Engineering Economic Analysis Chapter 9 Other Analysis Techniques Donald G. Newnan San Jose State University Ted G. Eschenbach University of Alaska Anchorage Jerome P. Lavelle North Carolina State University Neal A. Lewis University of New Haven Copyright Oxford University Press 2017

Chapter Outline Future Worth Analysis Benefit-Cost Ratio Analysis Payback Period Sensitivity & Breakeven Analysis Graphing with Spreadsheets for Sensitivity & Breakeven Analysis Doing What-If Analysis with Spreadsheets Copyright Oxford University Press 2017

Learning Objectives Apply future worth, benefit-cost ratio, payback period, & sensitivity analysis methods Link future worth analysis to present worth & annual worth methods Develop the benefit-cost ratio Understand the concept of “payback period” Conduct sensitivity & breakeven analyses Use spreadsheets for sensitivity & breakeven analyses Copyright Oxford University Press 2017

Vignette: Clean & Green Buildings in U.S. account for 75% of electricity consumption 45% of energy use 40% of CO2 emissions 40% of raw materials use 13% of potable water consumption Green Building Council (2016) Designers & engineers have been developing environment-friendly construction materials & building techniques Copyright Oxford University Press 2017

Vignette: Clean & Green Advantages of “Green” buildings Improve workers’ productivity Reduce health & safety costs Improve indoor environmental quality Reduce energy & maintenance costs Myth Cost more to build Harder to recoup investment in a timely manner Increasing by 10% annually Copyright Oxford University Press 2017

Future Worth Analysis Alternatives compared using future worth at given time Emphasizes final outcome Firm’s final wealth Retirement savings Easily converted to/from PW, EAW, & EAC Copyright Oxford University Press 2017

Example 9-1 Future Worth Calculation A 20-year-old quits $35/week smoking habit. What in savings account paying 5% compounded semiannually at age 65? Work-week habit costs $7/day. What if $2/day alternative substituted 4 days/week? (Happy Money says more happiness from weekly treat than daily habit) Stop: Semiannual saving = $35 𝗑 26 = $910 Habit to treat: $5 saved on 4 days = $20/wk = $520 every 6 mo. Copyright Oxford University Press 2017

Example 9-2 Future Worth Analysis New Plant Year Remodel $85,000 $850,000 200,000 1 250,000 1,200,000 2 3     Copyright Oxford University Press 2017

Benefit-Cost Ratio Analysis At given MARR, an acceptable alternative satisfies NPW = PW(Benefits) – PW(Costs) ≥ 0 EUAW = EUAB – EUAC ≥ 0 As a ratio: Copyright Oxford University Press 2017

Benefit/Cost Ratio Example for Road Benefits = + outcomes for public Faster, safer travel PW = $3.8M Disbenefits = − outcomes for public Traffic delays during construction PW = −$0.9M Costs = paid by government Building & maintaining roads PW = −$2M B/C ratio = (3.8M − 0.9M)/2M = 1.45 Copyright Oxford University Press 2017

Benefit-Cost Ratio Analysis Situation Criterion Neither input nor output fixed One alternative: B/C ≥ 1 Two or more alternatives: Incremental analysis of B/C ratios Fixed input; constant C Maximize B/C; highest B Fixed output; constant B Maximize B/C; lowest C Copyright Oxford University Press 2017

Example 9-3 Benefit-Cost Ratio Analysis Copyright Oxford University Press 2017

Example 9-4 Benefit-Cost Ratio Analysis D E F Initial Cost $4000 $2000 $6000 $1000 $9000 $10,000 PW of Benefit 7330 4700 8730 1340 9000 9500 B/C 1.83 2.35 1.46 1.34 1.00 0.95 Rearrange the alternatives in order of increasing investment D B A C E Initial Cost $1000 $2000 $4000 $6000 $9000 PW of Benefit 1340 4700 7330 8730 9000 B/C 1.34 2.35 1.83 1.46 1.00 Calculate ΔB/ΔC of the incremental investments, if ΔB/ΔC≥1, choose the higher-cost alternative  do A B-D A-B C-A E-A Initial Cost $2000 – 1000 $4000 – 2000 $6000 – 4000 $9000 – 4000 PW Benefit 4700 – 1340 7330 – 4700 8730 – 7330 9000 – 7330 ΔB/ ΔC 3.36 1.32 0.70 0.33 Copyright Oxford University Press 2017

New Public Swimming Pool Pool costs $1.2M to build & $200K/year to operate. Benefit is $450K/year. Using equivalent annual values at i =6% & n =25 years, what is B/C ratio? 1.53 1.81 2.25 4.79 I don’t know Copyright Oxford University Press 2017

New Public Swimming Pool Pool costs $1.2M to build & $200K/year to operate. Benefit is $450K/year. Using equivalent annual values at i =6% & n =25 years, what is B/C ratio? 1.53 1.81 2.25 4.79 I don’t know EAC costs = 1.2M(A/P,6%,25) + 200K = 93.9K + 200K = $293.9K EAW benefits = 450K B/C ratio = 450K / 293.9K = 1.53 Copyright Oxford University Press 2017

