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ECGD3110ECGD3110Systems Engineering & EconomySystems Engineering & Economy

Lecture 7Lecture 7OtherOther Analysis MethodsAnalysis Methods

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Other Analysis MethodsOther Analysis Methods

Future Worth Analysis (FWA)Future Worth Analysis (FWA)

Benefit-Cost Ratio Analysis (BCRA)Benefit-Cost Ratio Analysis (BCRA)

Payback PeriodPayback Period

Sensitivity and Breakeven AnalysisSensitivity and Breakeven Analysis

Selection of Minimum MARRSelection of Minimum MARR

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Other Analysis TechniquesOther Analysis Techniques

Future worth analysisFuture worth analysis is is equivalent toequivalent to present worth analysis; present worth analysis; the best alternative one way is also best the other way. There are many situations where we want to know the best alternative one way is also best the other way. There are many situations where we want to know what a what a futurefuture situation will be, if we take some particular course of action situation will be, if we take some particular course of action nownow. This is called . This is called future worth future worth analysisanalysis..

Since we can writeSince we can writePW of cost PW of cost PW of benefit PW of benefit or or EUAC EUAC EUAB EUAB we can equivalently writewe can equivalently write

(PW of benefit)/PW of cost (PW of benefit)/PW of cost 1 1, or , or EUAB/EUAC EUAB/EUAC 1 1..Economic analysis based on these ratios is called Economic analysis based on these ratios is called benefit-cost ratio analysisbenefit-cost ratio analysis ..

Payback periodPayback period is an is an approximateapproximate analysis method. For example, if a $1000 investment today generates analysis method. For example, if a $1000 investment today generates $500 annually in savings, we say its payback period is 1000/500 = 2 years. $500 annually in savings, we say its payback period is 1000/500 = 2 years.

Sensitivity analysisSensitivity analysis identifies how sensitive economic conclusions are to the values of the data, and allows identifies how sensitive economic conclusions are to the values of the data, and allows making decisions for an entire range of the data. making decisions for an entire range of the data.   

Breakeven analysisBreakeven analysis is closely related to sensitivity analysis, and determines conditions when two is closely related to sensitivity analysis, and determines conditions when two alternatives are equivalent (as well as when each is better than the other). It can be viewed as a type of alternatives are equivalent (as well as when each is better than the other). It can be viewed as a type of sensitivity analysis.sensitivity analysis.

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Benefit/Cost Ratio AnalysisBenefit/Cost Ratio Analysis

ExampleExample Each of the five mutually exclusive alternatives presented below will last for 20 years Each of the five mutually exclusive alternatives presented below will last for 20 years and has no salvage value. MARR = 6%.and has no salvage value. MARR = 6%.

The steps are the same as in incremental ROR, except that the criterion is now The steps are the same as in incremental ROR, except that the criterion is now B/B/C, C, and the cutoff is 1 instead of the MARR:and the cutoff is 1 instead of the MARR:

1) Be sure you identify all alternatives. 1) Be sure you identify all alternatives. 2) (Optional) Compute the B/C ratio for each alternative. Discard any with a B/C < 1. 2) (Optional) Compute the B/C ratio for each alternative. Discard any with a B/C < 1. (We can discard F).(We can discard F).3) Arrange the remaining alternatives in an ascending order of investment.3) Arrange the remaining alternatives in an ascending order of investment.

AA BB CC DD EE FF

CostCost $4000$4000 $2000$2000 $6000$6000 $1000$1000 $9000$9000 $10000$10000

PWBPWB $7330$7330 $4700$4700 $8730$8730 $1340$1340 $9000$9000 $9500$9500

B/CB/C 1.831.83 2.352.35 1.461.46 1.341.34 1.001.00 0.950.95

NPVNPV 33303330 27002700 17301730 340340 00 -500-500

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DD BB AA CC EE FF

CostCost $1000$1000 $2000$2000 $4000$4000 $6000$6000 $9000$9000 $10000$10000

PWBPWB $1340$1340 $4700$4700 $7330$7330 $8730$8730 $9000$9000 $9500$9500

B/CB/C 1.341.34 2.352.35 1.831.83 1.461.46 1.001.00 0.950.95

NPVNPV 340340 27002700 33303330 17301730 00 -500-500

Benefit/Cost Ratio AnalysisBenefit/Cost Ratio Analysis

4) Comparing 4) Comparing B/B/C with 1 for consecutive alternatives select the best C with 1 for consecutive alternatives select the best alternative.alternative.

