### CBA Cost-Benefit Analysis

### Discounting Skills List

**Instructions.** Most of the questions on this exam have to do with the community of Ourville which is considering some options for creating parks to enhance the quality of life of local residents. The amounts are expressed in simple numbers – e.g., $100 – which you can assume to be referring to realistic amounts – e.g., hundreds of thousands. In every case, use the question as an opportunity for demonstrating your competence – say what you know, explain your work, use complete sentences. The exam contains almost no mathematical calculations. Grading scale: (5)demonstrated excellence, (4)demonstrated understanding, (3)suggested understanding, (2)suggested misunderstanding, (1)demonstrated misunderstanding.

**1.** As a part of its considerations about the park project, Ourville needs to think about the opportunity costs associated with each tract of land being considered for the park. What is an opportunity cost? You are nominated to explain (BRIEFLY) in terms the public will understand what we mean by opportunity cost:

**2.** While discussing the value of the park options to residents the term "willingness to pay" comes up. Explain (BRIEFLY) to the public what this means.

**3.** One part of the staff report talks about discounting. A resident asks "where do discount rates come from?" Your (BRIEF) answer:

**4.** In your reports you mention Pareto and Kaldor-Hicks criteria. Your supervisor says you can't just refer to these – you need to explain (BRIEFLY) what they mean in everyday terms:

**5.** One option on the table for the community of Ourville is to build a park on the west side of town. Should we spend $100 to build a new park? Studies have determined that the park will provide $132 of benefits to the community's residents. What do you recommend and why?

**6.** Two options are on the table for the community of Ourville. Either option will cost $100. Option A — the West Park – provides $80 of benefits (total) to families who live close to the west park location and $52 (total) to families who live farther away on the east side of town. Option B – the East Park – provides $40 to the first group of families and $110 to the second group. What do you recommend and why?

**7.** The mayor of Ourville wants a more detailed analysis on option A. Apparently, the park could range in size from the very small to the very large. Budget concerns are not an issue for now. Examine the information below. What do you recommend and why? For example: What type of problem is this? What is the fundamental rule? How big should the park be?

**8.** Activists in Ourville force the city not to think of this as an either/or proposition. Experts are consulted and the following cost benefit information is obtained. Council allocates $200 for the parks project. How do you recommend they proceed and why? What kind of problem is this? How big should each park be?

9. The Ourville Alliance, a neighborhood group whose members include several MPPs, likes decision trees. And they think the benefits of the different park options are not certain. In fact, they think that Option A has a 75% chance of a net benefit of 60 and a 25% chance of being a bust and having a net benefit of only 20. By comparison, Option B has a 90% chance of having a net benefit of 50 and a 10% chance of a net benefit of only 10. Sketch in details, labels, etc. on this decision tree as necessary. What do you recommend and why?

**10.** Earlier in the process, two options were on the table for the community of Ourville. One proposal was for a pocket park that will cost only $10 and is projected to have $50 benefit — a benefit to cost ratio of 5 to 1. The other proposal is a more elaborate park that will cost $50 and have a benefit of $100 — a benefit to cost ratio of 2 to 1. The town budget could afford either project – either one pocket park or one larger park, but not both. What would you recommend and why?

11. What is the basic equation for the present value (PV) of a future value (FV) N years from now at a discount rate R?

12. In comparing options for the park projects in Ourville, staff have noted that equipment choices will have an impact on maintenance costs down the line. Two swing sets, in particular, are being considered. One is very expensive up front, but has a very favorable maintenance outlook. The other is less expensive, but might need repairs and even to be replaced during the expected lifetime of the sturdier set. Data is below (based on a 7% discount rate). We assume annual community benefits from using the park to be 2000 (except in the year where the cheaper swing set would have to be replaced). The town budget could afford either project, but not both. What do you recommend and why? Explain to a public audience what is going on here.

### Discards

- Given table of costs and benefits, calculate net and marginal.
- Flow chart, logic model, decision tree
- Answer two questions; read question 3; calculate NBs and PV until there are no more to do.

- Perhaps a single problem: compare two projects with stream of 4 years of costs and benefits
- Intuition Question: compare a project with high upfront costs to one that's more spread out; a project takes a long time to pay back but keeps on paying back; a project with high c/b ratio compared to one with high nb.
- A straightforward problem with advantages going to one group. Oakville is considering two approaches to its policy problem. Project A involves a parcel tax that will cost property owners an average of $100 and a total of 1,000,000 each year over three years. It will provide $50 of benefit to everyone in town, for a total of 1,000,000 each year for the next five years.
- Project B will charge

- Simple computation. Calculate present value of $100 in 5 years if discount rate is 6%.

$1.06^2=1.12$ | $1.06^3=1.19$ | $1.06^4=1.26$ | $1.06^5=1.34$ | $1.06^6=1.42$ | $1.06^7=1.50$ | $1.06^8=1.59$ | $1.06^9=1.69$ | $1.06^{10}=1.79$ |

1 | 2 | 3 | 4 | 5 | 6 |

-125 | -150 | -175 | -50 | -50 | -50 |

13 | 31 | 49 | 176 | 192 | 200 |

-112 | -119 | -126 | 134 | 142 | 150 |

-100 | -100 | -100 | 100 | 100 | 100 |

- Chart: Marginal net benefit on problems with scalable projects.