Econ 134A

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# Econ 134A - PowerPoint PPT Presentation

Econ 134A. Test 1 Solution sketches. Level of difficulty. On multiple choice questions… “Easy” denotes that about 80-100% of students get this question correct “Medium” denotes that about 60-80% of students get this question correct

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### Econ 134A

Test 1

Solution sketches

Level of difficulty
• On multiple choice questions…
• “Easy” denotes that about 80-100% of students get this question correct
• “Medium” denotes that about 60-80% of students get this question correct
• “Hard” denotes that about 40-60% of students get this question correct
Level of difficulty
• On Problems…
• I take a 10% sample
• “Easy” denotes that the average score is 80-100% of the points possible
• “Medium” denotes that the average score is 60-80% of the points possible
• “Hard” denotes that that average score is 40-60% of the points possible
Today is Oct. 27, ’11You invest \$2,500 today
• Find FV on July 27, 2013, 14% SAIR, compounded every three months
• Quarterly interest rate is 3.5%
• Difference between the two dates
• 1.75 years, or 7 quarters
• FV = \$2500(1.035)7 = \$3180.70
• Easy problem
Today is Oct. 27, ’11You invest \$2,500 today
• Find FV on Oct. 27, 2041, 2.31% SAIR, compounded continuously
• Difference between the two dates
• 30 years
• To compound continuously…
• \$2500*exp(0.0231*30) = \$4,999.26
• Easy problem
Today is Oct. 27, ’11You invest \$2,500 today
• Find FV on April 27, 2019, 5% SAIR, compounded every 30 months
• Compounding occurs every 30 months, or 2.5 years
• Add 12.5% interest every 2.5 years
• Difference between the two dates
• 7.5 years
• 3 periods of 2.5 years
• FV = \$2,500(1.125)3 = \$3,559.57
• Hard problem
Adelle Samuelson, \$35,000 real payment 7 years from now
• Inflation is 3% per year for three years
• Inflation is 4% per year for four years
• Nominal payment is
• \$35,000(1.03)3(1.04)4 = \$44,741.76
• Hard problem
Heath Wells deposits \$10,000 in a bank, 9% yearly interest
• Money in the bank for 5 years
• How much MORE interest is earned if compounded monthly, relative to simple interest?
• Compounded monthly
• \$10,000(1.0075)60 = \$15,656.81
• Simple interest
• \$10,000(1.45) = \$14,500
• Difference is \$1,156.81
• Medium problem
Biliana Marks and the will:\$3,000 per year forever…
• …starting 6 months from now
• EAIR is 8%
• A perpetuity that pays \$3,000 per year forever STARTING ONE YEAR FROM NOW has PV of \$3,000 / 0.08 = \$37,500
• We have to multiply the above value by sqrt(1.08) in order to value each payment six months earlier: \$37,500 (1.0392) = \$38,971.14
• Hard problem
LA Purchase: \$15M in 1803; \$219M in 2010 with inflation
• If annual inflation was the same every years over a 207-year period, what is yearly inflation rate?
• All numbers below in millions of dollars
• 15(1+r)207 = 219
• (1+r)207 = 219/15
• 1+r = 1.0130  r = 1.30%
• Easy-medium problem
• What is EAC if discount rate is 4%/yr.?
• PV of costs
• \$1,000 + \$100/1.04 = \$1,096.15
• If EAC is X, then
• X/1.04 + X/1.042 = \$1,096.15
• 1.8661X = \$1,096.15
• X = \$581.17
• Medium problem

