1. 13. Discounting
Reading:
BGVW, Chapter 10

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. 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

4. 2. It Really Matters!
Often has a large role in determining outcome of a project or regulation
Projects with long time spans are especially sensitive
Go to next page for example
Calculator  NPV

6. 3. Bottom Line Use real SDR 3.5% (for years 1 – 50)
Sensitivity analysis around 2% - 6%
Convert investment flows into consumption equivalents
Based on optimal growth theory
Using declining rates after yr. 50
50-100: 2.5%
: 1.5%
: 0.5%
> 300: 0%

7. 4. Three core rationales for discounting
Time-declining preference (SMRTP)
People are impatient and prefer things Today vs. Tomorrow
Opportunity cost of capital (Return on private investment)
Displacing private investments and we should ‘beat’ this with funds used by public sector
Intergeneration equity (Growth theories)
If incomes are rising (we have a little history of this happening), then we might ‘discount’ future higher income periods

8. 5. Interest rate theories for discounting
Why the market rate of interest is a good starting point
See next slide
Why adjustments need to made for taxes (and probably other stuff)
See second to next slide

11. Deriving SDR from the Market (Interest Rate Theories)
Government projects will displace investment (rz) and consumption (pz).
Marginal Rate of Return on Private Investment
Taking money out of private sector should at least match that return.
Will displace investment and consumption, but mostly investment so find private rate close to investment displacement rz
Corporate Bond Rate (Return on Equities?)
Marginal Rate of Time Preference
Will displace investment and consumption, but mostly consumption through taxes so use pz
Treasury Rates

12. Rate at which Government Borrows
Weighted average depending on degree of displacement
Is project taxed financed?
Debt financed?
Market conditions?

13. 6. Optimal Growth Rate Theories for Discounting
Ramsey directs us to look at optimal growth rate of consumption over time.

14. Ramsey objects to treating utility of different generations differently (though his theory allows for it), but with economic growth & declining marginal utility of consumption discounting still makes sense
“[His] model assumes that due to ongoing economic growth, society will consistently enjoy higher per capita consumption in the future than it does today. Consequently, as a result of declining marginal utility of consumption, society welfare would increase if consumption were ‘smoothed out’ (more equal) over time. Put another way, the future should have a lower weight than the present. The rate at which the weights decline across time should be proportional to the growth rate of per capita consumption: the higher the growth rate, the higher the SDR.” But, the rate will also depend on how fast mu of consumption falls as per capita consumption rises.

15. Using the Optimal Growth Rate Approach to Discounting
The optimal growth approach to discounting assumes that policy makers use a well-behaved social welfare function that describes the values society places on different amounts of per capita consumption, both public and private, over time. Policy makers choose the amount of public investment in order to maximize the well-being of society now and in the future.
Look to growth rates in economies (g) and maybe tax schedules (e)
Growth Rate
Consumption Discounting 15

16. 7. Time Declining Discounting
Empirical Evidence
Far off Environmental Disasters count for nothing
Individuals not alive today left out
Uncertainty of Growth
Do NOT want to average 1% and 7%  4%
You want to average NPV 16

17. 8. The Shadow Price of Capital
The shadow price of capital method entails distinguishing between project impacts that affect investment and those that affect consumption.
Convert displaced investment into consumption terms then discount all at the rate for consumption
Shadow Price
of Capital
Discounted Present Value of Investment Perpetuity 17

18. Generalized Formula
Amount Reinvested
Depreciation 18

19. 9. Bottom Line (Again) Use real SDR 3.5% (for years 1 – 50)
Sensitivity analysis around 2% - 6%
Convert investment flows into consumption equivalents
Based on optimal growth theory
Using declining rates after yr. 50
50-100: 2.5%
: 1.5%
: 0.5%
> 300: 0%