Class 4 Benefit Cost Analysis Reference source for the slides: .

Class 4

Benefit Cost Analysis

Reference source for the slides: http://www.agecon.purdue.edu/staff/shively/courses/AGEC406/index.htm

Benefit-Cost Analysis

First of two related lectures:

1. Overview of benefit-cost analysis

2. Specific benefit-cost tools

Static efficiency is defined as maximization of net benefits for a single time period.

Many economic decisions that occur over time are a series of static decisions.

Example: Shopping for Food Choose groceries each week, consume them,

then start over again next week.

Static vs. dynamic efficiency

A dynamic decision is one in which current decisions have impacts on net benefits

arising in the future.

Many economic decisions with environmental implications are dynamic.

Example: Forestry If you choose to harvest trees this year,

harvesting next year is no longer an option.

Static vs. dynamic efficiency

Benefit-Cost Analysis What is benefit-cost analysis?

BCA is an economic technique used to:

1.Evaluate a project or investment over time

2. Compare the merits of a set of projects

BCA is conducted by comparing economic benefits of an activity with economic costs of an activity.

Key Point

As a tool for economic analysis, BCA seeks to examine potential actions with the objective of increasing well being...

…seeking an activity or use that provides greater benefit than cost, or the greatest benefit among competing uses.

Key Point

Decisions are typically not made on the basis of BCA alone…

but BCA can be useful for providing information on economic features of projects or activities, and can therefore be useful for informing the debate.

Dam construction

Costs:

Materials = $500,000

Labor = $600,000

Total Cost = $1,100,000

BCA in a timeless world

Dam construction

Benefits:

Recreation = $400,000

Flood control = $300,000

Electricity = $500,000

Total Benefit =$1,200,000

BCA in a timeless world

Dam construction

Total Benefit =$1,200,000

Total Cost = 1,100,000

Net Benefit = 100,000

Benefit exceeds cost, so dam appears to be a good investment

BCA in a timeless world

BCA as “Approach”

To know whether society should build the dam, other information may be needed:

1. Are there non-economic impacts?

2. What is the opportunity cost of the dam?

Time and Discounting

Often the benefits and costs of a project accrue at different times. The technique used to deal with this issue is discounting.

Discounting

Discounting is a technique used to convert all benefits and costs to a common point in time, usually the present.

The value of a project, expressed in terms of the present, is called the Present Value.

Discounting

Discounting is based on the premise that a dollar of benefit received today is worth more than a dollar of benefit received in the future.

The bias arises because current resources can be invested.

Discounting is the opposite of compounding.

Discounting

The rate at which a current value is compounded is called the interest rate.

The rate at which a future value is discounted is called the discount rate.

Computing a present value

PV = Pt / (1 + r)t

PV = present value

Pt = value at time t

r = interest (discount) rate

t = year in which Pt is realized

Dam revisited

Total Benefits accrue when dam is finished (t = 1)

Total Costs accrue at start of construction (t = 0)

Discount rate = 10% Should the dam be built?

BCA with discounting

Total Benefits accrue when dam is finished (t = 1), soPt = $1,200,000 and PV of benefit is:

$1,200,000 / (1+0.10)1 = $1,090,909

Total Costs accrue at start of construction (t = 0), so Pt = $1,100,000 and PV of benefit is:

$1,100,000 / (1+0.10)0 = $1,100,000

PV(B) < PV(C) The dam shouldn’t be built.

Dam construction revisited

Total Benefits accrue in the future (i.e. when dam is finished). The process of discounting reduces the value of those benefits because they occur in the future.

Because the merit of a project can hinge on the choice of discount rate, it can be a source of debate.

There is no simple rule for choosing a discount rate. Often a “well known” interest rate is used.

Why the reversal?

Whenever benefits and costs accrue at different points in time, amounts should be converted to present values for comparison.

BCA is a decision-support tool, not a decision-making tool.

Discounting can be used regardless of the length of time under consideration, but discounting has implications for equity.

Key Points

Three BCA tools:

1. Net Present Value (NPV)

2. Benefit-Cost Ratio (BCR)

3. Net Present Value (NPV)

Net Present Value (NPV)

The net present value of benefits is the present value of those net benefits.

Net benefit is simply the sum of benefits minus the sum of costs.

NPV is the current value of all net benefits associated with a project

The net benefits are converted to present value by discounting.

NPV Formula

Tt

tt

tt

r

CostBenefitNPV

1 1

Key Point

If the project has a NPV > 0, then it is worth considering on its economic merits.

If the project has a NPV < 0, then it fails to return benefits greater than the value of the resources used.

NPV Example

Time Benefit Cost Net Benefit

0 100 150 -50

1 100 100 0

2 100 50 50

all 300 300 0

-50/(1+.1)0 + 0/(1+.1)1 + 50/(1+.1)2 = -8.68

Benefit Cost Ratio (BCR)

BCR is computed as the PV of Benefits divided by the present value of Costs.

Discounted benefits and discounted costs are calculated and summed separately, then divided.

BCR Formula

Tt

tt

t

Tt

tt

t

r

Costr

Benefit

BCR

1

1

1

1

Key Point

If the project has a BCR > 1, then it is worth considering on its economic merits.

If the project has a BCR < 1, then it fails to return benefits larger than its costs.

BCR Example

Num. = 100/(1.1)0 + 100/(1.1)1 +100/(1.1)2 = 273.54

Den. = 150/(1.1)0 + 100/(1.1)1 +50/(1.1)2 = 282.22

BCR = 273.54/282.22 = 0.97 < 1

Internal Rate of Return (IRR)

The IRR is the maximum interest rate that could be paid for the project resources that would leave enough money to cover investment costs and still allow society to break even.

The IRR is the discount rate at which the PVof benefits equals the present value of costs.

IRR Formula

Solve for the IRR by finding i that solves:

PV(Benefits) = PV(Costs)

Use algebra or a spreadsheet

Key Point

The IRR must exceed the chosen discount rate for the project to be accepted.

IRR Example

100/(1 + i)0 + 100/(1 + i)1 +100/(1 + i)2 =

150/(1 + i)0 + 100/(1 + i)1 +50/(1 + i)2

i = 0

Advantages of BCA

1. Provides a framework

2. BCA is quantitative

3. BCA is based on facts

4. The methods provide clarity

5. Results allow comparability

Disadvantages of BCA

1. Requires valuation

2. Discount rate sensitivity

3. Plagued by uncertainty

4. Silent on equity

5. BCA is anthropocentric