94

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Investment Opportunity Schedule (IOS)Projects Ranked by IRR

Example:In the absence of capital rationing the projects as ranked by IRR would be:

Project A would be unacceptable because forecast IRR < WACC.



Annual ATCF

BenefitsUseful

Life NPV IRR PID $70,000 $20,000 7 $27,368 21.08% 1.39C $4,000,000 $1,040,000 6 $529,471 14.40% 1.13E $1,000,000 $290,000 5 $99,328 13.82% 1.10F $960,000 $200,000 8 $106,985 12.99% 1.11B $3,000,000 $700,000 6 $48,682 10.55% 1.02

$9,030,000 $811,835

A $1,500,000 $290,000 7 -$88,159 8.19% 0.94

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Investment Opportunity Schedule (IOS)Projects Ranked by PI

Example:In the absence of capital rationing the projects as ranked by PI would be:

Project proposal A would be unacceptable because the forecast PI is less than 1.0.



Annual ATCF

BenefitsUseful

Life NPV IRR PID $70,000 $20,000 7 $27,368 21.08% 1.39C $4,000,000 $1,040,000 6 $529,471 14.40% 1.13F $960,000 $200,000 8 $106,985 12.99% 1.11E $1,000,000 $290,000 5 $99,328 13.82% 1.10B $3,000,000 $700,000 6 $48,682 10.55% 1.02

$9,030,000 $811,835

A $1,500,000 $290,000 7 -$88,159 8.19% 0.94

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Ranking of ProjectsIn the Absence of Capital Rationing

Project NPV IRR PI1 C D D2 F C C3 E E F4 B F E5 D B B

Capital Budget $9,369,000 $9,369,000 $9,369,000Total NPV $679,803 $679,803 $679,803

Clearly, in the absence of capital rationing, all three methods choose value maximizing projects and reject value-destroying projects.

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Investment Opportunity Schedule (IOS)Projects Selected by NPV under Capital Rationing Limit of $6 million

Example:Under capital rationing the projects selected by NPV would be:



Annual ATCF

BenefitsUseful

Life NPV IRR PIC $4,000,000 $1,040,000 6 $529,471 14.40% 1.13F $960,000 $200,000 8 $106,985 12.99% 1.11E $1,000,000 $290,000 5 $99,328 13.82% 1.10

$5,960,000 $735,785B $3,000,000 $700,000 6 $48,682 10.55% 1.02D $70,000 $20,000 7 $27,368 21.08% 1.39

A $1,500,000 $290,000 7 -$88,159 8.19% 0.94

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Investment Opportunity Schedule (IOS)Projects Selected by IRR under Capital Rationing Limit of $6 million

Example:Under capital rationing the projects selected by IRR would be:



Annual ATCF

BenefitsUseful

Life NPV IRR PID $70,000 $20,000 7 $27,368 21.08% 1.39C $4,000,000 $1,040,000 6 $529,471 14.40% 1.13E $1,000,000 $290,000 5 $99,328 13.82% 1.10

$5,070,000 $656,168F $960,000 $200,000 8 $106,985 12.99% 1.11B $3,000,000 $700,000 6 $48,682 10.55% 1.02

A $1,500,000 $290,000 7 -$88,159 8.19% 0.94

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Investment Opportunity Schedule (IOS)Projects Selected by PI under Capital Rationing Limit of $6 million

Example:Under capital rationing the projects selected by PI would be:



Annual ATCF

BenefitsUseful

Life NPV IRR PID $70,000 $20,000 7 $27,368 21.08% 1.39C $4,000,000 $1,040,000 6 $529,471 14.40% 1.13

$4,070,000 $556,840F $960,000 $200,000 8 $106,985 12.99% 1.11E $1,000,000 $290,000 5 $99,328 13.82% 1.10B $3,000,000 $700,000 6 $48,682 10.55% 1.02

A $1,500,000 $290,000 7 -$88,159 8.19% 0.94

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Ranking of ProjectsAssuming a Limit on Capital Expenditures to $6,000,000

Project NPV IRR PI1 C D D2 F C C3 E E

Capital Budget $5,960,000 $5,070,000 $4,070,000Total NPV $735,785 $656,168 $556,840

Capital rationing is an artificial limit on capex.Only NPV ranking will ensure maximization of shareholder wealth

under these constrained conditions.

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International Considerations

• Capex decisions involving direct foreign investment must take into account additional factors:– Political risk– Potential legal and regulatory issues– Adjust for foreign exchange risk– Adjust for foreign taxation– How can the project be financed if local capital

markets are poorly developed?

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International Investment

• Export Development Canada (EDC) is a federal crown corporation that helps Canadian firms export and make foreign direct investment decisions (FDI)

• EDC provides insurance products to help mitigate some of the risks of FDI

• FDI outside Canada is a growing phenomenon in Canada as Canadian companies increasingly are seeking international investment opportunities.

• EDC is encouraging Canadian companies to look beyond the U.S. as FDI targets.

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Summary and Conclusions

In this chapter you have learned:– How capital decisions are made in companies– About capital expenditure evaluation tools including

NPV, IRR, profitability index, payback period and discounted payback period

– Why NPV is the preferred evaluation approach– How to adjust analysis for conditions of capital

rationing, risk differences across corporate divisions, and effects of foreign direct investment.

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