Chapter 11 – Benefit/Cost Analysis of Public Projects.

Chapter 11 – Benefit/Cost Analysis

of Public Projects

Overview• Differences between private sector and public sector

– Public projects affect many groups of people– Decision making is a political process, not a business process (MARR)

• How to use B/C ratios– B is the PW or AW of benefits, C is the PW or AW of costs– B/C>1 is the requirement– The B/C>1 test is for independent projects

• Multiple projects or alternative plans– Do not compare B/C ratios directly. A project with B/C=4 is not necessarily a

better project than one with B/C=2.– To compare projects or plans (mutually exclusive), need to use delta-method

• Defining the B(benefit)/C(cost) ratio– Is a + cash flow an increase in Benefit or a decrease in Cost?– Is a – cash flow an increase in Cost or a decrease in Benefit?– Does it matter? Not for testing B/C>1

• Criticism– Analysis can be very subjective– B/C ratios do not consider “fairness” or distribution of benefits/costs

Private sector vs. Public sector

Private PublicPurpose Make money

Provide goods&services at a profit

Protect and serve

Protect health, lives, property. Provide non-profit services and jobs.

Finance Private investors (voluntary)

Taxation

(not voluntary)

Ownership Private property

Partnerships & Corporations

The “people”

The “government”

Conflict of interests Not usually Common

Project Life Usually 5 – 20 years Long 20-60 yrs

Nature of Benefits Profit

Measured in $

Many benefitsSome benefits hard to measure in $

How is decision made? Business process that compares profit and costs

Political process that compares benefits, costs and distribution

The B/C ratio

B is usually the sum of benefits to anyone.C is usually the sum of costs to the government or sponsor of the project.

B and C need to be in the same units, such as: year 0 dollars (Present Worth) or dollars/year (Annual Worth)

A project should produce more benefits than costs, so that B>C, or dividing by C, B/C>1

Why B/C ratios?

• The B/C ratio is a simple way to explain the effects of a project to government authorities and the public.

• People who support a project usually argue that B/C is greater than 1, and large.

• People who oppose a project usually argue that B/C is less than 1. (In addition, there may be distributional reasons for opposing a project. For example, maybe the rich benefit but the poor pay the costs)

B/C Ratios, Corruption, and Inefficiency

Requiring B/C>1 helps to limit the effects of corruption and inefficiency

• Corruption tends to force Costs above Benefits – government project buys hammers for us$1000 from senator’s

friend (increased C)– government allocates money to clean up parks, but the money

is stolen internally with no benefit (decreased B)

• Inefficiency tends to raise costs (increased C)– Log-rolling in legislature tends to focus on every district

getting something, rather than on B/C analysis.– Public projects often have too many supervisors, when

compared with projects in private businesses– complex procedures (“red tape”) for simple tasks

Example #1

• Buying a new ambulance for a public hospital– Benefits: (value of lives saved, value of increased taxes paid

by those whose live, increase in public safety) AW of Benefits = $4 million/year

– Costs: (ambulance capital recovery, drivers’ salary, medical team salary, overhead) AW of Costs = $3 million/year

– B/C = $4 million/$3 million = 1.3333

the benefits justify the costs

Example #2

• Building a boat harbor for HKUST– Benefits: (recreation, attract more faculty and students,

attract more tourists, increased business for restaurants, boat tours and rental, and hotels)

PW = $200 million

– Costs: (enclose portion of bay, repair after typhoons, additional labor for supervision and security, additional insurance) PW = $500 million

B/C = $200 million/$500 million = 0.4the benefits do not justify the costs

Multiple projects or alternative plans

• If any or all the projects can be chosen, the projects are independent. Choose all the projects with B/C > 1

• If only one project can be chosen, the projects are mutually exclusive. You can not compare B/C ratios directly, but you can use a delta method similar to the delta method used for IRR in Chapter 4.

Example #3 – Independent Projects

Project PW of Benefit

(millions)

PW of Cost

(millions)

B/C ratio Fund?

W 30 10 3.0 Yes

B/C>1

X 35 20 1.75 Yes

B/C>1

Y 65 40 1.625 Yes

B/C>1

Z 50 100 0.5 No

B/C<1

Example #4 – Choose 1 Project(mutually exclusive)

Project PW of Benefit

(millions)

PW of Cost

(millions)

B/C ratio Fund?

W 30 10 3.0 ?

X 35 20 1.75 ?

Y 65 40 1.625 ?

Z 50 100 0.5 No

B/C<1

Delta method

Eliminate all projects with B/C<1.Baseline is initially the project (or plan) with B/C>1 and the lowest cost. Repeat steps 1-3 below until done.Step 1: Compute B/C for each of the projects relative to the baseline.

B = Project Benefit – Baseline BenefitC = Project Cost – Baseline Cost

Step 2: Eliminate all projects where B/C<1Step 3: If B/C>1 for some projects, replace the baseline by the remaining

project with the lowest cost. Go back and repeat step 1 with the new baseline.

If no projects are remaining, or if B/C<1 for all remaining projects, you are done.

When you are done, the baseline you have is the preferred project.

Delta Method (Example #4)Project PW of

Benefit

(millions)

PW of Cost

(millions)

B/C ratio Fund?

W 30 10 3.0 ?

X 35 20 1.75 ?

Y 65 40 1.625 ?

Z 50 100 0.5 No

B/C<1

We eliminate Z, since B/C<1 for Z.

The baseline should have B/C>1 and lowest cost.

Therefore, the baseline will initially be W.

