Stocks and Their Valuation Answer Key Part 5

ANSWERS AND SOLUTIONS 1. Required return Answer: e Diff: E 2. Required return Answer: d Diff: E 3. Required return Answer: a Diff: E The total return is made up of a dividend yield and capital gains yield. For Stock A, the total required return is 10 percent and its capital gains yield (g) is 7 percent. Therefore, A’s dividend yield must be 3 percent. For Stock B, the required return is 12 percent and its capital gains yield (g) is 9 percent. Therefore, B’s dividend yield must also be 3 percent. Therefore, statement a is true. Statement b is false. Market efficiency just means that all of the known information is already reflected in the price, and you can’t earn above the required return. This would depend on betas, dividends, and the number of shares outstanding. We don’t have any of that information. Statement c is false. The expected returns of the two stocks would be the same only if they had the same betas. 4. Constant growth model Answer: a Diff: E Statement a is true; the other statements are false. The constant growth model is not appropriate for stock valuation in the absence of a constant growth rate. If the required rate of return differs for the two firms due to risk differences, then the firms’ stock prices would differ. 5. Constant growth model Answer: a Diff: E Statement a is true; the other statements are false. If a stock’s required return is 12 percent and its capital gains yield is 5 percent, then its dividend yield is 12% - 5% = 7%. The expected future dividends should be discounted at the required rate of return. 6. Constant growth model Answer: c Diff: E Statement c is true; the others are false. Statement a would be true only if the dividend yield were zero. Statement b is false; we’ve been given no information about the dividend yield. Statement c is true; the constant rate at which dividends are expected to grow is also the expected growth rate of the stock’s price. 7. Constant growth model Answer: e Diff: E Statement a is false: P0 = D1/(ks - g). g is different for the two stocks, but the required return and expected dividend are the same, so the prices will be different also. Statement b is false: ks = D1/P0 + g. A has a higher g, so its dividend yield must be lower because the firms have the same required rate of return. Statement c is false. Therefore, statement e is the correct answer. 8. Constant growth model Answer: c Diff: E N The correct answer is statement c. For Stock X, ks = D1/P0 + g 0.12 = D1/P0 + 0.06, or D1/P0 = 0.06. For Stock Y, ks = D1/P0 + g 0.10 = D1/P0 + 0.04, or D1/P0 = 0.06. So, both Stock X and Stock Y have the same dividend yield. So, statements a and b are incorrect. That also makes statements d and e incorrect. Since both stocks X and Y have the same price today, and Stock X has a higher dividend growth rate than Stock Y, the price of Stock X will be higher than the price of Stock Y one year from today. So, statement c is the correct choice. 9. Constant growth model Answer: e Diff: E N The correct answer is statement e. At a price of $50, ks = D1/P0 + g = $3.00/$50 + 0.06 = 12%. So, statement a is correct. $89.54. So, statement b is also correct. D1/P0 = $3.00/$50.00 = 6%, so statement c is correct. Thus, statement e is the correct choice. 10. Constant growth model P̂10 = $50(1.06)10 = Answer: e Diff: E If Stock X has a required return of 12 percent and a dividend yield of 5 percent, we can calculate its growth rate: ks = D1/P0 + g 12% = 5% + g 7% = g. If Stock Y has a required return of 10 percent and a dividend yield of 3 percent, we can calculate its growth rate: ks = D1/P0 + g 10% = 3% + g 7% = g. Since both stocks have the same price and Stock X has a higher dividend yield than Stock Y, its dividend per share must be higher. Therefore, statement a is true. We just showed above, that both stocks have the same growth rate, so statement b must be false. One year from now, the stocks will both trade at the same price. They are starting at the same price today, and will be growing at the same rate this year, so they will end up with the same stock price one year from now. Therefore, statement c must also be true. Since both statements a and c are true, the correct choice is statement e. 11. Constant growth model and CAPM Answer: a Diff: E N The correct answer is statement a. From the information given and the CAPM equation, we know that Stock A’s and Stock B’s required returns are 12.9% and 11.7%, respectively. The required return is equal to a dividend yield and a capital gains yield. Since these are constant growth stocks, their capital gains yields are equivalent to their dividend growth rates of 7%. Therefore, the dividend yields for Stock A and Stock B are 5.9% and 4.7%, respectively. Statement b is incorrect; we cannot determine which stock has the higher price without knowing their expected dividends. Statement c is incorrect; from the answer given for statement a, we know that Stock B’s dividend yield doesn’t equal its expected dividend growth rate. 12. Miscellaneous issues Answer: c Diff: E Statement c is true; the others are false. Two classes of common stock can have different voting rights, as well as pay different dividends. An IPO occurs when a firm goes public for the first time. Statement c is the exact definition of a preemptive right. 