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UNIT 6

Project Evaluation

When cost and benefit cash flows have been estimated and combined, aproject proposal is ready for evaluation. This unit shows how to calculatethe most widely used measures of project profitability, and discusses theiruse in evaluating and ranking projects.

Learning Objectives When you have completed this unit you should:

A. Know how to calculate payback, return on investment, net presentvalue, and internal rate of return for a project.

B. Understand the advantages and disadvantages of each method.

C. Know how to use each method to evaluate and rank proposedprojects.

6-1. Is It Worth Doing?

Many more projects are proposed than are approved. How can the pro-

posals that are most profitable to the organization be selected? Each pro-posal must be evaluated and, if resources are limited, compared againstother proposals. Evaluation decides whether the project qualifies as profit-able, measured against a specified organization guideline (e.g., three-yearpayback, or positive net present value at 10% discount rate). If the organi-zation has unlimited resources, a favorable evaluation is sufficient forproject approval. Otherwise, the proposal must compete against otherqualified proposals for limited resources.

To evaluate proposed investments, one must first express them on a com-mon basis and then apply some sort of economic criterion, or profitabilityindex. The usual common basis is estimated cash flow. No one economiccriterion dominates the field. There are several, and each has its particularstrengths, weaknesses, and impassioned champions and detractors. Thecriteria discussed in this unit are the four most widely used. They includepayback, return on investment, net present value, and internal rate ofreturn.

6-2. Project Cash Flow Table

A control improvement project starts as an idea. The idea takes on differ-ent representations as it is developed. Representations may be as concrete

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58 UNIT 6: Project Evaluation

as a pilot plant demonstration of a proposed control scheme or as abstractas a mathematical proof. The financial representation of a project is astring of numbers, the expected yearly cash flows. These cash flows are thealgebraic sums of the benefit cash flows discussed in Unit 4 and the costcash flows covered in Unit 5. The combined cash flow table for a conven-tional project starts with negative numbers, then switches to positive.

Example 6-1: The first costs of a four-unit control consolidation aredescribed in Example 5-2. The cash flows for the first costs of this projectare listed in the second column of Table 6-1. If benefits from the consolida-tion are $40,000 per unit per year, the benefit cash flows will be $80,000 forthe second year, during which only two units will be run from the consoli-dated control room, and $160,000/year thereafter for the life of the project.Benefit cash flows are listed in the third column of Table 6-1. Combinedcash flows, the year-by-year algebraic sums of cost and benefit cash flows,are listed in column four.

6-3. Nondiscounted Evaluation Methods

The earliest widely used evaluation methods are payback and return oninvestment.The payback period (PP) is the time required to recover theoriginal capital investment from cash flow. The original capital investmentis the project first cost, and for payback calculation purposes, the cashflows are benefits minus operating costs. PP thus can be defined as thevalue that satisfies Eq. (6-1).

(6-1)

Cash Flows, $

Year Costs Benefits Combined

0 -200,000 0 -200,000

1 -190,000 0 -190,000

2 -140,000 80,000 -60,0003 0 160,000 160,000

4 0 160,000 160,000

5 0 160,000 160,000

6 0 160,000 160,000

7 0 160,000 160,000

8 0 160,000 160,000

Table 6-1. Cash Flows for Control Consolidation

C CF td0

PP=

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UNIT 6: Project Evaluation 59

where:

FC = project first cost

CF = operating cash flow, not including first costsTime is usually measured from the start of operations rather than from thefirst expenditure.

Return on investment (ROI) uses the same first cost and cash flow defini-tions. It is expressed as a percentage and measured by the ratio of averageyearly operating cash flow to first cost, as shown in Eq. (6-2).

(6-2)

where:

CFi = cash flow for ith year

n = project operating lifetime, in years

Example 6-2: A straightforward project has an estimated first cost,invested at the start of the project, of $100,000. The project will take oneyear before operation starts, so operating cash flows start in year 2. Theyare estimated to be $40,000 per year for eight years. The overall cash flowdiagram is shown as Fig. 6-1. Payout period is 2.5 years, the time afterstart-up at which operating cash flow equals first cost. ROI = 100 x$40,000/100,000 = 40%.

