1. 6. Discounting
Reading:
BGVW, Chapters 6

2. 1. Introduction
Benefits and costs usually extend over many time periods, need means to compare
“Discount ” benefits and costs in future time periods to get flows in a common metric. Treat future flows as worth less than current flows

3. 2. Basics
Future Value
Future value of $10,000 in one year if interest rate is 8%
Future value of $10,000 in two years if interest rate is 8%
Compounding

4. Present Value
Present Value of $10,000 received in one year if interest rate is 8%

5. Present Value of $10,000 received in 2 years if interest rate is 8%
Larger n, smaller PV
Larger i, smaller PV

6. 3. Net Present Value
PV Benefits

7. PV Costs
Net PV

8. Example in Figure 6.4

9. 5. Timing and Terminal Values
Comments
Higher the discount rate the lower the future counts
If you go out far enough the flow values go to zero
5. Timing and Terminal Values
NPV rise if benefits are realized earlier and costs are realized later
Terminal Values
National park (long lived, pertetuity values make sense)
World’s fair (short lived, decommissioning makes sense)
Salvage values (eg., buses)
Simple Projections
Depreciation
--sensitivity analysis

10. 6. Real vs. Nominal
Accounting for inflation in the measures of benefits and costs
Nominal dollars: current dollars, money as we see it
Real dollars: adjusts for inflation, purchasing power held constant

11. Usually done w/ CPI
Example: Convert $X received in 1999 to real 1990 dollars:

12. This also implies real discount rates and nominal discount rates
This also implies real discount rates and nominal discount rates. That latter are not adjusted for inflation.
If inflation is rising at 4% per year and interest is 7%, we say the real rate of interest (real economic growth) is 3%.
Formula (Really 2.91%, not 3%)
Can use either real or nominal, just be consistent

13. 7. Internal Rates of Return
The discount rate at which NPV is zero is the internal rate of return of the project.
Sometimes compared w/ cost of return on government money if invested elsewhere
Problems:
same problem as b/c ratio
can have multiple rates

14. 8. Sensitivity Analysis over Discount Rates
Adjust discount rate and see how project outcome varies
Extremely common
Calculator

15. 9. Shortcuts in Discounting
Annuities/Perpetuities/Growth Rates
Pages
Value of Perpetuity (forever)
Value of an Annuity that Grows or Declines (forever) – growth is g

16. Value of Perpetuity (n years)
Value of an Annuity that Grows or Declines (forever) – grow is g