Presentation on theme: "Evaluating Projects with Benefit/Cost Ratio Method"— Presentation transcript:
1 Evaluating Projects with Benefit/Cost Ratio Method
2 Conventional B/C Ratio with PW: B/C = PW(benefits of the proposed project) PW(total costs of the proposed project)= PW(B)I + PW(O&M)B = benefits of the proposed projectI = initial investment in the proposed projectO&M = operating and maintenance costs ofthe proposed projectIf B/C 1 => project is acceptableB/C < 1 => project is unacceptable
3 Modified B/C Ratio with PW: B/C = PW(B) - PW(O&M)IB = benefits of the proposed projectI = initial investment in the proposed projectO&M = operating and maintenance costs ofthe proposed project
4 Conventional B/C Ratio with AW: B/C = AW(benefits of the proposed project) AW(total costs of the proposed project)= AW(B)CR + AW(O&M)B = benefits of the proposed projectCR = capital recovery amount = I (A/P) - S(A/F)O&M = operating and maintenance costs ofthe proposed projectIf B/C 1 => project is acceptableB/C < 1 => project is unacceptable
5 Modified B/C Ratio with AW: B/C = AW(B) - AW(O&M)CRB = benefits of the proposed projectCR = capital recovery amount = I (A/P) - S(A/F)O&M = operating and maintenance costs ofthe proposed project
6 Conventional B/C Ratio with PW & Salvage Value B/C = PW(benefits of the proposed project) PW(total costs of the proposed project)= PW(B)I - PW(S) + PW(O&M)B = benefits of the proposed projectI = initial investment in the proposed projectS = salvage value of investmentO&M = operating and maintenance costs ofthe proposed project
7 Modified B/C Ratio with PW & Salvage Value B/C = PW(B) - PW(O&M)I - PW(S)B = benefits of the proposed projectI = initial investment in the proposed projectS = salvage value of investmentO&M = operating and maintenance costs ofthe proposed project
8 A city is considering extending the runways of its Municipal Airport so that commercial jets can use the facility. The land necessary for the runway extension is currently farmland, which can be purchased for $350,000. Construction costs for the runway extension are projected to be $600,000, and the additional annual maintenance costs for the extension are estimated to be $22,500. If the runways are extended, a small terminal will be constructed at a cost of $250,000. The annual operating and maintenance costs for the terminal are estimated at $75,000. Finally, the projected increase in flights will require the addition of two air traffic controllers, at an annual cost of $100,000. Annual benefits of the runway extension have been estimated as follows:$325,000 rental receipts from airlines leasing space at the facility$65,000 airport tax charged to passengers$50,000 convenience benefit for residents of Bugtussle$50,000 additional tourism dollars for Bugtussle
12 Consistency of B/C Methods The magnitude of B/C value may be differentThe conclusion from all methods are consistent; that is if conventional B/C with PW > 1 then modified B/C with PW, conventional B/C with AW, and modified B/C with AW will be > 1. And vice versa.
14 Disbenefit in the B/C ratio Disbenefits - negative consequences to the public resulting from the implementation of a public-sector project.Traditionally disbenefits is treated as negative benefits (i.e., subtract disbenefits from benefits in the numerator of the B/C ratio). Alternatively, the disbenefits could be treated as costs (i.e., add disbenefits to cost in the denominator of the B/C ratio).
16 ExampleBy previous example, In addition to the benefits and costs, suppose that there are disbenefits associated with the runway extension project. Specifically, the increased noise level from commercial jet traffic will be a serious nuisance to homeowners living along the approach path to the Bugtussle Municipal Airport. The annual disbenefit to citizens of Bugtussle caused by this "noise pollution" is estimated to be $100,000. Given this additional information, reapply the conventional B/C ratio, with equivalent annual worth, to determine whether or not this disbenefit affects your recommendation on the desirability of this project.
