Chapter 11 – Benefit/Cost Analysis of Public Projects

1. Chapter 11 – Benefit/Cost Analysis of Public Projects

2. Overview • Differences between private sector and public sector • Public projects affect many groups of people • Decision making is a political process, not a business process (MARR) • How to use B/C ratios • B is the PW or AW of benefits, C is the PW or AW of costs • B/C>1 is the requirement • The B/C>1 test is for independent projects • Multiple projects or alternative plans • Do not compare B/C ratios directly. A project with B/C=4 is not necessarily a better project than one with B/C=2. • To compare projects or plans (mutually exclusive), need to use delta-method • Defining the B(benefit)/C(cost) ratio • Is a + cash flow an increase in Benefit or a decrease in Cost? • Is a – cash flow an increase in Cost or a decrease in Benefit? • Does it matter? Not for testing B/C>1 • Criticism • Analysis can be very subjective • B/C ratios do not consider “fairness” or distribution of benefits/costs

3. Private sector vs. Public sector

4. The B/C ratio B is usually the sum of benefits to anyone. C is usually the sum of costs to the government or sponsor of the project. B and C need to be in the same units, such as: year 0 dollars (Present Worth) or dollars/year (Annual Worth) A project should produce more benefits than costs, so that B>C, or dividing by C, B/C>1

5. Why B/C ratios? • The B/C ratio is a simple way to explain the effects of a project to government authorities and the public. • People who support a project usually argue that B/C is greater than 1, and large. • People who oppose a project usually argue that B/C is less than 1. (In addition, there may be distributional reasons for opposing a project. For example, maybe the rich benefit but the poor pay the costs)

6. B/C Ratios, Corruption, and Inefficiency Requiring B/C>1 helps to limit the effects of corruption and inefficiency • Corruption tends to force Costs above Benefits • government project buys hammers for us$1000 from senator’s friend (increased C) • government allocates money to clean up parks, but the money is stolen internally with no benefit (decreased B) • Inefficiency tends to raise costs (increased C) • Log-rolling in legislature tends to focus on every district getting something, rather than on B/C analysis. • Public projects often have too many supervisors, when compared with projects in private businesses • complex procedures (“red tape”) for simple tasks

7. Example #1 • Buying a new ambulance for a public hospital • Benefits: (value of lives saved, value of increased taxes paid by those whose live, increase in public safety) AW of Benefits = $4 million/year • Costs: (ambulance capital recovery, drivers’ salary, medical team salary, overhead) AW of Costs = $3 million/year • B/C = $4 million/$3 million = 1.3333 the benefits justify the costs

8. Example #2 • Building a boat harbor for HKUST • Benefits: (recreation, attract more faculty and students, attract more tourists, increased business for restaurants, boat tours and rental, and hotels) PW = $200 million • Costs: (enclose portion of bay, repair after typhoons, additional labor for supervision and security, additional insurance) PW = $500 million B/C = $200 million/$500 million = 0.4 the benefits do not justify the costs

9. Multiple projects or alternative plans • If any or all the projects can be chosen, the projects are independent. Choose all the projects with B/C > 1 • If only one project can be chosen, the projects are mutually exclusive. You can not compare B/C ratios directly, but you can use a delta method similar to the delta method used for IRR in Chapter 4.

10. Example #3 – Independent Projects

11. Example #4 – Choose 1 Project(mutually exclusive)

12. Delta method Eliminate all projects with B/C<1. Baseline is initially the project (or plan) with B/C>1 and the lowest cost. Repeat steps 1-3 below until done. Step 1: Compute B/C for each of the projects relative to the baseline. B = Project Benefit – Baseline Benefit C = Project Cost – Baseline Cost Step 2: Eliminate all projects where B/C<1 Step 3: If B/C>1 for some projects, replace the baseline by the remaining project with the lowest cost. Go back and repeat step 1 with the new baseline. If no projects are remaining, or if B/C<1 for all remaining projects, you are done. When you are done, the baseline you have is the preferred project.

13. Delta Method (Example #4) We eliminate Z, since B/C<1 for Z. The baseline should have B/C>1 and lowest cost. Therefore, the baseline will initially be W.

14. Delta Method Step 1 (Example #4) We calculated the B/C relative to W.

15. Delta Method Step 2(Example #4) We need to eliminate any project with B/C <1. In this case, we eliminate X. The additional cost of 10 million does not justify additional benefits of only 5 million.

