Discounting

Planning Analysis:
Discounting

Discounting

When Evaluating Costs of Alternatives, the Policy Analyst’s Problem:

determing the long term impacts of projects....for this purpose cost analysis

comparing two or more alternative projects... one way is to look at costs

in a perfect world...benefits all occur at once...not in the real world

An Example:

Year	0	1	2	3	4	5
A	-5	+5	+3	+6	+2	+1
B	-5	+5	+1	+2	+6	+6

Which is better?

There is a standard method of analyzing this problem: discounting

Some Key Concepts

dollar today is worth more than tomorrow: why? (inflation, opportunity, risk)

two main questions of discounting:

what is the value today of $1 given to me in year n, if the discount rate is r?

what is the value today of $1 given to me each year for n years, if the discount rate is r?

Key Terms

discount rate: rate used to approximate time preferance for money

nominal discount rate: (interest rates....inflation)...current dollars....often 5-10%

real discount rate: (nominal - inflation)...constant dollars...often -4%

The most common task of policy analysts is discounting future benefits and costs using some discount rate.

Net Present Value is a technique analysts can use to compare projects/alternatives

two key tools, tables on pages 330 and 331 of P&S.

Some Examples

given 4% and 5 years, what is the discount factor = .8219

Interpretation: a dollar five years from now discounted at 4% is worth $0.82 in today.

given a steady stream of benefits or costs, what is discount factor given $1, 5%, and 10 years = 7.7217

Interpretation: A dollar of benefits each year for 10 years discounted at 5% is worth $7.72 in today's dollars.

given a varied stream of benefits and costs, what is the npv of the cost stream below at a 4% discount rate?

	0	1	2	3	4	5
Ben	0	300	300	400	400	600
Costs	1000	100	200	200	100	200
Ben-Costs	-1000	200	100	200	300	400

DF?	1	.9615.	.9246	.8890	.8548	.8219

DB/C	-1000	192.3	92.46	177.80	256.44	321.76

NPV	+47.76

given a steady stream of benefits and costs, what is the npv of the cost stream below assuming a 20 year period and a 4% discount rate?

	1	2	3	4	5-20
B	2000	2000	2000	2000	2000
C	1000	1000	1000	1000	1000

NPV= 2000-1000

= 1000 X 13.5903 =

$13,590.30

you win $1 million in the lottery, you can receive a cash payment of $400,000 today or the full million in 10 years. you assume you can invest the money and earn an 8% return. What do you do?

find df for 8% at 10 yrs = 0.4632

multiply DF by $1 million = $463,200

you are given $1,000 each year for 20 years to invest in an IRA at 10%. what is the value today (PV) of your IRA in 20 years?

DF = 8.5136

multiply DF by 1000 = 8,513.60

Summary

Evaluating long term costs? use discounting

NPV is a useful tool...

sensitivity analysis (dr, term affect NPV)

if costs or benefits are shifted down the line in one alternatively, higher discount rate many adjust ranking...why? compounding

UDV and annual equivalent value are useful for comparison.