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 = (PV B ‑ PV c ) 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 = (PV B / PV C ) 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