HUM 2115: Engineering Economy

Benefit-Cost Ratio

Rafat Rahman
Lecturer, Industrial & Production Engineering
Ahsanullah University of Science and Technology

1
Introduction
▪ A public sector project is a product, service, or system authorized, financed, and operated by the federal,

state, or local governmental agencies.

▪ Some examples are:

Highways Universities Prisons

Hospitals Sports arenas Public housing
Emergency relief Utilities Transportation

▪ Public projects provide service to citizenry at no profit.

▪ Such public works are numerous, and although they may be of any size, they are frequently much larger

than private ventures.

▪ Since they require the expenditure of capital, such projects are subject to the principles of engineering

economy with respect to their design, acquisition, and operation. 2

Introduction
▪ The benefit/cost ratio is relied upon as a fundamental analysis method for public sector projects.
▪ The B/C analysis was developed to introduce greater objectivity into public sector economics, and
as one response to the U.S. Congress approving the Flood Control Act of 1936.
▪ The benefit-cost analysis can be used to choose among alternatives in allocating funds for such
projects as the construction of a mass-transit system, building an irrigation dam, highway
maintenance, or implementing an air-traffic control system.
▪ If the projects are on the same scale with respect to cost, it is merely a question of choosing the
project where the benefits exceed the costs by the greatest amount.
▪ As in the case for the internal rate of return criterion, when comparing mutually exclusive
alternatives, an incremental benefit-cost ratio must be used.

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Perspective and Terminology for Analyzing Public Projects
▪ For any project, the proper perspective is to consider the net benefits to the owners of the
enterprise.
▪ For government projects, the true owners are ultimately the taxpayers.
▪ Benefits (B) are favorable consequences of the project to the public (owners). Advantages to
the public (time savings, improved reliability, enhanced safety, environmental protection,
leisure opportunities, increased business revenue, etc.)
▪ Costs (C) represent monetary disbursements required of the government.
▪ Disbenefits (D) represent negative consequences of a project to the public (owners).
Disadvantages to the public (delay, environmental damage, reduction in quality of life, etc.)

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Applying the benefit-cost ratio method
▪ The B/C ratio method involves the calculation of a ratio of benefits to costs.
▪ Whether evaluating a project in the private sector or in the public sector, the time value of
money must be considered to account for the timing of cash flows (or benefits) occurring
after the inception of the project.
▪ The consideration of the time value of money means this is really a ratio of discounted
benefits to discounted costs.
▪ B/C ratio is the ratio of the equivalent worth of benefits to the equivalent worth of costs
(PW, FW or AW).
▪ A project is acceptable when the B/C ratio is greater than or equal to 1.0

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Benefit-Cost Ratio Method
1. Benefit/Cost Ratio Method for Single Project
2. Comparison of Mutually Exclusive Projects by incremental B/C Ratios

• General formula

𝐁𝐞𝐧𝐞𝐟𝐢𝐭𝐬 −𝐃𝐢𝐬𝐛𝐞𝐧𝐞𝐟𝐢𝐭𝐬 𝐁−𝐃 B−D *Initial cost (Ci)

1. Conventional B/C = = = Ci + CO&M
𝐂𝐨𝐬𝐭 𝐂 *Annual M&O costs (CM&O)
C= Ci + CM&O
𝐁𝐞𝐧𝐞𝐟𝐢𝐭𝐬 −𝐃𝐢𝐬𝐛𝐞𝐧𝐞𝐟𝐢𝐭𝐬 −𝐌𝐚𝐢𝐧𝐭𝐞𝐧𝐚𝐧𝐜𝐞 & 𝐎𝐩𝐞𝐫𝐚𝐭𝐢𝐧𝐠 𝐂𝐨𝐬𝐭
2. Modified B/C = 𝐈𝐧𝐢𝐭𝐢𝐚𝐥
𝐂𝐨𝐬𝐭
𝐁−𝐃−𝐎&𝐌
=
Ci
▪ If B/C ≥ 1.0, accept the project
▪ If B/C < 1.0, project is not economically acceptable

