Evaluating Evaluating ProjectsProjects

withwithBenefit/Cost Benefit/Cost Ratio MethodRatio Method

Conventional B/C Ratio with PW:Conventional B/C Ratio with PW:

B/C = B/C = PW(benefits of the proposed project)PW(benefits of the proposed project) PW(total costs of the proposed project)PW(total costs of the proposed project)

= PW(B)= PW(B)

I + PW(O&M)I + PW(O&M) B = benefits of the proposed projectB = benefits of the proposed project

I = initial investment in the proposed project I = initial investment in the proposed project

O&M = operating and maintenance costs of O&M = operating and maintenance costs of

the proposed projectthe proposed project

If B/C 1 => project is acceptable

B/C < 1 => project is unacceptable

Modified B/C Ratio with PW:Modified B/C Ratio with PW:

B/C = PW(B) - PW(O&M) B/C = PW(B) - PW(O&M)

II B = benefits of the proposed projectB = benefits of the proposed project

I = initial investment in the proposed project I = initial investment in the proposed project

O&M = operating and maintenance costs of O&M = operating and maintenance costs of

the proposed projectthe proposed project

Conventional B/C Ratio with AW:Conventional B/C Ratio with AW:

B/C = B/C = AW(benefits of the proposed project)AW(benefits of the proposed project) AW(total costs of the proposed project)AW(total costs of the proposed project)

= AW(B)= AW(B)

CR + AW(O&M)CR + AW(O&M)

B = benefits of the proposed projectB = benefits of the proposed project

CR = capital recovery amount = I (A/P) - S(A/F)CR = capital recovery amount = I (A/P) - S(A/F)

O&M = operating and maintenance costs of O&M = operating and maintenance costs of

the proposed projectthe proposed project

If B/C 1 => project is acceptable

B/C < 1 => project is unacceptable

Modified B/C Ratio with AW:Modified B/C Ratio with AW:

B/C = AW(B) - AW(O&M) B/C = AW(B) - AW(O&M)

CRCR

B = benefits of the proposed projectB = benefits of the proposed project

CR = capital recovery amount = I (A/P) - S(A/F) CR = capital recovery amount = I (A/P) - S(A/F)

O&M = operating and maintenance costs of O&M = operating and maintenance costs of

the proposed projectthe proposed project

Conventional B/C Ratio with PW Conventional B/C Ratio with PW & Salvage Value& Salvage Value

B/C = B/C = PW(benefits of the proposed project)PW(benefits of the proposed project) PW(total costs of the proposed project)PW(total costs of the proposed project)

= PW(B)= PW(B)

I - PW(S) + PW(O&M)I - PW(S) + PW(O&M)

B = benefits of the proposed projectB = benefits of the proposed project

I = initial investment in the proposed project I = initial investment in the proposed project

S = salvage value of investmentS = salvage value of investment

O&M = operating and maintenance costs of O&M = operating and maintenance costs of

the proposed projectthe proposed project

Modified B/C Ratio with PW & Modified B/C Ratio with PW & Salvage Value Salvage Value

B/C = PW(B) - PW(O&M) B/C = PW(B) - PW(O&M)

I - PW(S)I - PW(S)

B = benefits of the proposed projectB = benefits of the proposed project

I = initial investment in the proposed projectI = initial investment in the proposed project

S = salvage value of investment S = salvage value of investment

O&M = operating and maintenance costs of O&M = operating and maintenance costs of

