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Last name of TA
Your name and Perm # ________________________________________________________________
Day and time of your section
Econ 134A
Test 3, Version A
John Hartman
December 7, 2011
Instructions: (First thing: Write your name, perm #, TA name, and day and time of your section above, and
bubble in your test form; if you do not do any of these, this is one way you can lose 3 points.)
You have 140 minutes to complete this test, unless you arrive late. Late arrival will lower the time available to you,
and you must finish at the same time as all other students.
Each question shows how many points it is worth. Show all work in order to receive credit. You will receive partial
credit for incorrect solutions in some instances in the PROBLEMS section. Clearly circle your answer(s) or else you
may not receive full credit for a complete and correct solution.
Cheating will not be tolerated during any test. Any suspected cheating will be reported to the relevant authorities on
this issue.
You are allowed to use a nonprogrammable four-function or scientific calculator that is NOT a communication
device. You are NOT allowed to have a calculator that stores formulas, buttons that automatically calculate IRR,
NPV, or any other concept covered in this class. You are NOT allowed to have a calculator that has the ability to
produce graphs. If you use a calculator that does not meet these requirements, you will be assumed to be cheating.
Unless otherwise specified, you can assume the following: Negative internal rates of return are not possible; all
interest is to be compounded as directed unless mentioned otherwise.
You are allowed to turn in your test early if there are at least 10 minutes remaining. As a courtesy to your
classmates, you will not be allowed to leave during the final 10 minutes of the test.
Your test should have 17 multiple-choice questions and 4 problems (35 points). The maximum possible point total is
89 points. If your test is incomplete, it is your responsibility to notify a proctor to get a new test.
Until all tests are collected, you are not to speak unless given the okay from one of the proctors. You are allowed to
talk to others once your test is collected and you have left the test room.
Grading:
For your reference, an example of a well-labeled graph is below:
Filling in scantron & front page of test correctly
and completely, & showing photo ID
3/3
(automatic unless you do not do any of these)
Multiple choice portion
_____/51
Other portions of test
_____/35
Total score
_____
MULTIPLE CHOICE: Answer the following questions on your scantron. Each correct answer is worth 3 points.
All incorrect or blank answers are worth 0 points. If there is an answer that does not exactly match the correct
answer, choose the closest answer.
1. Which of the following was referred to as a “$300 million sock puppet” in lecture?
A. General Motors
B. The United States government
C. Irving Fisher
D. pets.com
E. John Hartman
This information was given in lecture: pets.com.
Use the following information for the next two problems:
Suppose that the daily price for each share of Wobbly, Inc., stock is a random walk with each day’s movement
in price independent of the previous day’s. Every day, the stock can either go up or down by $1, each with 50%
probability. However, over the past five days, the stock has gone up by $1 every day. (For the questions below,
if your answer does not exactly match one of the answers, pick the closest answer.)
2. What is the probability that the stock will go up each of the next five days?
A. 100%
B. 50%
C. 10%
D. 3%
E. 0.1%
Each day’s outcome is independent of the previous days outcome: Probability is (½)5 = 3.125%
3. Compared to today, what is the probability that the stock will be the same price two days from now?
A. 100%
B. 75%
C. 50%
D. 25%
E. 0%
There are four possible outcomes, each with probability ¼: (up, down), (down, up), (up, up), (down, down). The
first two lead to the same price two days from now, so there is a 50% probability that the stock will be the same
price two days from now.
4. Suppose that you want to make a synthetic T-Bill as follows: Shares of T-Bolla stock are currently selling for
$250. A call option on T-Bolla with one year to maturity and a $250 strike price sells for $17. A put with the
same terms sells for $6. What is the implied risk-free rate?
A. 2.4%
B. 4.6%
C. 6.8%
D. 9.2%
E. 35.3%
See p. 685 to derive stock price + price of put – price of call = present value of exercise price. So the PV of the
exercise price is 250 +6 – 17 = 239. To calculate the risk-free rate, take 250/239 – 1 = 4.60%.
5. Suppose that taxable bonds are currently yielding 21%, while at the same time, non-taxable bonds of
comparable risk yield 8%. What is the break-even tax rate?
A. 8%
B. 13%
C. 38%
D. 62%
E. 163%
.21 (1 – t*) = .08  t* = 61.9%
6. If Stock A has an expected return of 6% and a standard deviation of 8%, and Stock B has an expected return
of 9% and a standard deviation of 12%, what is the minimum standard deviation possible of a portfolio of these
two stocks? Assume that the two stocks have a correlation of -1.
A. 9%
B. 8%
C. 6%
D. 4%
E. 0%
See Figure 11.4: The point of lowest s.d. when two stocks have a correlation of -1 is 0%.
7. A bond pays $2 every year forever, starting three months from today. The effective annual discount rate is
14%. What is the present value of this stream of payments?
A. $16.29
B. $15.84
C. $15.79
D. $15.76
E. $14.29
Interest rate every 3 months is (1.14)1/4 – 1 = 3.3299%. PV of an annuity with first payment 1 year from today is
2 / .14 = $14.29. PV of an annuity with first payment 3 months from today is (2/.14) (1.033299)3 = $15.76.