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B/C ratios for Present Worth
▪ Formulas of the B–C ratio using the Present Worth (PW)-

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B/C ratios for Annual Worth
▪ Formulas of the B–C ratio using the Annual Worth (AW)-

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B/C ratios for Annual Worth
▪ Disbenefits (D) can be included in the B-C ratio in either the numerator or denominator, as shown
with AW below-

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B/C ratios Example
❑ The Wartol Foundation, a nonprofit educational research organization, is contemplating an investment of

$1.5 million in grants to develop new ways to teach people the rudiments of a profession. The grants
would extend over a 10-year period and would create an estimated savings of $500,000 per year in
professor salaries, student tuition, and other expenses. In this case the program would be an addition to
ongoing and planned activities. An estimated $200,000 a year would thus have to be released from other
programs to support the educational research. To make this program successful, a $50,000 per year
operating expense will be incurred by the foundation from its regular O&M budget. The foundation uses
a rate of return of 6% per year on all grant investments. Use benefit cost analysis to evaluate the project
and decide if this project is acceptable.

1. Conventional B/C

2. Modified B/C
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B/C ratios Example
Solution:
Here, 1.Conventional B/C =
𝑩−𝑫
=
500,000 −200,000
𝑪 203,801.94+50,000
Benefits, B = $500,000 per year
= 1.182
Disbenefits, D = $ 200,000 per year
▪ The project is acceptable because B/C > 1.0
Operating expenses = $50,000 per year
Rate of return i = 6% per year
𝑩−𝑫−𝑶&𝑴 500,000 −200,000 −50,000
2.Modified B/C = =
Time Period, n = 10 𝑪𝒊 203,801.94

Initial investment Ci = $1500000 (A/P,6%,10) = 1.226

=1,500,000 (0.13587) ▪ The project is acceptable because B/C > 1.0
=$203,801.94 per year

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B/C ratios Example
❑ The city of Columbia 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 a farmland that 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:

Apply the B/C ratio method with a study period of 20 years and a MARR of 10% per year to determine
whether the runways at Columbia Municipal Airport should be extended. 12
B/C ratios for Annual Worth

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B/C ratios Method

Added benefits vs. reduced cost

▪ As with the different types of ratios, the
question arises if classifying certain
cash flows as either added benefits or
reduced costs.
▪ While the numerical value of the ratio
may change, there is no impact on
project acceptability regardless of how
the cash flows are handled.

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B/C ratios Example
❑ A project is being considered by the Tennessee Department of Transportation to replace an
aging bridge across the Cumberland River on a state highway. The existing two-lane bridge is
expensive to maintain and creates a traffic bottleneck because the state highway is four
lanes wide on either side of the 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 B/C analysis, using a MARR of 8% and a study period of 25 years, to determine
whether the new bridge should be constructed.

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B/C ratios Example

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Incremental B/C ratios Method
The procedures for incremental B/C analysis of multiple alternatives are as follows:
1. Determine the equivalent total cost for all alternatives. Use AW, PW, or FW equivalencies.
2. Determine the equivalent total benefits (and any disbenefits estimated) for each alternative.
3. Order the alternatives by equivalent total cost, smallest first.
4. Calculate the B/C for the first ordered alternative. If B/C <1.0, eliminate it.
5. By comparing each alternative to ‘do-nothing’ in order, we eliminate all that have B/C < 1.0.
The lowest-cost alternative with B/C ≥ 1.0 becomes the defender and the next higher-cost
alternative is the challenger in the next step.

