## 6/27/14

### Introduction Cost Benefit Analysis

This post goes over the basics of cost benefit analysis, also referred to as CBA. While not comprehensive, it introduces the ideas and processes behind a typical cost benefit analysis. CBAs are useful to help us decide whether one outcome is better than another from society's point of view.

Examples:
Should we build townhouses in a local city park?
Should we build a new fountain downtown?
Should we increase taxes on the rich to fund higher eduation?
Should your University spend 10 million on a new rec center?
Should we pave that grass in front of the building to make a new parking lot?

How can we study these issues? Cost benefit analysis can help in figuring out these tricky problems:
The steps of CBA:

1) Project/policy identification:
-what are we studying?
-who/what do we care about?
-whose welfare are we measuring?

2)Identify Impacts
-Any project has resource tradeoffs, and we need to identify these.
-Identify physical impact of the policy, we desire accurate measurements but traditionally deal w/uncertainty

3)Valuing impacts
-identify monetary values of all relevant effects.
-Indirectly we're comparing social benefits to social costs (maximizing welfare and MB=MC)
-markets help identify some values, but remember that they are prone to market failure.
-Ch. 4 will teach us some methods for valuing the environment.

4)Discounting cost and benefit flows
-helps to understand what a present value (PV) is.
-the discount rate deals with the time value of money, not inflation, but similar to an interest rate.
-for example, if I give you \$1,000 today, how much money will I have to give you one year from today to make you give up the \$1,000 today?
To accurately compare different benefits and costs over time we need to find the relevant PV. This is done using the following equation:

PV(X_t )=X_t[(1+r)]^(-t)

Where PV is the present value
Xt represents either costs or benefits in time period t
r is the discount rate
and t represents the time period

Example:
-calculate the present value for an asset that pays \$500 a year for 5 years at a discount rate of 5%.
476.2+453.5+431.92+411.4+391.8=2164.74

-calculate the present value cost to maintain a  pool for \$1,000 a year for 5 years at a discount rate of 10%.
909.1+826.4+751.3+683+620.9=3790.79

5) Applying the net present value (NPV) test: also known as Kaldor-Hicks compensation test:
Is it possible for the "gainers" to compensate the "losers" to make them just as well off so that nobody "loses".

-to do this we have to calculate the NPV:

where Bt is benefits in time period t
and Ct is costs in time period t

We take the sum of all time period and if NPV>0 then it is a good project and it satisfies the Kaldor-Hicks criterion.

6) Sensitivity analysis:
-Will a change in certain parameters cause the NPV to change signs? If the NPV does change signs, this would change whether or not performing the project is worth it.

This post does not cover everything associated with cost benefit analysis but provides a brief introduction to the concepts and methods performed in most cost benefit analyses.