Thus, for the example, the increments B-D and A-B are attractive. We Thus, for the example, the increments B-D and A-B are attractive. We prefer B to D, and we prefer A to B. Increment C-A is not attractive, as prefer B to D, and we prefer A to B. Increment C-A is not attractive, as B/B/C = 0.76 < 1. Comparing A to E, again A is best. Finally A is the best C = 0.76 < 1. Comparing A to E, again A is best. Finally A is the best project.project.

B-DB-D A-BA-B C - AC - A E-AE-A

Incremental CostIncremental Cost $1000$1000 $2000$2000 $2000$2000 $5000$5000

Incremental BenefitIncremental Benefit $3360$3360 $2630$2630 $1400$1400 $1670$1670

Incr.B/Incr. CIncr.B/Incr. C 3.363.36 1.321.32 0.760.76 0.330.33

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A, B, C, and D are above the 45-degree line; their B/C ratio is > 1. F is below the line: B/C ratio is < 1. We can discard F if we wish.

Benefit/Cost Ratio AnalysisBenefit/Cost Ratio Analysis

PWB/PWC = 1PWB/PWC = 1

PWB

PWC

D

B

A

C EF

B-DB-D A-BA-B C - AC - A E-AE-A

Incremental CostIncremental Cost $1000$1000 $2000$2000 $2000$2000 $5000$5000

Incremental BenefitIncremental Benefit $3360$3360 $2630$2630 $1400$1400 $1670$1670

Incr.B/Incr. CIncr.B/Incr. C 3.363.36 1.321.32 0.760.76 0.330.33

Examine each separable increment of investment.B/C < 1 increment is not attractiveB/C 1 increment is desirable.

Begin with D & B: B/C > 1. B “wins”.Next consider A: B/C > 1. A “wins”.C: B/C < 1; discard C. E: B/C < 1; discard E. F was discarded earlierConclude A is best.

Note: Alt. B has the highest B/C ratio

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Payback PeriodPayback Period

WarningWarning1. Payback period is an 1. Payback period is an approximateapproximate, rather than an exact, , rather than an exact, analysis calculationanalysis calculation..  2. All costs and all profits, or savings of the investment prior to payback, are included 2. All costs and all profits, or savings of the investment prior to payback, are included without considering differences in their without considering differences in their timingtiming..3. All the economic consequences beyond the payback period are completely ignored.3. All the economic consequences beyond the payback period are completely ignored.4. Payback period may or may not select the same alternative as an exact economic analysis 4. Payback period may or may not select the same alternative as an exact economic analysis method.method.

Payback period is used becausePayback period is used because1.1. the concept can be readily the concept can be readily understoodunderstood,,2.2. the calculations can be readily made and the calculations can be readily made and understoodunderstood by people unfamiliar with the use of by people unfamiliar with the use of

the time value of money.the time value of money.

It’s “better than nothing.” Use it as a last resort to communicate.It’s “better than nothing.” Use it as a last resort to communicate.

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A firm is buying production equipment for a new A firm is buying production equipment for a new plant.plant.Two alternative machines are being consideredTwo alternative machines are being considered..

Payback Period: ExamplePayback Period: Example YeaYearr

TempoTempomachinemachine

DuraDuramachinemachine

00 --$30,000$30,000 --$35,000$35,000

11 12,00012,000 1,0001,000

22 9,0009,000 4,0004,000

33 6,0006,000 7,0007,000

44 3,0003,000 10,00010,000

55 00 13,00013,000

66 00 16,00016,000

77 00 19,00019,000

88 00 22,00022,000

00 57,00057,000

Tempo PBP Analysis

$0

$20,000

$40,000

0 1 2 3 4 5 6 7 8

Year

Benefits

Costs

Dura PBP Analysis

$0

$50,000

$100,000

0 1 2 3 4 5 6 7 8

Year

Benefits

Costs

Tempo Dura IRR 0.00% 18.99%

PBP analysis would choose Tempo (PBP = 4 yrs.) instead of Dura (PBP = 5 yrs.). However, with IRR analysis we can see that Tempo is not a very attractive investment. Although, Tempo does return its investment more quickly than Dura.

