Transcript Discounting - University of California, Santa Barbara

Discounting
How should the future benefits of a
project be weighed against present
costs?
“Construction company owner
wins $314.9 million Powerball”
Winner opts for $170 million lump-sum
payoff instead of 30 annual payments.
Question: Why would someone choose
$170 million over $315 million?
Answer: The time value of money.
Future earnings must be discounted.
Outline
What is discounting?
Why do we discount?
The mechanics of discounting.
The importance & controversy of
discounting.
Discounting in practice.
What is discounting?
Public and private decisions have
consequences for future:
Private: Farmer invests in water-saving
irrigation. High up-front cost, benefits
accrue over time.
Public: Dam construction, Regulating
emissions of SOx, etc.
Need method for comparing costs &
benefits over time.
Why do we discount?
Put $100 in bank today, get about $105
next year.
Why does money earn positive interest?
People generally prefer to consume sooner
rather than later (impatience),
Productivity of capital (if we divert some
money to investment, may yield higher
future consumption).
Mechanics of discounting
Money grows at rate r.
Invest V0 at time 0: V1=V0(1+r)
V2=V1(1+r),…
Future Value Formula: Vt=V0(1+r)t.
Present Value Formula: V0 = Vt/(1+r)t.
Other formulae available in handout.
The drip irrigation problem
Farmer has to decide whether to invest
in drip irrigation system:
Cost = $120,000.
Water savings = 1,000 Acre-feet per year
Water cost = $20 per acre foot.
Calculate everything in present value
(alternatively, could pick some future
date and use future value formula)
Investing in drip irrigation
(r=.05)
Year
Costs
Benefits
0
120,000
20,000
Cumulative
Net Gain
-100,000
1
0
19,048
-80,952
2
0
18,141
-62,811
3
0
17,277
-45,534
When does he break even?
Drip Irrigation Project
200000
Net Payoff
150000
100000
50000
0
-50000 0
5
10
15
-100000
-150000
Year
20
25
Where does inflation come in?
Inflation is the increase in the cost of a
“basket of goods” at different times.
Your grandpa always says “An ice cream
cone only cost a nickel in my
day”….that’s inflation.
Want to compare similar values across
time by controlling for inflation
Correct for inflation: “Real”
Don’t correct for inflation: “Nominal”
The “Consumer Price Index”
CPI is the way we control for inflation.
CPIt = 100*(Ct/C0)
Ct = cost of basket of goods in year t.
C0 = cost of basket of goods in year 0.
E.g.
Year
1990
1991
1992
CPI
100
104.2
107.4
Some other discounting concepts
Net Present Value (NPV): The present
value of B-C over the life of the project.
Internal Rate of Return (IRR): The
interest rate at which project would
break even.
Scrap Value: The value of capital at the
end of the planning horizon.
Importance of discounting
Discounting the future biases analysis
toward present generation.
If benefits accrue later, project less likely
If costs accrue later, project more likely
Speeds up resource extraction
“Risk-adjusted discount rate”
Risky projects may justify increasing
discount rate.
Social vs. private discount rate
Private discount rate easily observed
It is the outcome of the market for money.
Depends on risk of default on loan.
Social rate may be lower
People care about future generations
Public projects pool risk – spread losses
among all taxpayers.
Argues for using “risk-free” rate of return.
Social discount rate in practice
Small increase in r can make or break a
project.
Typical discount rates for public projects
range from 4% - 10%.
Usually do “sensitivity analysis” to
determine importance of discount rate
assumptions.
Be clear about your assumptions on r.