1. Copyright Oxford University Press 2009 Chapter 9 Other Analysis Techniques

2. Copyright Oxford University Press 2009 Future Worth Analysis Benefit-Cost Ratio or Present Worth Index Analysis Payback Period Sensitivity, Breakeven, and What-if Analysis Chapter Outline

3. Copyright Oxford University Press 2009 Apply future worth analysis, and benefit- cost ratio analysis (present worth Index analysis) Understand the meaning of “payback period” Conduct sensitivity, breakeven, or what-if analysis for Engineering Economy problems Learning Objectives

4. Copyright Oxford University Press 2009 Example 9-1 Future Worth Calculation How much could one accumulate by age 65 if $35 is saved each week from age 20? The saving account pays 5% interest, compounded semiannually?

5. Copyright Oxford University Press 2009 Example 9-2 Future Worth Analysis YearNew PlantRemodel 0$85,000$850,000 1200,000250,000 21,200,000250,000 3200,000250,000 0 1 23 85K 200K 1,200K FW New Plant 23 850K 0 1 250K FW Remodel 250K

6. Copyright Oxford University Press 2009 Benefit-Cost Ratio Analysis At a given minimum attractive rate of return (MARR), an alternative is acceptable, provided These criteria could also be stated as a ratio:

7. Copyright Oxford University Press 2009 Benefit-Cost Ratio Analysis SituationCriterion Neither input nor output fixed: Typical situation Incremental B/C Ratio Analysis: Compute incremental B/C ratio If ΔB/ΔC≥1, choose higher-cost alternative If ΔB/ΔC<1, choose lower-cost alternative Fixed input: amount of money or other input resources are fixed Maximize B/C Fixed output: fixed task, benefit, or other outputs Maximize B/C

8. Copyright Oxford University Press 2009 Example 9-3 Benefit-Cost Ratio Analysis Device A 4 0 1 23 5 P=1000 A = 300 4 0 1 23 5 P=1350 300 Device B 350 450 400 500 Incremental (B-A) 4 0 1 23 5 P = 350 50 150 100 200

9. Copyright Oxford University Press 2009 Example 9-4 Benefit-Cost Ratio Analysis Machine XMachine Y Initial cost$200$700 Uniform annual benefit95120 End-of-useful-life salvage value50150 Useful life, in years612

10. Copyright Oxford University Press 2009 Example 9-5 Benefit-Cost Ratio Analysis ABCDEF Initial Cost$4000$2000$6000$1000$9000$10000 PW of Benefit733047008730134090009500 B/C1.832.351.461.341.000.95 1.Rearrange the alternatives in order of increasing cost 2.Calculate ΔB/ΔC of the incremental investments, if ΔB/ΔC≥1, choose the higher-cost alternative DBACE Initial Cost$1000$2000$4000$6000$9000 PW of Benefit13404700733087309000 B/C1.342.351.831.461.00 B - DA - BC - AE - A Initial Cost$2000-1000$4000-2000$6000-4000$9000-4000 PW of Benefit4700-13407330-47008730-73309000-7330 ΔB/ΔC3.361.320.700.33

11. Copyright Oxford University Press 2009 Graphical Representation of Benefit-Cost Ratio Analysis B/C = 1.0 B/C = 2.0 B/C = 1.5 B/C = 0.5 PW of Benefits PW of Costs

12. Copyright Oxford University Press 2009 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 $0$2,000$4,000$6,000$8,000$10,000 PW of Costs PW of Benefits Graphical Representation of Benefit-Cost Ratio Analysis B/C = 1.0 B/C = 2.0 B/C = 1.5 B/C = 0.5 D B A C E F

13. Copyright Oxford University Press 2009 Variations on Benefit-Cost Ratio Government B/C ratio in Public Sector: Present Worth Index in Private Sector: All B/C ratios use same criterion: B/C ≥ 1 Various B/C ratios may differ in value, but they provide consistent recommendations

14. Copyright Oxford University Press 2009 Example 9-6 Government B/C Ratio Analysis Right turn lanes Left turn lanesIncremental Initial cost$8.9M$3M Uniform annual benefit1.6M$2.2M Annual maintenance$150K75K Disbenefit$900K2.1M Useful life, in years15

15. Copyright Oxford University Press 2009 Example 9-7 Present Worth Index Analysis MinimalTotalIncremental Initial cost$8.9M$3M Uniform annual benefit1.6M$2.2M Annual maintenance$150K75K Disbenefit$900K2.1M Useful life, in years15

16. Copyright Oxford University Press 2009 It is the period of time required for the project’s profit or other benefits to equal the project’s cost It is an approximate economic analysis method The effect of timing is ignored All economic consequences after payback are ignored May not consistent with equivalent worth and rate of return methods Payback Period

17. Copyright Oxford University Press 2009 Payback Period = 2.33 years Example 9-8 Payback Period Year012345 A-$1000+200 +1200 B-$2783+1200 Alternative B Alternative A Payback Period = 2.5 years

18. Copyright Oxford University Press 2009 Example 9-9 Payback Period AlternativesCostUniform Annual BenefitSalvage Value Atlas$2000$450$100 Tom Thumb$3000$600$700 Payback Period = 5 years Tom Thumb Atlas Payback Period = 4.4 years

19. Copyright Oxford University Press 2009 Example 9-10 Payback Period AlternativesCostAnnual BenefitUseful Life Tempo$30,000$12,000, 9000, 6000,…4 Dura$35,000$1000, 4000, 7000,…8 Payback Period = 5 years Dura Tempo Payback Period = 4 years

20. Copyright Oxford University Press 2009 Sensitivity Analysis –Projections of expenditures and returns ultimately affect economic decisions –To what extend do variations in the data affect the decision? Breakeven Analysis –It is a form of sensitivity analysis –In what conditions, two alternatives are viewed as “indifferent”? –One application is “staged construction” Sensitivity and Breakeven Analysis

21. Copyright Oxford University Press 2009 Example 9-11 Breakeven Analysis Construction Cost Full- capacity $140,000 Two-stage $100,000 now + 120,000 n years from now Full capacity Two-stage Breakeven point

22. Copyright Oxford University Press 2009 Example 9-12 Breakeven Analysis ABC Initial Cost$2000X$5000 Uniform Annual Benefit410639700 For Alternative B to be selected, NPW B ≥ NPW C 7329 – X ≥ 3029 X ≤ 4300

23. Copyright Oxford University Press 2009 Example 9-13 Breakeven Analysis Right turn lanesLeft turn lanes Initial cost$8.9M$11.9M Uniform annual benefit1.6M2.2M Annual maintenance0.15M0.225M Disbenefit0.9M2.1M Breakeven for Right turn lanes Breakeven for Left turn lanes Breakeven for Incremental Investment