16. Delta Method Step 3(Example #4) B/C >1 for Y Therefore we replace the baseline with Y. If there were more projects, we would repeat steps 1-3 with the baseline=Y Since there are no more projects, we are done. The best choice is Y. If we move from W to Y, we gain 35 million in added benefits and pay only 30 million in added costs. This is justified. B/C >1

17. Choice of Y not obvious from simple B/C ratio The simple B/C ratio does NOT tell you the best project. You must use a more complex method, such as the delta method, to compare projects.

18. Alternative definitions of B/C ratio B- Benefits I – Initial Investment O&M – Operating and Maintenance Costs ---------------------------------- Conventional B/C Ratio with PW: B/C=PW(B)/(I+PW(O&M)) Modified B/C Ratio with PW: B/C=(PW(B)-PW(O&M))/I

19. What’s the difference? Conventional B/C Ratio with PW: B/C=PW(B)/(I+PW(O&M)) Modified B/C Ratio with PW: B/C=(PW(B)-PW(O&M))/I Yearly O&M costs are treated as part of the C term Yearly O&M costs are treated as a reduction of the benefits Next: Does it matter?

20. Does it matter? The conventional and modified formulas will produce different numbers. However, when conventional B/C is greater than 1, so is Modified B/C. When modified B/C is greater than 1, so is conventional B/C. The numbers change. The funding decisions do not.

21. Classifying benefits and costsDoes it matter which side an item is on? Suppose X is a negative cash flow We only want projects where B>C+X We could compare B/(C+X) to 1.0 If B/(C+X)>1.0, then B>C+X

22. Classifying benefits and costsDoes it matter which side an item is on? Suppose X is a negative cash flow We only want projects where B>C+X We could compare B/(C+X) to 1.0 If B/(C+X)>1.0, then B>C+X But this is equivalent to saying we want B-X>C We could compare (B-X)/C to 1.0 If (B-X)/C>1.0, then B-X>C B/(C+X) and (B-X)/C are different numbers, but we can compare either of these numbers to 1.0 to make our decision.

23. Harmful effects of public projects Are these costs or negative benefits? • Building a dam will ruin a recreational white-water river and flood useful land • Making a road wider will increase pollution and noise in the neighborhood • A new park may attract beggars and vagrants As long as they are included in the analysis, it does not matter if these are considered costs (+C) or deductions from benefits (-B). The standard is that these are deductions from benefits, or disbenefits. Costs are usually only costs to the government or builder of the project.

24. Criticisms of B/C Method • Answers of studies seem to be strongly linked to the study sponsor • Easy to manipulate • Decision makers and public, may care about the results but not about the analyses or the process. • B/C ratios do not say who pays and who benefits. makes rational debate difficult

25. The Political Process Because a project may have supporters and opponents, various tricks can be used to affect the B/C analysis. These include • Unrealistic assumptions (100 year life, etc) • Different methods of valuing controversial items that are hard to measure • Omitting harmful effects • Manipulating MARR to stress short-term costs or long-term benefits

26. Which MARR? Some alternatives MARRs: • The interest rate paid by the government when they borrow the money to finance the project (ranges from 3% for the US federal government to 8% for bond issues by small towns) • The opportunity cost of capital to the government agency (varies) • The opportunity cost of capital to the taxpayer (estimated at 7%/year = 10% investment-3% taxes for the US by USA Office of Management and Budget) • The risk-free market rate (hovers around 3%)

27. Distribution of benefits and costs Destroying a squatter village to construct new luxury high rise and transport station == Benefits accrue to the rich with costs to the poor ------------------------------------------------------------------ Power plants; waste disposal == Benefits accrue to a general population with disbenefit to a smaller community near the facility who must endure pollution -------------------------------------------------------------------- Raising taxes to support welfare programs for unmarried mothers, drug addicts, or poor immigrants == Benefits accrue to unpopular segments of the poor, with the costs paid by productive members of society.

28. Summary • B/C analysis provides, at best, a way to avoid bad projects. • To compare projects, you can not use B/C ratios directly. You must use a delta method. • B/C analysis of public projects can be controversial. Some of the numbers involve substantial guesswork. • B/C analysis does not measure the distribution of benefits and costs, which can be an important political factor.