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Cost Benefit Analysis

In 1981, President Ronald Reagan required CBA for all major rules.

CBA asks two major questions:

• What are the costs of a decision?
• What are the benefits of a decision?
• Do the benefits outweigh the costs?

These are the general steps of CBA:

1. Define the situation
   • including geographic scope!
2. Identify the costs
3. Identify the benefits
4. Discount future costs and benefits to identify net present value (NPV)
5. Interpret results

Net Present Value

Some costs / benefits occur in the future, and some occur now. $1 now is not worth the same as $1 in two years.

The Present Value of X money is the amount you would be willing to pay now to receive X in the future.

Let’s define some terms:

• $r$ is the interest rate
• $FV$ is the future value of some money
• $PV$ is the present value
• $t$ is a number of years

If we have $100, we can determine how much that will be worth in $t=10$ years, given an interest rate of $r=5%$.

\[FV = PV * (1+r)^t\\ FV = 100 * (1+0.05)^{10}\\ FV = 100 * 1.05^{10}\\ FV = 100 * 1.62889462678\\ FV = 162.89\]

If we are instead given the future value, we can determine the present value.

\[PV = FV / (1+r)^t\]

Other things that affect the discount rate

• inflation
• future generations

Benefit - Cost Ratio

Divide the PV of benefits by the PV of costs. This represents efficiency.