Cost Benefit Analysis and

Discounting

Cost Benefit Analysis: What is it?

Good overviews of CBA: Paul Portney*; Matthew Kotchen**.

Portney: “it is an attempt to identify and express in dollar terms all of the effects of proposed government policies or projects”

It is a useful tool to assess the social welfare impacts of a project or policy.

Many economists favor using it when assessing a project – though it still raises concerns in many quarters and can be difficult to get right.

•See: Paul R. Portney, "Benefit-Cost Analysis." The Concise Encyclopedia of Economics. 2008. Library of Economics and Liberty. 4 September 2013. <http://www.econlib.org/library/Enc/BenefitCostAnalysis.html>.** Kotchen, Matthew J., “Cost Benefit Analysis”, Encyclopedia of Climate and Weather 2nd Edition, Stephen Schneider(ed.), New York: Oxford University Press, 2010. <http://environment.yale.edu/kotchen/pubs/CBAchap.pdf>.

Cost Benefit Analysis: How do we do it?

Add up costs and add up benefits; if net benefits are positive do the project!

Simple, right?

Not quite! Issue of measurement of costs and benefits.

Often times, costs simpler – tend to be one-off and are market transactions e.g. one time cost of constructing a dam

Benefits can be trickier e.g. what is the value of cleaner air after an emissions standard policy is implemented?

Cost Benefit Analysis: How do we do it?

Methodological points:

Need to turn to non-market valuation techniques (travel cost method, contingent valuation).

Need to be cognizant of timing of costs and benefits – costs and benefits can be out in the future.

Cost Benefit Analysis: Debatable Issues

1. Discount rate – the value of future events

2. Distribution of income – wealth may affect willingness to pay for a benefit

3. Compensation (Kaldor-Hicks criterion) – always winners and losers but will losers be compensated?

Discounting: What is it?

Many times we want to assess value of events in the future e.g. costs and benefits that occur in the future.

Projects span time – activities occur over many months/years.

How do we think about activities that have value but occur at times other than the present?

Idea: reduce all future values to a common present value.

Discounting: What is it?

We need to convert future values into a present value.

To do this we discount the future back to the present.

Why? Because: money today is worth more than money tomorrow.

The discount rate is a product of society’s time value of money (composed of the pure rate of time preference and the goods discount rate).

Discounting: How do we do it?

Use this formula to convert all future values to present values:

PV = FVt/(1 + r)t

Where PV is present value, FV is future value, r is the discount rate and t is time.

Discounting: How do we do it?

Let’s use that formula.

What is the value of a $100 tomorrow (one period in the future)?

Assume discount rate, r, is set to 0.05

Then,

PV = FVt/(1 + r)t

PV = 100/(1 + 0.05)1

PV = $95.2381

Discounting: How do we do it?

By the way: opposite of discounting is compounding

If we have a present value and wish to see what the future value is, we use compounding

FVt = PV(1 + r)t

Discounting: The Debate!

Choice of discount rate is at the heart of CBA controversies

It is a key issue as it determines whether a project is beneficial or not, whether a project should be implemented or not

Two major schools of thought:

Descriptive: We observe the rate of return in the market (e.g. Nordhaus)

Prescriptive: We derive the discount rate based on philosophical/ethical basis (e.g. Stern)

Discounting: The Debate!

Regardless of how it is derived, the important thing is how high it is set.

High discount rate = we don’t value the future as much as the present

Low discount rate = we value the future almost as much as the present

Case Study: Irrigation as an Adaptation to Climate Change

Climate change affects temperature and precipitation among other climate phenomena

Changes in the hydrological cycle will be some of the most obvious changes that will affect agriculture

Irrigation systems are a way to adapt to changes in the hydrologic cycle (especially changes in the quantity and timing of precipitation)

“The prices of staple foods are at near historic lows, and stockpiles are adequate. This is a situation that would be inconceivable without the last half-century's investments in irrigation.”

“Irrigation is the largest recipient of public agricultural investment in the developing world.”

