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Chapter 9 - Benefit-Cost Ratio and Other Analysis Methods Click here for Streaming Audio To Accompany Presentation (optional) EGR 403 Capital Allocation Theory Dr. Phillip R. Rosenkrantz Industrial & Manufacturing Engineering Department Cal Poly Pomona EGR 403 - The Big Picture • Framework: Accounting & Breakeven Analysis • “Time-value of money” concepts - Ch. 3, 4 • Analysis methods – – – – Ch. 5 - Present Worth Ch. 6 - Annual Worth Ch. 7,7A,8 - Rate of Return (incremental analysis) Ch. 9 - Benefit Cost Ratio & other methods • Refining the analysis – Ch. 10, 11 - Depreciation & Taxes – Ch. 12 - Replacement Analysis EGR 403 - Cal Poly Pomona - SA12 2 Chapter 9 - Other Analysis Methods • • • • Future worth analysis Benefit-cost ratio analysis Payback period Sensitivity and breakeven analysis EGR 403 - Cal Poly Pomona - SA12 3 Future Worth Analysis • Answers the question, what will the future situation be, if we take some particular course of action now? – Example 9.1, FW = P(F/P,i , n), FW = A(F/A, i, n) Vices Smoking Cigarettes Cigars Spirits Beer Liquor Wine Semi-annual consumption Semi-annual in units Cost/ unit sub total 26 26 $ 15.00 $ $ 1.00 $ 26 $ 6.00 6 $ 15.00 13 $ 8.00 Semi-annual total Present age Retirement age Years to retirement 20 65 45 $ $ $ $ FW if saved FW if invested in market 390.00 26.00 $128,370.16 $1,225,019.32 $8,558.01 $81,667.95 156.00 90.00 104.00 766.00 $51,348.06 $490,007.73 $29,623.88 $282,696.77 $34,232.04 $326,671.82 $252,132.16 $2,406,063.59 Annual i 5.00% Compounded semi-annually EGR 403 - Cal Poly Pomona - SA12 12.00% 4 Future Worth Analysis When constructing a building, the issue is: • not the dollars out of pocket, • but the invested cost at start- up. • Example 9-2: The remodel project costs less out of pocket, but has a higher “up front” cost. That makes it less desirable. Interest rate Purchase site Design & site preparation Construction Equipment installation Out of pocket costs FW at start-up 8.00% Year 0 1 2 3 Alternatives Remodel Construct available new plant factory $ 85 $ 850 $ 200 $ 250 $ 1,200 $ 250 $ 200 $ 250 Select: $ 1,685 $ 1,600 Remodel available factory $ 1,836 $ 1,882 Construct new plant EGR 403 - Cal Poly Pomona - SA12 5 Benefit-Cost Ratio Analysis • If the PW of benefits PW of costs 0. The alternative is considered acceptable. • Restated: Benefit-cost ratio B/C =. PW of benefit/PW of cost 1. • Fixed input, maximize B/C. Example 9-3 Year 0 1 2 3 4 5 PW of: Cost Benefit $ $ $ $ $ $ MARR = 7.00% Alternative A B (1,000.00) $ (1,000.00) 300.00 $ 400.00 300.00 $ 350.00 300.00 $ 300.00 300.00 $ 250.00 300.00 $ 200.00 ($1,000.00) ($1,000.00) $ 1,230.06 $ 1,257.75 B/C = 1.23 1.26 Select: B Other alternatives for comparison: PW $ 230.06 $ 257.75 EUAC $56.11 $62.86 FW $322.67 $361.50 IRR 15.24% 17.47% EGR 403 - Cal Poly Pomona - SA12 6 Benefit-Cost Ratio Analysis • If the EUAB - EUAC 0. The alternative is considered acceptable. • Restated: Benefit-cost ratio: B/C = EUAB/EUAC 1 Or, using PW: B/C = PWB/PWC • Neither input or output fixed - use incremental B/C. • Note: Salvage Value is considered a “negative cost”, not a benefit • B/C Ratio Analysis is popular in government • Very easy to use with databases and spreadsheets EGR 403 - Cal Poly Pomona - SA12 7 Benefit Cost Ratio Analysis Example Reject increment if incremental B/C Ratio is < 1 Cost PWB B/C Increment incr Cost incr PWB incr B/C Keep D 1000 1340 1.34 B 2000 4700 2.35 A 4000 7330 1.83 C 6000 8730 1.46 E 9000 9000 1 B-D 1000 3360 3.36 B A-B 2000 2630 1.36 A C-A 2000 1400 