13. Preemptive right 14. Classified stock 15. Efficient markets hypothesis Answer: b Diff: E Answer: e Diff: E Answer: e Diff: E Statements a through d are false; therefore, statement e is true. Statement a is false. Strong-form efficiency states that current market prices reflect all pertinent information, whether publicly available or privately held. If it holds, even insiders would find it impossible to earn abnormal returns in the stock market. Statement b is false; this describes semistrong-form efficiency. Statement c is false; some investors may be able to analyze and react more quickly than others to releases of new information. However, the buy-sell actions of those investors quickly bring market prices into equilibrium. 16. Efficient markets hypothesis Answer: d Diff: E Stocks are usually riskier than bonds and should have higher expected returns. Therefore, statement a is false. In equilibrium, stocks with more market risk should have higher expected returns than stocks with less market risk. Therefore, statement b is false. The semistrong form of market efficiency says that all publicly available information, including past price history, is already accounted for in the stock’s price. Therefore, statement c is false. Remember, when trying to find the price of a stock, we discount all future cash flows by the required return. If the price is equal to the present value of those cash flows, then the NPV of the stock must be equal to 0. Therefore, statement d is true. Net present value is stated in dollars and the required return is stated as a 17. percent. It is impossible for the two to equal each other. Therefore, statement e is false. Efficient markets hypothesis Answer: e Diff: E Statement a is false; riskier securities have higher required returns. Statement b is false for the same reason as statement a. Statement c is false; semistrong-form efficiency says that you cannot make abnormal profits by trading off publicly available information. So statement e is the correct answer. 18. Efficient markets hypothesis Answer: e Diff: E Weak-form efficiency means that you cannot profit from recent trends in stock prices (that is, technical analysis doesn’t work). Therefore, statement a must be false. Semistrong-form efficiency means that all public information is already accounted for in the stock price. Because bonds and stocks have different risk levels and tax implications, there is no reason to expect them to have the same return. Therefore, statement b must be false. Similarly, because different stocks have different risk levels, there is no reason to expect all stocks to have the same return. Therefore, statement c is also false. The correct choice is statement e. 19. Efficient markets hypothesis Answer: c Diff: E Statement c is true; the other statements are false. Semistrong-form market efficiency implies that only public information, not private, is rapidly incorporated into stock prices. Markets can be efficient yet still price securities differently depending on their risks. 20. Efficient markets hypothesis 21. Efficient markets hypothesis Answer: a Diff: E Answer: e Diff: E N The correct answer is statement e. If prices rapidly reflect all available public information, then the market is semistrong-form efficient not weak-form efficient. Therefore, statement a is incorrect. If the market is weak-form efficient, then you cannot beat the market by using technical analysis or charting. Therefore, statement b is incorrect. Different stocks will have different risk and will have different required and expected returns, so statement c is incorrect. 22. Efficient markets hypothesis Answer: a Diff: E Statement a is true; the other statements are false. Historical information cannot be used to beat the market under weak-form efficiency. Public information cannot be used to beat the market under semistrongform efficiency. 23. Preferred stock concepts Answer: e Diff: E 24. Preferred stock concepts Answer: e Diff: E 25. Both statements a and b are true; therefore, statement e is the correct choice. 