Name______Perm #______

Econ 134A (common final for both lectures)John Hartman

Test 3, Form AMarch 18, 2017

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 8 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.At the beginning of the February 8 lecture, I read the cover story of the January 30 issue of Barron’s magazine titled Next Stop: Dow ______. (Hint: This number is a projection of the Dow Jones Industrial Average by the year 2025.)

A. 10,000B. 15,000C. 20,000D. 25,000E. 30,000

2. A European call option for a stock has an exercise price of $60, and an expiration date of one year from today. This stock has a 10% chance of having each of the following values: $48, $49, $50, $51, $52, $53, $54, $55, $56, and $57. What is the present value of the call option? The effective annual interest rate for this stock is 50%.

A. $0B. $1C. $2D. $3E. $4

3. A firm currently has a capital structure of **one part debt to two parts equity**. The beta of this firm would be 1.25 if it would be an all-equity firm with no debt. (In other words, the beta of the firm if unlevered is 1.25.) The beta value of any debt issued is 0.9. How much would the equity beta decrease by if the firm decides to change to having **one part debt to three parts equity**?

A. 0.01B. 0.05C. 0.1D. 0.25E. 0.5

4. Which of the following types of efficiency has the most assumptions?

A. Semi-strong efficiency

B. Strong efficiency

C. Weak efficiency

D. All three have the same level of assumptions

E. There is no way to tell which form has the most assumptions

5. Bridgette receives a loan of $50,000 today. She must completely pay the loan back in 48 monthly payments, starting eight months from today. The effective annual interest rate on the loan is 15%. How much will each payment be?

A. $1,370 B. $1,420 C. $1,470D. $1,480 E. $1,500

6. If a rare coin sells for $100,000 today and it sold for $100 forty years ago, what is the geometric average rate of return over the last forty years?

A. 17%

B. 19%

C. 25%

D. 32%

E. Unable to determine the geometric average from the information given

7. A stated annual interest rate of 9.5%, compounded every hour, is equivalent to an effective annual interest rate of _____. (Assume 365 days in a year.)

A. 9.65%B. 9.75%C. 9.85%D. 9.95%E. 10.05%

8.Two stocks, Y and Z, have a correlation coefficient of 1. Suppose that you invest 80% of your money in stock Y and 20% of your money in stock Z. What is the standard deviation of this portfolio if the standard deviation of stock Y’s return is 30% and the standard deviation of stock Z’s return is 15%?

A. 15%B. 18%C. 21%D. 24%E. 27%

9. Three stocks have annual returns of 12%, 24%, and 32%. The variance of this sample is _____.

A. 0.0044B. 0.0064C. 0.01D. 0.03E. 0.08

10. What is the annuity factor of a 50-year annuity with an effective annual interest rate of 18%? Assume annual payments, with 50 payments made starting one year from today.

A. 5.5B. 5.25C. 5D. 4.75E. 4.5

**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. Buzzy will invest in a portfolio, with ¾ of the money invested in Dull Doldrum Dolly Company, and ¼ of money in a risk-free bond. Dull Doldrum Dolly Company stock could have a rate of return of 0%, 15%, or 30%, each with one-third probability. The risk-free bond has a rate of return of 10%.

(a) (3 points) If Dull Doldrum Dolly Company has a beta value of 2, what is the expected return of a stock with the same beta value as the market portfolio?

(b) (4 points) What is the standard deviation of Buzzy’s portfolio?

12. (6 points) Dakota has just received $800,000 for a house mortgage. The loan will be paid back as follows: The first payment of $1,000 will be paid one month from today. 359 subsequent monthly payments will be made, each 0.4% higher than the previous payment. A final balloon payment will be made 400 months from today to completely pay off the loan. How much will this balloon payment be? Assume a stated annual interest rate of 18%, compounded monthly.

13. Solve each of the following:

(a) (3 points) Give an example in which for a given year, the capital gain for a stock is negative but the percentage return is positive.

(b) (3 points) A stated annual interest rate of 15%, compounded 5 times per year is equivalent to what stated annual interest rate if compounded 6 times per year?

14. (7 points) Suppose that Stock F and Stock G have a correlation value of ρ = –1. Stock F has an expected return of 12% and standard deviation 15%. Stock G also has an expected return of 12% and standard deviation 15%. Today, each stock is valued at $200 per share. Over the next year, Stock F will go up by $9. How much will Stock G go up by next year? (Please completely justify your answer to get full credit.)

15. Nola is considering an investment that will require her to receive $500 today and $1,195 two years from today. She will also need to pay $1,595 one year from today as part of the investment.

(a) (4 points) Find all internal rates of return.

(b) (2 points) For what discount rates will there be positive net present values for this investment? You must completely justify your answer to receive credit.

16. (6 points) Marilyn owns a European call option for TMIWD, Inc. The option has an exercise price of $130, with an expiration date one year from today. If Marilyn assumes that TMIWD stock’s value on the expiration date comes from a uniform distribution, with all prices between $100-$140 equally likely, what is the perceived expected value of the option? Assume that Marilyn is risk neutral, and assume an effective annual discount rate of 25% for this option. (Note that with this uniform distribution, any price from $100 to $140 is equally probable in 1-cent increments, but no other price can occur with positive probability. You can use a continuous distribution as an approximation if you want.)

17. (6 points) Travis buys two put options with an exercise price of $50 (per share) today, three call options with an exercise price of $150 (per share), and four shares of stock currently valued at $90 (per share). The expiration date of all of these options is one year from today. Each option is for buying or selling one share. The effective annual discount rate for these options is 20%. Draw a well-labeled graph that shows the value of a combination of the five options and four shares of stock, as a function of the value of the stock at expiration. The vertical intercept should have the present value of the combination of the assets. The horizontal intercept should have the future 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.

18. (5 points) Suppose you start a bank account one year from today. If you make annual deposits of $100 into an account that pays an effective annual interest rate of 15%, when will you have an account balance of $50,000? (Round to the nearest number of years. The deposits will occur on the same date each year starting one year from today.)

**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