Part I Principles A B C D E

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Part I. Principles A. B. C. D. E. Markets Market failure Discounting & PV Dynamic efficiency Pollution solutions

C. Discounting and Present Value (Appendix 2 A)

Time preference • Suggests people prefer to realize benefits sooner than later (and realize costs later than sooner) • Individuals not indifferent between $1 benefits today and $1 benefits tomorrow • Discounting – procedure by which $’s of benefits in different periods can be expressed by common metric: Present value (PV)

Option of buying a $100 bond • With payoff 1 year from now • How much would it have to pay in 1 year for you to buy it today? • If $110, your “rate of time preference, ” or “discount rate” is 10% • Makes you indifferent between $100 today and $110 next year (you view the PV of $110 a year from now to be $100)

PV Formula • FV = value that occurs t periods into future • r = discount rate • PV = present value

Bond example • • PV = $100 FV = $110 t = 1 year r=? r = 0. 1

Another example • • PV = ? FV = $10, 000 t = 12 years r = 0. 04 PV = $6, 246

Interpretation? • A person with a discount rate of 4% is indifferent between receiving $6, 246 today and $10, 000 12 years into the future.

What if discount rate increases? • • PV = ? FV = $10, 000 t = 12 years r = 0. 08 PV = $3, 971

Interpretation? • The higher the discount rate, the less person likes receiving benefits in the future. They “discount” the future more. Want immediate benefits. • Therefore, when the discount rate is doubled, the PV goes down. $10, 000 in 12 years now only worth $3, 971 today instead of $6, 246.

Discounting/PV in environ. econ. • Using benefit-cost analysis to determine if environmental projects are a good idea • Each year of the project there will be costs and benefits – some years more costs, some years more benefits • Is the project a good idea? If PV of benefits – PV of costs > 0

Benefit-cost analysis • – benefits in year t • – costs in year t • T – number of years project yields costs/ benefits • TNB – total net benefits

BCA – example • Assume that a dam costs $20 million to build in one year, and that, beginning in the second year, the dam yields net benefits of $2 million per year for 30 years 1. If the discount rate is equal to 5%, what is the net present value of the dam? 2. Is the project worthwhile?

Calculation • • Excel is very helpful here! Net PV = $10. 74 million PV of benefits – PV of costs > 0 Project worthwhile

Example continued • What if net benefits are only 1 million per year for 30 years – is the project still worth it? • Net PV = $ – 4. 63 million • PV of benefits – PV of costs < 0 • Project NOT worthwhile

Discrete case only • Will return to benefit-cost analysis in Part II of class (environmental decision making) • In Appendix 2 A, responsible only for discrete discounting/compounding (can stop at equation 2 a. 6)

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