1. Econ 134A
Spring 2016 Test 3
Based on Form A

2. Q1
Stock X has a beta of 2 and a rate of return of 20%. Stock Y has a beta of 1.5 and a rate of return of 16%. What is the market rate of return?
A 24% B 22% C 18% D 14% E 12%
Beta rate of return
20% %
12% (recall linear relationship)
Answer: E

3. Q2
A stated annual interest rate of 24%, compounded continuously, is equivalent to a stated annual interest rate of ____%, compounded every three months?
e^.24=
(1+r)^4=
1+r= r=
SAIR=4× =

4. Q3
A bond has a face value of $500 and will pay out a 12% coupon six months and 18 months from today. The bond will also mature 18 months from today. If the effective annual interest rate of this bond if 15%, what is the present value of this bond?

5. Use the following information to answer the next three questions: No Sins Trucks stock exhibits price changes that are a random walk. In any given day, the value of the stock goes up by $2 with probability 0.6 and down by $3 with probability 0.4. The stock’s current value is $90.

6. Q4
What is the probability that the value of the stock will be the same three days from today?
A 0% B 6% C 22% D 29% E 43%
No possible combination
Answer A

7. Q5
What is the probability that the value of the stock exceed $95 three days from today?
Pr(U,U,U)= (0.6)^3=.216

8. Q6 What is expected value of the stock three days from today?
Expected change each day= $2(.6)+$3(.4)=$0
Answer: $90

9. Q7
In your first job, suppose that your boss tells you to use the discounted payback period method, with the cutoff date 5 years, 6 months from now. In other words, the payback period is 5 years, 6 months. The effective annual discounted rate is 10%. Which of the following offers should you accept if you use this method, and provide the reason why?
A (400/.1) (1- 1/(1.1^5))=1516
B 700/(1.1^4) +700/(1.1^5) = 913
C 2000/(1.1^.5)=1906
D 0
E 1,000/(1.1^3)+1,000/(1.1^5)=1372
Answer C

10. Q8
A sample of stocks has rates of return of 20%, 30%, and 28%. The standard deviation of this sample is X%. What is X?
X= (20%+30%+28%)/3=26%
Var=1/2 [(.2-.26)^2+(.3-.26)^2+( )^2]=.0028
Sd=

11. Q9
Which of the following would be information incorporated into the value of a stock if we believed in the strong form of efficiency?(If more than one of the first four answers is correct, pick E)
Answer:E (all information is believed to be used with the strong form of efficiency)

12. Q10
Heidi wants to borrow $30,000 from a local bank to buy a new car. She can afford to make monthly payments up to $800 per month. Assuming that interest is compounded monthly, what is the largest annual interest rate she can afford on a 48 month loan?
30000=(800/r)× [1- 1/((1+r)^48)]
This is hard to solve mathematically, but we can try different values.
If r=.1, then the right side of equation is $31,542.
.125$30,098pick E

13. Q11
Pinch an Inchworm, Inc. currently has $80,000 of stock issued, with no bonds. The current cost of equity is 20%. If the company sells $20,000 of bonds and uses this money to purchase $20,000 worth of stock, what is the new cost of equity? Assume that the cost of debt is 10% and that there are no other securities issues by Pinch an Inchworm. You can also assume that the weighted average cost of capital is constant.
.2=.1(20,000/80,000)+X(60,000/80,000)
.2=.025+(3/4) X X=

14. Q12
Lucy Bongo Drinks, Inc. always acts as a cash cow unless indicated otherwise. Without any re-investment of their earnings they will earn $5 per share every year forever. The effective annual interest rate for owning this stock is 20%. Assume that the next dividend payment will be made later today. Suppose that Lucy Bongo Drinks, Inc. could retain all of its earnings 4 years from today, and earn 25% on these earnings over the following year. (In other words, no dividend would be paid 4 years from today if Luck Bongo Drinks retains all of its earnings, and would continue to act as a cash cow in later years. )
(a)What is the present value of this stock if it continues to act as a cash cow?
5+5/.2=$30

15. Q12
(b) Should Lucy Bongo Drinks retain its earnings 4 years from today? Why or why not?
Yes, return on earnings > discount rate OR NPV>0
(c) How much does the present value of Lucy Bongo Drinks change if the company retains its earnings 4 years from today?
-5/(1.2^4)+5(1.25)/(1.2^5)=$

16. Q13
Two families, the Greens and the Browns, are buying a house today. The Greens will completely pay back a loan on their house monthly over the next 10 years, starting in one month. The Browns will do so monthly over the next 30 years, also starting in one month. Each family will take out a mortgage of $100,000 and will make equal monthly payments to pay back the loan. The stated annual interest rate for both families is 12%, compounded monthly.

