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Benefit / Cost Analysis in Public Sector
Public Sector projects are owned, used, and financed by the citizens. Examples of public works projects: Hospitals, parks, utilities, schools, sports arenas, freeways, food stamps, emergency relief. Typically Public Sector projects are Large-scale Long life spans (30-50+ years) No profits; any expenses are paid by public, and any revenue goes back to public For example, Saints may move to L.A. In order to do so, they would need an updated football arena. This would be a huge project, and something that might fall in the realm of the Public Sector. In addition to the football arena, local infrastructure (roads, freeways, etc.) will have to be modified to alleviate congestion. To do economic analysis, we often have to estimate: Costs โ expenditures to the government entity for construction, operation and maintenance, less any salvage value Benefits โ advantages to be experienced by the owners, the public Disbenefits โ undesirable or negative consequences to the owners of the alternative is implemented. May be indirect economic disadvantages of the alternative. In order to determine whether such a project is worthwhile or not we conduct a Benefit-Cost Analysis.
- Identify all user's benefits (favorable outcomes) and disbenefits (unfavorable outcomes) arising from the project
- Quantify as much as possible these benefits and disbenefits in dollar terms so that benefits and costs can be compared
- Identify sponsor's costs and quantify them
- Determine the equivalent net benefits and net costs at the base period
- Accept project if the equivalent net benefits exceed the equivalent net costs Thus we can say that B > C or B / C > 1
Benefits
What are benefits and disbenefits of a project e.g., a new highway will alleviate congestion, allowing people to get to work faster. New businesses will spring up along the highway (gas stations, restaurants). However, because of a decrease in traffic along the old route, some businesses there may be lost. B = benefits โ disbenefits for simplicity we define benefits as either primary or secondary primary โ directly attributable to the project secondary โ indirectly attributable e.g., govt wants to build a superconductor lab primary benefit โ new technologies and applications to US businesses secondary benefit โ international trade of these technologies and the increase in local economy due to the presence of a large scientific population.
Costs
Identify and classify the expenditures required and any savings to be realized. C = initial capital expenditures + operating and maintenance costs Since we are going to have a ratio, B / C, the sign convention changes, and we take costs as positive values (and revenues in the cost term as negative values) e.g., a new toll highway, will have construction costs, resurfacing costs and revenues in the forms of tolls.
MARR
Typically the projects we are looking at with this kind of analysis are public, and thus the rate of return is different than for private ventures. The purpose of government spending is not the same as private industry (i.e., make money). The interest rate we apply for public projects is called the โSocial Discount Rateโ. Two possibilities for social discount rate
- social discount rate should reflect only the prevailing government borrowing rate. for projects with no private counterparts (reservoirs, dams, noncommercial access roads), the rate is set at the rate that government borrows money
- social discount rate should represent the rate that could have been earned had the funds not been removed from the private sector. if public projects are
๎ญ B = Bb โ Ba ๎ญ C = Cb โ Ca
- BC (b-a) = BC^ ๎ i^ ๎ b โ a =^ ๎ญ B ๎ญ C
- If BC(i)b-a > 1, then chose alternative B (the difference, if less than 1, chose alternative A.
- Move down the list, like the challenger defender we did last week. Addendums: If delta (I + C') = 0, then we cannot use benefit-cost ratio. In this case, we select the alternative with the largest B value With unequal service lives, instead of PW analysis on all terms, we use AW analysis Let's consider a flood control project: in $1000 Channel Improvements Dam and Reservoir No Flood control First Cost $1,500 $2,500 0 Flood Damage First Year 220 50 500 Increasing Gradient 10 5 8 O&M: first year 70 95 increasing gradient 5 8 Annual Benefit to Fisheries 29 Disbenefit to recreation 20 Disbenefit to agriculture 21 Assume a study period of 25 years and an i value of 11% Rank according to first cost: NFC < CI < D&R Let's determine BC(i)ci-nfc: What are benefits of improving channel? cost of floods decreases from 500 to 220 in first year. Some recreation is lost Del B = (-220 - - 500)(P/A,11%,25) + (-10 - -8)(P/G,11%,25) + (-20)(P/A,11%,25) = 2,070. Del C = (1500-0) + (70-0)(P/A,11%,25) + (5-0)(P/G, 11%,25) = 2,388. Del B / Del C = 2070.06 / 2388.7 = 0.885. This tells us that the added benefits of
improving the channel ( a decrease in flood damage) do not outweigh the costs associated with improving the channel (construction, maintenance, loss of recreation land) Let's determine BC(i)dr-nfc Del B = (-50 - - 500)(P/A,11%,25) + (-5 - -8)(P/G,11%,25) + 29(P/A,11%,25) โ 21 (P/A,11%,25) = 4,036. Del C = (2500-0) + (95-0)(P/A,11%,25) + (8-0)(P/G, 11%,25) = 3,778. Del B / Del C = 4036.78 / 3778.75 = 1. Therefore, the added expense of building and maintaining the dam, results in a benefit to the region in terms of reduced flooding and increased fishing. We can think of the B/C as in terms of a $ benefit per $ cost. So a B/C of $1.07, intuitively tells us that every $1 spent on construction and maintenance yields 1.07 in benefits (namely a reduction in flooding) Depending on how we look at projects, we can have different opinions on whether something is a cost or a disbenefit. Consider the following: A city wishes to issue a $5 M bond to purchase greenbelt to preserve land and protect against flooding. The following cash flows are expected:
- Annual cost of $5 M bond over 15 years at 6% interest rate:
- Annual maintenance, upkeep and program management
- Annual parks development budget
- Annual loss in commercial development
- State sales tax rebates not realized
- Annual municipal income from park use
- Savings in flood control projects
- Property damage not experienced due to flooding We have several points of view we can take when classifying these as costs, benefits and disbenefits viewpoint of the public (purchasing and operating the park is our goal): Cost: 1, 2, 3 Benefit: 6, 7, 8 Disbenefit: 4, 5
initial cost $M annual benefit
CC B/C
A 6 350,000 360000 0.
B 8 420,000 480000 0.
C 3 125,000 180000 0.
D 10 400,000 600000 0.
E 5 350,000 300000 1.
F 11 700,000 660000 1.
we eliminate all but E and F We do incremental analysis on the choices rank from low to high cost: E F del CC = 660,000-300,000 = 360, del B = 700,000 โ 350,000 = 350, del B / del CC = 0.97, so no go. Let's say that a new site becomes available, G. initial cost: 10 M, annual benefit 700, 10 M 6% = 600, G - E B / C = 700,000 / 600,000 = 1. compare this with option E: del CC = 600,000 โ 300,000 = 300, del B = 700,000 โ 350,000 = 350, B / C = 1. Therefore, we chose G Must still check against F F โ G del CC = 660,000 โ 600,000 = 60, del B = 700,000 โ 700,000 = 0 B / C = 0 therefore we stay with G In this case, we pay for F to get same economic benefit. no go. problems 11, 16, 25, 33
Chapter 10 We have now seen 5 different way to evaluate projects and chose the best one: PW AW FW ROR B/C PW, AW, FW to be used evaluate alternatives in private sector. Don't often worry about FW Alternatives with Equal lives: AW or PW public sector: B/C based on AW or PW Unequal lives of alternatives: AW public sector: B/C based on AW Long to infinite: AW or PW, using capitalized cost, A = P*i public sector B/C based on AW