Payback and ROI have similar advantages and disadvantages. Both areeasy to understand and easy to compute. Neither explicitly takes intoaccount the time value of money, since future cash flows are not dis-counted as a function of time. As a result, these methods are biased in thevalues placed on some cash flows compared to the discount methods cov-ered in 6.4. Payback places no value on cash flows beyond those requiredto cover first cost. ROI places equal value on immediate and remote cashflows. These biases are not important if all the projects being comparedhave similar lifetimes and cash flow trajectories. They can produce baddecisions when comparing dissimilar projects. Payback and ROI have been largely superseded by the discounted evaluation methods discussedin the next section.

ROI 100 CF i( ) n i 1=

n

FC( ) =

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6-4. Discounted Evaluation Methods

The evaluation methods recommended by most economists are net presentvalue (NPV) and internal rate of return (IRR). Both of these methods takeinto account the time value of money by discounting future cash flows as a

function of time. The time value of money is simply the effect of interest.The future value (FV) of a present value (PV) after n years is determined by Eq. (6-3), the compound interest formula.

FVn = PV (1 + k)n (6-3)

where k is the yearly fractional interest rate.

Table 6-2 shows a few future values of one dollar as a function of interestrate and time. Discount factors for future values are calculated by rear-ranging Eq. (6-3) into Eq. (6-4) to solve for PV.

PV = FVn/(l + k) n (6-4)

Fig. 6-1. Cash Flow Diagram for Example 6-2

Interest Rate

Year 5% 10% 20%

1 1.050 1.100 1.200

5 1.276 1.611 2.488

10 1.629 2.594 6.192

Table 6-2. Compounded Future Value of $1

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The present value of one dollar of future value is the discount factor thatmust be applied when evaluating future cash flow. Some discount factorsare plotted in Fig. 6-2 and listed in Table 6-3. Note that the entries in thistable are simply the inverse of the entries in Table 6-2.

Fig. 6-2. Discount Factor for Future Values

Interest Rate

Year 5% 10% 20%

1 0.952 0.909 0.833

5 0.784 0.621 0.402

10 0.614 0.386 0.161

Table 6-3. Discount Factors

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If interest rate k is set at the cost of capital, the net present value of a stringof cash flows (CFi) over n years can be calculated by repeated applicationof Eq. (6-4), as follows:

(6-5)

The project represented by the string of cash flows should be approved ifNPV is positive, since a positive value of NPV indicates that investment inthe project will earn at a rate greater than k. For instance, if capital can beobtained by borrowing at 10%, a project with an NPV of $20,000 at k = 0.10will yield $20,000 over and above interest costs.

The calculation procedure for internal rate of return uses the NPV calcula-tion as a means to a different end. An unknown rate of return (r) is substi-tuted for cost of capital (k) in Eq. (6-5), producing Eq. (6-6).

(6-6)

The internal rate of return (IRR) is that value of r which will result in azero value of NPV. Eq. (6-6) cannot be solved explicitly for r, so findingIRR is a trial-and-error procedure. Those projects with an IRR greater thana specified target rate should be approved.

Example 6-3: The cash flows for Example 6-2, shown in Fig. 6-1, can also be used to calculate NPV and IRR. If a pretax cost of capital of 15% isassumed, NPV can be calculated from Eq. (6-5) as follows:

NPV = -100,000 + 0 + 40,000/(1.15)2...40,000/(1.15)9 = $56,081

IRR must be greater than 15%, since NPV is positive at that rate of return.A rate of 30% produces a negative NPV of -10,009, so IRR must be lessthan 30%, but closer to 30% than 15%. Two interpolations yield an IRR of26.8%. Fig. 6-3 shows the effect of rate of return on NPV.

NPV of a nonconventional project may equal zero at more than one dis-count rate, producing multiple internal rates of return. A necessary butnot sufficient condition is at least two changes of sign for cash flow. SeeExercise 6-10 for an example. Methods have been proposed (Ref. 1) to deal

NPV CF0 CF1 1 k+( ) CF2 1 k+( )2

CFn 1 k+( )n + + +

CF0 CF i 1 k+( )i ( )

i 1=

n+

=

=

NPV CF0 CFi 1 r+( )i

( )i 1=

n

+=

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with these cases by identifying a single relevant rate of return for use indetermining project acceptability.

