## Exam

# University of Economics - FIN 201CF Final. Graded A

University of Economics - FIN 201CF Final 1. The excess return required from a risky asset over that required from a risk-free asset is called the: 2. The average squared difference between the actual return and the average return is called the: 3. The standard deviation for a set of stock returns can be calculated as the: 4. A symmetric, bell-shaped frequency distribution that is completely defined by its mean and standard deviation is the _____ distribution. 5. The average compound return earned per year over a multi-year period is called the _____ average return. 6. The return earned in an average year over a multi-year period is called the _____ average return. 7. The excess return you earn by moving from a relatively risk-free investment to a risky investment is called the: . 8. The capital gains yield plus the dividend yield on a security is called the: 9. A portfolio of large company stocks would contain which one of the following types of securities? 10. Based on the period of 1926 through 2008, _____ have tended to outperform other securities 11. Which one of the following types of securities has tended to produce the lowest real rate of return for the period 1926 through 2008? 12. On average, for the period 1926 through 2008: 13. Over the period of 1926 through 2008, the annual rate of return on _____ has been more volatile than the annual rate of return on _____. 14. Which one of the following is a correct ranking of securities based on their volatility over the period of 1926 to 2008? Rank from highest to lowest. 15. Over the period of 1926 to 2008, small company stocks had an average return of __%. 16. Over the period of 1926 to 2008, the average rate of inflation was _____%. 17. The average annual return on long-term corporate bonds for the period of 1926 to 2008 was _____%. Answers available at 18. The average annual return on small company stocks was about _____ percentage points greater than the average annual return on large-company stocks over the period of 1926 to 2008. 19. The average risk premium on U.S. Treasury bills over the period of 1926 to 2008 was _____%. 20. Which one of the following is a correct statement concerning risk premium? Answers available at 21. The risk premium is computed by ______ the average return for the investment. 22. The Zolo Co. just declared that it is increasing its annual dividend from $1.00 per share to $1.25 per share. If the stock price remains constant, then: 23. Which of the following statements are correct concerning the variance of the annual returns on an investment? I. The larger the variance, the more the actual returns tend to differ from the average return. II. The larger the variance, the larger the standard deviation. III. The larger the variance, the greater the risk of the investment. IV. The larger the variance, the higher the expected return. Answers available at 24. The variance of returns is computed by dividing the sum of the: 25. Which of the following statements concerning the standard deviation are correct? I. The greater the standard deviation, the lower the risk. II. The standard deviation is a measure of volatility. III. The higher the standard deviation, the less certain the rate of return in any one given year. IV. The higher the standard deviation, the higher the expected return. Answers available at 26. The standard deviation on small company stocks: I. is greater than the standard deviation on large company stocks. II. is less than the standard deviation on large company stocks. III. had an average value of about 33% for the period 1926 to 2008. IV. had an average value of about 20% for the period 1926 to 2008. Answers available at 27. Estimates using the arithmetic average will probably tend to _____ values over the long-term while estimates using the geometric average will probably tend to _____ values over the short-term. 28. A capital gain occurs when: . 29. Capital market history shows us that the average return relationship from lowest to highest between securities is: stocks. 30. How much of total world stock market capitalization is from the United States in 2008? Answers available at 31. In predicting the expected future return of the market, one of the dangers is that: 32. The dollar value of the world stock market capitalization, from largest to smallest is: Answers available at 33. Which country has the lowest stock market risk premium? 