the proposed projectthe proposed project

A city is considering extending the runways of its Municipal A city is considering extending the runways of its Municipal Airport so that commercial jets can use the facility. The Airport so that commercial jets can use the facility. The landland necessary for the runway extension is currently farmland, which necessary for the runway extension is currently farmland, which can be purchased for can be purchased for $350,000$350,000. . Construction costsConstruction costs for the for the runway extension are projected to be runway extension are projected to be $600,000$600,000, and the , and the additional annual additional annual maintenance costsmaintenance costs for the extension are for the extension are estimated to be estimated to be $22,500$22,500. If the runways are extended, a small . If the runways are extended, a small terminal will be terminal will be constructed constructed at a cost of at a cost of $250,000$250,000. The annual . The annual operating and operating and maintenance costsmaintenance costs for the terminal are estimated for the terminal are estimated at at $75,000$75,000. Finally, the projected increase in flights will require . Finally, the projected increase in flights will require the addition of two air the addition of two air traffic controllerstraffic controllers, at an annual cost of , at an annual cost of $100,000$100,000. Annual . Annual benefits benefits of the runway extension have been of the runway extension have been estimated as follows:estimated as follows:$325,000 rental receipts from airlines leasing space at the $325,000 rental receipts from airlines leasing space at the

facilityfacility$65,000 airport tax charged to passengers$65,000 airport tax charged to passengers$50,000 convenience benefit for residents of Bugtussle$50,000 convenience benefit for residents of Bugtussle$50,000 additional tourism dollars for Bugtussle$50,000 additional tourism dollars for Bugtussle

SolutionSolutionI = land cost + runway construction cost I = land cost + runway construction cost

+ terminal construction cost+ terminal construction cost

= 350,000 + 600,000 + 250,000 = = 350,000 + 600,000 + 250,000 = 1,200,0001,200,000

B = rent + tax + convenience benefit + B = rent + tax + convenience benefit + tourismtourism

= 325,000 + 65,000 + 50,000 + 50,000 = 325,000 + 65,000 + 50,000 + 50,000 = 490,000= 490,000

O&M = runway O&M + terminal O&M + O&M = runway O&M + terminal O&M +

controller controller

= 22,500 + 75,000 + 100,000 = = 22,500 + 75,000 + 100,000 = 197,500197,500

Conventional B/CConventional B/CB/C = PW(B)/[I + PW(O&M)]B/C = 490,000 (P/A, 10%, 20)/[1,200,000 +

197,500 (P/A,10%,20)] = 1.448 > 1Modified B/CModified B/C

B/C = [PW(B) - PW(O&M]/ IB/C = [490,000 (P/A, 10%, 20) -

197,500 (P/A,10%,20)]/ 1,200,000 = 2.075 > 1

B/C with PWB/C with PW

B/C with AWB/C with AW

Conventional B/C:Conventional B/C:B/C = AW(B)/[CR + AW(O&M)]B/C = AW(B)/[CR + AW(O&M)]B/C = 490,000/[1,200,000 (A/P,10%,20) + B/C = 490,000/[1,200,000 (A/P,10%,20) + 197,500] = 1.448 > 1197,500] = 1.448 > 1

Modified B/C:Modified B/C:B/C= [AW(B) - AW(O&M]/CRB/C= [AW(B) - AW(O&M]/CRB/C = [490,000 - 197,500]/[1,200,000 (A/P,10%,20)]B/C = [490,000 - 197,500]/[1,200,000 (A/P,10%,20)]

= 2.075 > 1= 2.075 > 1

Consistency of B/C MethodsConsistency of B/C Methods

The magnitude of B/C value may be The magnitude of B/C value may be differentdifferent

The conclusion from all methods are The conclusion from all methods are consistent; that is if conventional consistent; that is if conventional B/C with PW > 1 then modified B/C B/C with PW > 1 then modified B/C with PW, conventional B/C with AW, with PW, conventional B/C with AW, and modified B/C with AW will be > and modified B/C with AW will be > 1. And vice versa.1. And vice versa.

