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# Rate of Return on a Stock

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As an equity analyst you are concerned with what will happen to the required return to Universal Toddler Industries's stock as market conditions change. Suppose rRF = 5%, rM = 12%, and bUTI = 1.4.

(a) Under current conditions, what is rUTI, the required rate of return on UTI stock?
(b) Now suppose rRF (1) increases to 6% or (2) decreases to 4%. The slope of the SML remains constant. How would this affect rM and rUTI?
(c) Now suppose rRF remains at 5% but rM (1) increaes to 14% or (2) falls to 11%. The slope of the SML does not remain constant. How would these changes affect rUTI?

Answer is:

a. ri = 14.8%
b. (1) rM = 13%; ri = 15.8%
(2) rM = 11%; ri = 13.8%
c (1) ri = 17.6%
(2) ri = 13.4%

I need to be able to show I came up with these answers.

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#### Solution Preview

(a)
rUTI = rRF + bUTI*(rM - rRF)
=> rUTI = 5% + 1.4*(12%-5%)
=> rUTI = 14.8%

(b)
If rRF increases to 6%
rM ...

#### Solution Summary

The solution provides step by step solution to the question being asked. Standard formula is used to determine the answer and steps are shown clearly and concisely.

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## Problem set- Multiple choice questions

1. The New York Stock Exchange is primarily

a. A secondary market.
b. An organized auction market.
c. An over-the-counter market.
d. Answers a and b are correct.
e. Answers b and c are correct.
Answer:

2. Your uncle would like to restrict his interest rate risk and his default risk, but he would still like to invest in corporate bonds. Which of the possible bonds listed below best satisfies your uncle's criteria?

a. AAA bond with 10 years to maturity.
b. BBB perpetual bond.
c. BBB bond with 10 years to maturity.
d. AAA bond with 5 years to maturity.
e. BBB bond with 5 years to maturity.
Answer:

3. Which of the following could explain why a business might choose to organize as a corporation rather than as a sole proprietorship or a partnership?

a. Corporations generally face fewer regulations.
b. Corporations generally face lower taxes.
c. Corporations generally find it easier to raise capital.
d. Corporations enjoy unlimited liability.
e. Statements c and d are correct.
Answer:

4. Which of the following are examples of a primary market transaction?

a. A company issues new common stock.
b. A company issues new bonds.
c. An investor asks his broker to purchase 1,000 shares of Microsoft common stock.
d. All of the statements above are correct.
e. Statements a and b are correct.
Answer:

5. You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?

a. The discount rate decreases.
b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same.
c. The discount rate increases.
d. Answers b and c above.
e. Answers a and b above.

Answer:

6. Which of the following factors are likely to increase market interest rates?

a. Corporations increase their demand for capital.
b. Households become less willing to save.
c. Expected inflation increases.
d. Statements a and c are correct.
e. Statements a, b, and c are correct.

Answer:

7. Which of the following bank accounts has the highest effective annual return?

a. An account which pays 10 percent nominal interest with monthly com-pounding.
b. An account which pays 10 percent nominal interest with daily com-pounding.
c. An account which pays 10 percent nominal interest with annual com-pounding.
d. An account which pays 9 percent nominal interest with daily com-pounding.
e. All of the investments above have the same effective annual return.

Answer:

8. If \$100 is placed in an account that earns a nominal 4 percent, compounded quarterly, what will it be worth in 5 years?

a. \$122.02
b. \$105.10
c. \$135.41
d. \$120.90
e. \$117.48

Answer:

9. If a 5-year ordinary annuity has a present value of \$1,000, and if the interest rate is 10 percent, what is the amount of each annuity payment?

a. \$240.42
b. \$263.80
c. \$300.20
d. \$315.38
e. \$346.87

Answer:

10. You recently received a letter from Cut-to-the-Chase National Bank that offers you a new credit card that has no annual fee. It states that the annual percentage rate (APR) is 18 percent on outstanding balances. What is the effective annual interest rate? (Hint: Remember these companies bill you monthly.)

a. 18.81%
b. 19.56%
c. 19.25%
d. 20.00%
e. 18.00%

Answer:

11. Which of the following would not cause an increase in net operating working capital?

a. Inventory increases.
b. Accounts receivable increases.
c. Short-term investments increase.
d. Accounts payables decrease.
e. Accruals decrease.