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Lesson from Example: liquidity and profitability can be very different criteria.

Final Conclusions about PBP AnalysisThis analysis provides a measure of the speed of the return of the investment. If a company is short of working capital, or experiences a rapidly changing technology, the speed of return can be important.  PBP analysis should not be confused with careful economic analysis.PBP analysis does not always mean the investment is economically desirable.

Payback Period: SummaryPayback Period: Summary

1. Payback period is an approximate, rather than an exact, analysis calculation.

2. All costs and all profits, or savings of the investment prior to payback, are included without considering differences in their timing.

3. All the economic consequences beyond the payback period are completely ignored.

4. Payback period may or may not select the same alternative as an exact economic analysis method.

5. Payback period is used because the concept can be readily understood, the calculations can be readily made and understood by people unfamiliar with the use of the time value of money.

6. PBP analysis is “better than nothing.” Use it as a last resort to communicate.

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Sensitivity and Breakeven AnalysisSensitivity and Breakeven Analysis

Motivating SituationMotivating Situation

garbage garbage model model garbage garbage

All engineering economic analysis is based on models. If the data the models use is All engineering economic analysis is based on models. If the data the models use is inaccurate, the results will not be useful. inaccurate, the results will not be useful. The data often represents The data often represents projectionsprojections of future consequences, and there may be of future consequences, and there may be considerable uncertainty about the accuracy of the data.considerable uncertainty about the accuracy of the data.An important question is: An important question is:

“ To what extent do variations in the data affect the decisionbased on the model ”

Some data may have little or no effect on the decision. Other data may have a big effect Some data may have little or no effect on the decision. Other data may have a big effect on the decision. A decision is said to be on the decision. A decision is said to be sensitive to the estimatesensitive to the estimate when small variations when small variations in a particular estimate would change the selection of the alternative.in a particular estimate would change the selection of the alternative.

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Hypothetical Example.Hypothetical Example. We must make a choice of a replacement machine. We must estimate:  We must make a choice of a replacement machine. We must estimate:  1) the annual maintenance cost and  1) the annual maintenance cost and  2) the salvage value.  2) the salvage value.  Perhaps we find thatPerhaps we find that1)1) our decision is sensitive to changes in the annual maintenance estimate;our decision is sensitive to changes in the annual maintenance estimate;2) 2) the decision is insensitive to the salvage-value estimate over the full range of its the decision is insensitive to the salvage-value estimate over the full range of its

possible values.possible values.This tells us we need to do a very good job with:This tells us we need to do a very good job with:1) but having an accurate estimate for1) but having an accurate estimate for2) is not too important. 2) is not too important. The following are examples where sensitivity analysis can help.The following are examples where sensitivity analysis can help.1.1. Should we install a cable with 400 circuits now, or a 200-circuit cable now and another Should we install a cable with 400 circuits now, or a 200-circuit cable now and another

200-circuit cable later?200-circuit cable later?2.2. A 10-cm water main is needed to serve a new area. Should the 10-cm main be installed A 10-cm water main is needed to serve a new area. Should the 10-cm main be installed

now, or should a 15-cm main be installed in order to provide an adequate water supply now, or should a 15-cm main be installed in order to provide an adequate water supply to adjoining areas to be developed later?to adjoining areas to be developed later?

3.3. A firm needs a 10,000-mA firm needs a 10,000-m22 warehouse now. It estimates it will need an extra 10,000-m warehouse now. It estimates it will need an extra 10,000-m22 one in four years. It could build a 10,000-mone in four years. It could build a 10,000-m22 warehouse now and enlarge it later, or it warehouse now and enlarge it later, or it could build a 20,000-mcould build a 20,000-m22 warehouse now. warehouse now.