34. In estimating the future equity risk premium, it is important to include assumptions about: 35. One year ago, you purchased a stock at a price of $32.50. The stock pays quarterly dividends of $.40 per share. Today, the stock is worth $34.60 per share. What is the total amount of your dividend income to date from this investment? Dividend income = $.40 4 = $1.60 36. Six months ago, you purchased 100 shares of stock in ABC Co. at a price of $43.89 a share. ABC stock pays a quarterly dividend of $.10 a share. Today, you sold all of your shares for $45.13 per share. What is the total amount of your capital gains on this investment? Capital gains = ($45.13 - $43.89) 100 = $124 37. A year ago, you purchased 300 shares of IXC Technologies, Inc. stock at a price of $9.03 per share. The stock pays an annual dividend of $.10 per share. Today, you sold all of your shares for $28.14 per share. What is your total dollar return on this investment? Answers available at Total dollar return = ($28.14 - $9.03 $.10) 300 = $5,763 38. You purchased 200 shares of stock at a price of $36.72 per share. Over the last year, you have received total dividend income of $322. What is the dividend yield? Dividend per share = $322 200 = $1.61; Dividend yield = $1.61 $36.72 = 4.4% 39. Winslow, Inc. stock is currently selling for $40 a share. The stock has a dividend yield of 3.8%. How much dividend income will you receive per year if you purchase 500 shares of this stock? Dividend income = $40 .038 500 = $760 40. One year ago, you purchased a stock at a price of $32 a share. Today, you sold the stock and realized a total return of 25%. Your capital gain was $6 a share. What was your dividend yield on this stock? Capital gains yield = $6 $32 = 18.75%; Dividend yield = 25% - 18.75% = 6.25% 41. You just sold 200 shares of Langley, Inc. stock at a price of $38.75 a share. Last year you paid $41.50 a share to buy this stock. Over the course of the year, you received dividends totaling $1.64 per share. What is your capital gain on this investment? Answers available at Capital gain = ($38.75 - $41.50) 200 = -$550 (capital loss) 42. You purchased 300 shares of Deltona, Inc. stock for $44.90 a share. You have received a total of $630 in dividends and $14,040 in proceeds from selling the shares. What is your capital gains yield on this stock? Cost = 300 $44.90 = $13,470; Capital gains yield = ($14,040 - $13,470) $13,470 = 4.23% 43. Today, you sold 200 shares of SLG, Inc. stock. Your total return on these shares is 12.5%. You purchased the shares one year ago at a price of $28.50 a share. You have received a total of $280 in dividends over the course of the year. What is your capital gains yield on this investment? Answers available at Dividend yield = $280 (200 $28.50) = 4.91%; Capital gains yield = 12.5% - 4.91% = 7.59% 44. Six months ago, you purchased 1,200 shares of ABC stock for $21.20 a share. You have received dividend payments equal to $.60 a share. Today, you sold all of your shares for $22.20 a share. What is your total dollar return on this investment? Total dollar return = ($22.20 - $21.20 $.60) 1,200 = $1,920 45. Eight months ago, you purchased 400 shares of Winston, Inc. stock at a price of $54.90 a share. The company pays quarterly dividends of $.50 a share. Today, you sold all of your shares for $49.30 a share. What is your total percentage return on this investment? Total percentage return = ($49.30 - $54.90 $.50 $.50) $54.90 = -8.4% (loss) 46. A stock had returns of 8%, -2%, 4%, and 16% over the past four years. What is the standard deviation of this stock for the past four years? Average return = (.08 - .02 .04 .16) 4 = .065; Total squared deviation = (.08 - .065)2 (-.02 - .065)2 (.04 - .065)2 (.16 - .065)2 = . . . . = .0171; Standard deviation = (.0171 (4 - 1) = .0057 = . = 7.5% 47. A stock has an expected rate of return of 8.3% and a standard deviation of 6.4%. Which one of the following best describes the probability that this stock will lose 11% or more in any one given year? Lower bound of 99% probability range = .083 - (3 .064) = -.109 = -10.9%; Probability of losing 11% or more is less than 0.5%. 