8. Sally Rutters receives a perpetuity, payable once every three years. The first payment of $100 is made today.
Each subsequent payment is 8% higher than the previous one. If the effective annual discount rate is 5%, what
is the present value of this stream of payments? (Pick the closest answer if your answer does not exactly match.)
A. $1400
B. $1500
C. $1700
D. $2000
E. Infinity
Payment made in 3 years: $108; using the growing perpetuity formula (with effective rate every 3 years of
(1.05)3 – 1 = 15.7625%), we get the PV of all future payments: $108/(.157625 - .08) = $1391. To get the PV of
all payments, we take the current payment’s value and add the PV all future payments: $100 + $1391 = $1491.
9. Gold Picker, Inc. currently has a stock price of $40 per share. The next dividend is expected to be $2 one year
from today, and grow at 4% per year forever. Executives of Gold Picker, Inc. are trying to determine what the
growth rate has to change to in order for the value of the stock to double. (This assumes that the dividend paid
one year from today does not change.) If you were to advise them, what would your answer be? (Note: Your
answer needs to be the new growth rate.)
A. 13%
B. 9%
C. 8%
D. 7%
E. 6.5%
First, we need to calculate r: $2/(r - .04) = $40  r = .09. Next, we can use this to calculate the new growth
rate needed to double the stock’s value to $80: $2/(.09 – g*) = $80  g* = 6.5%.
10. A stock is currently priced at $80. The stock will either increase or decrease by 9% over the next year. The
risk-free rate and the expected return of the stock are both 5%. There is a call option on the stock with a strike
price of $85. What is the risk-neutral value of the call option?
A. $0
B. $4.76
C. $5.33
D. $6.85
E. $7.20
Let p = prob. of stock price going up. Then .05 = .09p - .09(1-p)  p = 7/9. When the price falls, the call
option is worthless; when the price goes up, the call option is worth (87.20-85) / 1.05 = $2.09. PV of this option
is then 7/9 of $2.09, or $1.63. The closest value is $0, so this should be the answer that is chosen.
11. A bond pays coupons once per year. You buy a bond today that makes its only remaining coupon payment
of $100 one year from today. The face value of the bond is $600. If the bond sells for $640 today, what is the
return on the bond over the next year? (You can assume that there is no risk of default.)
A. -7%
B. 7%
C. 9%
D. 16%
E. 17%
All money received is one year from today: $600 + $100 = $700. If you pay $640 today, then your return after
one year is ($700 - $640) / $640 = 9.375%.
12. A risk-neutral investor has the utility function U(x) = x – 4.75, with x being number of percentage points of
the investor’s returns. Suppose that the risk-free rate is 9.5%. Further suppose that the current difference
between the expected return on the market and the risk-free rate is 4.75%. If the investor has to choose one of
the five securities below, which of the following investments would this investor want to maximize expected
utility?
A. A risk-free security
B. A security that gives the same return and risk as the market
C. A security with a beta of -1
D. A security with an expected return of 19%
E. A security with a beta of 2.1
The expected returns of each of the answers are (A) 9.5%, (B) 14.25%, (C) 4.75%, (D) 19%, (E) 19.475% 
Pick a security with the highest returns, since the higher the returns, the higher the utility: (E).
13. Suppose that you use two data points to try to estimate beta for a security. (Your estimate of beta will be
determined from the line that goes through both points.) When the S&P 500 has a return of -3%, the return of
this security is -2%. When the S&P has a return of 8%, the return of this security is 12%. What is your
estimated beta based on these two data points? (Pick the closest answer.)
A. 4.0
B. 1.3
C. 1.0
D. 0.8
E. 0.5
Beta will be the slope of the line, with the return % on the vertical axis: Slope = rise/run = [12-(-2)] / [8-(-3)]
= 1.2727.
14. A firm’s overall cost of capital is currently 15% and its beta is 2.0. The risk-free rate is currently 5%. The
firm is currently trying to determine if it should invest in a new project with a beta of 2.5. What is the discount
rate of this new project if a rational investor is indifferent about investing in this new project?
A. 20%
B. 17.5%
C. 15%
D. 12.5%
E. 5%
The market premium here is 5% ([15 – 5] / 2). If the new project has a beta of 2.5, then the point at which this
firm is indifferent about doing the project is 5% + 5%(2.5) = 17.5%.
15. In your first job interview, suppose that your boss tells you to use the discounted payback period method,
with the cutoff date 10 years, 6 months from now. In other words, the payback period is 10 years, 6 months. The
effective annual discount rate is 8%. Which of the following offers should you accept if you use this method?
A. $300 per year forever, with the first payment made today
B. $1,000 per year forever, with the first payment made seven years from today
C. A one-time payment of $2,400 today
D. $10,000 per year forever, with the first payment made 12 years from today
E. $750 every two years forever, with the first payment made two years from today
Find the PV of each offer, counting payments made only in the first 10 years, 6 months. (Note that you have to
discount each future payment appropriately.) (A) $2313, (B) $2087, (C) $2400, (D) $0, (E) $2420. Choose $750
every two years forever, with the first payment made two years from today.