If PW(B) / [ I + PW(O&M)] > 1 =>If PW(B) / [ I + PW(O&M)] > 1 =>

PW(B) > I + PW(O&M) => PW(B) > I + PW(O&M) =>

PW(B) - PW(O&M) > I => PW(B) - PW(O&M) > I =>

[PW(B) - PW(O&M)] / I > 1[PW(B) - PW(O&M)] / I > 1 If PW(B) / [ I + PW(O&M)] > 1 =>If PW(B) / [ I + PW(O&M)] > 1 =>

PW(B) > I + PW(O&M) => PW(B) > I + PW(O&M) =>

PW(B)(A/P) >[ I + PW(O&M)](A/P) =>PW(B)(A/P) >[ I + PW(O&M)](A/P) =>

AW(B) > I(A/P) + AW(O&M) =>AW(B) > I(A/P) + AW(O&M) =>

AW(B) > AW(B) > I(A/P) - S(A/F)I(A/P) - S(A/F) + AW(O&M) => + AW(O&M) =>

AW(B) > AW(B) > CRCR + AW(O&M) => + AW(O&M) =>

AW(B) / [CR + AW(O&M)] > 1AW(B) / [CR + AW(O&M)] > 1

Disbenefit in the B/C ratioDisbenefit 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).

Conventional B/C with AW & Conventional B/C with AW & DisbenefitDisbenefit

B/C = B/C = AW(benefits) - AW(disbenefits)AW(benefits) - AW(disbenefits) AW(costs) AW(costs)

= AW(B) - AW(D)= AW(B) - AW(D)

CR + AW(O&M) CR + AW(O&M)

B/C = B/C = AW(benefits)AW(benefits) AW(costs) + AW(disbenefits) AW(costs) + AW(disbenefits)

= AW(B) = AW(B)

CR + AW(O&M) + AW(D)CR + AW(O&M) + AW(D)

ExampleExample

By previous example, In addition to the benefits and By previous example, In addition to the benefits and costs, suppose that there are disbenefits associated with costs, suppose that there are disbenefits associated with the runway extension project. Specifically, the the runway extension project. Specifically, the increased noise level from commercial jet traffic will increased noise level from commercial jet traffic will be a serious nuisance to homeowners living along the be a serious nuisance to homeowners living along the approach path to the Bugtussle Municipal Airport. The approach path to the Bugtussle Municipal Airport. The annual disbenefit to citizens of Bugtussle caused by this annual disbenefit to citizens of Bugtussle caused by this "noise pollution" is estimated to be $100,000. Given "noise pollution" is estimated to be $100,000. Given this additional information, reapply the conventional this additional information, reapply the conventional B/C ratio, with equivalent annual worth, to determine B/C ratio, with equivalent annual worth, to determine whether or not this disbenefit affects your whether or not this disbenefit affects your recommendation on the desirability of this project.recommendation on the desirability of this project.

Disbenefits Reduce BenefitsDisbenefits Reduce Benefits..B/C = [AW(B) - AW(D)] / [CR + AW(O&M)]B/C = [AW(B) - AW(D)] / [CR + AW(O&M)]B/C = [490,000 - 100,000]/[$1,200,000 B/C = [490,000 - 100,000]/[$1,200,000 (A/P,10%,20) + 197,500](A/P,10%,20) + 197,500]B/C = 1.152B/C = 1.152

Disbenefits Treated as Additional CostDisbenefits Treated as Additional CostB/C = AW(B)/[CR + AW(O&M) + AW(D)] B/C = AW(B)/[CR + AW(O&M) + AW(D)] B/C = 490,000 / [1,200,000 (A/P,10%,20) + B/C = 490,000 / [1,200,000 (A/P,10%,20) + 197,500 + 100,000] 197,500 + 100,000] B/C = 1.118B/C = 1.118

ConsistencyConsistency Let B = the equivalent annual worth of Let B = the equivalent annual worth of

project benefitsproject benefits C = the equivalent annual worth of project C = the equivalent annual worth of project