48. A stock has returns of 3%, 18%, -24%, and 16% for the past four years. Based on this information, what is the 95% probability range for any one given year? Answers available at Average return = (.03 .18 - .24 .16) 4 = .0325; Total squared deviation = (.03 - .0325)2 (.18 - .0325)2 (-.24 - .0325)2 (.16 - .0325)2 = . . . . = .; Standard deviation = (. (4 - 1) = . = .19346 = 19.346%; 95% probability range = 3.25% (2 19.346%) = -35.4 to 41.9% 49. A stock had returns of 8%, 14%, and 2% for the past three years. Based on these returns, what is the probability that this stock will earn at least 20% in any one given year? Average return = (.08 .14 .02) 3 = 8%; Total squared deviation = (.08 - .08)2 (.14 - .08)2 (.02 - .08)2 = .00 .0036 .0036 = .0072; Standard deviation = (.0072 (3 - 1) = .06 = 6%; Upper end of the 95% probability range = 8% (2 6%) = 20%; Probability of earning at least 20% in any one year is 2.5%. 50. A stock had returns of 11%, 1%, 9%, 15%, and -6% for the past five years. Based on these returns, what is the approximate probability that this stock will earn at least 23% in any one given year? Average return = (.11 .01 .09 .15 - .06) 5 = 6%; Total squared deviation = (.11 - .06)2 (.01 - .06)2 (.09 - .06)2 (.15 - .06)2 (-.06 - .06)2 = .0025 .0025 .0009 .0081 .0144 = .0284; Standard deviation = (0.284 (5 - 1) = .0071 = .084; Upper end of the 95% probability range = .06 (2 .084) = 22.8%; Probability of earning more than 23% in any one year is just slightly less than 2.5%. 51. A stock had returns of 8%, 39%, 11%, and -24% for the past four years. Which one of the following best describes the probability that this stock will NOT lose more than 43% in any one given year? Average return = (.08 .39 .11 - .24) 4 = 8.5%; Total squared deviation = (.08 - .085)2 (.39 - .085)2 (.11 - .085)2 (-.24 - .085)2 = . . . . = .1993; Standard deviation = .1993 (4 - 1) = . = 25.7747%; Lower bound of the 95% probability range = 8.5% - (2 25.7747%) = -43.05; Probability of NOT losing more than 43% in any given year is 97.5%. 52. Over the past five years, a stock produced returns of 14%, 22%, -16%, 2%, and 10%. What is the probability that an investor in this stock will NOT lose more than 8% nor earn more than 21% in any one given year? Average return = (.14 .22 - .16 .02 .10) 5 = 6.4%; Total squared deviation = (.14 - .064)2 (.22 - .064)2 (-.16 - .064)2 (.02 - 0.064)2 (.10 - .064)2 = . . . . . = .08352; Standard deviation = .08352 (5 - 1) = .02088 = 14.45%; 68% probability range = 6.4% 14.45% = -8.05% to 20.85%; Answer is 68%. 53. What are the arithmetic and geometric average returns for a stock with annual returns of 4%, 9%, -6%, and 18%? Arithmetic average = (.04 .09 - .06 .18) 4 = 6.25%; Geometric return = (1.04 1.09 .94 1.18).25 - 1 = 5.89% 54. What are the arithmetic and geometric average returns for a stock with annual returns of 21%, 8%, -32%, 41%, and 5%? Arithmetic average = (.21 .08 - .32 .41 .05) 5 = 8.6%; Geometric return = (1.21 1.08 .68 1.41 1.05).20 - 1 = 5.6% 55. A stock had returns of 6%, 13%, -11%, and 17% over the past four years. What is the geometric average return for this time period? Geometric average = (1.06 1.13 .89 1.17).25 - 1 = 5.7% 56. A stock had the following prices and dividends. What is the geometric average return on this stock? Return for year 2 = ($24.90 - $23.19 $.23) $23.19 = 8.3657%; Return for year 3 = ($23.18 - $24.90 $.24) $24.90 = -5.9438%; Return for year 4 = ($24.86 - $23.18 $.25) $23.18 = 8.3261%; Geometric return = (1. . 1.).3333 - 1 = 3.4% 57. You bought 100 shares of stock at $20 each. At the end of the year, you received a total of $Invest = $20(100) = $2,000 $Return = ($2,500 $400 - $2,000)/$2,000 = .45 = 45% 58. You bought 100 shares of stock at $20 each. At the end of the year, you received a total of $400 in dividends, and your stock was worth $2,500 total. What was your total dollar capital gain and total dollar return? C. $500; $900 $CG = $2,500 - $2,000 = $500 $Total Return = CG DIV = $500 $400 = $900 59. Excelsior shares are currently selling for $25 each. You bought 200 shares one year ago at $24 and received dividend payments of $1.50 per share. What was your percentage capital gain this year? %CG = ($25 - $24)/$25 = .04167 = 4.17% 60. Excelsior share are currently selling for $25 each. You bought 200 shares one year ago at $24 and received dividend payments of $1.50 per share. What was your total rate of return? % Total Return = [($25 $1.50)/ $24] - 1 = . = 10.42% 61. The prices for IMB over the last 3 years are given below. Assuming no dividends were paid, what was the 3-year holding period return? Given the following information: Year 1 return = 10%, Year 2 return = 15%, Year 3 return = 12%. HPR = (1.10) (1.15) (1.12) = 1.4168 - 1 = 41.68% 62. Kids Toy Co. has had total returns over the past five years of 0%, 7%, -2%, 10%, and 12%. What was the arithmetic average return on this stock? Arithmetic average = (0 7 - 2 10 12)/5 = 5.40% 63. The returns on your portfolio