Answer:

12. If you buy a factory for \$250,000 and the terms are 20 percent down, the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance, what are the 30 equal annual payments?

a. \$20,593
b. \$31,036
c. \$24,829
d. \$50,212
e. \$ 6,667

Answer:

13. Which of the following are likely to occur if Congress passes legislation which forces Carter Manufacturing to depreciate their equipment over a longer time period:

a. The company's physical stock of assets would increase.
b. The company's reported net income would decline.
c. The company's cash position would decline.
d. All of the answers above are correct.
e. Answers b and c are correct.

Answer:

14. A 5-year corporate bond yields 9 percent. A 5-year municipal bond of equal risk yields 6.5 percent. Assume that the state tax rate is zero. At what federal tax rate are you indifferent between the two bonds?

a. 27.78%
b. 38.46%
c. 41.22%
d. 54.33%
e. 72.22%

Answer:

15. Your corporation has the following cash flows:

Operating income \$250,000
Interest received 10,000
Interest paid 45,000
Dividends received 20,000
Dividends paid 50,000

Answer:

If the applicable income tax rate is 40 percent (federal and state combined), and if 70 percent of dividends received are exempt from taxes, what is the corporation's tax liability?

a. \$ 74,000
b. \$ 88,400
c. \$ 91,600
d. \$100,000
e. \$106,500

Answer:

16. Byrd Lumber has 2 million shares of stock outstanding. On the balance sheet the company has \$40 million worth of common equity. The company's stock price is \$15 a share. What is the company's Market Value Added (MVA)?

a. (\$80 million)
b. (\$20 million)
c. (\$10 million)
d. \$20 million
e. \$80 million

Answer:

17. Other things held constant, (1) if the expected inflation rate decreases, and (2) investors become more risk averse, the Security Market Line would shift

a. Down and have steeper slope.
b. Up and have less steep slope.
c. Up and keep same slope.
d. Down and keep same slope.
e. Down and have less steep slope.

Answer:

18. Stock A has a beta of 1.5 and Stock B has a beta of 0.5. Which of the following statements must be true about these securities? (Assume the market is in equilibrium.)

a. When held in isolation, Stock A has greater risk than Stock B.
b. Stock B would be a more desirable addition to a portfolio than Stock A.
c. Stock A would be a more desirable addition to a portfolio than Stock B.
d. The expected return on Stock A will be greater than that on Stock B.
e. The expected return on Stock B will be greater than that on Stock A.

Answer:

19. Calculate the required rate of return for Mercury Inc., assuming that investors expect a 5 percent rate of inflation in the future. The real risk-free rate is equal to 3 percent and the market risk premium is 5 percent. Mercury has a beta of 2.0, and its realized rate of return has averaged 15 percent over the last 5 years.

a. 15%
b. 16%
c. 17%
d. 18%
e. 20%

Answer:

20. A money manager is managing the account of a large investor. The investor holds the following stocks:

Stock Amount Invested Estimated Beta
A \$2,000,000 0.80
B 5,000,000 1.10
C 3,000,000 1.40
D 5,000,000 ???

The portfolio's required rate of return is 17 percent. The risk-free rate, rRF, is 7 percent and the return on the market, rM, is 14 percent. What is Stock D's estimated beta?

a. 1.256
b. 1.389
c. 1.429
d. 2.026
e. 2.154

Answer:

21. You hold a diversified portfolio consisting of a \$10,000 investment in each of 20 different common stocks (i.e., your total investment is \$200,000). The portfolio beta is equal to 1.2. You have decided to sell one of your stocks which has a beta equal to 0.7 for \$10,000. You plan to use the proceeds to purchase another stock which has a beta equal to 1.4. What will be the beta of the new portfolio?

a. 1.165
b. 1.235
c. 1.250
d. 1.284
e. 1.333

Answer:

22. Which is the best measure of risk for an asset held in isolation? Which is the best measure for an asset held in a diversified portfolio?

a. Variance; correlation coefficient.
b. Standard deviation; correlation coefficient.
c. Beta; variance.
d. Coefficient of variation; beta.
e. Beta; beta.