70 percent of dividends received, not paid out, are tax deductible. Common stock concepts Answer: d Diff: E Statements b and c are true; therefore, statement d is the correct choice. A greater proportion of common stock in the capital structure increases the likelihood of a takeover bid. 26. Common stock concepts Answer: e Diff: E We don’t know anything about the dividends of either stock. Stock Y could have a dividend yield of 0 percent and a capital gains yield of 12 percent, while Stock X has a dividend yield of 10 percent and a capital gains yield of 0 percent. Therefore, statement a is false. If the two stocks have the same dividend yield, Stock Y must have a higher expected capital gains yield than X because Y has the higher required return. Therefore, statement b is false. Remember the DCF formula: P0 = D1/(ks g). If D1 and g are the same, and we know that Y has a higher required return than X, then Y’s dividend yield must be larger than X’s. In order for this to be true Y’s price must be lower than X’s. Therefore, statement c is false. Since statements a, b, and c are false, then the correct answer is statement e. 27. Declining growth stock Answer: e Diff: E Statement e is the correct choice; all the statements are true. Statement a is true; P0 = $2/(0.15 + 0.05) = $10. Statement b is true; Div yield5 = D6/P5 or [$2.00(0.95)5]/[$10.00(0.95)5] = $1.547562/$7.74 = 20%. Statement c is true; $10(0.95)5 = $7.74. 28. Dividend yield and g Answer: d Diff: E ks = D1/P0 + g. Both stocks have the same ks and the same P0, but may have a different D1 and a different g. So statements a, b, and c are not necessarily true. Statement d is true, but statement e is clearly false. 29. Dividend yield and g Answer: c Diff: E Statements a and b are both false because the required return consists of both a dividend yield (D1/P0) and a growth rate. Statements a and b don’t mention the growth rate. Statement c is true because if the required return for Stock A is higher than that of Stock B, and if the dividend yield for Stock A is lower than Stock B’s, the growth rate for Stock A must be higher to offset this. Statement d is not necessarily true because the growth rate could go either way depending upon how high the dividend yield is. Statement e is also not necessarily true. 30. Market equilibrium Answer: b Diff: E N The correct answer is statement b. The realized return is an historical return. It is what has already happened in the past. There is no reason that the expected return in the future should equal the return it has realized in the past. Therefore, statement a is incorrect. If the expected return does not equal the required return, then markets are not in equilibrium. If you are expecting a higher return than you require (given the level of risk) for a stock, then the stock will be a “bargain.” This You will be getting a higher return than you require. disequilibrium will not last, and the stock price will adjust until its expected return equals its required return. Therefore, statement b is correct. Different investments should have different expected returns. You will have a different expected return for an oil company stock than you would for an airline company stock, depending on what is happening to oil prices. There is no reason for you to expect the same returns on all of your investments. Therefore, statement c is incorrect. Investments should not have the same realized returns. Realized returns are historical, and all stocks have different price histories. Therefore, statement d is incorrect. 31. Market efficiency and stock returns Answer: c Diff: M Statement c is true; the other statements are false. If beta increased, but g remained the same, the new stock price would be lower. Market efficiency says nothing about the relationship between expected and realized rates of return. 32. Efficient markets hypothesis Answer: e Diff: M Statement e is true; the other statements are false. If the stock market is weak-form efficient, you could use private information to outperform the market. Semistrong-form efficiency means that current market prices reflect all publicly available information. 33. Efficient markets hypothesis Answer: c Diff: M 34. Efficient markets hypothesis Answer: e Diff: M Statement e is the correct choice. Semistrong-form efficiency implies that past stock prices cannot be used to forecast future returns. 