Chapter 11 – Benefit/Cost Analysis of Public Projects

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

Private sector vs. Public sector PrivatePublic PurposeMake money Provide goods&services at a profit Protect and serve Protect health, lives, property. Provide non-profit services and jobs. FinancePrivate investors (voluntary) Taxation (not voluntary) OwnershipPrivate property Partnerships & Corporations The people The government Conflict of interestsNot usuallyCommon Project LifeUsually 5 – 20 yearsLong yrs Nature of BenefitsProfit Measured in $ Many benefits Some benefits hard to measure in $ How is decision made?Business process that compares profit and costs Political process that compares benefits, costs and distribution

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

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)

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 senators 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

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 = the benefits justify the costs

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

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.

Example #3 – Independent Projects ProjectPW of Benefit (millions) PW of Cost (millions) B/C ratioFund? W Yes B/C>1 X Yes B/C>1 Y Yes B/C>1 Z No B/C<1

Example #4 – Choose 1 Project (mutually exclusive) ProjectPW of Benefit (millions) PW of Cost (millions) B/C ratioFund? W ? X ? Y ? Z No B/C<1

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.

Delta Method (Example #4) ProjectPW of Benefit (millions) PW of Cost (millions) B/C ratioFund? W ? X ? Y ? Z No B/C<1 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.

Delta Method Step 1 (Example #4) ProjectPW of Benefit (millions) PW of Cost (millions) B C B/ C W (baseline) X Y We calculated the B/ C relative to W.

Delta Method Step 2 (Example #4) ProjectPW of Benefit (millions) PW of Cost (millions) B C B/ C W (baseline) X =520-10=100.5 Y = = 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.

Delta Method Step 3 (Example #4) ProjectPW of Benefit (millions) PW of Cost (millions) B C B/ C W (baseline) Y 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

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. ProjectPW of Benefit (millions) PW of Cost (millions) B/C ratioFund? W X Y Yes, from Delta Analysis Z No B/C<1

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

Whats 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?

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.

Classifying benefits and costs Does 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

Classifying benefits and costs Does 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.

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.

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

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

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%)

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.

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.