Evaluating Projects
with
Benefit/Cost Ratio
Method
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 project
I = initial investment in the proposed project
O&M = operating and maintenance costs of
the proposed project
If B/C  1 => project is acceptable
B/C < 1 => project is unacceptable
Modified B/C Ratio with PW:
B/C = PW(B) - PW(O&M)
I
B = benefits of the proposed project
I = initial investment in the proposed project
O&M = operating and maintenance costs of
the proposed project
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 project
CR = capital recovery amount = I (A/P) - S(A/F)
O&M = operating and maintenance costs of
the proposed project
If B/C  1 => project is acceptable
B/C < 1 => project is unacceptable
Modified B/C Ratio with AW:
B/C =
AW(B) - AW(O&M)
CR
B = benefits of the proposed project
CR = capital recovery amount = I (A/P) - S(A/F)
O&M = operating and maintenance costs of
the proposed project
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 project
I = initial investment in the proposed project
S = salvage value of investment
O&M = operating and maintenance costs of
the proposed project
Modified B/C Ratio with PW &
Salvage Value
B/C = PW(B) - PW(O&M)
I - PW(S)
B = benefits of the proposed project
I = initial investment in the proposed project
S = salvage value of investment
O&M = operating and maintenance costs of
the proposed project
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
Solution
I = land cost + runway construction cost
+ terminal construction cost
= 350,000 + 600,000 + 250,000 = 1,200,000
B = rent + tax + convenience benefit + tourism
= 325,000 + 65,000 + 50,000 + 50,000 = 490,000
O&M = runway O&M + terminal O&M +
controller
= 22,500 + 75,000 + 100,000 = 197,500
B/C with PW
Conventional B/C
B/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 > 1
Modified B/C
B/C = [PW(B) - PW(O&M]/ I
B/C = [490,000 (P/A, 10%, 20) 197,500 (P/A,10%,20)]/ 1,200,000
= 2.075 > 1
B/C with AW
Conventional B/C:
B/C = AW(B)/[CR + AW(O&M)]
B/C = 490,000/[1,200,000 (A/P,10%,20) +
197,500] = 1.448 > 1
Modified B/C:
B/C= [AW(B) - AW(O&M]/CR
B/C = [490,000 - 197,500]/[1,200,000 (A/P,10%,20)]
= 2.075 > 1
Consistency of B/C Methods


The magnitude of B/C value may be
different
The 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.


If PW(B) / [ I + PW(O&M)] > 1 =>
PW(B) > I + PW(O&M) =>
PW(B) - PW(O&M) > I =>
[PW(B) - PW(O&M)] / I > 1
If PW(B) / [ I + PW(O&M)] > 1 =>
PW(B) > I + PW(O&M) =>
PW(B)(A/P) >[ I + PW(O&M)](A/P) =>
AW(B) > I(A/P) + AW(O&M) =>
AW(B) > I(A/P) - S(A/F) + AW(O&M) =>
AW(B) > CR + AW(O&M) =>
AW(B) / [CR + AW(O&M)] > 1
Disbenefit in the B/C ratio


Disbenefits - negative consequences to the public
resulting from the implementation of a publicsector 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 &
Disbenefit
B/C = AW(benefits) - AW(disbenefits)
AW(costs)
= AW(B) - AW(D)
CR + AW(O&M)
B/C =
=
AW(benefits)
AW(costs) + AW(disbenefits)
AW(B)
CR + AW(O&M) + AW(D)
Example
By 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.
Disbenefits Reduce Benefits
.
B/C = [AW(B) - AW(D)] / [CR + AW(O&M)]
B/C = [490,000 - 100,000]/[$1,200,000
(A/P,10%,20) + 197,500]
B/C = 1.152
Disbenefits Treated as Additional Cost
B/C = AW(B)/[CR + AW(O&M) + AW(D)]
B/C = 490,000 / [1,200,000 (A/P,10%,20) +
197,500 + 100,000]
B/C = 1.118
Consistency
Let B = the equivalent annual worth of
project benefits
 C = the equivalent annual worth of project
costs
 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

Example
A 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) - (18,500 - 10,000)]
B/C = 1.275
Treating maintenance costs saving as an Increased Benefit:
B/C = [25,000 + (18,500 - 10,000)]/[300,000(A/P,8%,25)]
B/C = 1.192
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).
Example


The required investments, annual operating and
maintenance costs, and annual benefits for two mutually
exclusive alternative projects are shown below, which
project should be selected?
Capital investment
AnnualO&M cost
Annual benefit
Conventional B/C:
Modified B/C:
Project A
110,000
12,500
37,500
1.475
1.935
Project B
135,000 i = 10%
45,000 N = 20 yrs
80,000
1.315
2.207
Incremental B/C Ratio
Should Be Used
Example
Three 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
8,500,000
B
10,000,000
C
12,000,000
Annual O&M. costs
750,000
Salvage value
1,250,000
Annual benefit
2,150,000
725,000
1,750,000
2,265,000
700,000
2,000,000
2,500,000
Capital investment
PW(Costs, A) = 8,500,000 + 750,000(P/A,10%,50)
- 1,250,000(P/F,10%,50) = 15,925,463
PW(Costs, B) = 10,000,000 + 725,000(P/A,10%,50)
- 1,750,000(P/F,10%,50) = 17,173,333
PW(Costs, C) = 12,000,000 + 700,000(P/A,10%,50)
- 2,000,000(P/F,10%,50) = 18,923,333
PW(Benefit,A) = 2,150,000(P/A,10%,50) = 21,316,851
PW(Benefit, B) = 2,265,000(P/A,10%,50) = 22,457,055
PW(Benefit, C) = 2,750,000(P/A,10%,50) = 24,787,036
B/C(A) = 21,316,851/15,925,463 = 1.3385 > 1.0 .A is Acceptable
B/C(B - A) = (22,457,055 - 21,316,851)/(17,173,333 - 15,925,463)
= 0.9137 < 1.0 . . Project B not Acceptable
B/C(C - A) = (24,787,036 - 21,316,851)/(18,923,333 - 15,925,463)
= 1.1576 > 1.0 . . Project C is Acceptable
Decision: Recommend Project C
Example
Two 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 II
Capital investment
$750,000
Annual O&M costs
120,000
Annual benefit
245,000
Useful life of project (years) 35
$625,000
110,000
230,000
25
AW(Costs, I) = 750,000(A/P,9%,35) + 120,000
= 190,977
AW(Costs, II) = 625,000(A/P,9%,25) + 110,000
= 173,629
B/C(II) = 230,000/ 173,629 = 1.3247 > 1.0 . .
Project II is Acceptable
 B/C(I - II) = (245,000- 230,000)/(190,977 - 173,629)
= 0.8647 < 1.0 . .
Project I not Acceptable
Select 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
Homework
Page 267
Problem # 8, 12, 18