over the last 5 years were -5%, 20%, 0%, 10% and 5%. What is the arithmetic average return? Arithmetic average = (-5 20 0 10 5)/5 = 6% 64. If the expected return on the market is 16%, then using the historical risk premium on large stocks of 8.6%, the current risk-free rate is: Risk-free rate = 16% - 8.6% = 7.4% 65. The total annual returns on large company common stocks averaged 12.3% from 1926 to 2008, small company stocks averaged 17.4%, long-term government bonds averaged 5.8%, while Treasury Bills averaged 3.8%. What was the average risk premium earned by long-term government bonds, and small company stocks respectively? Long Term Government = 5.8% - 3.8% = 2.0% Small Stocks = 17.5% - 3.8% = 13.7% 66. The returns on your portfolio over the last 5 years were -5%, 20%, 0%, 10% and 5%. What is the standard deviation of your return? Standard Deviation = [(-.05 - .06)2 (.20 - .06)2 (0 - .06)2 (.10 - .06)2 (.05 - .06)2]/4 = .0370/4 = .00925 = .09617 = 9.62% 67. Suppose you own a risky asset with an expected return of 12% and a standard deviation of 20%. If the returns are normally distributed, the approximate probability of receiving a return greater than 32% is approximately: Z = (32 - 12)/20 = 1; 32 is 1 standard deviation above the mean. The probability of being within 1 standard deviation is approximately 68%; therefore, probability above the mean is approximately 32%/2 = 16%. 68. The return pattern on your favorite stock has been 5%, 8%, -12%, 15%, 21% over the last five years. What has been your average return and holding period return over the last 5 years? Average return = (5 8 - 12 15 21)/5 = 37/5 = 7.4% HPR = [(1.05)(1.08)(.88)(1.15)(1.21)] - 1 = (1.3886) - 1 = .3886 = 38.9% 69. The long term inflation rate average was 3.2% and you invested in long term corporate bonds over the same period which earned 6.1%. What was the average risk premium you earned? Average risk premium = 6.1% - 3.2% = 2.9% 70. The market portfolio of common stocks earned 14.7% in one year. Treasury bills earned 5.7%. What was the real risk premium on equities? Risk premium = 14.7% - 5.7% = 9.0% 71. You have a sample of returns observations for the Malta Stock Fund. The 4 returns are 7.25%, 5.6%, 12.5%, 1.0%. What is the average return and variance of these returns? Answers available at Average return = (.0725 .056 .125 .01)/4 = .2635/4 = . = 6.6% Variance = [(7.25 - 6.6)2 (5.6 - 6.6)2 (12.5 - 6.6)2 (1 - 6.6)2]/3 = 67.5925/3 = 22.53 1. A portfolio is: 2. The percentage of a portfolio's total value invested in a particular asset is called that asset's: 3. Risk that affects a large number of assets, each to a greater or lesser degree, is called _____ risk. 4. Risk that affects at most a small number of assets is called _____ risk. 5. The principle of diversification tells us that: 6. The _____ tells us that the expected return on a risky asset depends only on that asset's nondiversifiable risk. 7. The amount of systematic risk present in a particular risky asset, relative to the systematic risk present in an average risky asset, is called the particular asset's: 8. The linear relation between an asset's expected return and its beta coefficient is the: 9. The slope of an asset's security market line is the: 10. You are considering purchasing stock S. This stock has an expected return of 8% if the economy booms and 3% if the economy goes into a recessionary period. The overall expected rate of return on this stock will: 11. Which one of the following statements is correct concerning the expected rate of return on an individual stock given various states of the economy? 12. The expected return on a stock that is computed using economic probabilities is: 13. The characteristic line is graphically depicted as: 14. The beta of a security is calculated by: 15. If investors possess homogeneous expectations over all assets in the market portfolio, when riskless lending and borrowing is allowed, the market portfolio is defined to: 16. Which one of the following is an example of a nondiversifiable risk? 17. The risk premium for an individual security is computed by: 18. Standard deviation measures _____ risk. 19. When computing the expected return on a portfolio of stocks the portfolio weights are based on the: 20. The portfolio expected return considers which of the following factors? I. the amount of money currently invested in each individual security II. various levels of economic activity III. the performance of each stock given various economic scenarios IV. the probability of various states of the economy 21. The expected return on a portfolio: 22. If a stock portfolio is well diversified, then the portfolio variance: 23. Which one of the following statements is correct concerning the standard deviation of a portfolio? 