1 / 26

# 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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'Econ 134A' - vic

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### Econ 134A

Test 1

Solution sketches

• 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

• 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

• 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

• 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

• 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

Taeil Smith deposits \$500 today: yrHow long until it grows to \$32K?

• 500 (1.08)T = 32,000

• (1.08)T = 64

• T = log1.08 64

• T = log 64/log 1.08 = 54.04

• Easy problem

• 3 easy problems

• 1 easy-medium problem

• 2 medium problems

• 3 hard problems

Problem: yrYou 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

• (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

• (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

• (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

• 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

• 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

• 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

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

• 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

99 yrth 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

50 yrth 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