Cost-Benefit Analysis

2

Cost Benefit Analysis

Identify & evaluate all costs & benefits Discount Assess project(s) by calculating

Benefit/Cost Ratio (B/C) Net Present Value (NPV) Internal Rate of Return (IRR)

3

Evaluation

Identification (what are they?) Evaluation (what are they worth?) Measurement issues:

Direct & indirect (i.e. externalities) effects Tangible & intangible effects Pecuniary effects

4

Discounting

Policies & projects last a long time Frequently costs & benefits occur at different

times Money has a time value, i.e. ceteris paribus,

current dollars are more valuable than future dollars

Thus, we need to place current & future costs & benefits on an equal basis for comparison

5

Discounting, cont.

This is done by “discounting,” that is by reducing future dollars to present value by applying a discount (or a negative interest) rate

Discount Rate v. Interest Rate

$100,000 invested at a 3% interest rate today will be worth roughly $115,927 in five years

$100,000 in anticipated benefits five years from now is worth roughly $86,260 today, when discounted by 3%

6

The Discount Rate Matters

$100,000 in anticipated benefits five years from now is worth roughly $86,260 today, when discounted by 3%

$100,000 in anticipated benefits five years from now is worth roughly $78,352 today, when discounted by 5%

The difference grows larger as Multiple years are accounted for Benefits accrue further into the future

7

What To Use As A Discount Rate?

There are various approaches to selecting one “Givens” (i.e. some authority imposes one) Bank interest rates Rates of return on certain investments (e.g.

government bonds) “Social” discount rates

8

9

Net Present Value

The difference between total discounted benefits and total discounted costs

NPV = (PVB ‑ PVc) NPV: decision criteria

For a single project, a positive NPV indicates acceptability

For multiple (competing) projects, the project(s) with the highest NPVs should receive highest priority

10

Benefit/Cost Ratio

B/C = (PVB / PVC) Benefit/Cost ratio: decision criteria

For a single project, a B/C ratio which is greater than 1 indicates acceptability

For multiple (competing) projects, the project(s) with the highest B/C ratios (greater than 1) should receive highest priority

Internal Rate of Return

The discount rate at which the present value of benefits is equal to the present value of costs

Internal Rate of Return: decision criteria For a single project, an IRR which is greater than

the selected (for B/C and/or NPV analysis) discount rate indicates acceptability

For multiple (competing) projects, the one with the largest IRR is the most desirable

11

12

NPV & B/C Comparison

NPV measures totals, indicates the amount by which benefits exceed (or do not exceed) costs (total benefit or loss)

B/C measures the ratio (or rate) by which benefits do or do not exceed costs (efficiency)

13

NPV & B/C Comparison, cont.

They are clearly similar, but not identical With multiple projects, some may do better

under NPV analysis, others under B/C

Internal Rate of Return

It has a certain attraction, but also has some problems The argument that an IRR which is greater than

the selected discount rate is desirable can be questioned - discount rates can be arbitrary!

Calculation (by hand) is tedious & prone to error (but modern spreadsheets are a help)

Under certain conditions there may be more than one correct solution to an IRR problem

14