24. The standard deviation of a portfolio will tend to increase when: 25. Systematic risk is measured by: 26. Which one of the following is an example of systematic risk? 27. The systematic risk of the market is measured by: 28. Unsystematic risk: . 29. Which one of the following is an example of unsystematic risk? 30. The primary purpose of portfolio diversification is to: . 31. Which one of the following would indicate a portfolio is being effectively diversified? 32. The majority of the benefits from portfolio diversification can generally be achieved with just _____ diverse securities. 33. Which one of the following measures is relevant to the systematic risk principle? 34. A security that is fairly priced will have a return _____ the Security Market Line. 35. The intercept point of the security market line is the rate of return which corresponds to: 36. A stock with an actual return that lies above the security market line: 37. The market risk premium is computed by: 38. The excess return earned by an asset that has a beta of 1.0 over that earned by a risk-free asset is referred to as the: Answers available at 39. The efficient set of portfolios: 40. Diversification can effectively reduce risk. Once a portfolio is diversified, the type of risk remaining is: 41. A well-diversified portfolio has negligible: 42. The Capital Market Line is the pricing relationship between: 43. Total risk can be divided into: 44. Beta measures: 45. The dominant portfolio with the lowest possible risk is: 46. The measure of beta associates most closely with: 47. An efficient set of portfolios is: 48. A stock with a beta of zero would be expected to have a rate of return equal to: 49. The combination of the efficient set of portfolios with a riskless lending and borrowing rate results in: riskless asset and the tangency portfolio. 50. According to the Capital Asset Pricing Model: 51. The diversification effect of a portfolio of two stocks: 52. The separation principle states that an investor will: individual risk tolerance. 53. When a security is added to a portfolio the appropriate return and risk contributions are: 54. When stocks with the same expected return are combined into a portfolio: 55. The correlation between stocks A and B is the: 56. You have plotted the data for two securities over time on the same graph, i.e., the monthly return of each security for the last 5 years. If the pattern of the movements of each of the two securities rose and fell as the other did, these two securities would have: 57. If the covariance of stock 1 with stock 2 is - .0065, then what is the covariance of stock 2 with stock 1? 58. You have a portfolio of two risky stocks which turns out to have no diversification benefit. The reason you have no diversification is the returns: 59. A portfolio will usually contain: 60. If the correlation between two stocks is 1, then a portfolio combining these two stocks will have a variance that is: 61. The opportunity set of portfolios is: 62. The correlation between two stocks: 63. If the correlation between two stocks is -1, the returns: 64. Diversification can effectively reduce risk. Once a portfolio is diversified the type of risk remaining is: 65. For a highly diversified equally weighted portfolio with a large number of securities, the portfolio variance is: 66. A well-diversified portfolio has eliminated most of the: 67. A typical investor is assumed to be: 68. The total number of variance and covariance terms in a portfolio is N2. How many of these would be (including non-unique) covariances? 69. The relationship between the covariance of the security with the market to the variance is called the: 70. According to the CAPM: 71. The elements along the diagonal of the variance/covariance matrix are: 72. The elements in the off-diagonal positions of the variance/covariance matrix are: 73. The beta of an individual security is calculated by: . 