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Incremental B/C ratios Method
6. Calculate incremental costs (C) and benefits (B) using the relations-

7. Calculate the ∆B/∆C for the first challenger compared to the defender. If ∆B/∆C ≥ 1.0, the
challenger becomes the defender, and the previous defender is eliminated. Conversely, if
B/C ≤1.0, remove the challenger and the defender remains against the next challenger.
8. Repeat steps 6 and 7 until only one alternative remains. It is the selected one. In all the steps
above, incremental disbenefits may be considered by replacing ∆B with ∆(B-D).

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Incremental B/C ratios Example
❑ Three mutually exclusive alternative public-works projects are currently under consideration.
Their respective costs and benefits are included in the table that follows. Each of the
projects has a useful life of 50 years, and MARR is 10% per year.
Which, if any, of these projects should be selected?

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Incremental B/C ratios Example
Solution:
Project A: PW(Costs) = $8,500,000 + $750,000(P/A, 10%, 50) −$1,250,000(P/F, 10%, 50)
= $15,925,463
PW(Benefit) = $2,150,000(P/A, 10%, 50) = $21,316,851
Project B: PW(Costs) = $10,000,000 + $725,000(P/A, 10%, 50) −$1,750,000(P/F, 10%, 50)
= $17,173,333
PW(Benefit) = $2,265,000(P/A, 10%, 50) = $22,457,055
Project C: PW(Costs) = $12,000,000 + $700,000(P/A, 10%, 50) −$2,000,000(P/F, 10%, 50)
= $18,923,333
PW(Benefit, C) = $2,500,000(P/A, 10%, 50) = $24,787,036
Now, B/C(A) = $21,316,851/$15,925,463 = 1.3385 > 1.0
B/C(B) = $ 22,457,055/$17,173,333 = 1.3077 > 1.0 All the projects are acceptable!
B/C(C) = $ 24,787,036/$18,923,333 = 1.3099 > 1.0 20
Incremental B/C ratios Example
Therefore, the ranking in order of increasing total equivalent worth of costs are thus-
Project A < Project B < Project C

Now, comparing Project A and Project B to calculate incremental B/C ratio-

∆B/∆C of (B - A) = ($22,457,055 − $21,316,851)/($17,173,333 − $15,925,463)
= 0.9137 < 1.0
Therefore, increment required for Project B is not acceptable.
Comparing Project A and Project C-
∆B/∆C of (C - A) = ($24,787,036 − $21,316,851)/($18,923,333 − $15,925,463)
= 1.1576 > 1.0
Therefore, increment required for Project C is acceptable.
Decision: Recommend Project C
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Incremental B/C ratios Example
❑ Two mutually exclusive alternative public-works projects are under consideration. Their
respective costs and benefits are included in the table that follows. 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 MARR is 9% per year, which, if either, of these projects should be selected? The effect
of inflation is negligible.

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Incremental B/C ratios Example
Solution:
Project I: AW(Costs) = $750,000(A/P, 9%, 35) + $120,000 = $190,977
Project II: AW(Costs) = $625,000(A/P, 9%, 25) + $110,000 = $173,629
B/C (I) = $245,000/$ 190,977 = 1.2823 > 1.0
B/C (II) = $230,000/$173,629 = 1.3247 > 1.0
Both the projects are acceptable
Therefore, the ranking in order of increasing total equivalent worth of costs are thus-
Project II < Project I
Now, comparing Project II and Project I to calculate incremental B/C ratio-
∆B/∆C of (I–II) = ($245,000 − $230,000)/($190,977 − $173,629) = 0.8647 < 1.0
Therefore, increment required for Project I is not acceptable.
Decision: Project II should be selected. 23
Incremental B/C ratios Example
❑ A government is planning a hydroelectric project for a river basin. In addition to the production of
electric power, this project will provide flood control, irrigation and recreation benefits. The estimated
benefits and costs that are expected from the three alternatives under consideration are given in the
following table.

If the interest rate is 10% and the life of projects is estimated to be 40 years, by comparing the BC
ratios, determine which project should be selected.
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B-C ratios Example

25
B-C ratios Example

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