You could also have used the annuity formula here

• 500 (1.08)T = 32,000
• (1.08)T = 64
• T = log1.08 64
• T = log 64/log 1.08 = 54.04
• Easy problem
Summary of MC problems
• 3 easy problems
• 1 easy-medium problem
• 2 medium problems
• 3 hard problems
Problem:You invest \$500 today
• You get back…
• \$214.70 in one year
• \$350.30 in two years
• (a) What is NPV if EAIR is 15%
• -500 + 214.7/1.15 + 350.3/1.152
• -\$48.43
• Easy problem
Invest \$500 today, get back \$214.70 & \$350.30
• (b) Based on the answer in (a), is the annual IRR >, <, or = to 15%
• It must be less than 15%
• Since all future cash flows have positive value, a discount rate that falls will lead to a higher NPV (since these future payments are discounted less)
• Medium problem
Invest \$500 today, get back \$214.70 & \$350.30
• (c) Calculate the annual IRR
• -500 + 214.7/(1+r) + 350.3/(1+r)2 = 0
• There are multiple ways to solve this; I like to solve it by first multiplying both sides by (1+r)2
• -500(1+r)2 + 214.7(1+r) + 350.3 = 0
• -500r2 – 785.3r + 65 = 0
• Use the quadratic formula on the formula sheet to get r = 0.07882 or -1.6494
• IRR = 7.882%
• Hard problem
Invest \$500 today, get back \$214.70 & \$350.30
• (d) Suppose that you receive an additional payment in 3 years
• How much does this payment need to be in order for the NPV of the project to be \$100? (Call this payment X in calculations below)
• -500 + 214.7/1.2 + 350.3/1.22 + X/1.23 = 100
• -77.82 + X/1.23 = 100
• X/1.23 = 177.82
• X = \$307.27
• Medium problem
Problem: Junk bond with 4 coupon payments of \$500 each
• What is PV of this bond if effective annual discount rate is 6% for 1st 2 years and 14% thereafter?
• 500 + 500/1.06 + 500/1.062 + 500/[(1.06)2(1.14)]
• \$1,807.05
• Medium problem
Problem: Sammy Waffle wins the Wacky Lottery
• 10 payments
• \$10,000 two years, four years, and six years from today
• \$13,000 eight years from today
• Payments made in years 10, 12, 14, 16, 18, and 20 (each 3% higher than the previous payment)
• What is the PV of these payments if the effective annual discount rate is 5%?
• Medium problem
Sammy Waffle wins the Wacky Lottery
• Payments in…
• Yr. 10: \$13,390
• Yr. 12: \$13,791.70
• Yr. 14: \$14,205.45
• Yr. 16: \$14,631.61
• Yr. 18: \$15,070.56
• Yr. 20: \$15,522.68
Present value of payments

2 years from today

\$9,070.29

4 years from today

\$8,227.02

6 years from today

\$7,462.15

8 years from today

\$8,798.91

10 years from today

\$8,220.30

12 years from today

\$7,679.73

14 years from today

\$7,174.72

16 years from today

\$6,702.91

18 years from today

\$6,262.13

20 years from today

\$5,850.33

Total PV of the 10 payments

\$75,448.50

Sammy Waffle wins the Wacky Lottery

You can also use the annuity formula to calculate the PV of the last 6 or 7 payments

Summary of problems
• 2 points of easy problems
• 24 points of medium problems
• 6 points of hard problems
• Note that the curve is set at the end of the quarter
• You can look at the syllabus to see what the likely distribution of grades is
• Even though there are 62 points possible, divide your score by 61 to get your grade
• For those of you with low grades, Test 1 may be the score you drop
• Average
• 43.40 points
• 43.40/61 = 71.1%
• THE GRADE DISTRIBUTION BELOW IS MEANT TO BE AN APPROXIMATE GUIDELINE
• Do not use this as an absolute guide for determining your grade
99th percentile

61 points

Those with 62 points will get 100% and be bumped up if on the border of two grades at the end of the quarter

80th percentile

53 points

Most students w/53+ points are approximately in the A+ to B+ range

60th percentile

48 points

Most students between 48-52 points are approximately in the B+ to B range

50th percentile (median)

44.5 points

The median student at the end of the quarter will likely get a B or B-

40th percentile

42 points

Someone here is approximately at a B- or C+

20th percentile

35 points

Students with 35 points or below are in danger to get a C- or below for the class if there is no improvement on the other two tests