74. A risk that affects a large number of assets, each to a greater or lesser degree is called: 75. As we add more securities to a portfolio, the ____ will decrease: 76. Diversification will not lower the ____ risk: 77. You want your portfolio beta to be 1.20. Currently, your portfolio consists of $100 invested in stock A with a beta of 1.4 and $300 in stock B with a beta of .6. You have another $400 to invest and want to divide it between an asset with a beta of 1.6 and a risk-free asset. How much should you invest in the risk-free asset? BetaPortfolio = 1.20 = ($100 $800 1.4) ($300 $800 .6) (x $800 1.6) (($400 - x) $800 0) = .175 .225 .002 0; .8 = .002x; x = $400; Risk - free asset = $400 - $400 = $0 78. You have a $1,000 portfolio which is invested in stocks A and B plus a risk-free asset. $400 is invested in stock A. Stock A has a beta of 1.3 and stock B has a beta of .7. How much needs to be invested in stock B if you want a portfolio beta of .90? BetaPortfolio = .90 = ($400 $1,000 1.3) ($x $1,000 .7) (($600 - x) $1,000 0) = .52 .0007x 0; .0007x = .38; x = $542.86 = $543 79. You recently purchased a stock that is expected to earn 12% in a booming economy, 8% in a normal economy and lose 5% in a recessionary economy. There is a 15% probability of a boom, a 75% chance of a normal economy, and a 10% chance of a recession. What is your expected rate of return on this stock? E(r) = (.15 .12) (.75 .08) (.10 -.05) = .018 .06 - .005 = .073 = 7.3% 80. The Inferior Goods Co. stock is expected to earn 14% in a recession, 6% in a normal economy, and lose 4% in a booming economy. The probability of a boom is 20% while the probability of a normal economy is 55% and the chance of a recession is 25%. What is the expected rate of return on this stock? E(r) = (.20 -.04) (.55 .06) (.25 .14) = -.008 .033 .035 = .06 = 6.0% 81. You are comparing stock A to stock B. Given the following information, which one of these two stocks should you prefer and why? E(r)A = (.60 .09) (.40 .04) = .054 .016 = .07 = 7% E(r)B = (.60 .15) (.40 -.06) = .09 - .024 = .066 = 6.6% You should select stock A because it has a higher expected return and also appears to be less risky. 82. Zelo, Inc. stock has a beta of 1.23. The risk-free rate of return is 4.5% and the market rate of return is 10%. What is the amount of the risk premium on Zelo stock? Risk premium = 1.23 (.10 - .045) = .06765 = 6.77% 83. If the economy booms, RTF, Inc. stock is expected to return 10%. If the economy goes into a recessionary period, then RTF is expected to only return 4%. The probability of a boom is 60% while the probability of a recession is 40%. What is the variance of the returns on RTF, Inc. stock? E(r) = (.60 .10) (.40 .04) = .06 .016 = .076 Var = .60 (.10 - .076)2 .40 (.04 - .076)2 = . . = . 84. The rate of return on the common stock of Flowers by Flo is expected to be 14% in a boom economy, 8% in a normal economy, and only 2% in a recessionary economy. The probabilities of these economic states are 20% for a boom, 70% for a normal economy, and 10% for a recession. What is the variance of the returns on the common stock of Flowers by Flo? E(r) = (.20 .14) (.70 .08) (.10 .02) = .028 .056 .002 = .086 Var = .20 (.14 - .086)2 .70 (.08 - .086)2 .10 (.02 - .086)2 = . . . = . 85. Kurt's Adventures, Inc. stock is quite cyclical. In a boom economy, the stock is expected to return 30% in comparison to 12% in a normal economy and a negative 20% in a recessionary period. The probability of a recession is 15%. There is a 30% chance of a boom economy. The remainder of the time, the economy will be at normal levels. What is the standard deviation of the returns on Kurt's Adventures, Inc. stock? E(r) = (.30 .30) (.55 .12) (.15 -.20) = .09 .066 - .03 = .126 Var = .30 (.30 - .126)2 .55 (.12 - .126)2 .15 (-.20 - .126)2 = . . . = . Std dev = . = .15825 = 15.83% 86. What is the standard deviation of the returns on a stock given the following information? E(r) = (.10 .16) (.60 .11) (.30 -.08) = .016 .066 - .024 = .058 Var = .10 (.16 - .058)2 .60 (.11 - .058)2 .30 (-.08 - .058)2 = . . . = . Std dev = . = .09152 = 9.15% 87. You have a portfolio consisting solely of stock A and stock B. The portfolio has an expected return of 10.2%. Stock A has an expected return of 12% while stock B is expected to return 7%. What is the portfolio weight of stock A? .102 = [.12 x] [.07 (1 - x)] = .12x .07 - .07x; .032 = .05x; x = 64% 88. You own the following portfolio of stocks. What is the portfolio weight of stock C? Portfolio weightC = (400 $46) [(100 $22) (600 $17) (400 $46) (200 $38)] = $18,400 $38,400 = 47.9% 89. You own a portfolio with the following expected returns given the various states of the economy. What is the overall portfolio expected return? E(r) = (.15 .18) (.60 .11) (.25 -.10) = .027 .066 - .025 = .068 = 6.8% 90. What is the expected return on a portfolio which is invested 20% in stock A, 50% in stock B, E(r)Boom = (.20 .18) (.50 .09) (.30 .06) = .036 .045 .018 = .099 E(r)Normal = (.20 .11) (.50 .07) (.30 .09) = .022 .035 .027 = .084 E(r)Bust = (.20 -.10) (.50 .04) (.30 .13) = -.020 .020 .039 = .039 E(r)Portfolio = (.20 .099) (.70 .084) (.10 .039) = .02376 .0588 .0039 = .0825 = 8.25% 91. What is the expected return on this portfolio? Portfolio value = (520 $25) (300 $48) (250 $26) = $13,000 $14,400 $6,500 = $33,900; E(r) = ($13,000 $33,900 .08) ($14,400 $33,900 .15) ($6,500 $33,900 .06) = .03068 .06372 .01150 = .1059 = 10.59% 92. What is the expected return on a portfolio comprised of $3,000 in stock K and $5,000 in stock L if the economy is normal? E(r)Normal = [$3,000 ($3,000 $5,000) .05] [$5,000 ($3,000 $5,000) .06) = .01875 .0375 = .05625 = 5.63% 93. What is the expected return on a portfolio comprised of $4,000 in stock M and $6,000 in stock N if the economy enjoys a boom period? E(r)Boom = [($4,000 ($4,000 $6,000) .18] [$6,000 ($4,000 $6,000) .10] = .072 .06 = .132 = 13.2% 94. What is the portfolio variance if 30% is invested in stock S and 70% is invested in stock T? E(r)Boom = (.30 .12) (.70 .20) = .036 .14 = .176 E(r)Normal = (.30 .06) (.70 .04) = .018 .028 = .046 E(r)Portfolio = (.40 .176) (.60 .046) = .0704 .0276 = .098 VarPortfolio = [.40 (.176 - .098)2] [.60 (.046 - .098)2] = . . = . 95. What is the variance of a portfolio consisting of $3,500 in stock G and $6,500 in stock H? E(r)Boom = [$3,500 ($3,500 $6,500) .15)] [$6,500 ($3,500 $6,500) .09) = .0525 .0585 = .111 E(r)Normal = [$3,500 ($3,500 $6,500) .08)] [$6,500 ($3,500 $6,500) .06) = .028 .039 = .067 E(r)Portfolio = (.15 .111) (.85 .067) = .01665 .05695 = .0736 VarPortfolio = [.15 (.111 - .0736)2] [.85 (.067 - .0736)2] = . . = . = . 96. What is the standard deviation of a portfolio that is invested 40% in stock Q and 60% in stock R? E(r)Boom = (.40 .18) (.60 .09) = .072 .054 = .126 E(r)Normal = (.40 .09) (.60 .05) = .036 .03 = .066 E(r)Portfolio = (.25 .126) (.75 .066) = .0315 .0495 = .081 VarPortfolio = [.25 (.126 - .081)2] [.75 (.066 - .081)2] = . . = . Std dev = . = .02598 = 2.6% 97. What is the standard deviation of a portfolio which is comprised of $4,500 invested in stock S and $3,000 in stock T? E(r)Boom = [$4,500 ($4,500 $3,000) .12)] [$3,000 ($4,500 $3,000) .04) = .072 .016 = .088 E(r)Normal = [$4,500 ($4,500 $3,000) .09)] [$3,000 ($4,500 $3,000) .06) = .054 .024 = .078 E(r)Bust = [$4,500 ($4,500 $3,000) .02)] [$3,000 ($4,500 $3,000) .09) = .012 .036 = .048 E(r)Portfolio = (.10 .088) (.65 .078) (.25 .048) = .0088 .0507 .012 = .0715 VarPortfolio = [.10 (.088 - .0715)2] [.65 (.078 - .0715)2] [.25 (.048 - .0715)2] = . . . = . Std dev = . = .01388 = 1.4% 98. What is the standard deviation of a portfolio which is invested 20% in stock A, 30% in stock B and 50% in stock C? E(r)Boom = (.20 .15) (.30 .10) (.50 .05) = .03 .03 .025 = .085 E(r)Normal = (.20 .09) (.30 .06) (.50 .07) = .018 .018 .035 = .071 E(r)Bust = (.20 -.14) (.30 .02) (.50 .08) = -.028 .006 .04 = .018 E(r)Portfolio = (.10 .085) (.70 .071) (.20 .018) = .0085 .0497 .0036 = .0618 VarPortfolio = [.10 (.085 - .0618)2] [.70 (.071 - .0618)2] [.20 (.018 - .0618)2] = . . . = . Std dev = . = . = 2.2% 99. What is the beta of a portfolio comprised of the following securities? ValuePortfolio = $2,000 $3,000 $5,000 = $10,000 BetaPortfolio = ($2,000 $10,000 1.20) ($3,000 $10,000 1.46) ($5,000 $10,000 .72) = .24 .438 .36 = 1.038 100. Your portfolio is comprised of 30% of stock X, 50% of stock Y, and 20% of stock Z. Stock X has a beta of .64, stock Y has a beta of 1.48, and stock Z has a beta of 1.04. What is the beta of your portfolio? BetaPortfolio = (.30 .64) (.50 1.48) (.20 1.04) = .192 .74 .208 = 1.14 101. Your portfolio has a beta of 1.18. The portfolio consists of 15% U.S. Treasury bills, 30% in stock A, and 55% in stock B. Stock A has a risk-level equivalent to that of the overall market. What is the beta of stock B? BetaPortfolio = 1.18 = (.15 0) (.30 1.0) (.55 B) = 0 .3 .55B; .88 = .55B; B = 1.6 The beta of a risk-free asset is zero. The beta of the market is 1.0. 