Name______Perm #______
Econ 134AJohn Hartman
Test 3, Form ADecember 7, 2015
Instructions:
YOU WILL TURN IN THE ENTIRE TEST, INCLUDING THE MULTIPLE-CHOICE QUESTIONS.
You have 160 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.
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.
- Equivalent annual cost problems are in real dollars.
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 10 multiple choice questions (20 points) and 6 problems (49 points). The maximum possible point total is 70 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:
MULTIPLE CHOICE: Answer the following questions on your scantron. Each correct answer is worth 2 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.If Joe believes that all information (including private information) relevant to a stock is incorporated into a stock’s price, then he believes in what form(s) of efficiency?
A.Weak form efficiency only
B.Semi-strong form efficiency only
C.Strong form efficiency only
D.Both weak and strong form efficiency only
E.Weak and semi-strong, and strong form efficiency
2. A stock has a value right now of $80. Each day starting tomorrow, the stock’s price changes in the same fashion as a random walk as follows: there is a 50% chance that the price goes up by $2, and a 50% chance that the price goes down by $2. Each day’s movement in price is independent of the previous day’s movement. You own a call option with an exercise price of $83.50, and the call option can only be exercised three days from now. What is the probability that the call option will have positive value three days from now?
A. 0%B. 12.5%C. 25%D. 50%E. 87.5%
3. Assume an effective annual discount rate of 10%. If someone invests $500 in a project today, and then receives $700 3 years later from the investment, what is the profitability index of this investment?
A. 0.85B. 0.95C. 1.05D. 1.15E. 1.25
4. A zero-coupon bond has a face value of $600, to be paid 8 months from today. If the yield to maturity is 5% (as an effective annual interest rate), what is the current price of the bond?
A. $550B. $560C. $570D. $580E. $590
5. An asset promises to pay $20 per year forever, starting six months from today. The stated annual discount rate for this asset is 14%, compounded twice per year. What is the present value of this stream of payments?
A.$148.05B. $147.70C. $152.50D. $152.85E. $153.20
6. Suppose that the daily price of each share of Paradise Profit Walk Shoes stock is a random walk with each day’s movement in price independent of the previous day’s price change. Every day, the stock can either go up or down by $5, each with 50% probability. The stock is currently valued at $50. What is the probability that the value of the stock three days from now will be exactly $60?
A. 0%B. 25%C. 50%D. 75%E. 100%
7. Which supermarket chain talked about in lecture is selling its Santa Barbara area stores?
A. Smart FinalB. VonsC. HaggenD. RalphsE. Gelson’s
8. Joanna owns an investment in which she receives $1,000 today, she must pay $2,200 one year from today, and she receives $1,202 two years from today. She finds that there are two internal rates of return, L and U. Both L and U are positive and L < U. For which positive discount rates will the net present value of this investment be positive?
A. Between L and U only
B. Less than L only
C. More than U only
D. Less than U only
E. Less than L and More than U
9. An asset’s returns were analyzed over a four-year time period. During these four years, the rates of return were 5%, 12%, 5%, and 5%. What is the standard deviation of this sample?
A. 2.5%B. 3%C. 3.5%D. 4%E. 4.5%
10. Hal borrows $10,000 today and will make 10 monthly payments to completely pay back the loan, starting one month from today. He will reduce the principal by the same amount each month. How much will the payment be 5 months from today if Hal’s stated annual interest rate is 24%, compounded monthly?
A. $1,120B. $1,100C. $1,080D. $1,060E. $1,040
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.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.
11. (7 points) Stock Z has a 40% probability of a 2% return in a given year, a 50% probability of a 15% return in a given year, and a 10% probability of a 20% return in a given year. The beta value for Stock Z is 2. The return of a risk-free asset is 8%. What is the return of an asset with a beta value equal to 1?