The advantage of these discount-based methods over payback and ROI is

their consistent valuation of future cash flows. Their historical disadvan-tage, which limited their acceptance for a long time, is more difficult calcu-lation. This objection is now irrelevant. Many calculator and personalcomputer programs, especially spreadsheets, can be used for NPV andIRR calculation.

NPV and IRR are equivalent methods for project evaluation, and thechoice between them for this purpose is a matter of taste. If the target rateis set equal to the cost of capital and no other restrictions apply, the use ofNPV or IRR will produce identical results. They will not necessarily pro-duce identical rankings, so care should be taken to use the appropriatemethod when projects must be rank ordered. These situations are dis-cussed in Section 6-6.

6-5. Using a Spreadsheet

Calculation of NPV using pencil and paper is slow and tedious. Calcula-tion of IRR is even more repetitive, since it involves a trial-and-error pro-cedure. For any problems more complex than evaluation of a single set of

Fig. 6-3. Effect of Rate of Return on NPV in Example 6-3

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cash flows, the easiest way to get NPV and IRR values is through the useof a spreadsheet program. The most popular spreadsheets, including thewidely used Excel , have built-in NPV and IRR functions.

Operation of a computer spreadsheet is essentially an information entryprocess. Calculation and display are automatically and immediately per-formed when information is received. When an entry in one cell ischanged, all the dependent cells are altered to reflect that change. This fea-ture allows rapid evaluation of alternatives.

Spreadsheets are particularly useful for contingency or what-if studies.Once the original cash flows and function calls have been entered, eachchange in cash flow immediately produces changes in the displayed val-ues of NPV and IRR. Fig. 6-4 is a typical project evaluation printout from aspreadsheet. Cash flows, discount rate, NPV, and IRR are shown. Only thecash flow entries need to be altered to find the effects of a changed situa-tion. The effect of a delayed start-up is shown in Fig. 6-5. The delay wipesout cash flow for the first year, affecting NPV and IRR. Only the entry foryear one cash flow had to be changed. NPV and IRR were automaticallyrecalculated. All the engineering economy textbooks cited in Appendix Ahave detailed descriptions of spreadsheet use for project evaluation.

6-6. Selection Among Proposals

The situation in which all projects are independent and the choice amongthem is unlimited is an idealized state, more commonly encountered intextbooks than in the real world. There are several ways to classify theconstraints that often limit project selection.

Fig. 6-4. Spreadsheet Project Evaluation Printout

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Choice may be limited because multiple projects seek the same object. Aproposal to replace existing controls with a DCS cannot be evaluated inde-pendently of a proposal to replace the same controls with multiple PLCs.Acceptance of one proposal forecloses the opportunity for the other one.Choice may also be limited by resource availability. The scarce resourcemay be skilled labor (the process engineer who knows the plant has onlyenough time to work on one control project) or productive capacity (theonly two plants making left-handed widgets cannot both be shut down forcontrol retrofits). In most cases the scarce resource is capital.

Capital investment literature uses a somewhat different classificationscheme. Opportunity-limited situations are lumped with those limited byavailability of resources other than capital. The conflicting projects aremutually exclusive.The decision that must be made is no longer whether aproject qualifies for investment under organization guidelines, but whichone among qualifying proposals is most attractive. In this situation NPVand IRR can produce different results. The literature includes many dis-cussions (see Ref. 2 for example) of the conditions for which the two meth-ods have ranking conflicts.

Example 6-4: Cash flows for mutually exclusive proposals A and B arelisted in Table 6-4. The required rate of return is equal to the cost of capitalat 10%, so both proposals qualify easily. NPV of proposal A at 10% cost ofcapital is $6,699; IRR is 22%. NPV of proposal B is $7,136; IRR is 18.3%. Ifprojects are ranked by NPV, proposal B will be selected. If IRR is used,proposal A will be selected.

NPV is considered to be the sounder methodology for ranking of mutuallyexclusive proposals. It assumes that cash flows can be reinvested at thecost of capital, while IRR assumes that cash flows can be reinvested to earn

Fig. 6-5. Spreadsheet Project Evaluation Printout after Cash Flow Change

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the calculated rate of return. The NPV assumption is more conservativeand more likely.

