Topics Today 102308

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Topics Today (10/23/08)

• Discounting and CBA.
• Long-term discounting.
• Read 9, 10 from outside reading list.
• Homework 5 is on website.

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Cost-Benefit Analysis

• Cost-Benefit Analysis a comparison of total
  benefits and total costs associated with
  alternative policies.
• Net Benefits Total Benefits Total Costs.
• CBA involves computing net benefits for each
  policy alternative.

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Cost-Benefit Analysis

• Most environmental policies / projects generate
  benefits and costs which will extend for long
  periods of time.
• Q How do we compare a cost today to a benefit 25
  years from today?

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Discounting

• A benefit/cost that falls in the future is not
  worth the same as a benefit/cost that falls today
• Two rationales for discounting
• Rationale 1. Time preferencepeople prefer to
  have a good now to having it later, and they are
  willing to sacrifice for it.
• Ex/ Your want to see a new concert or play or
  sporting event, or youre applying for a permit
  to gain access to a wilderness area. Think of
  one of these which would you really want.
  Then think about what it would be worth to you to
  do it
• You find out, though, that there are no
  seats/permits available for two years. Would you
  be willing to pay a little extra to not wait for
  two years? This is the time preference
  explanation of discounting.

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Discounting

• This logic carries over into environmental goods
• Suppose the Wisconsin DNR is considering the
  establishment of another flock of Whooping Cranes
  at Horicon Marsh. It could do it now, or in five
  years. Which would you prefer?

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Discounting

• Rationale 2 the opportunity cost of foregone
  investment.
• Would you prefer 100 in real purchasing power
  this year or next year?
• Its better to take the money up-front, put it in
  the bank, and earn interest.
• Suppose the interest rate was 5 and there was no
  inflation.
• If you banked the 100, next year youll have
  105.
• Where did the 5 come from? The bank loaned out
  your money to someone who invested it in other
  assets machines, homes, roads, schools, etc.
• Waiting until next year has an opportunity cost
  of foregone investment equal to 5.

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Discounting

• Q What happens to 100 ten years from now with
  investment?
• If you accept it today and put it in the bank at
  5 interest, next year it would be worth
  100(1.05)105.
• In year 2, it would be worth 105(1.05)
  100(1.05)(1.05)110.25.
• In year 10, it would be worth 100(1.05)10
  162.89.
• (Value today)(1r)T(Value T years from now).
• Value today is often called present value of X,
  T years from now.
• PV(X)X / (1r)T

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Discounting

• Taking the 100 today and putting it in the bank
  at 5 interest gives you 162.89 ten years from
  now.
• If you choose to forego the 100 today then you
  forego 62.89 opportunity cost of foregone
  investment.
• Key Point investment is productive.

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Discounting

• What would happen if the interest rate were 2
  rather than 5?
• If you stuck the 100 in the bank at 2 interest
  youd end up with 100(10.02)10121.90.
• If you took the 100 ten years from now, your
  opportunity cost of foregone investment would
  only be 21.90.
• The opportunity cost of foregone investment is
  lower with lower discount rates.

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Discounting and Infinite Horizons

• Many projects generate costs and benefits which
  are assumed to extend into perpetuity.
• Q What is the present value of an infinite sum
  of 10 net benefits?
• PV(xt)xt / (1r)t.
• The net present value of an infinite sum of 10
  payments equals 10(1r)-0(1r)-1...(1r)-8.
• This infinite sequence converges to 10 10/r.
• The net present value of an infinite sum of 10
  annual payments at 10 discount is equal to 110.
  

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Discounting
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Discounting

• Ex/ Compact fluorescent lightbulbs vs.
  Incandescent lightbulbs.
• Compact fluorescent bulbs use roughly 1/3 to 1/5
  the electricity of incandescent bulbs.
• At Amazon.com
• I could buy a compact fluorescent for about 14.
• I could buy an incandescent for about 0.60.
• Suppose youre a hotel manager who needs to buy
  1000 bulbs. Should you choose compact fluorescent
  or incandescent?

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Discounting
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Discounting
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Discounting
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Discounting

• Higher discount rate smaller present value of
  future benefits / costs.
• How do businesses choose their discount rate?
• Its typically the market rate of interest on
  investments of similar risk.
• Their opportunity cost of capital.
• What discount rate should public agencies choose?
  Well come back to this question.