0.70 A E-A 5000 1670 0.33 A EGR 403 - Cal Poly Pomona - SA12 8 Benefit Cost Ratio Analysis Example First Increment is B-D. Incremental B/C > 1, so choose higher cost alternative Cost PWB B/C Increment incr Cost incr PWB incr B/C Keep D 1000 1340 1.34 B 2000 4700 2.35 A 4000 7330 1.83 C 6000 8730 1.46 E 9000 9000 1 B-D 1000 3360 3.36 B A-B 2000 2630 1.36 A C-A 2000 1400 0.70 A E-A 5000 1670 0.33 A EGR 403 - Cal Poly Pomona - SA12 9 Benefit Cost Ratio Analysis Example Reject increment if incremental B/C Ratio is < 1 Cost PWB B/C Increment incr Cost incr PWB incr B/C Keep D 1000 1340 1.34 B 2000 4700 2.35 A 4000 7330 1.83 C 6000 8730 1.46 E 9000 9000 1 B-D 1000 3360 3.36 B A-B 2000 2630 1.36 A C-A 2000 1400 0.70 A E-A 5000 1670 0.33 A EGR 403 - Cal Poly Pomona - SA12 10 Payback Period: Important Points • • • • Approximate economic analysis method. Prior to payback the effect of timing is ignored. After payback all economic consequences are ignored. Will not necessarily produce a recommended alternative consistent with equivalent worth and rate of return methods. EGR 403 - Cal Poly Pomona - SA12 11 Payback Period • The period of time required for the profit or other benefits of an investment to equal the cost of the investment. • How many years are required to get my money back? 9-6 Alternative Year 0 1 2 3 4 5 Payback: Select: A $ (1,000.00) $ 200.00 $ 200.00 $ 1,200.00 $ 1,200.00 $ 1,200.00 2.5 EGR 403 - Cal Poly Pomona - SA12 B $ (2,783.00) $ 1,200.00 $ 1,200.00 $ 1,200.00 $ 1,200.00 $ 1,200.00 2.3 B 12 What is wrong here? Payback and IRR analysis do not agree. Payback Analysis Example 9-8 Alternative With alternative A we get our money back in 4 years but never make a return on the investment. With alternative B we get our money back in 5 years and make a return on the investment of 19%. How should we make a decision? 1. Liquidity vs. profitability. 2. Life of project. Year A B 0 ($30,000.00) $ (35,000.00) 1 $12,000.00 $ 1,000.00 2 $9,000.00 $ 4,000.00 3 $6,000.00 $ 7,000.00 4 $3,000.00 $ 10,000.00 5 $0.00 $ 13,000.00 6 $0.00 $ 16,000.00 7 $0.00 $ 19,000.00 8 $0.00 $ 22,000.00 Salvage $0.00 $ Payback: 4.00 5.00 Select: A IRR = 0% 19% Select: B EGR 403 - Cal Poly Pomona - SA12 13 Sensitivity and Break-even Analysis • Economic data represent projections of expenditures and returns. • These projections ultimately affect our decisions. • To more fully consider our choice of a decision, we should play a “what if” game to determine the amount of change in a data point that might change the decision. EGR 403 - Cal Poly Pomona - SA12 14 Consider Problem 6-21 • Diesel engine is preferred based on values assumed. • How much would changes in assumptions have to be in order to change the preferred alternative? Prob 6-21 Diesel Gas Vehicle Cost 13000 12000 Fuel 685.71 910.71 Repairs 300 200 Resale 2000 3000 Insurance 500 500 EUAC $4,780.22 $5,157.70 n 4 3 EGR 403 - Cal Poly Pomona - SA12 15 How much would price of diesel fuel need to go up before Gas would be the preferred alternative? Diesel Cost $0.48 $0.50 $0.55 $0.60 $0.65 $0.70 $0.75 EUAC $4,780.22 $4,808.79 $4,880.22 $4,951.65 $5,023.08 $5,094.51 $5,165.93 EGR 403 - Cal Poly Pomona - SA12 Price of Diesel would have to go up to $.75 to change decision. 16 What is the impact of the variability of resale value on the analysis? By varying the resale value, we find that at about $4200 resale value for the gasoline powered vehicle the EUAC is almost equal Resale (Gas) $2,000 $3,000 $4,000 $5,000 $4,200 EUAC 5,471.81 5,157.70 4,843.59 4,529.48 4,780.77 EGR 403 - Cal Poly Pomona - SA12 17