The other restricted situation treated in the capital investment literature is

limited availability of capital, known as capital rationing.Theoretically,capital should be available for any worthwhile project (i.e., one that willearn a higher rate than the cost of capital). Actually, capital may be limitedfor any number of reasons. Firms may limit capital expenditures becauseof credit limits or fear of the market effects of increased borrowing. Divi-sions and individual plants, where most decisions on control improve-ment projects are made, are almost always subject to limits on the amountof capital that can be committed without approval of higher authority.There are usually more qualifying proposals than can be funded withavailable capital, so some means must be found to discriminate amongthem and select the most profitable.

Net present value is not very useful as a tool for this selection process. Theproject with the largest NPV is expected to make the most money, but itmay not be the most efficient use of capital. The discount rate for NPVmight be raised until total capital outlay for qualified proposals is equal to

or less than the capital limit, but this is equivalent to reinventing internalrate of return. It is simpler to use IRR directly. Projects are selected bystarting with the highest IRR and proceeding down the list until the capi-tal limit is reached. Another possible method for ranking projects uses theratio of the net present value of net cash inflows to the initial investment.This ratio is called the profitability index (Ref. 3). Profitability rankingsshould be similar to those obtained using IRR.

Cash Flows, $

Year Project A Project B

0 -25,000 -25,000

1 10,000 0

2 10,000 5,000

3 10,000 10,000

4 10,000 30,000

Table 6-4. Mutually Exclusive Proposals

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References

1. Hartman, J.C. and Schafrick, I.C., 2004. The Relevant InternalRate of Return. Engineering Economist 49, 3, pp. 139-155.

2. Barney, L.D. and Danielson, M.G., 2004. Ranking MutuallyExclusive Projects: the Role of Duration. Engineering Economist49, 1, pp. 43-61.

3. Peterson. S. and Pugh, D., 2005. How to Make a Good CapitalDecision. InTech 52. 3, p. 50.

4. Park C. S., 2002.Contemporary Engineering Economics (3d ed.), p.809. Prentice-Hall.

Exercises

6-1. Payback is sometimes known as the fish-bait method of projectevaluation. Why?

6-2. Calculate payback, ROI, NP and IRR for the project for which cash flowsare listed in Table 6-2. Use a 10% discount rate.

6-3. The discount factor for earnings 5 years hence is known to be 0.497. What

is the percentage discount rate?6-4. A firm evaluates proposals using a discount rate of 20%. This rate is

considerably higher than the cost of capital, which is available at 10%. Listsome possible reasons for this behavior.

6-5. Payback, ROI, NP and IRR for the cash flows shown in Fig. 6-1 werecalculated in Examples 6-2 and 6-3. Which of these profitability measureswould be affected if the project started earning immediately instead of one year after initial expenditures?

6-6. Two projects, A and B, are proposed for the same unit. Each project consistsof installation of a PLC to control a different part of the unit. Expected cash flows for the projects are listed in Table 6-5. The criterion for projectapproval is positive net present value at a discount rate of 15%. Which projects should be approved?

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6-7. If the PLCs for the projects in Exercise 6-6 lose power, failure may becatastrophic. The PLCs should, therefore, be powered by an uninterruptible power supply (UPS). An already installed UPS has the capacity to handleone but not both PLCs. A new UPS to handle one PLC would cost $5000.In this situation, which projects should be approved?

6-8. Under what circumstances can capital rationing make projects mutuallyexclusive? Give an example.

6-9. In the example given in the solution to Exercise 6-8, what will happen if thecapital limit is less than $800,000? greater than $1,500,000?

6-10. Since you have demonstrated your mastery of the subject by reaching thisexercise, you havebeen asked to write a sequel to this unit. You are offeredan immediate $1000 cash payment, and royalty payments after completionof the book are estimated to be $2000/year for 3 years. The book will take one year to complete, and during that year you must forgo a consulting projectthat would have earned you $5000. Is this an attractive proposal? Whatrange of discount rates would result in positive NPV?

Cash Flows, $

Year Project A Project B

0 -10,000 -10,000

1 3,000 -5,000

2 3,000 5,000

3 3,000 5,000

4 3,000 5,000

5 3,000 5,000

6 3,000 5,000

7 3,000 5,000

Table 6-5. Cash Flows for Exercise 6-6

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