Transcript Econ 134A

Econ 134A
Test 1
Solution sketches
Level of difficulty
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On multiple choice questions…
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“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
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On Problems…
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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, ’11
You invest $2,500 today
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Find FV on July 27, 2013, 14% SAIR,
compounded every three months
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Quarterly interest rate is 3.5%
Difference between the two dates
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1.75 years, or 7 quarters
FV = $2500(1.035)7 = $3180.70
Easy problem
Today is Oct. 27, ’11
You invest $2,500 today
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Find FV on Oct. 27, 2041, 2.31% SAIR,
compounded continuously
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Difference between the two dates
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To compound continuously…
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30 years
$2500*exp(0.0231*30) = $4,999.26
Easy problem
Today is Oct. 27, ’11
You invest $2,500 today
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Find FV on April 27, 2019, 5% SAIR,
compounded every 30 months
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Compounding occurs every 30 months, or 2.5
years
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Difference between the two dates
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Add 12.5% interest every 2.5 years
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
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Inflation is 3% per year for three years
Inflation is 4% per year for four years
Nominal payment is
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$35,000(1.03)3(1.04)4 = $44,741.76
Hard problem
Heath Wells deposits $10,000
in a bank, 9% yearly interest
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Money in the bank for 5 years
How much MORE interest is earned if
compounded monthly, relative to simple
interest?
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Compounded monthly
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Simple interest
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$10,000(1.0075)60 = $15,656.81
$10,000(1.45) = $14,500
Difference is $1,156.81
Medium problem
Biliana Marks and the will:
$3,000 per year forever…
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…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
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If annual inflation was the same every
years over a 207-year period, what is
yearly inflation rate?
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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
Rosie buys a robot, $1,000 today;
$100 maintenance cost in 1 yr
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What is EAC if discount rate is 4%/yr.?
PV of costs
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If EAC is X, then
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$1,000 + $100/1.04 = $1,096.15
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:
How long until it grows to $32K?
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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
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3
1
2
3
easy problems
easy-medium problem
medium problems
hard problems
Problem:
You invest $500 today
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You get back…
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$214.70 in one year
$350.30 in two years
(a) What is NPV if EAIR is 15%
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-500 + 214.7/1.15 + 350.3/1.152
-$48.43
Easy problem
Invest $500 today, get back
$214.70 & $350.30
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(b) Based on the answer in (a), is the
annual IRR >, <, or = to 15%
It must be less than 15%
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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
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(c) Calculate the annual IRR
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-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
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(d) Suppose that you receive an additional
payment in 3 years
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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
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What is PV of this bond if effective
annual discount rate is 6% for 1st 2
years and 14% thereafter?
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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
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10 payments
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$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
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Payments in…
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Yr.
Yr.
Yr.
Yr.
Yr.
Yr.
10:
12:
14:
16:
18:
20:
$13,390
$13,791.70
$14,205.45
$14,631.61
$15,070.56
$15,522.68
Sammy Waffle wins the Wacky
Lottery
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Present value of
payments
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$8,227.02
$7,462.15
$8,798.91
10 years from today
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$8,220.30
$5,850.33
Total PV of the 10
payments
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You can also use the annuity
formula to calculate the PV of
the last 6 or 7 payments
$6,262.13
20 years from today
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$6,702.91
18 years from today
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$7,174.72
16 years from today
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$7,679.73
14 years from today
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8 years from today
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$9,070.29
6 years from today
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4 years from today
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12 years from today
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2 years from today
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$75,448.50
Summary of problems
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2 points of easy problems
24 points of medium problems
6 points of hard problems
Grade distribution
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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
Remember that you drop your lowest grade
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For those of you with low grades, Test 1 may be
the score you drop
Grade distribution
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Average
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43.40 points
43.40/61 = 71.1%
THE GRADE DISTRIBUTION
BELOW IS MEANT TO BE AN
APPROXIMATE GUIDELINE
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Do not use this as an absolute guide for
determining your grade
Grade distribution
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99th percentile
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61 points
This is what you divide
your score by to
determine your grade
Those with 62 points will
get 100% and be
bumped up if on the
border of two grades at
the end of the quarter
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80th percentile
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53 points
Most students w/53+
points are approximately
in the A+ to B+ range
60th percentile
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48 points
Most students between
48-52 points are
approximately in the B+
to B range
Grade distribution
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50th percentile (median)
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44.5 points
The median student at
the end of the quarter
will likely get a B or B-
40th percentile
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42 points
Someone here is
approximately at a B- or
C+
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20th percentile
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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