Graphical Representation of Benefit-Cost Ratio Analysis Incremental B/C = 1 is 45⁰ line Do A since B/CD > 1 B/CB – D > 1 B/CA – B > 1 B/CC – A & B/CE – A < 1 Not B largest B/C Not E largest project with B/C > 1 Copyright Oxford University Press 2017

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 Copyright Oxford University Press 2017

Example 9-5 Government B/C Ratio Analysis Right turn lanes Left turn lanes Incremental Initial cost $8.9M $3M Annual maintenance 150K 75K Uniform annual benefit 1.6M $2.2M Construction disbenefit 900K 2.1M Useful life, in years 15 i=10%     Copyright Oxford University Press 2017

Example 9-6 Present Worth Index (Cost ≡ Initial Minimal Total Incremental Initial cost $8.9M $3M Annual maintenance 150K 75K Uniform annual benefit 1.6M $2.2M Disbenefit 900K 2.1M Useful life, in years 15 i=10%     Ratios differ from Exp. 9-5 because maintenance cost in numerator. Copyright Oxford University Press 2017

Payback Period Time required for project’s profit & benefits to equal project’s cost Approximate economic analysis method Ignores time value of money Ignores all cash flows after payback May not be consistent with equivalent worth & rate of return methods Copyright Oxford University Press 2017

When Can Payback be Used If payback time measured in months & benefits continue for years Most common in start-up enterprises which are VERY short of capital Most projects with good payback periods look good on other measures Not always, so payback is unreliable Copyright Oxford University Press 2017

Example 9-7 Payback Period Year 1 2 3 4 5 A −$1000 +200 +1200 B −$2783 Payback Period =2.33 years Payback Period =2.5 years Alternative A Alternative B Copyright Oxford University Press 2017

Example 9-8 Payback Period Product: n = 5, A = −4000 Machine A: P = −$10,000 S = $0 Machine B: P = −$15,000 S = $9000 Payback A = $10,000/($4000/yr) = 2.5 years Payback B = $15,000/($4000/yr) = 3.75 years Minimizing payback Machine A Copyright Oxford University Press 2017

Example 9-8 TVM solution Incremental IRR = 12.5%  B better at rates below 12.5% Above i = 12.5% A better At 15%, incremental PW = −$525  A better Copyright Oxford University Press 2017

Payback: A new computer systems costs $20,000 Savings each year: Year Savings 1 $8,000 2 $6,000 3 $4,000 4 $4,000 5 $3,000 Payback period is: 2.6 years 3.0 years 3.5 years 3.6 years 4.0 years Copyright Oxford University Press 2017

Payback: A new computer systems costs $20,000 Savings each year: Year Savings 1 $8,000 2 $6,000 3 $4,000 4 $4,000 5 $3,000 Payback period is: 2.6 years 3.0 years 3.5 years 3.6 years 4.0 years After 3 years, savings total $18,000. $2000 is needed to payback, out of $4000 received in year 4. Payback = 3 + 2000/4000 = 3.5 years. Copyright Oxford University Press 2017

Discounted Payback Period Adds time value of money to payback Computes interest on cumulative investment or project balance Still ignores cash flows after payback Copyright Oxford University Press 2017

Example 9-9 Discounted Payback Period Alternatives Cost Uniform Annual Benefit A $10,000 $3000 B $12,000 $3500 i=10% A preferred because shorter discounted payback period Copyright Oxford University Press 2017

Sensitivity & Breakeven Analysis Sensitivity Analysis: Projected expenditures & returns  which decision To what extent do uncertainties/variations in data affect decision? Breakeven Analysis Form of sensitivity analysis changing 1 variable When are 2 alternatives economically equivalent? Common example is project life since often one of most uncertain values Copyright Oxford University Press 2017

Example 9-10 Breakeven Analysis Construction Cost Full-capacity $140,000 Two-stage $100,000 now + $120,000 n years from now   Breakeven n = 14.27 years Copyright Oxford University Press 2017

Example 9-11 Breakeven Analysis Right turn lanes Left turn lanes Incremental Initial cost $8.9M $3M Uniform annual benefit 1.6M $2.2M Annual maintenance $150K 75K Disbenefit $900K 2.1M Useful life, in years 15 i=10% Copyright Oxford University Press 2017

Example 9-12 Automatic graph from spreadsheet Construction Cost Full-capacity $140,000 Two-stage $100,000 now + $120,000 n years from now Automatic graph from spreadsheet Copyright Oxford University Press 2017

Example 9-13 What-if Analysis Can Change Multiple Variables Initial Estimate Adjustment First cost $70,000 +10% Units / year 1200 −20% Net unit revenue $25 −15% Life, in years 8 −3 Interest rate 12% None Initial B/C = 2.13 but only 0.96 with adjustments Copyright Oxford University Press 2017