costscosts X = the equivalent annual worth of a cash

flow (either an added benefit or a reduced

cost) not included in either B or C

B/C = (B + X) / C > 1 => B + X > C =>

B > C - X => B/ (C - X) > 1 if C - X > 0

ExampleExampleA project is being considered to replace an aging bridge. The A project is being considered to replace an aging bridge. The new new bridgebridge can be can be constructedconstructed at a cost of at a cost of $300,000$300,000, and estimated , and estimated annual maintenance costsannual maintenance costs are are $10,000$10,000. The . The existing bridgeexisting bridge has has annual maintenance costsannual maintenance costs of of $18,500$18,500. The . The annual benefitannual benefit of the new of the new four-lane bridge to motorists, due to the removal of the traffic four-lane bridge to motorists, due to the removal of the traffic bottleneck, has been estimated to be bottleneck, has been estimated to be $25,000$25,000. Conduct a . Conduct a benefit/cost analysis, using an interest rate of 8% and a study period benefit/cost analysis, using an interest rate of 8% and a study period of 25 years, to determine whether the new bridge should be of 25 years, to determine whether the new bridge should be constructed.constructed.

Treating maintenance costs saving as a Treating maintenance costs saving as a Reduced Cost: Reduced Cost:

B / C = 25,000 / [300,000(A / P,8%,25) - (18,500 - 10,000)]B / C = 25,000 / [300,000(A / P,8%,25) - (18,500 - 10,000)]

B/C = 1.275B/C = 1.275

Treating maintenance costs saving as an Treating maintenance costs saving as an Increased Benefit: Increased Benefit:

B/C = [25,000 + (18,500 - 10,000)]/[300,000(A/P,8%,25)]B/C = [25,000 + (18,500 - 10,000)]/[300,000(A/P,8%,25)]

B/C = 1.192B/C = 1.192

Comparison of Mutually Exclusive Projects by B/C Ratios

Maximizes the B/C ratio does Maximizes the B/C ratio does NOTNOT guarantee that the best project is guarantee that the best project is selected.selected.

Inconsistent ResultInconsistent Result from Conventional from Conventional B/C ratio and Modified ratio. (the B/C ratio and Modified ratio. (the conventional B/C ratio might favor a conventional B/C ratio might favor a different project than would the modified different project than would the modified B/C ratio).B/C ratio).

ExampleExample The required investments, annual operating and The required investments, annual operating and

maintenance costs, and annual benefits for two mutually maintenance costs, and annual benefits for two mutually exclusive alternative projects are shown below, which exclusive alternative projects are shown below, which project should be selected?project should be selected?

Project A Project BProject A Project B Capital investment 110,000 135,000 i = 10%Capital investment 110,000 135,000 i = 10%

AnnualO&M costAnnualO&M cost 12,500 12,500 45,000 N = 20 yrs45,000 N = 20 yrsAnnual benefitAnnual benefit 37,500 37,500 80,00080,000Conventional B/C:Conventional B/C: 1.4751.475 1.315 1.315 Modified B/C:Modified B/C:1.9351.935 2.2072.207

Incremental B/C Incremental B/C Ratio Should Be Ratio Should Be UsedUsed

Three mutually exclusive alternative public works projects Three mutually exclusive alternative public works projects are currently under consideration. Each of the projects has a are currently under consideration. Each of the projects has a useful life of 50 years, and the interest rate is 10 % per year. useful life of 50 years, and the interest rate is 10 % per year. Which, if any, of these projects should be selected?Which, if any, of these projects should be selected?

AA B B C CCapital investment 8,500,000 10,000,000 12,000,000Capital investment 8,500,000 10,000,000 12,000,000

Annual O&M. costsAnnual O&M. costs 750,000 725,000 700,000 750,000 725,000 700,000Salvage valueSalvage value 1,250,000 1,750,000 1,250,000 1,750,000 2,000,0002,000,000Annual benefitAnnual benefit 2,150,000 2,265,000 2,150,000 2,265,000 2,500,0002,500,000

ExampleExample

PW(Costs, A) = 8,500,000 + 750,000(P/A,10%,50)PW(Costs, A) = 8,500,000 + 750,000(P/A,10%,50)

- 1,250,000(P/F,10%,50) = 15,925,463- 1,250,000(P/F,10%,50) = 15,925,463

PW(Costs, B) = 10,000,000 + 725,000(P/A,10%,50)PW(Costs, B) = 10,000,000 + 725,000(P/A,10%,50)