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Discounting

• Ex/ Pandora is deciding how to dispose of some
  hazardous waste.
• She can contain it safely at a cost of 175 or
  bury it in the local landfill for free.
• If she buries it, ten years from now there will
  be 450 in damages to her neighbor, Bucky.
• What is the present value of 450 in ten years at
  a discount rate of 10?
• PV(450)450/(10.1)10173.50.

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Discounting

• Ex/ Pandoras waste (cont.)
• With a 10 discount rate, is it efficient for
  Pandora to bury her waste?
• If Pandora buries the waste, then she can invest
  her 175 and have 175(10.1)10453.90 in ten
  years.
• Pandora could compensate Bucky 450 ten years
  from now and still have 3.90.
• So it is efficient for Pandora to bury her waste.
  
• This is an example of an environmental bond
  investing money specifically to compensate future
  generations for environmental damage.

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Cost-Benefit Analysis (CBA)

• Process of a CBA with discounting
• Net benefit test when net benefits change over
  time.
• Future costs and benefits are put into present
  value terms.
• Present value X / (1r)T

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Cost-Benefit Analysis (CBA)

• Process of a CBA with discounting
• Apply the net present value test
• Is the sum of discounted gains greater than the
  sum of discounted losses?
• NPV ? Bt(1r)-t - ? Ct(1r)-t where the
  summations run from time t0 (today) to time tT
  (the life of the project).
• Is NPV 0 for some groups and groups?

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Cost-Benefit Analysis (CBA)

• Ex/ Suppose Wisconsin is considering an ecosystem
  restoration plan.
• The ecosystem slowly recovers until a threshold
  is reached in year 4.
• Benefits are significantly higher in year 4.

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Cost-Benefit Analysis (CBA)

• Ex/ Ecosystem Restoration (cont.)
• The NPV of the project varies with the discount
  rate this is sensitivity analysis.
• What discount rate is appropriate?

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Choosing Discount Rates

• Historically, long-term interest rates on
  government bonds are used as a measure of the
  opportunity cost of foregone investment.
• Long-term rates are typically adjusted by a risk
  premium.
• Riskier projects have higher discount rates.

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CBA, Climate Change, and Uncertain Discounting

• Time profile of benefits from reducing 1 ton of
  carbon emissions in 2000.

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CBA, Climate Change, and Uncertain Discounting

• Benefits from reducing climate change are
  long-term ( 100 years).
• Few markets exist for investments with maturities
  exceeding 30 years.
• What is correct discount rate in 100 years?
• Newell, R., and W. Pizer. 2002. Discounting the
  Benefits of Climate Change Policies Using
  Uncertain Rates. Resources, 146(15) 15-20. 7
  in outside reading list.

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CBA, Climate Change, and Uncertain Discounting

• Market interest rate on U.S. long-term government
  bonds.

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CBA, Climate Change, and Uncertain Discounting

• P.V. of 100 in 100 years.
• 7 discount PV 0.12.
• 1 discount PV 36.97.
• Expected value (equal probability) 0.50.12
  0.536.97 18.55.
• P.V. of 100 in 101 years.
• 7 discount PV 0.11.
• 1 discount PV 36.61.
• Expected value (equal probability) 0.50.11
  0.536.61 18.36.

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CBA, Climate Change, and Uncertain Discounting

• Expected value drops by 1 (18.36 / 18.55
  1.01) in 1 years time.
• Effective discount rate is 1.
• The change in value between 100 years and 101
  years depends solely on the low discount rate.

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CBA, Climate Change, and Uncertain Discounting

• High rates discount future benefits so much that
  they add little to expected value.
• Ex/ Suppose uncertainty is from a discount rate
  of 1 to 10.
• Expected P.V. of 100 in 100 years 18.49.
• Expected P.V. of 100 in 101 years 18.31.
• Expected P.V. drops by 1 (18.31 / 18.49).
• Effective discount rate is 1.

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CBA, Climate Change, and Uncertain Discounting

• Newell and Pizers simulation experiment

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CBA, Climate Change, and Uncertain Discounting

• Newell and Pizers simulation experiment
• They generated tens of thousands of future
  interest rate paths.
• This generates tens of thousands of equally
  plausible future discount rates.
• They averaged the value of 100 at differ points
  in time using the simulated discount rates.

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CBA, Climate Change, and Uncertain Discounting
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CBA, Climate Change, and Uncertain Discounting
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CBA, Climate Change, and Uncertain Discounting

• Uncertain discount rates raise estimates of
  future valuations relative to constant discount
  rates.
• Unexpectedly low discount rates raise valuations
  by a large amount.
• Unexpectedly high discount rates reduce
  valuations by a small amount.