Sensitivity and Breakeven AnalysisSensitivity and Breakeven Analysis

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Sensitivity and Breakeven Analysis: ExampleSensitivity and Breakeven Analysis: Example

Stage Construction with n as a sensitivity parameterStage Construction with n as a sensitivity parameter ..We can build a project to full capacity now, or construct it in two stages.We can build a project to full capacity now, or construct it in two stages.Full-capacity construction in one stage costs $140,000.Full-capacity construction in one stage costs $140,000.The first stage construction costs $100,000. The first stage construction costs $100,000. The second stage construction, n years later, costs $120,000.The second stage construction, n years later, costs $120,000.

Other informationOther informationEither facility will last until 40 years from now, regardless of when it is installed, and will Either facility will last until 40 years from now, regardless of when it is installed, and will have zero salvage value then.have zero salvage value then.The annual cost of operation and maintenance is the same for either alternative.The annual cost of operation and maintenance is the same for either alternative.The interest rate is 8% a year.The interest rate is 8% a year.

Our choice between I and II may depend on the value of n. Our choice between I and II may depend on the value of n. We shall do a sensitivity analysis for all values of n of interest.We shall do a sensitivity analysis for all values of n of interest.

I. Construct full capacity now:I. Construct full capacity now:

PWPWII= $140,000= $140,000II. Build in two stages:II. Build in two stages:

PWPWIIII(n) =100,000+120,000(P/F,8%,n)=100,000+120,000/(1+i)-(n) =100,000+120,000(P/F,8%,n)=100,000+120,000/(1+i)-nn=100000+120000/(1.08)-=100000+120000/(1.08)-nn. .

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Sensitivity and Breakeven Analysis: Example – cont.Sensitivity and Breakeven Analysis: Example – cont.

Year I II 10 $140,000 $155,583 11 $140,000 $151,466 12 $140,000 $147,654 13 $140,000 $144,124 14 $140,000 $140,855 15 $140,000 $137,829 16 $140,000 $135,027 17 $140,000 $132,432 18 $140,000 $130,030 19 $140,000 $127,805 20 $140,000 $125,746 21 $140,000 $123,839 22 $140,000 $122,073 23 $140,000 $120,438 24 $140,000 $118,924 25 $140,000 $117,522 26 $140,000 $116,224 27 $140,000 $115,022 28 $140,000 $113,910 29 $140,000 $112,879 30 $140,000 $111,925

Breakeven Chart, Ex. 9-9

$0

$50,000

$100,000

$150,000

$200,000

$250,000

Year

I

II

We see the breakeven point between I and II is about 15 years.We see the breakeven point between I and II is about 15 years.(exactly n = 14.275).(exactly n = 14.275).

If n < 15 years, I is cheaper (one-stage).If n < 15 years, I is cheaper (one-stage).If n If n 15 years, II is cheaper (two-stage construction). 15 years, II is cheaper (two-stage construction).

The decision on how to construct the project is sensitive to the age at which the second stage is needed The decision on how to construct the project is sensitive to the age at which the second stage is needed onlyonly if the if the range of estimates includes 15 years. In this case we need a really accurate estimate of n to make a good range of estimates includes 15 years. In this case we need a really accurate estimate of n to make a good decision.decision.

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Example:Example: We have 3 mutually exclusive alternatives, each with a 20-year life, and no salvage value. MARR = 6%. We have 3 mutually exclusive alternatives, each with a 20-year life, and no salvage value. MARR = 6%. Initial CostInitial Cost Ann.BenefitAnn.Benefit

Alt. AAlt. A $2,000$2,000 $410$410Alt. BAlt. B $4,000$4,000 $639$639Alt. CAlt. C $5,000$5,000 $700$700Based on this data, we found Alt. B was preferred.Based on this data, we found Alt. B was preferred.

Question:Question: How sensitive is our choice to the estimate of the initial cost of B? How sensitive is our choice to the estimate of the initial cost of B?

