Cost Benefit Analysis

Gopalakrishnan K 028Manish Murthy 139

PGDM-Operations

Introduction CBA estimates and totals up the equivalent money value of the benefits and costs to the community of projects to establish whether they are worthwhile

Federal Navigation Act of 1936

U.S. Corps of Engineers carry out projects for the improvement of the waterway system

Consistent set of methods for measuring benefitsand costs and deciding whether a project is worthwhile

Principles of CBA Computation of components of costs and benefits sometimes intuitive and sometimes not So, common unit of measurement – most convenient unit is money

All benefits and costs of a project should be measured in terms of their equivalent money value

Benefits that are not directly expressed in terms of dollars but some money the recipients of the benefits would consider

E.g. Free monthly visit to a doctor

Principles of CBA Benefits and costs of a project have to be expressed in terms of dollars of a particular time

Net benefit of the projects is just the sum of the present value of the benefits less the present value of the costs

Discounted present value of that benefit of theproject

CBA Valuations Should Represent Consumers or Producers Valuations As Revealed by Their Actual Behaviour

Should reflect preferences revealed by choices which have been made

E.g. Improvements in transporation

Choices involving tradeoffs between time and money

Challenging part of CBA is finding past choices which reveal the tradeoffs and equivalencies in preferences

CBA Valuations Should Represent Consumers or Producers Valuations As Revealed by Their Actual Behaviour

Should reflect preferences revealed by choices which have been made

E.g. Improvements in transporation

Choices involving tradeoffs between time and money

Challenging part of CBA is finding past choices which reveal the tradeoffs and equivalencies in preferences

Market Choices Consumers buy things which are at least as beneficial as the money they relinquish

For any consumer buying some of a commodity, the marginal benefit is equal to the market price

Relationship between the market price and the quantity consumed is called the demand schedule

Gross Benefits of an Increase in Consumption is an Area Under the Demand Curve

Market Choices

When the increase in consumption is small compared to the total consumption the gross benefit is adequately approximated, as is shown in a welfare analysis

CBA Some Measurements of Benefits Require the Valuation of Human Life

Choices can be used to estimate the personal cost people place on increased risk and thus the value to them of reduced risk

The impact of a project is the difference between what the situation in the study area would be with and without the project

An alternative to the project must be explicitly specified and considered in the evaluation of the project

CBA The impacts of a project are defined for a particular study area, be it a city, region, state, nation or the world

Sometimes an impact of a project can be measured in two or more ways. E.g. : highway

Decision Criteria for Projects

Ratio of benefits to costs greater than 1(PV)

Highest net PV value (mutually exclusive projects)

Discount rate – based on trial and error – net PV = funds available

Benefit-Cost ratio – arbitrary – operating costs net out from benifits

Example – Highway Project

Four-lane highway 101 and the traffic to San Jose – no median divider – inordinate number of heads-on collision – Blood Alley

Highway extension to San Jose is proposed as a new project

Time Saving & Lowers risk

Increased traffic

AnalysisNo Extension, 101 Extension

"Blood Alley" Only and "Blood Alley"Rush Hours   Passenger Trips   (per hour)   Trip Time   (minutes)   Value of Time   ($/minute)Nonrush Hours   Passenger Trips   (per hour)   Trip Time   (minutes)   Value of Time   ($/minute)Traffic Fatalities   (per year)

12 6

500 555.55

35 25

$0.08 $0.08

TRIP DATA

3,000 4,000

50 30

$0.10 $0.10

Monetary Benefits Hourly Benefit

Yearly Benefit – 260 weekdays @ 6 rush hours/weekday – 1560 Rush & 7200 nonrush

Trips Which Would Trips GeneratedBe Taken Anyway By the Project

Rush Hour 6,000.00 1,000.00 7,000.00Nonrush Hour 400 22.22 422.22

TYPE Total

Trips Which Trips GeneratedWould Be By the Project

Taken AnywayRush Hour $9,360,000 $1,560,000 $10,020,000Nonrush Hour $2,880,000 $160,000 $3,040,000Total $12,240,000 $1,720,000 $13,960,000

TYPE Total

Total Value BenefitsRisk Saving

Accept $400 increase for every increase in 1/1000th increase in risk of death

Implicit valuation of life is $400,000

Total Value of Benefits

Assumed to be constant over 30 years

VALUE OF BENEFITSPER YEAR

Time Saving $13,960,000Reduced Risk $2,400,000Total Saving $16,360,000

TYPE OF BENEFIT

CostsCost of Construction - $200m for 4 yearsMaintenance - $1m/year after constructionRight-of-way - $100mAssumed to recover right-of-way cost at

end of 30 yearsTIME BENEFITS RIGHT-OF CONSTRUCTION MAINTENANCE(year) ($millions) -WAY COSTS ($millions)

($millions) ($millions)0 0 100 0 0

1-4 0 0 50 05-29 16.36 0 0 130 16.36 -100 0 1

Net Present Value Interest Rate on long term bonds is 8%

Rate of Inflation is 6%

Real rate of interest is 2%

All benefits & costs discounted at 2% to time zero

Formula

Net Present ValuePRESENT VALUE

($ millions)Benefits 304.11

CostsRight-of-Way 44.79Construction 190.39Maintenance 18.59Total Costs 253.77

Net Benefits 50.35

Key TakeawaysBenefit/Cost ratio at 2% discount

– 1.2

At 3% discount, <~1

Right-of-way may have increasing value with time – discounted PV for alternate use may be more like $150m instead of $100m

Summary Monetary representation of postive and negative

impacts helps determining worthiness of the project

Valuation based on consumer and product market choices

Care to include all impacts including inflation

Worthwhile project is one whoseDiscounted value of benefits exceeds discounted value

of costsBenefit/cost ratio greater than oneInternal rate of return greater than cost of capital