12. (9 points; this problem is meant to be challenging) Carlos is about to buy a $1,000,000 house in a small Iowa town. He will pay 30% of the house’s cost in cash, and finance the other 70% of the cost with a mortgage. He will pay off the loan over 40 years, and he will make yearly payments to pay off the mortgage starting one year from today. Carlos will pay back the loan with a partial amortization re-payment schedule over the first 20 years, followed by a new financing schedule to completely pay off the balloon payment 20 years from today over the following 20 years.
The loan for the first 20 years has 40-year amortization with a 5% interest rate. This will result in a balloon payment 20 years from today, which will be financed with a new loan over the following 20 years. The first payment for the second loan will occur 21 years from today. The interest rate over the last 20 years will be 7.5%.(Note that the last payment 40 years from today will completely pay off the loan.)
How much will each payment be? There are many steps needed to justify your answer, so please make sure the grader can understand your math and reasoning behind the solution. You can use the next page if you need more room to solve this problem. (Note that all interest rates in this problem are effective annual interest rates.)
(You can continue the work from the problem on the previous page here.)
13. (7 points) Stock Q’s value today is $50. Over the course of the next year, the value of the stock could go up by $2, $4, $6, $8, or $10, each with 20% probability. Hillary holds a European call option for Stock Q with an exercise price of $55.50, and an expiration date of one year from today. What is the present value of the option if the appropriate discount rate for the option is 20%?
14. Laura has run a regression of the security market line, just as you did in your econometrics assignment, with beta and expected returns entered as decimals. (For example, an expected return of 5% is entered as 0.05 for the regression) Based on her sample size, she finds in her regression results that her point estimate for the slope is 0.1 with a standard error of 0.009. Her point estimate for the y-intercept is 0.06 with a standard error of 0.005. Explain all answers below with words, an equation, and/or a graph.
(a) (3 points) What is the estimated rate of return for a risk-free asset? Explain your answer in 25 words or less.
(b) (4 points) What is the estimated rate of return for an asset with beta equal to 1? (Note: I am referring to the meaning of beta referred to in this class, not the beta meaning that is commonly referred to in econometrics classes.)
15. There are three known states of the world, L, M, and N. Each state occurs with one-third probability. When State L occurs, Stock A has a rate of return of 6% and Stock B has a rate of return of 19%. When State M occurs, Stock A has a rate of return of 14% and Stock B has a rate of return of 2%. When State N occurs, Stock A has a rate of return of 10% and Stock B has a rate of return of 15%.
(a) (1 point) What is the average rate of return for each stock. (Note: Both must be correct to receive credit.)
(b) (3 points) What is the standard deviation for the rate of return of each stock?
(c) (4 points) What is the correlation coefficient for the rate of return for these two stocks?
16. (6 points) Lesley buys two shares of stock at a price of $100 today, and one put option with an exercise price of $90 two years from now. (In other words, the expiration date of the option is two years from now.) The put option is for selling 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 two shares of stock and the put option 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 at the front page of the test to see a well-labeled graph.) Explain your answer in words, math, and/or using additional graphs.
17. (5 points) Aubrey’s Waffles currently has $200,000 of stock issued, with no bonds. The current cost of equity is 10%. If the company sells $25,000 of bonds and uses this money to purchase $25,000 worth of stock, what is the new cost of equity? Assume that the cost of debt is 5% and that there are no other securities issued by Aubrey’s Waffles. You can also assume that the weighted average cost of capital is constant.
NOTE: YOU CAN TEAR THIS SHEET OFF AND USE AS EXTRA SCRATCH PAPER. PLEASE NOTE THAT ANYTHING ON THIS SHEET WILL NOT BE GRADED UNLESS EXPLICITLY SPECIFIED ON THE TEST.
Perpetuity
Annuity
Growing perpetuity
Growing annuity
Quadratic formula
ax2 + bx + c = 0
Logarithmic rule
ab= c b = log c / log a
Variance of a sample
Variance of a distribution, with each outcome having the same probability of occurring
Covariance formula
Correlation of A and B
, where SD stands for standard deviation
Variance of a portfolio