35. Efficient markets hypothesis 36. Market equilibrium 37. Ownership and going public Answer: d Diff: M Answer: a Diff: M Answer: c Diff: M 38. Dividend yield and g Answer: b Diff: M 39. Statement b is true; the other statements are false. The stock’s required return must equal the sum of its expected dividend yield and constant growth rate. A stock’s dividend yield can exceed the expected growth rate. Constant growth model Answer: d Diff: M Statement d is true; the other statements are false. ks = Dividend yield + Capital gains. 14% = Dividend yield + 8%; therefore, Dividend yield = 6%. Dividend yield = Dividend/Price; Dividend = 0.06 × $50 = $3. Future stock price = $50 × 1.08 = $54. 40. Preferred stock value Answer: d Diff: E Vp = Dp/kp = $5/0.20 = $25. 41. Preferred stock value Answer: d Diff: E The dividend is calculated as 10% × $120 = $12. We know that the cost of preferred stock is equal to the dividend divided by the stock price or 8% = $12/Price. Solve this expression for Price = $150. (Note: Nonpartici-pating preferred stockholders are entitled to just the stated dividend rate. There is no growth in the dividend.) 42. Preferred stock yield Answer: c Diff: E Annual dividend = $2.50(4) = $10. kp = Dp/Vp = $10/$50 = 0.20 = 20%. 43. Preferred stock yield Answer: a Diff: E Annual dividend = $0.50(4) = $2.00. kp = Dp/Vp = $2.00/$20.00 = 0.10 = 10%. 44. Stock price Answer: d Diff: E 0 ks1= 16% 2 Years | | | P0 = ? 0 D2 = 9.25 2 P̂ = 150.00 CF2 = 159.25 Numerical solution: 159 . 25 = $118.35. P0 = 1 . 16 ) 2 Financial calculator solution: Inputs: N = 2; I = 16; PMT = 0; FV = 159.25. Output: PV = -$118.35. P0 = $118.35. 45. Future stock price--constant growth Answer: d Diff: E The stock price will grow at 7 percent for 4 years, $25 × (1.07)4 = $32.77. 46. Future stock price--constant growth Answer: b Diff: E The stock price today is calculated as: $4/(0.12 - 0.08) = $100. If the growth rate is 8 percent, the price in 8 years will be: $100 × (1.08)8 = $185.09. 47. 48. 49. Future stock price--constant growth Step 1: Find g: P0 = D1/(ks - g) $20 = $2/(0.15 - g) g = 5%. Step 2: Find P at t = 7: P̂ 7 = P0(1 + g)7 P̂ 7 = $20(1.05)7 P̂ 7 = $28.14 ≈ $28. Future stock price--constant growth Answer: a Diff: E Answer: a Diff: E Step 1: Determine the constant growth rate, g: ks = D1/P0 + g 9%= $2/$40 + g 0.09= 0.05 + g 0.04= g. Step 2: Determine the expected price of the stock 5 years from today: P̂5 = P0 × (1 + g)n = $40 × (1.04)5 = $40 × 1.21665 = $48.67. Future stock price--constant growth The price today, P0 = Answer: e Diff: E N D̂1 $ 0 . 50 = = $10.00. ks − g . 12 −0 . 07 Since this is a constant growth stock, its price will grow at the same P̂4 = P0(1.07)4 = $10.00(1.07)4 = $13.108 ≈ $13.11. rate as dividends. So, 50. Constant growth stock Answer: b Diff: E ks = D1/P0 + g g = ks - D1/P0 g = 0.11 - $1/$20 = 0.06 = 6%. 51. Constant growth stock Answer: a Diff: E 52. $2.00(1.15 ) = $57.50. .19 - 0.15 Constant growth stock Answer: e Diff: E P0 = The required rate of return on the stock: 5% + (9% - 5%)1.3 = 10.2%. D1 = $2.40 × 1.06 = $2.544. The price of the stock today is $2.544/(0.102 - 0.06) = $60.57. 53. Constant growth stock Answer: c Diff: E P0 = D1/(ks - g) $30 = $3/(0.16 – g) $4.8 - $30g = $3 $1.8 = $30g g = 6%. 54. Constant growth stock Answer: d Diff: E We know that P0 = D1/ks - g) and we have all the information except D1, so we input the data into this equation. $30 = D1/(0.10 - 0.07) $30 = 33.33D1 D1 = $0.90. 55. 56. Constant growth stock Step 1: Calculate the price of the stock today, since it is a constant growth stock. D1 = $2.00; ks = 0.09; g = 0.05. P0 = D1/(ks - g) = $2.00/(0.09 - 0.05) = $50. Step 2: Determine the price of the stock five years from today: P̂5 = $50 × (1.05)5 = $63.81. Constant growth stock Answer: b Diff: E Answer: d Diff: E Step 1: Using the Gordon constant growth model, calculate today’s price: P0= D1/(ks - g) = $0.60/(0.12 - 0.07) = $12.00. Step 2: Calculate the price of the stock 5 years from today, assuming g = 7% per year: P̂5 = P0 × (1.07)5 = $12.00 × (1.07)5 = $16.83. 57. Constant growth stock Answer: b Diff: E N This is a constant growth stock, so you can use the Gordon constant growth model to calculate today’s price. Once you have today’s price, you can find the price in 10 years. 58. Step 1: Find the stock’s current price. P0= D1/(ks - g) = $0.45/(0.11 - 0.04) = $6.4286. Step 2: Find the stock’s price in 10 years, given its current stock price. P̂10 = P0(1 + g)n = $6.4286(1.04)10 = $9.52. Nonconstant growth stock 0 | 1.00 P0 = ? CFt 0 | Answer: d Diff: E 1 k = 12% | gs = 5% 1.05 2 1.1025 | gs = 5% gn = 10% 1.21275 P̂ = 60.6375 = 2 1.05 3 Years 61.7400 Numerical solution: 61 . 74 1 . 05 + = $50.16. P0 = 1 . 12 1 . 12 ) 2 Financial calculator solution: Enter in CFLO register CF0 = 0, CF1 = 1.05, and CF2 = 61.74. Then enter I = 12, and press NPV to get NPV = P0 = $50.16. 1 . 21275 0 . 12 −0 . 10