1 Benefit Cost Analysis Typically used for public projects The goal is to determine if benefits exceed costs: Benefit / Cost Ratio > 1 The goal is NOT to maximize B/C Ratio. Interest rates used are typically lower than those used by businesses. Typically 4% - 8% (6.5% is typical) OMB requires 10% (except water proj.)

2 Benefit Cost Analysis The challenge is to quantify the benefits and costs. The equation… B/C = (Benefits – Disbenefits) to the public (Costs) to sponsoring agency You can use NPW, EAW, even NFW – whichever is easier in a particular problem.

3 Benefit Cost Analysis Steps: 1. Define the planning horizon. 2. Specify the Discount Rate (MARR) to be used. 3. Develop the cost and benefit-disbenefit profiles in monetary terms. 4. Compare the benefits to costs using a specified measure of worth, such as annual equivalent or present worth. 5. If the B/C ratio is: > 1project is justified = 1barely justified – political < 1not justified 6. Repeat steps 3 – 5 for alternative viewpoints

4 ExampleExample A city library is to be expanded to include meeting rooms, more electronic volumes, computer facilities, and electronic check-in and check-out. The cost of the expansion will be $700,000 and the new equipment will cost another $175,000. Maintenance and renewal of the new addition and equipment will run approximately $100,000/year. The library is projected to be in operation for 20 years, with a residual value of 40% of first cost for the physical facilities. There is no salvage value for the equipment. Discount is 8%. An estimated 150,000 people will visit the library each year. How much additional benefit per person, per year, must the library visitors perceive in order to justify the expansion?

5 Perspective Matters Suppose the library charged an annual fee Suppose the entire county sponsored The equation… B/C = (Benefits – Disbenefits) to public (Initial Investment) by sponsor What is the viewpoint of a user? What is the viewpoint of a non-user?

6 Modified B/C Analysis The challenge is to quantify the benefits and costs. The equation… B/C = (Benefits – Disbenefits – M & O) public (Initial Investment) by sponsor You can use NPW, EAW, even NFW – whichever is easier in a particular problem.

7 Incremental B/C Analysis MUST be used when there are multiple alternatives to choose from! The equation is still… B/C = (Benefits – Disbenefits) to the public (Costs) to sponsoring agency You can use Incr. NPW or Incr. EAW – whichever is easier in a particular problem.

8 Incremental B/C Analysis Steps: 1. Define the set of feasible, mutually exclusive, public sector alternatives to be compared. 2. Define the planning horizon. 3. Develop the cost and benefit-disbenefit profiles in monetary terms for each alternative. 4. Specify the MARR to be used. 5. Order the alternatives from smallest to largest Cost 6. Compare the alternatives using a specified measure of worth, such as annual equivalent, capitalized cost, or present worth (with matching lifetimes). If the B/C ratio is: > 1higher cost project is justified ≤ 1lower cost project is still justified

Incremental Benefit Cost Analysis Example ABCDEFG Benefits Disbenefits Costs B – D C Not Feasible Cost Order: G E C A F B E – G: G – DN: C – E: A – E: (136 – 89) – (10 – 14) = 51 = 2.55 (70 – 50) 20 Upgrade to E (136 – 136) – (10 – 10) = 0 = 0 (90 – 70) 20 Keep Proj. E (174 – 136) – (4 – 10) = 44 = 1.47 (100 – 70) 30 Upgrade to A (From feasibility, (B – D) / C = 1.5Upgrade to G

Incremental Benefit Cost Analysis Example ABCDEFG Benefits Disbenefits Costs B – D C Not Feasible Cost Order: G E C A F B F – A: B – A: (178 – 174) – (2 – 4) = 6 = 0.6 (110 – 100) 10 Keep Proj. A (180 – 174) – (60 – 4) = – 50 = – 2.5 (120 – 100) 20 Best is Proj A

Class Problem Consider the five mutually exclusive alternatives. They have 20-year useful lives and no salvage value. If the minimum attractive rate of return is 6%, which alternative should be selected? 11 ABCDEF Cost$4000$2000$6000$1000$9000$10,000 PW Benefits $7330$4700$8730$1340$9000$9500 B/C Ratio

12 Graphical Solution Costs

13 Where are more examples in the class book? Chapter 9 section 7 Eschenbach, Ted G. Engineering Economy Applying Theory to Practice (Third Edition) Where can I find the class problem? Newnan, Donald G.; Lavelle, Jerome P.; Eschenbach, Ted G. (2009). Engineering Economic Analysis (10th Edition).. Oxford University Press.Online version available at: OVEL_DISPLAY_bookid=2394&VerticalID=0 Page References and Other interesting topics

Bonus Problem: B/C Build-Up Example  Snack Fridge Viability Data: 110 IE & EngM students 48% will use snack fridge instead of going home Users average (2) drinks & (1) snack each week Mark-up is 10%, drink price is $.50, snacks $.75 School year averages 32 weeks Fridge costs $495, lasts 8 yrs, 8% cpd annually If they save time & $$ on snacks & drinks, they can buy books, study more, and expect one of them to win a $5 500 national scholarship every 4 years. But the vending company will quit donating $300 per year to their Tech Society Perform a B/C analysis – IE student perspective