BENEFIT/COST ANALYSIS

Dr.K.AnanthanarayananAssociate professor

Department of Civil Engineering Indian Institute of Technology, Madras

BENEFIT COST ANALYSISCommonly Used method for evaluating the worth of a

proposed projectMethod consists of comparing annual worth of the

benefits of a proposed project, to the annual worth of costs

Present worth or final worth may be used, but annual worth is most commonly used

Example: Proposed estimated benefits = Rs 2,00,000/Yr Cost = Rs 1,00,000/Yr Benefit/cost = 2.0 A common use of the B/C ratio method is to rank various

public works proposals on the basis of their B/C ratio and select the one or ones with the highest B/C ratio

B/C ANALYSIS

The proper ranking of projects requires further examination, and merely ranking in order of numerical B/C ratios may lead to erroneous conclusions

B/C RATIOSCalculate all benefits and costs on an annual basisInitial costs converted to equivalent annual cost by

application of (A/P,i,n) factorSimilarly salvage value, gradient cost and income

converted to annual costs

SIGN CONVENTION

Conventional method – negative B/C ratio To make positive treat all increases in

benefits (such as reduction in user costs) as positive when in numerator , and all increases in costs as positive when in denominator

BENEFIT COST ANALYSIS

COST Rs

BEN

EFIT

S R

s

B/C = 1.0

B/C > 1.0

B/C <1.0

Rejected region

Accepted region

O Proj Z

O Proj x

O Proj y

USER BENEFITS When public facilities are constructed, the user enjoys

some savings in costs (such as travel costs) when the new facility in compared to the old one

Savings may be due to

Less time required to travel certain distance Lower fuel consumption Less wear

Fewer accidents, etc. Net user benefits Up=Total annual cost to the user for the present facility Uf =Total annual cost to the same number of users for the future

facility

Un = Up - Uf

OWNER’S COSTS Two categories

OWNER’S COST

MAINTENANCE COSTSCAPITAL COSTS

Capital costs - construction, acquisition or other capital costs

If replacement - how to handle the present value of the existing facility?

The present value is the cash salvage value that would be received now if the facility were sold or demolished

If the existing facility is maintained in place, this cash value is left invested in the existing facility

CAPITAL COSTS

The cost of the proposed facility is not reduced by the worth of the existing facility since the value of the existing facility is an owner’s asset

Cf = equivalent capital cost of proposed facility, usually expressed on an annualized basis.

Cp = Equivalent capital cost of the existing facility (present salvage value), usually expressed on an annualized basis

Cu = Net capital cost of replacing the present facility

with the future Facility

Cu = Cf - Cp

CAPITAL COSTS

MAINTENANCE COSTS Mf = Equivalent operating and maintenance

costs of the future facility Mp = Equivalent operating and maintenance

cost of the existing facility

Mn = Net operating and maintenance cost of the proposed facility over the present facility. Either positive or negative

Mn = Mf - Mp

SEVERAL METHODS FOR CALCULATING B/C RATIO

Major problem - deciding which items to include in costs and which items to include in benefits

Several variations of methods exist. Two common approaches 1.Conventional B/C method 2. Modified B/C method Both methods involve a comparison of a proposed

facility with an existing facility. If there is no existing facility, use the present cost of

reaching the same objective

CONVENTIONAL B/C METHOD

Benefits are determined for users Bn=Un = Net annual benefits (saving costs) through safety improvements, decreased gasoline consumption decreased tire wear, etc.

Up = User cost of present facility

Uf = User cost of the proposed facility Cn + Mn = costs consist of the annual equivalent costs to the owner of the facility, including capital cost and maintenance

Un = Up- Uf

CONVENTIONAL B/C

Net savings to users

Conventional B/C = Owner’s net Owner’s net capital cost O&M costs

Conventional B/C = ( Un / (Cn + Mn)) = ( Bn / (Cn + Mn))Sign notation: In the denominator any increase in

costs results in a net positive cost

MODIFIED B/C Method This method uses the same input data but net

operating and maintenance costs (Mn) are treated as negative benefits (or disbenefits) rather than as costs. Thus, they are placed in the numerator

Modified B/C = (( Un- Mn)/ Cn ) = (( Bn- Mn)/ Cn ) The modified B/C methods usually yields

more consistent results.

WHAT TO COMPARE

Benefit/ cost studies by their very nature involve a comparison of two or more alternatives.

One of these alternatives should be an existing facility or method or erroneous results may occur.

For example, it is possible to compare an expensive new bridge across a bay with a more expensive new tunnel. The result would be a recommendation for construction of the bridge, simply because the existing route involving a short trip around the end of the bay was not considered

Sometimes there is no existing facility Example: 1.Environmental regulation - sewerage treatment plant 2. New facility required due to increased population growth. User benefits in the B/C ratio are ordinarily supposed represent

the reduction in the user’s cost resulting from construction of the new facility.

Where there is no facility it is difficult to establish a legitimate reduction in cost.

Some people fill this void by with a substitute alternative of their of own selection to replace the missing existing facility

Raises some critical questions

WHAT TO COMPARE…....

FURTHER COMMENTS ON B/C RATIOS Under certain circumstances one or the other B/C

ratios may not be suitable at allSome extremes: 1. Zero savings to users, then Un = 0 Conventional B/C = Un / (Cn + Mn) = 0 Modified B/C = (Un – Mn) / Cn = - Mn / Cn Project should be justifiable, if savings in

maintenance and operating costs more than offset the capital costs. This could be demonstrated with the conventional B/C, but could not be by the modified B/C

FURTHER COMMENTS ON B/C RATIOS If the project results in savings to users (Un is

+), and maintenance & operating costs drop by more than the capital costs rise (Cn + Mn is -), then Conventional B/C = Un / (Cn + Mn) < 0

Modified B/C = (Un – Mn) / Cn > 1 The conventional B/C ratio becomes a –ve

number, where as the modified B/C properly accounts for the benefit of lower maintenance to the owner.

FURTHER COMMENTS ON B/C RATIOS

If there is no change in the capital investment required (Cn = 0)

Conventional B/C = Un / (Cn + Mn) = Un / Mn Modified B/C = (Un – Mn) / Cn = ∞ Conventional method should be used here.