17. Q13
(1) During the next 10 years, how much more will the Greens pay each month(relative to the Browns)?
Greens: 100,000=(C/0.01)×[1-1/(1.01^120)]
100,000= C
C=1,434.71
Browns: 100,000=(C/0.01)×[1-1/(1.01^360)]
100,000= C
C=1,028.61
Difference = $1, $1,028.61=$406.10

18. Q13
(2) How much more interest will the Browns pay (relative the Greens) over the life of each family’s respective loans?
Greens: $1,434.71×120=$172,165.20
-100,000=72, interest
Browns: $1,028.61×360=$370,299.60
-100,000=270, interest
Difference: $ 270, $72,165.20=$198,134.40

19. Q14
There are 3 states of the world, X,Y and Z. In state X, stock A has a rate of return of 6% and stock B has a rate of return of 20% . In state Y, stock A has a rate of return of 10% and stock B has a rate of return of 2%. In state Z, stock A has a rate of return of 14% and stock B has a rate of return of 11%. All three states have one-third probability of occurring. What is the standard deviation of a portfolio that has 50% of money invested in each of stocks A and B?

20. Q14
Ra=( )/3= Rb=( )/3=.11
σ2a= 1/3 [(.06-.1)^2+(.1-.1)^2+(.14-.1)^2]=.00106
σa= %
σ2b= 1/3 [(.2-.11)^2+( )^2+( )^2]=.0054
σb= %
Covariance=1/3[(.06-.1)(.2-.11)+(.1-.1)( )+(.14-.1)( )]=-.0012
Variance of portfolio:
(.5)^2(.00106)+2(.5)(.5)(-.0012)+(.5)^2(.0054) = =
Standard deviation of portfolio= %

21. Q15
Find the present value of each of the following restaurants’ future dividend payments. Assume the effective annual interest rate for each restaurant is 20%. Assume each company is infinitely lived unless mentioned otherwise.
Check Your Mailboat, Inc. will pay out a dividend of $5 every months, starting in 18 months.
PV=(1/(1.2^(15/12))) 5/ =$85.37
3-month rate=

22. Q15
(b) Mr. Buss’s Buses, Inc. will pay out a dividend of $9 every 2 years, starting in 5 years. The company will go out business 50 yeas from today, and pay its shareholders $1,000 per share. No dividend payments will be made after the company goes out of business.
Dividends in years 5,7,9,11,….,49(23 times)
Rate every 2 years (1.2)^2-1=44%
PV=1/(1.2^3)[(9/.44)(1-1/(1.44^23))] +1000/(1.2^50)= ×.10988
=11.94

23. Q16
Isaias buys one share of stock a price of $80 today and two put options with an exercise price of $40 two years from now. (In other words, the expiration date of the option is two years from now.) The put option is for selling for 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 one share of stock and the two shares put options as a function of the value of stock at expiration. The vertical intercept should have the value of the combination of the stock and the put. 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 art the front page of the test to see a well-labeled graph.) Explain your answer in words, math, and / or using additional graphs.

24. Q16 Stock value X<=40: Value of puts each @ 40-x, 2 puts: 80-2x
Value of 1 share x
Total 80-x
Stock value X>40:
Value of puts 2 puts: 0
Total x

25. Q16

26. Q17
Mary Ann has just won the Super Wacky lottery jackpot. She is given two choices: (1) receive a monthly payment of $10,000 (starting today) or (2) receive a one-time lump sum payment of $1,000,000. If Mary Ann’s stated annual discount rate is 6%, compounded monthly, what is the minimum number of monthly payments she must receive in order to do better with the first option?
1,000,000=(10,000/.005)× [1-1/((1+.005)^T)]+10,000
990,000=10,000/.005 [1-1/(1.005^T)]
2,000,000/(1.005^T)=1,010,000
2,000,000/1,010,000=1.005^T T=
137 payments needed

27. Q18
Pump With Pride and Love, Inc. stock currently sells for $60 per share. Each of the next 4 years, the value of the stock will go up or down by $5, each with 50% probability. Ron buys a European call option with expiration date 4 years from today. The exercise price on this option is $69. What is the present value of this option if the effective annual interest rate is 25%?
UUUU$80Pr=.5^4=1/16
UUUD, UUDU, UDUU and DUUU $70 Pr=4×(.5)^4=1/4
PV of the option=(1/16) (1/(1.25^4))(11)+(1/4) (1/(1.25^4))(1)
= =.384