1. Engineering Economics in Canada Chapter 10 Public Sector Decision Making

2. Copyright © 2006 Pearson Education Canada Inc. 10-2 Review The market prices that guide most decisions may not reflect all the social benefits and costs adequately. When we consider the broader social context, the concept of profitability is extremely difficult to define.

3. Copyright © 2006 Pearson Education Canada Inc. 10-3 Market Failure A market is a group of buyers and sellers linked by trade in a particular product or service. When prices do not reflect all social benefits and costs of a decision, we say that there has been market failure. Market failure occurs when a market, left on its own, fails to make decisions in which resources are allocated efficiently.

4. Copyright © 2006 Pearson Education Canada Inc. 10-4 Benefit-Cost Ratios The same comparison methods that are used for private sector projects are appropriate for government sector projects. This section is devoted to a discussion of several benefit-cost ratios that are commonly used in public sector decision making. We then point out several problems associated with the use of benefit-cost ratios

5. Copyright © 2006 Pearson Education Canada Inc. 10-5 Benefit-Cost Ratios… Benefit-cost ratios can be based on either the present worths or the annual worths of benefits and costs of projects. The conventional benefit-cost ratio (BCR) is given by: BCR = PW(user’s benefits) PW(sponsor’s costs) a project is considered desirable if its BCR > 1, which is to say, its benefits exceed its costs.

6. Copyright © 2006 Pearson Education Canada Inc. 10-6 Benefit-Cost Ratios… A modified benefit-cost ratio (MBCR), BCRM = PW( user’s benefits – PW(sponsor’s op. costs) PW(sponsor’s capital costs) Though the MBCR is less used than the conventional BCR, it has the advantage that it provides a measure of the net gain per dollar invested by the project sponsor.

7. Copyright © 2006 Pearson Education Canada Inc. 10-7 Example 10.2 The town of Helen Lake, Manitoba plans to pave a parking lot near its main shopping area. The main beneficiaries will be the merchants and their customers. The present worth of expected benefits is $3 000 000. The cost to the town of buying the lot, clearing, paving, and painting is expected to be $500 000. The present worth of expected maintenance costs over the lifetime of the project is $50 000. In the construction period, there will be some disbenefits to the local merchants and customers due to disruption of traffic in the Main Street area. –The present worth of the disruption is expected to be about $75 000. What is the benefit-cost ratio?

8. Copyright © 2006 Pearson Education Canada Inc. 10-8 Example 10.2 Answer BCR = PW(user’s benefits) PW(sponsor’s costs) = $3 000 000 - $75 000 $500 000 + $50 000 =5.3 The benefit-cost ratio exceeds 1 and thus the proposal is economically justified.

9. Copyright © 2006 Pearson Education Canada Inc. 10-9 Example 10.3 A fire department in a medium-sized city is considering a new system. An indirect effect would be a reduction in required fire-fighting equipment. User Benefits: PW(benefits ) = $37 500 000 Sponsor’s Costs: PW(operating costs)= $ 3 750 000 PW(capital costs for the city )= $13 500 000 PW(red.equip. requirements) = $ 2 250 000 What is the benefit-cost ratio for the system? What is the modified benefit-cost ratio for the dispatch system? Is the project economically justifiable?

10. Copyright © 2006 Pearson Education Canada Inc. 10-10 Example 10.3 Answer BCR = $37 500 000 ($13 500 000 + $3 750 000 – $2 250 000) = 2.5 BCRM = ($37 500 000 – $3 750 000) ($13 500 000 – $ 2 250 000) = 3.0 We see that both the conventional and modified cost-benefit ratio are greater than 1. The project, under either criterion, is economically justified.

11. Copyright © 2006 Pearson Education Canada Inc. 10-11 Comparison on Independent Projects For independent projects then the following decision rule may be used: –Accept all projects with a benefit-cost ratio greater than one. In other words, accept a project if BCR= PW(user’s benefits) > 1, or PW(sponsor’s costs) BCRM= PW(user’s ben.) – PW(sponsor’s op.costs) > 1 PW(sponsor’s capital costs) This rule is equivalent to accepting all projects with a present worth of benefits greater than the present worth of costs.

12. Copyright © 2006 Pearson Education Canada Inc. 10-12 Comparison of Mutually Exclusive Projects To use benefit-cost ratios to choose among mutually exclusive projects, we must evaluate the increment between projects, just as we did with the IRR method. Suppose we have two mutually exclusive projects, X and Y, with present worths of benefits, B X and B Y, and present worths of costs, C X and C Y. We discard projects with a BCR < 1.