18 Consistency Let B = the equivalent annual worth of project benefits C = the equivalent annual worth of projectcostsX = the equivalent annual worth of a cashflow (either an added benefit or a reducedcost) not included in either B or CB/C = (B + X) / C > 1 => B + X > C =>B > C - X => B/ (C - X) > 1 if C - X > 0
19 ExampleA project is being considered to replace an aging bridge. The new bridge can be constructed at a cost of $300,000, and estimated annual maintenance costs are $10,000. The existing bridge has annual maintenance costs of $18,500. The annual benefit of the new four-lane bridge to motorists, due to the removal of the traffic bottleneck, has been estimated to be $25,000. Conduct a benefit/cost analysis, using an interest rate of 8% and a study period of 25 years, to determine whether the new bridge should be constructed.Treating maintenance costs saving as a Reduced Cost:B / C = 25,000 / [300,000(A / P,8%,25) - (18, ,000)]B/C = 1.275Treating maintenance costs saving as an Increased Benefit:B/C = [25,000 + (18, ,000)]/[300,000(A/P,8%,25)]B/C = 1.192
20 Comparison of Mutually Exclusive Projects by B/C Ratios Maximizes the B/C ratio does NOT guarantee that the best project is selected.Inconsistent Result from Conventional B/C ratio and Modified ratio. (the conventional B/C ratio might favor a different project than would the modified B/C ratio).
21 ExampleThe required investments, annual operating and maintenance costs, and annual benefits for two mutually exclusive alternative projects are shown below, which project should be selected?Project A Project BCapital investment , , i = 10%AnnualO&M cost 12,500 45, N = 20 yrsAnnual benefit ,500 80,000Conventional B/C:Modified B/C:
23 ExampleThree mutually exclusive alternative public works projects are currently under consideration. Each of the projects has a useful life of 50 years, and the interest rate is 10 % per year. Which, if any, of these projects should be selected?A B CCapital investment ,500, ,000, ,000,000Annual O&M. costs 750, , ,000Salvage value ,250, ,750, ,000,000Annual benefit ,150, ,265, ,500,000
24 PW(Costs, A) = 8,500, ,000(P/A,10%,50)- 1,250,000(P/F,10%,50) = 15,925,463PW(Costs, B) = 10,000, ,000(P/A,10%,50)- 1,750,000(P/F,10%,50) = 17,173,333PW(Costs, C) = 12,000, ,000(P/A,10%,50)- 2,000,000(P/F,10%,50) = 18,923,333PW(Benefit,A) = 2,150,000(P/A,10%,50) = 21,316,851PW(Benefit, B) = 2,265,000(P/A,10%,50) = 22,457,055PW(Benefit, C) = 2,750,000(P/A,10%,50) = 24,787,036B/C(A) = 21,316,851/15,925,463 = > 1.0 .A is AcceptableB/C(B - A) = (22,457, ,316,851)/(17,173, ,925,463)= < Project B not AcceptableB/C(C - A) = (24,787, ,316,851)/(18,923, ,925,463)= > Project C is AcceptableDecision: Recommend Project C
25 ExampleTwo mutually exclusive alternative public works projects are under consideration. Their respective costs and benefits are included in the table below. Project I has an anticipated life of 35 years, and the useful life of Project II has been estimated to be 25 years. If the interest rate is 9%, which, if either, of these projects should be selected?Project I Project IICapital investment $750,000 $625,000Annual O&M costs 120, ,000Annual benefit , ,000Useful life of project (years)
26 Project II is Acceptable AW(Costs, I) = 750,000(A/P,9%,35) + 120,000= 190,977AW(Costs, II) = 625,000(A/P,9%,25) + 110,000= 173,629B/C(II) = 230,000/ 173,629 = >Project II is Acceptable B/C(I - II) = (245, ,000)/(190, ,629)= <Project I not AcceptableSelect Project II
27 Criticisms and Shortcomings of the Benefit/Cost Ratio Method Often used as a tool for after-the-fact justifications rather than for project evaluationSerious distributional inequities (i.e., one group reaps the benefits while another incurs the costs) may not be accounted for in B/C studiesQualitative information is often ignored in B/C studies