Alternative Alternative A: A: NPWNPWAA = PW of benefit – PW of cost = 410 (P/A,6%,20) - 2000 = 410 (11.470) –2000 = 2703 = PW of benefit – PW of cost = 410 (P/A,6%,20) - 2000 = 410 (11.470) –2000 = 2703

Alternative B:Alternative B: Let x = initial cost of B (maybe $4000), Let x = initial cost of B (maybe $4000), NPWNPWBB = 639 (P/A,6%,20) – x = 7329 – x = 639 (P/A,6%,20) – x = 7329 – x

Alternative C:Alternative C: NPWNPWCC = 700 (P/A,6%,20) – 5000 = 3029 = 700 (P/A,6%,20) – 5000 = 3029

We have We have NPW NPWBB NPW NPWAA, NPW, NPWCC 7329 – x 7329 – x 2703,3029 2703,3029 7329 – x 7329 – x 3029 3029 7329 – 3029 7329 – 3029 x x 4300 4300 x x

For B to have the largest NPW means that the initial cost of B can be at most 4300. For B to have the largest NPW means that the initial cost of B can be at most 4300.

It can be ANY number less than 4300.It can be ANY number less than 4300.

Sensitivity and Breakeven Analysis: ExampleSensitivity and Breakeven Analysis: Example

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4300 = 4300 = breakevenbreakeven

NPVC= 3029

NPVA= 2703

NPVB= 7329 - x

X: Initial cost of B

Sensitivity and Breakeven Analysis: Example Sensitivity and Breakeven Analysis: Example – cont.– cont.

NPV

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SummarySummaryFuture WorthFuture Worth..

A future worth calculation occurs when the point in time at which the comparison between alternatives will be A future worth calculation occurs when the point in time at which the comparison between alternatives will be made is in the future. The best alternative according to future worth should also be best according to present made is in the future. The best alternative according to future worth should also be best according to present worth.worth.

Benefit-Cost Ratio AnalysisBenefit-Cost Ratio Analysis.. We compute a ratio of benefits to costs, using either PW or ACF calculations. Graphically, the method is We compute a ratio of benefits to costs, using either PW or ACF calculations. Graphically, the method is similar to PW analysis. Sometimes, with neither input nor output fixed, we use incremental benefit-cost similar to PW analysis. Sometimes, with neither input nor output fixed, we use incremental benefit-cost analysis (analysis (B/B/C). Benefit-cost ratio analysis is often used in government.C). Benefit-cost ratio analysis is often used in government.

Payback PeriodPayback Period.. The payback period is the period of time needed for the profit or other benefits of an investment to equal its The payback period is the period of time needed for the profit or other benefits of an investment to equal its cost. This method is simple to use and understand, but is a poor analysis technique for ranking alternatives. It cost. This method is simple to use and understand, but is a poor analysis technique for ranking alternatives. It provides a measure of the speed of return of the investment, but is not an accurate measure of its profitability.provides a measure of the speed of return of the investment, but is not an accurate measure of its profitability.

Sensitivity and Breakeven AnalysisSensitivity and Breakeven Analysis.. We use these techniques to determine how sensitive a decision is to estimates of various parameters. Breakeven We use these techniques to determine how sensitive a decision is to estimates of various parameters. Breakeven analysis determines conditions for which alternatives are equivalent. Usually we can visualize the analysis with analysis determines conditions for which alternatives are equivalent. Usually we can visualize the analysis with breakeven charts. Sensitivity analysis is an examination of a range of values for some parameter, to determine breakeven charts. Sensitivity analysis is an examination of a range of values for some parameter, to determine their effect on a particular decision.their effect on a particular decision.

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SELECTION OFSELECTION OF

A MINIMUM ATTRACTIVE RATE OF RETURNA MINIMUM ATTRACTIVE RATE OF RETURN

MARRMARRmin.min.