Answer:

23. You are an investor in common stock and currently hold a well-diversified portfolio which has an expected return of 12 percent with a beta of 1.2. You plan to buy 100 shares of AT&E at \$10 a share. AT&E has an expected return of 20 percent with a beta of 2.0. The total value of your current portfolio is \$9,000. What will be the expected return and beta of the portfolio after the purchase of the new stock?

a. rp = 20.0%; bp = 2.00
b. rp = 12.8%; bp = 1.28
c. rp = 12.0%; bp = 1.20
d. rp = 13.2%; bp = 1.40
e. rp = 14.0%; bp = 1.32

Answer:

24. You hold a diversified portfolio consisting of a \$5,000 investment in each of 20 different common stocks. The portfolio beta is equal to 1.12. You have decided to sell a lead mining stock (b = 1.0) at \$5,000 net and use the proceeds to buy a like amount of a steel company stock (b = 2.0). What is the new beta of the portfolio?

a. 1.12
b. 1.17
c. 1.22
d. 1.10
e. 1.02

Answer:

25. Calculate the required rate of return for Mercury, Inc., assuming that investors expect a 5 percent rate of inflation in the future. The real risk-free rate is equal to 3 percent and the market risk premium is 5 percent. Mercury has a beta of 2.0, and its realized rate of return has averaged 15 percent over the last 5 years.

a. 15%
b. 16%
c. 17%
d. 18%
e. None of the above
Answer:

26. One of the basic relationships in interest rate theory is that, other things held constant, for a given change in the required rate of return, the the time to maturity, the the change in price.

a. longer; smaller.
b. shorter; larger.
c. longer; greater.
d. shorter; smaller.
e. Answers c and d are correct.

Answer:

27. You are holding a stock which is currently in equilibrium. The required rate of return on the stock is 15 percent when the required return on an average stock is 10 percent. What will be the percentage change in the required return on the stock if the required return on an average stock increases by 30 percent while the risk-free rate is unchanged? Your stock has a beta of 2.

a. +20%
b. +30%
c. +40%
d. +50%
e. +60%

Answer:

28. Assume that all interest rates in the economy decline from 10 percent to 9 percent. Which of the following bonds will have the largest percentage increase in price?

a. A 10-year bond with a 10 percent coupon.
b. An 8-year bond with a 9 percent coupon.
c. A 10-year zero coupon bond.
d. A 1-year bond with a 15 percent coupon.
e. A 3-year bond with a 10 percent coupon.

Answer:

29. Consider a \$1,000 par value bond with a 7 percent annual coupon. The bond pays interest annually. There are 9 years remaining until maturity. What is the current yield on the bond assuming that the required return on the bond is 10 percent?

a. 10.00%
b. 8.46%
c. 7.00%
d. 8.52%
e. 8.37%

Answer:

30. A share of common stock has just paid a dividend of \$3.00. If the expected long-run growth rate for this stock is 5 percent, and if investors require an 11 percent rate of return, what is the price of the stock?

a. \$50.00
b. \$50.50
c. \$52.50
d. \$53.00
e. \$63.00

Answer:

31. Assume that you wish to purchase a bond with a 30-year maturity, an annual coupon rate of 10 percent, a face value of \$1,000, and semiannual interest payments. If you require a 9 percent nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

a. \$905.35
b. \$1,102.74
c. \$1,103.19
d. \$1,106.76
e. \$1,149.63

Answer:

32. A bond has an annual 8 percent coupon rate, a maturity of 10 years, a face value of \$1,000, and makes semiannual payments. If the price is \$934.96, what is the annual nominal yield to maturity on the bond?

a. 8%
b. 9%
c. 10%
d. 11%
e. 12%

Answer:

33. Van Buren Company has a current ratio = 1.9. Which of the following actions will increase the company's current ratio?

a. Use cash to reduce short-term notes payable.
b. Use cash to reduce accounts payable.
c. Issue long-term bonds to repay short-term notes payable.
d. All of the answers above are correct.
e. Answers b and c are correct.

