Public Center Decision Making (B-C Ratio)

Benefit to cost analysis Here, we consider public sector projects which take into account social impact more than private sector projects…

Before conducting a B/C analysis, it is important to identify

• Who will benefit
• Who will pay for the project Usually, members of society are the users/beneficiaries of project services and the government is the sponsor

We classify the costs of public projects into initial capital costs, and ongoing operating and administrative costs.

Tip

If the project generates savings, these are deducted from costs to produce a net cost to the sponsor…

• Some costs are directly attributed to the project and some are stimulated indirectly

We also need to consider social costs which can be negative these should be subtracted from the benefit to obtain a new measure of the social benefit of a project.

Expected Benefit

For an expected benefit, a standard approximation of the actual benefit is halfway between the highest / lowest benefit. (ex. when we are computing savings it would be $\left(\frac{1}{2}\right)\left(C_{before}-C_{after}\right)\cdot N_{\text{benefit (ex. an increase in visitors)}}$)

The Benefit-Cost Ratio

The purpose is to measure a project so that one can determine whether it causes a net increase in economic and social welfare

$B/CRatio=\frac{\text{Equivalent worth of net benefits}}{\text{Equivalent worth of costs}}$ Where this ratio can be of PW, FW, or AW…

This is $\text{Conventional B/C Ratio}=\frac{\text{EW net benefit}}{\text{EW initial costs+ EW O\&M costs}}$ There is also a modified variant… $\text{Modified B/C Ratio}=\frac{\text{EW net benefit - EW O\&M costs}}{\text{EW initial costs}}$

If B/C > 1, then invest, otherwise don’t. If the ratio is very close to 1, we need to do sensitivity analysis and further research.

We need to make sure that the sponsor vs beneficiaries are seperate (one is on the denominator and the other in the numerator)

Incremental B/C Ratio

The incremental B/C ratio should be used to compare mutually exclusive alternatives where we choose the one with the highest value.

1. Identify all relevant alternatives
2. Calculate the B/C ratio of each alternative and discard the ones with B/C ratio less than 1
   1. If they are all less than 1, we are doing an analysis for the least bad alternative
3. Rank-order the projects based on the present worth (or other scopes of analysis) of the costs from the lowest cost to the highest. The do nothing alternative always becomes the first on the ordered list
4. Identify the increment under consideration
   1. Calculate the B/C ratio for the incremental cash flows $\frac{B}{C}=\frac{\Delta B}{\Delta C}$
   2. Use the incremental B/C ratio to decide which alternative is better if $\frac{\Delta B}{\Delta C}>1$ increment
5. Do step 4 until all increments have been considered
6. Choose the best alternative from the set of mutually exclusive competing projects

If $\Delta C$ is 0, we choose the project with the greater equivalent worth of benefits If $\Delta B=0$ we choose the project with the lower equivalent worth of costs

Note

The MARR for public institutions are lower than private institutions, profits generated by public projects are not taxed

In evaluating public sector projects, the MARR is used in the same way as in evaluating private sector projects—it captures the time value of money.

No benefit cash flows

For questions where there is no benefit, you need to do an incremental analysis since that exposes the benefit (one will cost users less than the other) (incremental BC) $\frac{\Delta B}{\Delta C}$ where $\Delta B$ in this case would be $(0-\text{cost to the user of A})-(0-\text{cost to the user of B})$