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Sources of CapitalSources of Capital

Money generated from the operation Money generated from the operation of the firm (retained profits and of the firm (retained profits and depreciation)depreciation)

External sources of funds:External sources of funds:– Short term: banks (generally unsecured)Short term: banks (generally unsecured)– Long term: banks, insurance companies, Long term: banks, insurance companies,

pension funds, mortgage bonds pension funds, mortgage bonds (secured)(secured)

– Permanent: sale of company stockPermanent: sale of company stock

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Total capital invested (millions) 100.00$ Tax rate 40%

Capital Structure

%ROR

Interest paid

TaxesAT

Interest cost

Bank loan 20% 20.00$ 9% 1.80$ 0.72$ 1.08$ Mortgage bonds 20% 20.00$ 7% 1.40$ 0.56$ 0.84$

Common stock and retained earnings

60% 60.00$ 11% 6.60$ -$ 6.60$

9.80$ 1.28$ 8.52$

Cost of capital 8.52%

Example:

Cost of FundsCost of Funds

Cost of capital is the after-tax weighted Cost of capital is the after-tax weighted ROR of borrowed funds from all sources.ROR of borrowed funds from all sources.

2020

Capital available 1,200.00$

Project Number Cost

Estimated ROR

Select Projects

Capital to be Invested

ROR of Rejected Projects

2 50.00$ 45% 1 50.00$ 4 100.00$ 40% 1 100.00$ 3 50.00$ 38% 1 50.00$ 5 200.00$ 35% 1 200.00$ 1 150.00$ 30% 1 150.00$ 6 100.00$ 28% 1 100.00$ 8 250.00$ 25% 1 250.00$ 9 300.00$ 20% 1 300.00$ 7 200.00$ 18% 0 -$ 18%11 400.00$ 15% 0 -$ 15%10 300.00$ 10% 0 -$ 10%12 1,200.00$ 8% 0 -$ 8%

1,200.00$ Opportunity cost 18%

Example:

Investment OpportunitiesInvestment Opportunities

There are many investment There are many investment

opportunities in an active firm opportunities in an active firm

and often limited capital.and often limited capital.

Opportunity cost is the ROR of Opportunity cost is the ROR of

the best opportunity foregone.the best opportunity foregone.

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Selecting a MARRSelecting a MARR

MARR is generally the maximum of MARR is generally the maximum of

the:the:

– Cost of borrowed moneyCost of borrowed money

– Cost of capitalCost of capital

– Opportunity costOpportunity cost

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Year Alt A Alt B0 -80.00 -80.001 10.00 13.862 10.00 13.863 10.00 13.864 10.00 13.865 10.00 13.866 10.00 13.867 10.00 13.868 10.00 13.869 10.00 13.86

10 10.00 13.8611 20.00 10.0012 20.00 10.0013 20.00 10.0014 20.00 10.0015 20.00 10.0016 20.00 10.0017 20.00 10.0018 20.00 10.0019 20.00 10.0020 20.00 10.00

MARR 10% 10%NPW $28.83 $28.85

MARR (risk) 15% 15%

NPW ($5.00) $1.97

ROR 14.05% 15.48%

Additionally, MARR might be adjusted Additionally, MARR might be adjusted to reflect imminent inflation.to reflect imminent inflation.

Example:Example:

Adjusting MARR to Account for Adjusting MARR to Account for Risk and UncertaintyRisk and Uncertainty

Increase MARR to avoid Increase MARR to avoid marginal projects.marginal projects.

Assess all the projects using Assess all the projects using techniques other than techniques other than economic analysis.economic analysis.

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Representative Values of MARR Representative Values of MARR

Used in IndustryUsed in IndustryGroupGroup Small projectSmall project Large projectLarge project

StrugglingStrugglingLimited fundsLimited funds

One year paybackOne year payback= 60 % ROR= 60 % ROR

One year paybackOne year payback= 60 % ROR= 60 % ROR

StableStableAdequate fundingAdequate funding

Payback with a variable Payback with a variable lifelife

12 to 15%12 to 15%After-taxAfter-tax

In addition to these two factors, many other factors In addition to these two factors, many other factors also affect interest rates: public vs. private also affect interest rates: public vs. private organization, debt/equity position, risk posture, etc. organization, debt/equity position, risk posture, etc.