Answer:

34. The last dividend paid by a company was \$2.20. Klein's growth rate is expected to be 10 percent for one year, after which dividends are expected to grow at a rate of 6 percent forever. The company's stockholders require a rate of return on equity (rs) of 11 percent. What is the current price of the stock?

a. \$44.00
b. \$46.64
c. \$48.40
d. \$48.64
e. \$50.40

Answer:

35. If the expected rate of return on a stock exceeds the required rate,

a. The stock is experiencing supernormal growth.
b. The stock should be sold.
c. The company is probably not trying to maximize price per share.
d. The stock is a good buy.
e. Dividends are not being declared.

Answer:

36. The Wilson Corporation has the following relationships:

Sales/Total assets 2.0
Return on assets (ROA) 4%
Return on equity (ROE) 6%

What is Wilson's profit margin and debt ratio?

a. 2% and 0.33
b. 4% and 0.33
c. 4% and 0.67
d. 2% and 0.67
e. 4% and 0.50

Answer:

37. Assume that you plan to buy a share of XYZ stock today and to hold it for 2 years. Your expectations are that you will not receive a dividend at the end of Year 1, but you will receive a dividend of \$9.25 at the end of Year 2. In addition, you expect to sell the stock for \$150 at the end of Year 2. If your expected rate of return is 16 percent, how much should you be willing to pay for this stock today?

a. \$164.19
b. \$ 75.29
c. \$107.53
d. \$118.35
e. \$131.74

Answer:

38. Which of the following actions will increase a company's quick ratio?

a. Reduce inventories and use the proceeds to reduce long-term debt.
b. Reduce inventories and use the proceeds to reduce current liabilities.
c. Issue short-term debt and use the proceeds to purchase inventory.
d. Issue long-term debt and use the proceeds to purchase fixed assets.
e. Issue equity and use the proceeds to purchase inventory.

Answer:

39. Tapley Dental Supply Company has the following data:

Net income: \$240
Sales: \$10,000
Total assets: \$6,000
Debt ratio: 75%
TIE ratio: 2.0
Current ratio: 1.2
BEP ratio: 13.33%

If Tapley could streamline operations, cut operating costs, and raise net income to \$300, without affecting sales or the balance sheet (the additional profits will be paid out as dividends), by how much would its ROE increase?

a. 3.00%
b. 3.50%
c. 4.00%
d. 4.25%
e. 5.50%

Answer:

40. Southeast Packaging's ROE last year was only 5 percent, but its management has developed a new operating plan designed to improve things. The new plan calls for a total debt ratio of 60 percent, which will result in interest charges of \$8,000 per year. Management projects an EBIT of \$26,000 on sales of \$240,000, and it expects to have a total assets turnover ratio of 2.0. Under these conditions, the average tax rate will be 40 percent. If the changes are made, what return on equity will Southeast earn?

a. 9.00%
b. 11.25%
c. 17.50%
d. 22.50%
e. 35.00%

Answer:

41. Newburn Entertainment's stock is expected to pay a year-end dividend of \$3.00 a share. (D1 = \$3.00, the dividend at time 0, D0, has already been paid.) The stock's dividend is expected to grow at a constant rate of 5 percent a year. The risk-free rate, rRF, is 6 percent and the market risk premium, (rM - rRF), is 5 percent. The stock has a beta of 0.8. What is the stock's expected price five years from now?

a. \$60.00
b. \$76.58
c. \$96.63
d. \$72.11
e. \$68.96

Answer:

42. All treasury securities have a yield to maturity of 7 percent--so the yield curve is flat. If the yield to maturity on all Treasuries were to decline to 6 percent, which of the following bonds would have the largest percentage increase in price?

a. 15-year zero coupon Treasury bond.
b. 12-year Treasury bond with a 10 percent annual coupon.
c. 15-year Treasury bond with a 12 percent annual coupon.
d. 2-year zero coupon Treasury bond.
e. 2-year Treasury bond with a 15 percent annual coupon.

Answer:

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