16. A stock pays its next dividend of $3 one year from today. The dividend increases by $0.05 for each of the
next six years. (This increase is from the previous year’s dividend.) After the dividend payment seven years
from today, the company goes out of business and does not pay anything else to stock holders. How much is
this stock worth if your effective annual discount rate is 6%?
A. $20.80
B. $20.41
C. $19.26
D. $18.57
E. $17.52
$3/1.06 + $3.05/1.062 + $3.10/1.063 + … + $3.30/1.067 = $17.52
17. A zero-coupon bond pays its face value of $10,000 in 3 years. Today’s price for the bond is $8,912. What is
the yield to maturity, expressed as an annual percentage rate, using semiannual compounding? (Pick the closest
answer.)
A. 1.95%
B. 3.85%
C. 3.95%
D. 4.05%
E. 4.15%
Let r be the interest rate every six months. Then 8,912(1+r)6 = 10,000  r = 0.019383  The annual rate is
then 3.8766%.
PROBLEMS: For the following problems, you will need to write out the solution. You must show all work to
receive credit. Each problem (or part of problem) shows the maximum point value.
1. (9 points) $1 invested in 1925 would be worth $11.73 in 2008 if your investment went up by the inflation rate
every year. $1 invested in 1925 would be worth $9,548.94 in 2008 if invested in small company stocks. What is
the annual geometric mean of the real rate of return of small company stocks between 1925 and 2008? Round
your answer to the nearest hundredth of a percent.
There are many ways that this problem could be solved, all of which essentially do the same thing. Here is one
way: The real growth over the 83 years is $9,548.94/$11.73 = 814.06. To find the geometric mean over the 83
years, take the 83rd root of 814.06, and subtract one: 8.41%.
2. (6 points) Suppose that you believe that the true distribution of returns for Wrample, Inc., are as follows:
There is a 60% probability that Wrample’s return in any given year is 5%, a 20% probability that Wrample’s
return in any given year is –15%, and a 20% probability that Wrample’s return in any given year is 20%. What
is the standard deviation of Wrample’s returns? (Some hints: [1] This is not a case of using a sample. [2] If you
are not sure how to do this problem using one of the formulas on the formula sheet, you may want to have five
possible states of the world.) Round your answer to the nearest hundredth of a percent.
The simplest way to solve this is to assume five states of the world, with each state having 20% probability of
occurring: -15%, 5%, 5%, 5%, 20%. The expected return is 0.04. You then need to find the squared deviation of
each state (.0361, .0001, .0001, .0001, .0256). The average of these five outcomes is the variance: .0124. The
square root of the variance is the standard deviation: .11136, or 11.136%.
3. (6 points) Lesley buys a share of a stock at a price of $60 today, and a call option with an exercise price of
$55 two months from now. (In other words, the expiration date of the option is two months from now.) The call
option is for buying one share. For simplicity in this problem, you can assume that the discount rate is 0%.
Draw a well-labeled graph that shows the value of a combination of the stock and the call as a function of the
value of the stock at expiration. The vertical intercept should have the value of the combination of the stock and
the call. The horizontal intercept should have the value of the stock at the expiration. Make sure to label your
intercepts and other relevant numbers on each axis, where relevant. (Hint: You may want to look at the front
page of the test to see a well-labeled graph.) Explain your answer in words or using additional graphs.
Combined value of the
stock and the call ($)
The slope of the red line segments
1; the slope in blue is 2.
55
Stock value at
expiration ($)
55
To justify how you get this graph, you can either show that this is the sum of two graphs, or use the following
mathematical approach: If p < 55, then the call option is worthless. The value of the stock plus the value of the
call is p + 0 = p. When the value of the stock is greater than 55, then the combined value is p + (p – 55) = 2p –
55.
4. The Gobblenover machine can be purchased today for $20,000, and lasts for 25 years. There are additional
maintenance expenses at the end of each of the first 20 years. The first maintenance expense, paid one year
from today, will be $3,000. For each of the next 19 years, the maintenance cost will be 5% higher than the
previous year’s. For your calculations, you can assume that the annual discount rate is 8%. (Note: All costs
here are in real terms. This information has been incorporated into the discount rate.)
(a) (4 points) What is the present value of money spent throughout the life of the Gobblenover? Round your
answer to the nearest dollar.
$20,000, plus a growing annuity with C = $3,000, r = .08, g = .05, and T =20. This gives a total of $63,074.
(b) (6 points) What is the equivalent annual cost of the Gobblenover? Round your answer to the nearest dollar.
63,074 needs to be equal to an annuity paid out over 25 years: 63,074 = (C/r) [1 – 1/(1+r)T]. Let r = .08 and T
= 25 to get C = $5,909.
(c) (4 points) If you made the same rental payment at the beginning of each of the 25 years for the Gobblenover,
how much would each payment have to be in order to have the same present value as in part (a)? Round your
answer to the nearest dollar.
The easiest way to do this is to realize that this is the same as (b), except that each payment is made at the
beginning of the year instead of the end of the year: $5,909/1.08 = $5,471.