Econ 134Ajohn Hartman

Your name and Perm # ______

Econ 134AJohn Hartman

Test 3, Version ADecember 10, 2012

Instructions: (First thing: Write your name, perm #, TA name, and day and time of your section above, and bubble in your test form, name, and perm # on your scantron; 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.

Problems section: 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 yields and 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 8 multiple-choice questions and 6 problems (65 points). The maximum possible point total is 92points. 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.

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 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. A stock pays a dividend of $5 later today. The dividend will increase by 3% each year forever. What is the present value of the stock if the effective annual discount rate is 7%?

A. $71.43B. $73.57C. $125D. $128.75E. $133.75

5 + 5.15/(0.07 – 0.03) = $133.75

2. Patrick has just made a settlement in a court case. He will receive $3,000 every six months, starting one year from now. He will receive a total of 10 payments of $3,000 each. If his effective annual discount rate is 8%, what is present value of these payments?

A. $22,500B. $23,500C. $24,500D. $25,500E. $26,500

Find the stated rate every six months that will give you an effective rate of 8%: sqrt(1.08) – 1 = 3.9230%. Then do the following calculation: (1/1.039230) * (3000/1.039230) * (1 – 1/1.03923010) = $23,504.09. Note: 1/1.039230 is needed to discount the annuity formula used by 6 months.

3. Which of the following values could be the beta value of a risk-free asset?

A. –1B. 0C. 0.5D. 1E. 1.5

A risk-free asset must have a beta value of 0, based on the CAPM equation we derived in class. Any negative value of beta will give a return that is lower than the risk-free rate, and any positive value of beta will give a return that is higher than the risk-free rate.

4. Which of the following was NOT mentioned as a bubble in lecture?

A. The U.S. stock market in the 1920s

B. The Gold rush of the 1840s

C. Uranium markets in the 2000s

D. The Mississippi Company

E. The Tulip market during the Dutch Golden Age

All were mentioned in lecture as bubbles except the Gold rush of the 1840s.

For the next two problems, assume that there are two stocks, X and Y. Stock X has an expected return of 18% and a standard deviation of 23%. Stock Y has an expected return of 24% and a standard deviation of 28%. For each problem below, you will need to choose an answer that could be the lowest standard deviation of a portfolio of the two stocks. (In other words, only one of the answers could be the standard deviation of the minimum variance portfolio. Find that value.)

5. The two stocks are perfectly negatively correlated.

A. 0%B. 18%C. 23%D. 24%E. 28%

See Figure 11.4, p. 342, in the 9th edition, or Figure 11.4, p. 332 in the 3rd Core edition. You will see that if two stocks are perfectly negatively correlated, then their rho value (ρ) is -1. The lowest possible standard deviation in this instance is 0%.

6. The two stocks have a correlation strictly greater than –1 and strictly less than 1.

A. 0%B. 18%C. 23%D. 24%E. 28%

Using the same figure as in the previous problem, you will see that the lowest possible standard deviation must be positive, but less than the standard deviation of the least risky stock. So the answer must be more than 0%, but less than 23%. 18% is the only answer that could be correct.

7. Suppose that in the final interview before someone receives a job offer, the interviewees get the following problem: Use the discounted payback period method, with the cutoff date 13 years, 3 months from now. In other words, the payback period is 13 years, 3 months. The effective annual discount rate is 15%. Which of the following offers should be picked if someone uses this method?

A. 12 payments of $1000 every month, starting one month from today

B. A one-time payment of $10,000 today

C. $50,000 every 11 years forever, starting 11 years from today

D. $1,700 per year forever, starting today

E. A one-time payment of $100,000 made 15 years from today

You should find the present value of payments made in the next 13 years, 3 months, to be $11,134 for A, $10,000 for B, $10,747.16 for C, $11,191 for D, and $0 for E. Pick D, because it has the highest present value for the relevant payback period.

8. A stock is valued currently at $60 per share. Over the next year, the stock’s value could go down by 14%, up by 2%, up by 14%, up by 25%, or up by 35%. Each of these five outcomes has 20% probability of occurring. The effective annual discount rate is 8%. What is the risk-neutral value of a call option with an exercise price of $70, if the option can only be exercised one year from today? (Pick the closest answer.)

A. $0B. $3C. $5D. $8E. $15

The option will only have a positive value if the stock goes up by more than 16 2/3%. This only happens for the last two situations of the five mentioned above. If the stock goes up by 25%, the value one year from today will be $75; if by 35%, then the value will be $81. So the present value of this option is 0.2[(75-70)/1.08] + 0.2[(81-70)]/1.08 = $2.9630. So pick $3 for your answer.

