Economic Analysis in the Public Sector Benefit/Cost Analysis

1. Economic Analysis in the Public SectorBenefit/Cost Analysis

2. Introduction • Public investment decisions involve a great deal of expenditure, and their benefits are expected to occur over an extended period of time • Examples of public sector investment projects are • public transportation systems, • environmental regulations • flood control programs • Decision criteria is whether the project is in the best public interest

3. Economic Analyses Tools • benefit/cost analysis • to maximize benefits for a given set of costs • to maximize net benefits when both benefits and costs vary • risk-benefit analysis • to incorporate the risk in the benefit/cost • cost-effectiveness analysis • to minimize costs to achieve a certain level of benefits

4. Benefit/Cost Analysis Procedure 1. Identify all users’ benefits expected to arise from the project. 2. Quantify, as much as possible, these benefits in $ 3. Identify and quantify sponsor’s costs 4. Determine study period and interest rate 5. Compute the benefit/cost ratio

5. Example 1 • State of Michigan is considering a ban on the use of salt on highways. An alternative de-icer is sold for $600/ton. Salt costs $14/ton. • 2000 was a typical winter. Michigan • spent $9.2 million on salt (=> used 657,143 tons) • estimated • $427 million of highway corrosion damage, • $525 million of rust damage to vehicles, • $98.5 million of corrosion damage to utility lines, • $6.5 million of water supply damage • a total of $1057 million damage due to salt

6. Example 1 (cont’d) • Complete ban from salt in favor of the chemical de-icer yields • Direct User benefits /year = $1057 million • Direct Sponsor costs/year = ($600-$14) 657,143 = 385 million • Yearly Benefit/Cost Ratio • User benefits / Sponsor costs = 1057/385 = 2.75 > 1 • Indirect Benefits/Costs: • Higher state income tax • Unknown environmental changes • Unknown effects of the chemical de-icer

7. Selecting an Interest Rate • when projects span multiple years, you need an interest rate to factor in the time value of money • in the public sector, this rate is called social discount rate (or discount rate) For projects without private counterparts, • social discount rate should reflect only the public organization's borrowing rate For projects with private counterparts, • social discount rate should represent the rate that could have been earned had funds not been removed from the private sector

8. NPW Benefit/Cost Ratio • Given bn = benefit at time n, n = 1, ..., N cn = expense at time n, n = 0, ..., N i = discount rate K = initial investment period, bn=0 for n=1, .., K • Benefits versus Costs • NPW of benefits = B = Nn=0 bn (1+i) -n • NPW of costs = C = Nn=K+1 cn (1+i)-n • Investment versus Recurring Costs • Investment = I = Kn=0 cn(1+i) -n • Recurring Costs = C’ = Nn=K+1 cn(1+i) -n , C = I + C’

9. Ratios • Benefit/Cost Ratio = B/C = B / (I+C’) • Accept when this ratio is greater than 1 • Modified (Net) Benefit/Cost Ratio = (B - C’)/I • Accept when this ratio is greater than 1 • Notes: • B/C > 1 if and only if (B-C’)/I > 1 so the decision rule does not change. The value of the ratio itself might change. • B/(I+C’) > 1 if and only if NPW > 0 • You can also perform the same analysis with NAW

10. Example 2: Power Plant Design • Suppose the building of a 5,000-kwh power plant is being considered. The plant would only be used at 50% of capacity. The rest of the capacity would be lost. This would require a $5 million investment. O/M costs are estimated at $75,000 per year. Electricity is worth $0.05/kwh. Economic life is 35 years. Discount rate is 8%. • NAW of Benefits = (24hrs/day)(365 days/yr)(5,000 kw/hr)($0.05/kwh)(0.5) = $1,095,000/yr • NAW of Costs = $5,000,000(A/P, 8%,35) + $75,000 = $504,016 • B/C = 1,095,000/504,016 = 2.17 • Modified B/C = (1,095,000 - 75,000)/429,016 = 2.38

11. Example 3: Three Alternative Designs

12. Incremental Benefit/Cost Analysis • When mutually exclusive alternatives exist, each additional increase in investment should be justified based on • the additional benefits • the additional costs, and • the discount rate. • Perform Incremental Analysis Step 1: Ignore projects with B/C < 1 Step 2: Rank projects in increasing order of investment Step 3: Calculate the B/C ratio of the difference between the current alternative and the next alternative in rank order

13. Example 3 (cont’d)

14. Risk-Benefit Analysis • Economic impact of a variety of public projects can be differently affected by risk. • The extension of the benefit/cost analysis to include public -sector risk situations is called risk-benefit analysis. • Instead of using annual costs, we use expected annual costs.

15. Cost-Effectiveness Analysis • Combines non-monetary factors (effectiveness) and monetary aspects (costs) • Three conditions where cost-effectiveness analysis is trivial: • effectiveness of all alternatives is the same, so rank by decreasing costs • costs for all alternatives are equal, so rank by decreasing effectiveness • For any pair of alternatives, if both the cost and effectiveness of one dominate the other, then eliminate the dominated alternative

16. Cost-Effectiveness Analysis Procedure 1. Establish goals to be achieved by the projects 2. Identify constraints on achieving goal, such as budget, capacity 3. Identify all alternatives 4. Determine interest rate 5. Determining life-cycle cost of each alternative 6. Use incremental analysis to choose the best alternative

17. Example 4 • Three ways to construct an accident barrier on a densely populated highway are considered. • The goal is to reduce the number of head-on collisions. Construction and maintenance costs therefore have to be weighed against accident rates. • The study period is 10 years. • The interest (discount) rate is 6%

18. Example 4 (cont’d)

19. Pitfalls of the Cost-Effectiveness Method

20. Example 4 (cont’d) • Suppose you need at least a reduction of 50 accidents per year, then you will select the best alternative among: • the wire-mesh barrier with $/accident = 1943 • the concrete barrier with $/accident = 2127