13. Copyright © 2006 Pearson Education Canada Inc. 10-13 Comparison of Mutually Exclusive Projects If both projects have BCR’s > 1, we rank the projects in ascending order by the present worths of costs. Suppose C X ≥ C Y. We then form the ratio of the differences in benefits and costs: BCR(X-Y) = (B X – B Y )/(C X – C Y ) BCR(X-Y) > 1, X is preferred. Otherwise, Y is preferred. If C X = C Y (in which case the ratio is undefined), we choose the project with the greater present worth of benefits. If B X = B Y, we choose the project with the lower present worth of costs.

14. Copyright © 2006 Pearson Education Canada Inc. 10-14 Example 10.4 A city is considering increasing its airport capacity. Two mutually exclusive alternatives are being considered. –Alternative A is to construct a new airport 65 kilometres from the city. –Alternative B is to enlarge and otherwise upgrade the current airport that is only 15 kilometres from the city. Benefit and cost data are shown in Table 10.2. The city will use a MARR of 10% and a 10-year time horizon for this project. What are the benefit-cost ratios for the two alternatives? Which alternative should be accepted?

15. Copyright © 2006 Pearson Education Canada Inc. 10-15 Example 10.4 (con’t)…

16. Copyright © 2006 Pearson Education Canada Inc. 10-16 Example 10.4 Answer First, we convert all costs and benefits to PW PW(improved service of A) = $55(P/A,10%,10) = $55(6.1446) = $337.95 PW(improved service of B) = $28.5(6.1445) = $175.10 PW(increased travel cost of A) = $15(6.1445) = $92.17 The benefit-cost ratios for both alternatives are: BCR(A) = $337.95/($150+$50+$92.17) = 1.16 BCR(B) = $175.10/($10+$115+$25) = 1.1673 Both benefit-cost ratios exceed one, thus both are viable.

17. Copyright © 2006 Pearson Education Canada Inc. 10-17 Example 10.4 Answer (con’t)… To decide which alternative is better, we must compute the benefit-cost ratio of the incremental investment between the alternatives. Start with the project with the smallest present worth of costs (B), and compute the BCR associated with the marginal investment: BCR (A – B)= (B A – B B )/(C A – C B ) =($337.95 – $92.17 – $175.10) ($50 + $150) – ($10 + $115 + $25) = 1.4136 The ratio is greater than one. We interpret this to mean that the benefit-cost ratio ranks the new airport (A) ahead of the current airport (B).

18. Copyright © 2006 Pearson Education Canada Inc. 10-18 10.3.5 The MARR in the Public Sector Public sector organizations provide a mechanism for resources to be allocated to projects believed beneficial to society in general. Typical projects include health, safety, education programs, cultural development, and infrastructure development. Profits generated by public projects are not taxed. Private institutions and individuals are more concerned with generating wealth (profits) and are taxed by the government on this wealth. We would therefore expect the MARR for a public institution to be lower than that of a private institution, because the latter has a substantial extra expense acting to reduce its profits.

19. Copyright © 2006 Pearson Education Canada Inc. 10-19 Public Sector MARR In evaluating public sector projects, the MARR is used in the same way as in evaluating private sector projects—it captures the time value of money. In the private sector, the MARR expresses the minimum rate of return required on projects, taking into account that those profits will ultimately be taxed. The MARR used for public projects, often called the “social discount rate,” reflects the more general investment goal of maximizing social benefits.

20. Copyright © 2006 Pearson Education Canada Inc. 10-20 Public Sector MARR…(con’t) Some argue that the MARR should be the interest rate on capital borrowed by the government: the government bond rate. Others argue that the MARR should take into account that government spending on public projects consumes capital that might otherwise be used by taxpayers for private purposes. This line of thinking might lead to a social discount rate that is the same as the MARR for the taxpayers. In practice, the two viewpoints are captured by the Benefit-Cost Analysis Guide’s (Federal Treasury Board of Canada) recommendation that public projects be evaluated at a 10% (real) social discount rate and that the evaluation should include a sensitivity analysis at lower and upper bounds of 8% and 12% percent, respectively.

21. Copyright © 2006 Pearson Education Canada Inc. 10-21 Summary Introduction to Public Sector Decision Making Market Failure –Market Failure Defined –Remedies for Market Failure Decision Making in the Public Sector –The Point of View used for Project Evaluation –Identifying and Measuring the Costs of Public Projects –Identifying and Measuring the Benefits of Public Projects –Benefit-Cost Ratios –The MARR in the Public Sector