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. Provide at least four significant digits to each answer or you may not receive full credit for a correct solution.

1. Answer each of the following.

(a) (4 points) Evaluate the following statement as true or false, and state why in 50 words or less: “Anybody that believes in the weak form of efficiency believes that there is NEVER a random component in determining the price of the stock.”

False: Some people that believe in weak form efficiency believe that

Pt = Pt-1 + Expected return + Random errort

(Answers can vary, as long as there is some mention of a random component existing. An alternate acceptable reason for the justification is that prices follow a random walk.)

If anyone said true, then no points were given unless the explanation given is consistent with the above answer. If a correct reason was given with a true answer, then 2 points would be given.

(b) (6 points) A junk bond pays a coupon of $0.01 today, and will double its coupon every year for each the next 10 years. (Note that there are 11 coupon payments still to be made.) Because this bond has a high level of risk, assume that the effective annual discount rate is 125%. The bond matures in 10 years and has a face value of $5,000. What is the present value of this bond?

PV = 0.01 + 0.02[1/(1.25-1) – 1/(1.25-1) * (2/2.25)10] + 5000/2.2510 = $1.5690

2. Fattie’s Italian Food, Inc. would pay $8 per year in dividends per share if it acted as a cash cow. The company could retain $2 of their earnings every year into a project that will earn 14% the following year. Assume an effective annual discount rate of 12%. (Note: Assume that dividends are paid annually, with the next dividend payment paid today. Also assume that the new project will not change the company’s discount rate.)

(a) (3 points) How much would every share of stock be worth if the company acted as a cash cow?

PV = 8 + 8/0.12 = $74.67

(b) (6 points) How much would every share of stock be worth if the company retained $2 of their earnings this year only (i.e. today)? Assume that the company will act as a cash cow every year in the future.

PV = (8-2) + (8+2.28)/1.12 + (1/1.12)*(8/0.12) = $74.70

(c) (7 points) How much would every share of stock be worth if the company retained $2 of their earnings every year?

PV = (8-2) + 8.28/0.12 = $75

(d) (3 points) Should the company retain $2 of its earnings every year? (Assume the only other option is to be a cash cow in any given year.) Explain in 30 words or less.

Yes, the present value is higher by retaining earnings (see part c) versus being a cash cow (see part a).

ALTERNATE ANSWER: Yes, since the new project has a higher return than the discount rate.

3. (11 points) The town of No Fraud, FL, is considering buying a new machine to register votes for the next election in 2014. If the city council buys the machine today (year 0), the cost is $15,000. The machine lasts 20 years, but requires maintenance every year for 19 years, starting one year from today. The first maintenance cost one year from today will be $3,000, and will increase by 6% every year. The effective annual discount rate is 7%. What is the equivalent annual cost of this machine over its 20-year life? (Note: All costs are in real dollars.)

PV of all costs = 15,000 + 3,000[1/(0.07-0.06) – 1/(0.07-0.06) * (1.06/1.07)19] = $64,018.96 (Note that the growing annuity formula is used here.)

EAC calculation: $64,018.96 = (EAC/0.07) * [1 – 1/1.0720]  EAC = $6,042.94.

4. (8 points) Benyamin is quoted a price for a bond of $800. This bond has a face value of $790 and pays a 14% coupon once per year. Three coupons will be paid. One coupon will be paid later today, one will be paid a year from today, and one will be paid two years from today. If the bond matures two years from today, what is the yield on this bond (expressed as an effective annual rate)?

Find r such that 790(.14) + 790(.14)/(1+r) + 790(.14)/(1+r)2 + 790/(1+r)2 = 800 

689.4r2 + 1268.2r – 321.8 = 0. Use the quadratic formula to find that the only positive value for r is 22.5984%.

5. (9 points) Zach buys four shares of stock at a price of $130 (per share) today, and three call options with an exercise price of $150 (per share) three months from now. (In other words, the expiration date of the option is three months from now.) Each 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 four shares of stock and the three call options as a function of the value of the stock at expiration. The vertical intercept should have the value of the combination of the four shares of stock and the three call 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.

6. (8 points) Rydenapolis, Inc., produces race cars. This company has distributed 5,000 bonds with current value $60 each. This company also has distributed 16,000 shares of stock with current value of $25 each. (There is no other debt incurred or ownership in the company besides what is mentioned here.) The required return on equity is 12%, and the weighted average cost of capital is 8%. What is the cost of debt for Rydenapolis?

RWACC = S/(B+S) * RS + B/(B+S) * RB 0.08 = (400,000/700,000) * 0.12 + (300,000/700,000) * RB

RB = 0.0266667