2. Table of Contents
• PUBLIC PROJECTS
• DIFFICTLTIES IN EVALUATING
• INTRODUCTION TO B-C RATIO METHOD
• MUTUALLY EXCLUSIVE PROJECTS
• COMPARISION OF MUTUALLY EXCLUSIVE PROJECTS BY B-C RATIO METHOD
3. PUBLIC PROJECTS
• Authorized, Financed and Operated by government agencies.
• Much larger than private ventures and need huge capital.
• Relatively long project life (20-60 years).
• Mainly service oriented.
• Significant effect of politics.
4. SELF LIQUIDATING PROJECTS
• Public projects expected to earn direct revenue and repay its cost.
• Not expected to make a profit or pay taxes.
• Examples are toll bridges, highways, irrigation water, fresh water,
electric power, etc.
5. MULTIPLE-PURPOSE PROJECTS
• Most of the public projects are multi-purposed.
• Multiple-purpose projects like a dam to create a reservoir in a river may
have the following objectives:
i. Assist flood control.
ii. Provide drinking water.
iii. Generate electric power.
iv. Provide water for irrigation.
6. DIFFICULTIES IN EVALUATING
• Difficult in cost division due to multiple purposes.
• Monetary impacts due to the project are difficult to quantify.
• No profit standard to measure financial effectiveness.
• Very less connection between the project and its real owner.
• Huge political influence.
7. INTRODUCTION TO B-C RATIO
• It is the ratio of equivalent worth of benefits to the costs generally
used to choose alternatives.
• This method is majorly used in public project.
• Time value of money must be consider to account for timing of cash
• B-C ratio is also called as the savings- investment ratio(SIR).
There are two ways to calculate B-C:
1. Conventional B-C ratio with
2. Modified B-C ratio with PW(&AW);
9. 1. Conventional B-C ratio with PW:
B-C= PW(benefits of the proposed project)
PW(total costs of the proposed project)
PW(.)= present worth of (.);
B=benefits of the proposed project;
I=initial investment in the proposed project;
MV=market value at the end of useful life;
O&M=operating and maintenance costs of the proposed
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 454 CHAPTER 10 /
EVALUATING PROJECTS WITH THE BENEFIT–COST RATIO
METHOD will require the addition of two air traffic controllers at an
annual cost of $100,000.
14. 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 Columbia $50,000
Additional tourism dollars for Columbia 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
17. MUTUALLY EXCLUSIVE PROJECTS
● Mutually Exclusive refers to the events which cannot happen at the same
particular time. Ex: either head or tail when tossing a coin.
● Mutually Exclusive Projects is defined as a group of projects from which
at most, one project may be selected.
● A project is selected on the basis of certain parameter that includes
operation and management cost, profit from the application of project,
● Acceptance of one project results in rejection of all the other projects.
18. COMPARISION OF MUTUALLY EXCLUSIVE
PROJECTS BY B-C RATIO METHOD
● Mutually Exclusive Project are compared by Benefit-Cost Ratio i.e, B-C
ratio as it provides a ratio of benefits to costs rather than just the profit
● For the selection of the project by B-C ratio, the alternative with the B-C
ratio greater or equal to 1 is accepted while the other alternative with B-C
ratio less than 1 is rejected .
● Best alternative can be selected using an equivalent.worth method by
maximizing the PW or Aw or FW.
● The evaluation of the mutually exclusive project by B-C ratio is
conducted improperly by equivalent worth method which includes
convenient and modified B-C (as mentioned earlier).
● Therefore a comparison of mutually exclusive alternatives require an
incremental analysis to be conducted.
20. INCREMENTAL B-C ANALYSIS OF MUTUALLY
Process for the calculation of mutually exclusive project by incremental
analysis is as follows:
● When comparing mutually exclusive alternatives with B-C ratio method,
they are first ranked in order of increasing total equivalent worth of costs.
● This rank ordering will be identical whether the ranking is based on PW,
AW or FW of costs.
● Projects are ranked from smallest to largest according to costs obtained.
● The project with smallest cost is calculated for alternative.
● The b-c ratio of that particular project is calculated and if it is greater or equal to
1, it is regarded as the baseline alternative, otherwise we carry the process by
calculating b-c ratio of the following project.
● Then the following larger project is selected, the difference in the respective
benefits and costs of this project and baseline is used to calculate incremental b-
● If this project has b-c ratio greater or equal to 1 then this is set as new baseline
alternative , otherwise the last baseline is maintained.
● Similarly the process of calculating b-c ratio with incremental analysis is
followed until the last project is compared.
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? Solve by hand and by spreadsheet.
A B C
Capital investment $8,500,000 $10,000,000 $12,000,000
Annual operating and 750,000 725,000 700,000
Market value 1,250,000 1,750,000 2,000,000
Annual benefit 2,150,000 2,265,000 2,500,000
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) = $2,500,000(P/A, 10%, 50) = $24,787,036.
B–C(A) = $21,316,851/$15,925,463
= 1.3385 > 1.0.
Therefore, Project A is acceptable.
ΔB/ΔC 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.
ΔB/Δ 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
24. B-C ANALYSIS WITH UNEQUAL PROJECTS LIVES
● In mutually exclusive projects there are some project that have different
● The projects with varying useful lives is also possible to conduct an
incremental B-C analysis by using the AW of benefits and costs of the
● Process includes calculating AW for each project. The following process
is same as for the mutually exclusive project with same lives.
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.
Project I Project II
Capital investment $750,000 $625,000
Annual operating and maintenance 120,000 110,000
Annual benefit 245,000 230,000
Useful life of project (years) 35 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.
Therefore, Project II is acceptable.
ΔB/ΔC of (I–II) = ($245,000 − $230,000)/($190,977 − $173,629)
= 0.8647 < 1.0.
Therefore, increment required for Project I is not acceptable hence Project II should be selected.