Day and time of your section
________________________________________________________________
Your name and Perm #
Econ 234A
Test 2
John Hartman
March 21, 2013
Instructions:
You have 130 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. 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.
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 6 problems, some with multiple parts. The maximum possible point total is 67 points. If your test is incomplete, it is your responsibility to notify a proctor to get a new test.
For your reference, an example of a well-labeled graph is below:
Grading:
Filling in name, perm #, and day/time of section, & having photo ID
1 /1
(
)
Problems
Total score
_____/66
_____

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. Provide at least four significant digits to each answer or you may not receive full credit for a correct solution.
1. The Pointer 2100 machine can be purchased today for $10,000. Maintenance costs of $3,000 per year are also required 2 years, 5 years, and 8 years from today. The machine lasts for 10 years. Assume an effective annual discount rate of 13%. Note: All costs in this problem are in real dollars.
(a) (6 points) What is the equivalent annual cost of the machine?
PV of costs are 10,000 + 3,000/1.13
2
$15,106.20 = (EAC/0.13) [1 – 1.13
-10
+ 3,000/1.13
5
= 3,000/1.13
]

EAC = $2,783.92
8
= $15,106.20
(b) (6 points) Suppose you financed the machine as follows: You will loan all of the money needed to pay the present value of all costs of the machine today. You will make 9 payments to pay back the loan. These payments will be annually, starting two years from today. If each payment is the same, how much will each payment be?
$15,106.20 = (1/1.13) [(X/.13)(1 – 1.13
-9

X = $3,326.40
)] (annuity formula discounted by 1 year on right side)
2. (10 points) Natalie is celebrating her 40 th
birthday today. She has just sold a successful company she has run for the past 10 years, for $2,000,000. She will deposit this into an account today. The account that she opens today will earn 5% effective annual interest every year forever. She will also deposit $X on her
41 st
birthday, and 3% more each subsequent birthday until her 60 th
birthday. She will then withdraw
$500,000 each year, with the first withdrawal on her 61 st
birthday and the last withdrawal on her 90 th birthday. After the last withdrawal, the balance of the account will be zero. What is X?
2,000,000 + X[1/(.05-.03) – {1/(.05-.03)} (1.03/1.05)
20
] = 1.05
-20
(500,000/0.05)(1 – 1.05
-30
)

X = $56,177.25
3. (6 points) Chad is determined to deposit $250 into a bank account today that will earn 4.5% stated annual interest, compounded monthly. If no other deposits or withdrawals are made, when will the balance of the account reach $17,000? State your final answer in years.
250 (1 + 0.045/12)
T
= 17,000

1.00365
T
= 68

T = log 68/log 1.00375 = 1127.3 months, or 93.94 years.

4. (10 points) Randy buys one put option with an exercise price of $50 (per share) today, and one call option with an exercise price of $60 (per share). The expiration date of both of these options is one year from now. Each option is for buying or selling one share. The effective annual discount rate is 5%. Draw a well-labeled graph that shows the present value of a combination of the two options as a function of the value of the stock at expiration. The vertical intercept should have the present value of the combination of the two options. The horizontal intercept should have the value of the stock on the expiration date.
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, math, and/or using additional graphs. Include enough detail so that everything on the graph is unambiguous.
The PV of a put option is 50/1.05 = $47.62 if the value of the stock is 0 on the expiration date. For each additional dollar in value of the stock, the value of the put option goes down by $1/1.05, or $0.952381.
This continues until the value of the put option reaches $50, in which the put option has value of zero.
The call option will only have a positive value if the value of the stock exceeds $60. In this case, for each additional dollar in value of the stock, the value of the call option goes up by $1/1.05, or
$0.952381. Add these values together to get the graph below, also commonly known as a long strangle in the finance world:
Combined PV of both options
47.62
Slope here is
-0.952381
Slope here is 0.952381
50 60
Value of stock one year from today

5. Solve each of the following:
(a) (5 points) A firm currently has a capital structure of one part debt to three parts equity. The beta of this firm would be 1.3 if it would be an all-equity firm with no debt. (In other words, the beta of the firm if unlevered is 1.3.) The beta value of any debt issued is 0.3. How much would the equity beta change if the firm decides to change to having one part debt to one part equity?
Old: 1.3 = 0.75β equity
+ 0.25 (0.3)

β equity
New: 1.3 = 0.5β equity
+ 0.5 (0.3)

β equity
= 1.63333
= 2.3
The difference is 0.666667
(b) (4 points) This question is an example of discount interest: Sam borrows $50,000 today with a quoted interest rate of 8%. With discount interest, the bank deducts 8% of the loan amount up front, and gives this amount to Sam. Sam must then repay $50,000 one year from now. Is Sam truly being charged an effective annual interest rate of 8%? Justify your answer.
46,000 (1+r) = 50,000

r = 0.0869565
NO, since the EAIR is actually 8.69565% for this loan.
(c) (4 points) What happens to the value of a call option when the interest rate goes up? Explain your answer in 30 words or less.
Call option value goes up: The delay in potential value leads to a higher value for the option, since the money that could have been invested in the stock today can be invested at a higher interest rate between now and the option’s expiration date.
(d) (4 points) What happens to the value of a put option when the exercise price goes up? Explain your answer in 30 words or less.
Put option value goes up: 1. There is a higher likelihood of being in the money. 2. Conditional on being in the money, there is a higher payout.

6. There are 4 states of the world: A, B, C, and D. The respective probabilities of each state are 15%,
20%, 25%, and 40%. The respective annual returns for Asset G in each state of the world are 5%, 10%,
28%, and 12%. The respective annual returns for Asset H in each state of the world are 14%, 10%, 12%, and 8%.
(a) (2 points) What is the expected return of a portfolio with half of its funds in each of the two assets?
Exp. return of G = .15(.05) + .20(.1) + .25(.28) + .40(.12) = .1455
Exp. return of H = .15(.14) + .20(.1) + .25(.12) + .40(.08) = .103
Portfolio expected return = .5(.1455+.103) = .12425 = 12.425%
(b) (9 points) What is the standard deviation of a portfolio with half of its funds in each of the two assets?
Variance of a portfolio = .5
2 σ
G
2
+ 2(.5)(.5)
σ
G,H
+.5
2 σ
H
2
σ
G
2 = .15 (.05 - .1455) 2 + .2 (.1 - .1455) 2 + .25 (.28-.1455) 2 + .4 (.12 -.1455) 2 = .00656475
σ
H
2
= .15 (.14 - .103)
2
+ .2 (.1 - .103)
2
+ .25 (.12 - .103)
2
+ .4 (.08 - .103)
2
= .000491
σ
G,H
= .15(.05-.1455)(.14-.103) + .2(.1-.1455)(.1-.103) + .25(.28-.1455)(.12-.103) + .4(.12-.1455)(.08-
.103) = .0003035
Use these to find the variance of the portfolio to be 0.001915687

s.d. is the square root of the variance, which is 0.0437686, or 4.37686%.
ALTERNATE METHOD TO FIND THE VARIANCE OF THE PORTFOLIO:
.15(.095-.12425)
2
+ .2(.1-.12425)
2
+ .25(.2-.12425)
2
+ .4(.1-.12425)
2
= .001915687