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

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

C. Discounting and Present Value (Appendix 2A)

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 If the discount rate is equal to 5%, what is the net present value of the dam? 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 2A, responsible only for discrete discounting/compounding (can stop at equation 2a.6)

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