Delta Method Step 1 (Example #4)

Project PW of Benefit

(millions)

PW of Cost

(millions)

B C B/C

W

(baseline)

30 10 --- --- ---

X 35 20 5 10 0.5

Y 65 40 35 30 1.1666

We calculated the B/C relative to W.

Delta Method Step 2(Example #4)

Project PW of Benefit

(millions)

PW of Cost

(millions)

B C B/C

W

(baseline)

30 10 --- --- ---

X 35 20 35-30=5 20-10=10 0.5

Y 65 40 65-30=35 40-10=30 1.1666

We need to eliminate any project with

B/C <1.

In this case, we eliminate X.

The additional cost of 10 million does not justify additional benefits of only 5 million.

Delta Method Step 3(Example #4)

Project PW of Benefit

(millions)

PW of Cost

(millions)

B C B/C

W

(baseline)

30 10 --- --- ---

Y 65 40 35 30 1.1666

B/C >1 for Y

Therefore we replace the baseline with Y.

If there were more projects, we would repeat steps 1-3 with the baseline=Y

Since there are no more projects, we are done. The best choice is Y.

If we move from W to Y, we gain 35 million in added benefits and pay only 30 million in added costs. This is justified. B/C >1

Choice of Y not obvious from simple B/C ratio

The simple B/C ratio does NOT tell you the best project.

You must use a more complex method, such as the delta method, to compare projects.

Project PW of Benefit

(millions)

PW of Cost

(millions)

B/C ratio Fund?

W 30 10 3.0

X 35 20 1.75

Y 65 40 1.625 Yes, from Delta Analysis

Z 50 100 0.5 No

B/C<1

Alternative definitions of B/C ratio

B- BenefitsI – Initial InvestmentO&M – Operating and Maintenance Costs----------------------------------Conventional B/C Ratio with PW:

B/C=PW(B)/(I+PW(O&M))Modified B/C Ratio with PW:

B/C=(PW(B)-PW(O&M))/I

What’s the difference?

Conventional B/C Ratio with PW:

B/C=PW(B)/(I+PW(O&M))

Modified B/C Ratio with PW:

B/C=(PW(B)-PW(O&M))/I

Yearly O&M costs are treated as part of the C term

Yearly O&M costs are treated as a reduction of the benefits

Next: Does it matter?

Does it matter?Project PW(B) Initial Investment I PW(O&M) Conventional B/C Modified B/C Fund?A 40 10 25 1.14 1.50 YesB 40 25 10 1.14 1.20 YesC 30 20 25 0.67 0.25 NoD 30 25 20 0.67 0.40 No

The conventional and modified formulas will produce different numbers.

However, when conventional B/C is greater than 1, so is Modified B/C. When modified B/C is greater than 1, so is conventional B/C.

The numbers change. The funding decisions do not.

Classifying benefits and costsDoes it matter which side an item is

on?

Suppose X is a negative cash flow

We only want projects where B>C+X

We could compare B/(C+X) to 1.0

If B/(C+X)>1.0, then B>C+X

Classifying benefits and costsDoes it matter which side an item is

on?Suppose X is a negative cash flow

We only want projects where B>C+X

We could compare B/(C+X) to 1.0

If B/(C+X)>1.0, then B>C+X

But this is equivalent to

saying we want B-X>C

We could compare (B-X)/C to 1.0

If (B-X)/C>1.0, then B-X>C

B/(C+X) and (B-X)/C are different numbers, but we can compare either of these numbers to 1.0 to make our decision.

Harmful effects of public projectsAre these costs or negative benefits?• Building a dam will ruin a recreational white-water

river and flood useful land• Making a road wider will increase pollution and noise

in the neighborhood• A new park may attract beggars and vagrantsAs long as they are included in the analysis, it does not

matter if these are considered costs (+C) or deductions from benefits (-B).

The standard is that these are deductions from benefits, or disbenefits. Costs are usually only costs to the government or builder of the project.

Criticisms of B/C Method

• Answers of studies seem to be strongly linked to the study sponsor

• Easy to manipulate• Decision makers and public, may care about the

results but not about the analyses or the process.• B/C ratios do not say who pays and who

benefits.makes rational debate difficult

The Political Process

Because a project may have supporters and opponents, various tricks can be used to affect the B/C analysis. These include

• Unrealistic assumptions (100 year life, etc)• Different methods of valuing controversial items that

are hard to measure• Omitting harmful effects• Manipulating MARR to stress short-term costs or long-

term benefits

Which MARR?Some alternatives MARRs:

• The interest rate paid by the government when they borrow the money to finance the project (ranges from 3% for the US federal government to 8% for bond issues by small towns)

• The opportunity cost of capital to the government agency (varies)

• The opportunity cost of capital to the taxpayer (estimated at 7%/year = 10% investment-3% taxes for the US by USA Office of Management and Budget)

• The risk-free market rate (hovers around 3%)

Distribution of benefits and costsDestroying a squatter village to construct new luxury high rise and

transport station== Benefits accrue to the rich with costs to the poor------------------------------------------------------------------Power plants; waste disposal== Benefits accrue to a general population with disbenefit to a

smaller community near the facility who must endure pollution--------------------------------------------------------------------Raising taxes to support welfare programs for unmarried mothers,

drug addicts, or poor immigrants== Benefits accrue to unpopular segments of the poor, with the

costs paid by productive members of society.

Summary

• B/C analysis provides, at best, a way to avoid bad projects.

• To compare projects, you can not use B/C ratios directly. You must use a delta method.

• B/C analysis of public projects can be controversial. Some of the numbers involve substantial guesswork.

• B/C analysis does not measure the distribution of benefits and costs, which can be an important political factor.