- 1,750,000(P/F,10%,50) = 17,173,333- 1,750,000(P/F,10%,50) = 17,173,333

PW(Costs, C) = 12,000,000 + 700,000(P/A,10%,50)PW(Costs, C) = 12,000,000 + 700,000(P/A,10%,50)

- 2,000,000(P/F,10%,50) = 18,923,333- 2,000,000(P/F,10%,50) = 18,923,333

PW(Benefit,A) = 2,150,000(P/A,10%,50) = 21,316,851PW(Benefit,A) = 2,150,000(P/A,10%,50) = 21,316,851

PW(Benefit, B) = 2,265,000(P/A,10%,50) = 22,457,055PW(Benefit, B) = 2,265,000(P/A,10%,50) = 22,457,055

PW(Benefit, C) = 2,750,000(P/A,10%,50) = 24,787,036PW(Benefit, C) = 2,750,000(P/A,10%,50) = 24,787,036

B/C(A) = 21,316,851/15,925,463 = B/C(A) = 21,316,851/15,925,463 = 1.3385 > 1.0 1.3385 > 1.0 ..A is AcceptableA is Acceptable

B/B/C(B - A) = (22,457,055 - 21,316,851)/(17,173,333 - 15,925,463)C(B - A) = (22,457,055 - 21,316,851)/(17,173,333 - 15,925,463)

= = 0.9137 < 1.0 0.9137 < 1.0 . . . . Project B not AcceptableProject B not Acceptable

B/B/C(C - A) = (24,787,036 - 21,316,851)/(18,923,333 - 15,925,463)C(C - A) = (24,787,036 - 21,316,851)/(18,923,333 - 15,925,463)

= = 1.1576 > 1.0 1.1576 > 1.0 . . . . Project C is AcceptableProject C is Acceptable

Decision: Decision: Recommend Project CRecommend Project C

ExampleExample

Two mutually exclusive alternative public works Two mutually exclusive alternative public works projects are under consideration. Their respective projects are under consideration. Their respective costs and benefits are included in the table below. costs and benefits are included in the table below. Project I has an anticipated life of 35 years, and the Project I has an anticipated life of 35 years, and the useful life of Project II has been estimated to be 25 useful life of Project II has been estimated to be 25 years. If the interest rate is 9%, which, if either, of years. If the interest rate is 9%, which, if either, of these projects should be selected?these projects should be selected?

Project I Project IIProject I Project IICapital investmentCapital investment $750,000$750,000 $625,000$625,000Annual O&M costsAnnual O&M costs 120,000 120,000 110,000 110,000Annual benefitAnnual benefit 245,000 245,000 230,000 230,000Useful life of project (years)Useful life of project (years) 3535 25 25

AW(Costs, I) = 750,000(A/P,9%,35) + 120,000 AW(Costs, I) = 750,000(A/P,9%,35) + 120,000

= 190,977= 190,977

AW(Costs, II) = 625,000(A/P,9%,25) + 110,000 AW(Costs, II) = 625,000(A/P,9%,25) + 110,000

= 173,629= 173,629

B/C(II) = 230,000/ 173,629 = 1.3247 > 1.0 . . B/C(II) = 230,000/ 173,629 = 1.3247 > 1.0 . .

Project II is AcceptableProject II is Acceptable

B/B/C(I - II) = (245,000- 230,000)/(190,977 - 173,629)C(I - II) = (245,000- 230,000)/(190,977 - 173,629)

= 0.8647 < 1.0 . . = 0.8647 < 1.0 . .

Project I not AcceptableProject I not Acceptable

Select Project IISelect Project II

Criticisms and Shortcomings of the Benefit/Cost Ratio Method

Often used as a tool for after-the-fact justifications rather than for project evaluation

Serious distributional inequities (i.e., one group reaps the benefits while another incurs the costs) may not be accounted for in B/C studies

Qualitative information is often ignored in B/C studies

HomeworkHomework

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Problem # 8, 12, 18Problem # 8, 12, 18