Topics Today (3/13/13)  More on discounting  Used in BCA  Used in discussions of the optimal allocation of a resource (a mineral, a fish stock, etc.) over time  Pitfalls in Benefit Cost Analysis (in the context endangered species protection)  Double counting  Failure to properly account for opportunity costs  Sunk costs  Jobs  Taxes  Getting the baseline right (program evaluation)…discuss next time  Homework posted, due next Tuesday  Exams returned in discussionDiscounting  About the discounting formulae on the next page:  PV=Present value (value today)  FV(t) = Future value t periods in the future  i=discount rate (sometimes I use “r” for the discount rate) for the specified period length  A= an “annuity”; a fixed payment received every period  Note:usually in our exercises the period length is a year, whereas in real life the period length is a month (e.g. monthly car payments), in which case, for instance, an annual interest rate is converted to the monthly interest rate by dividing by 12 (e.g 6% annual rate is a 6%/12=.5% monthly rate) A=understanding is excellent B=understanding is good C=understanding is fair D=understanding is poor E= have never been exposed to itPresent value of a 1-time payment received t periods in the future, with a discount rate of i: • PV=FV/(1+i)^t Present value of a constant payment A received forever, starting next period: • PV=A/i Present value of a constant payment A received forever, starting this period: • PV=A+A/i Future value in t periods of a value PV received today: • FV=PV*(1+i)^t Present value of a constant payment A received for t periods: • PV=A/i –( A/i )/(1+i)^(t+1) Discounting 3Discounting example: buying a car  Purchasing a car Market value: $20,000Monthly interest rate: 1.50%# of payments 48Amount of payments: $700Present value: ($23,829.79)value of $700 per month forever: $46,666.67value of $700 per month forever, starting after the last payment:$22,836.88 Difference: $23,829.79Class exercise in discounting 00.10.20.30.40.50.60.70.80.91Prefer 100 to50 in 5 yearsPrefer 100 to80 in 5 yearsPrefer 100 to90 in 5 yearsPrefer 100 to100 in 5 yearsPrefer 90 to100 in 5 yearsPrefer 80 to100 in 5 yearsPrefer 60 to100 in 5 yearsPrefer 50 to100 in 5 yearsPercentage of the classResponses to the Lecture 15 clicker questions on discountingClass exercise in discounting Clicker questionDiscount rate yielding indifferencePercent of class saying "Yes"Percent change ImplicationPrefer 50 to 100 in 5 years14.9% 38%implies 38% prefer a discount rate greater than 14.9%Prefer 60 to 100 in 5 years10.8% 47% 9%implies 9% have a discount rate greater than 10.8% and less than 14.9%Prefer 80 to 100 in 5 years4.6% 67% 20%implies 20% have a discount rate greater than 4.6% and less than 10.8%Prefer 90 to 100 in 5 years2.1% 81% 14%implies 14% have a discount rate greater than 2.1% and less than 4.6%Prefer 100 to 100 in 5 years0.0% 91% 10%implies a discount rate of greater than 0% but less than 2.1%Discounting Effect of Discounting00.10.20.30.40.50.60.70.80.911 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 126 131 136 141 146Years in the Future in which $1 ReceivedPresent Value Interest rate (Discount rate)=0 Interest rate =3% Interest rate=10%7Discounting  What is the discount rate used by the U.S. in CBA analyses of projects?  Federal Office of Management and Budget requires about 2% discount rate for most CBA studies it reviews (with sensitivity analyses).  EPA typically uses 3% discount rate.  CBO typically uses 2%.  Discounting in environmental policy is controversial  Environmentalists often object to the notion of discounting –they argue for a very low or zero discount rate  Low discount rate makes the future relatively more important –implication for greater rates of conservation, greater current effort to reduce future environmental damages  But if your objective is environmental enhancement/preservation, a low discount rate is a double-edged sword… 8Discounting Example #1: For your graduation from UW, you’re given a U.S. Savings Bond by your favorite grandmother, redeemable for $300 in 30 years. The interest rate on the savings bond is 8%. So your kid brother doesn’t feel left out, she buys him a Tumble Time Tigger for $32. Discounting Question: A=Me; B=Brother; C=NIW 9Discounting  Discounting Example 2/ A new dam would cost $2 Billion to build, but would generate $100 million per year in irrigation benefits forever, starting next year. These are the only benefits and costs. The interest rate is 10%.  Question: should the dam be built? A=Yes; B=No; C=NIW 10Discounting  Discounting Example 3/ Cutting a stand of old growth would generate $10 million in net timber benefits. If the stand is cut, it would be financially mature again in 100 years (i.e. this is the next best time to get a second cutting). Leaving the stand in its old growth state generates $0.5 million per year forever, starting today. There is also existence value associated with keeping the stand in its current state. If the discount rate is 10%, what would the existence value have to be to justify on economic grounds keeping the stand in its current state? A=a little over $10 million ; B=a little over $5 million; C=a little over $4.5 million; D=a little over $9.5 million; E=$0 –cutting the stand is not justified even when the existence value is $0 11Endangered Species Protection  How many species exist?  Worldwide there is an estimated 14 million species, though this may vary between 3 million to 100 million  In the U.S., there are in excess of 200,000 species known to exist, many of these are insects and fungi.Endangered Species Protection  Condition of U.S. species  According to Stein, in 2001 in the U.S., of the approximately 21,000 known species of plants and vertebrate animals, there were:  70 known extinctions.  170 considered possibly extinct.  1,385 are critically imperiled.  1,737 are imperiled.  3,338 are considered vulnerable to extinction.  Roughly 1/3 of native U.S. plants and vertebrate animals is at risk of extinction.  There are currently 830 plants and animals on the U.S. threatened or endangered species lists (4%) Source: Stein, B.A. 2001. “A Fragile Cornucopia: Assessing the Status of U.S. Biodiversity.” Environment, 43(7): 11-22.CBA of Endangered Species