(World Bank (1995))

Senegal Irrigation Project

Nianga Irrigation Pilot Project (NIPP).

Life-span of about 30 years.

One of the analyses of this project provided a very clear schedule of costs and benefits.

Measured in thousands of 1975 CFA Francs (Senegalese currency)

* Weiler, Edward M. and Wallace E. Tyner (1981). Social Cost-Benefit Analysis of the Nianga Irrigation Pilot Project, Senegal. The Journal of Developing Areas , Vol. 15, No. 4 (Jul., 1981), pp. 655-670.

Cost and Benefit Stream of NIPP

Period of Time Benefit Schedule Cost Schedule Net Benefit Schedule

Note: we’re only considering agricultural output as a benefit and no others. However a whole slew of other benefits (unmeasured in this project) do exist.:(1) agricultural production; (2) production of rice seed; (3) increased knowledge of the agronomy of irrigated agriculture in the Fleuve Region; (4) improved technical skills of both the farmers who participate in the Pilot Project and those who receive training from the B.I.T. Center; and (5) shelter provided by the 17 houses at Cite SAED

Should we go ahead with this project?

We need to determine if the total benefits exceed the total costs

If benefits > costs then the project is worth doing

As discussed, we will discount all future costs and benefits to their present value

Results

Year Period

Total Agricultural

Benefits Total Cost

Benefits without Project

Net Benefits

Discount Rate PV(TB) 5% PV(TC) 5%

BC Ratio

1973 0 0.0 31,320.7 7,248.0 -38,568.7 0.05 0.0 31320.7 .

1974 1 0.0 354,174.0 7,248.0 -361,422.0 0.05 0.0 337308.571 .

1975 2 43,781.3 512,089.9 7,248.0 -475,556.6 0.05 39710.9 464480.635 .

1976 3 157,552.7 124,573.8 7,248.0 25,730.9 0.05 136099.9 107611.532 .

1977 4 164,809.6 144,853.9 7,248.0 12,707.7 0.05 135589.3 119171.662 .

… … … …. … …. … … … …

1998 25 215,364.2 113,642.0 7,248.0 94,474.2 0.05 63597.6 33558.7976 .

1999 26 215,364.2 113,642.0 7,248.0 94,474.2 0.05 60569.2 31960.7596 .

2000 27 215,364.2 113,642.0 7,248.0 94,474.2 0.05 57684.9 30438.8187 .

2001 28 215,364.2 113,642.0 7,248.0 94,474.2 0.05 54938.0 28989.3511 .

2002 29 215,364.2 113,642.0 7,248.0 94,474.2 0.05 52321.9 27608.9058 .

Sum: 2,746,329.56 2,490,685.93 1.10

PV of TB: 2,746,329.56PV of TC: 2,490,685.93BC Ratio: 1.10

Graph over Time: No Discounting and Discounting

B/C = 1.10

Agricultural Productivity and Climate Change

Benefits in NIPP are those of agricultural output (rice and tomatoes)

What if future climate change reduces the possible output?

This will require careful study – farmers may adapt their crop and input choice to a changed climate.

For the moment, let’s make some simple assumptions:

50% chance that climate change induces a 25% decline in agricultural revenues per year.

50% chance that climate change induces a 25% increase in agricultural revenues per year.

This change comes about in the 15th year of the project.

Graph over Time: High, Low and Expected Benefits with Climate Damages

Climate Change Kicks In

Result: E(B)/C = 1.10264

But,BH/C = 1.226883

BL/C = 0.978396

Scenario: High Benefits with Climate Damages

Climate Change Kicks In

Result: BH/C = 1.35

Hands-on Exercise

Let us conduct the above cost benefit analysis

We have already seen the results but we can do a couple of new things:

•Check the impact that the choice of discount rate has on our decision

•Check the impact of climate change based on when it begins to impact our project

Hands-on Exercise

Open Excel file titled “CBA and Discounting Exercise”

Base Case

Discount Rate

Climate Damage (20 yrs)

Climate Damage (15 yrs)