102. You would like to combine a risky stock with a beta of 1.5 with U.S. Treasury bills in such a way that the risk level of the portfolio is equivalent to the risk level of the overall market. What percentage of the portfolio should be invested in Treasury bills? BetaPortfolio = 1.0 = [(1 - w) 1.5] [w 0] = 1.5 - 1.5w; 1.5w = .5; w = .33 103. The market has an expected rate of return of 9.8%. The long-term government bond is expected to yield 4.5% and the U.S. Treasury bill is expected to yield 3.4%. The inflation rate is 3.1%. What is the market risk premium? Risk premium = 9.8% - 3.4% = 6.4% 104. The risk-free rate of return is 4% and the market risk premium is 8%. What is the expected rate of return on a stock with a beta of 1.28? E(r) = .04 (1.28 .08) = .1424 = 14.24% 105. The common stock of Flavorful Teas has an expected return of 14.4%. The return on the market is 10% and the risk-free rate of return is 3.5%. What is the beta of this stock? E(r) = .144 = .035 (.10 - .035); .109 = .065; = 1.68 106. The stock of Big Joe's has a beta of 1.14 and an expected return of 11.6%. The risk-free rate of return is 4%. What is the expected return on the market? E(r) = .116 = .04 1.14 (rm - .04); .1216 = 1.14rm; rm = .1067 = 10.67% 107. The expected return on HiLo stock is 13.69% while the expected return on the market is 11.5%. The beta of HiLo is 1.3. What is the risk-free rate of return? E(r) = .1369 = rf 1.3 (.115 - rf); .3rf = .0126; rf = .042 = 4.2% 108. The stock of Martin Industries has a beta of 1.43. The risk-free rate of return is 3.6% and the market risk premium is 9%. What is the expected rate of return on Martin Industries stock? E(r) = .036 (1.43 .09) = .1647 = 16.5% 109. Which one of the following stocks is correctly priced if the risk-free rate of return is 2.5% and the market risk premium is 8%? E(r)A = .025 (.68 .08) = .079 E(r)B = .025 (1.42 .08) = .139 Stock B is correctly priced. E(r)C = .025 (1.23 .08) = .123 E(r)D = .025 (1.31 .08) = .130 E(r)E = .025 (.94 .08) = .100 110. Which one of the following stocks is correctly priced if the risk-free rate of return is 3.6% and the market rate of return is 10.5%? E(r)A = .036 [.85 (.105 - .036)] = .095 E(r)B = .036 [1.08 (.105 - .036)] = .111 E(r)C = .036 [1.69 (.105 - .036)] = .153 Stock C is correctly priced. E(r)D = .036 [.71 (.105 - .036)] = .085 E(r)E = .036 [1.45 (.105 - .036)] = .136 111. The expected return on GenLabs is: E(r) = .05(-.5) .10(-.15) .2(.05) .3(.15) .2(.25) .15(.40) = .125 = 12.5% 112. The variance of GenLabs returns is: .05(-.50 - .125)2 .1(-.15 - .125)2 .2(.05 - .125)2 .3(.15 - .125)2 .2(.25 - .125)2 .15(.40 - .125)2 = .0428 113. The standard deviation of GenLabs returns is .05(-.50 - .125)2 .1(-.15 - .125)2 .2(.05 - .125)2 .3(.15 - .125)2 .2(.25 - .125)2 .15(.40 - .125)2 = .0428 Square root of (.0428) = .2069 114. Stock A has an expected return of 20%, and stock B has an expected return of 4%. However, the risk of stock A as measured by its variance is 3 times that of stock B. If the two stocks are combined equally in a portfolio, what would be the portfolio's expected return? Rp = 20(.5) .04(.5) = 12% 115. A portfolio is entirely invested into Buzz's Bauxite Boring equity, which is expected to return 16%, and Zum's Inc. bonds, which are expected to return 8%. 60% of the funds are invested in Buzz's and the rest in Zum's. What is the expected return on the portfolio? Rp = .60(R Buzz) .40(R Zum) = .60(16%) .40(8%) = 12.8% 116. The variance of Stock A is .004, the variance of the market is .007 and the covariance between the two is .0026. What is the correlation coefficient? Standard deviation of A = .06325, Standard deviation of the market = .08366 CORR = COV/(SDa.(SDm) = .0026/(.06325)(.08366) = .4913 117. A portfolio has 50% of its funds invested in Security One and 50% of its funds invested in Security Two. Security One has a standard deviation of 6%. Security Two has a standard deviation of 12%. The securities have a coefficient of correlation of 0.5. Which of the following values is closest to portfolio variance? Var. = .52(.06)2 .52(.12)2 2(.5)(.5)(.5)(.06)(.12) = .0009 .0036 .0018 = .0063 118. A portfolio has 25% of its funds invested in Security C and 75% of its funds invested in Security D. Security C has an expected return of 8% and a standard deviation of 6%. Security D has an expected return of 10% and a standard deviation of 10%. The securities have a coefficient of correlation of 0.6. Which of the following values is closest to portfolio return and variance? E(R) = .25(.08) .75(.10) = .095 = 9.5% Variance = .252(.06)2 .752(.10)2 2(.25)(.75)(.06)(.60)(.10) = .0072 119. A portfolio contains two assets. The first asset comprises 40% of the portfolio and has a beta of 1.2. The other asset has a beta of 1.5. The portfolio beta is: p = .4(1.2) .6(1.5) = 1.38 120. A portfolio contains four assets. Asset 1 has a beta of .8 and comprises 30% of the portfolio. Asset 2 has a beta of 1.1 and comprises 30% of the portfolio. Asset 3 has a beta of 1.5 and comprises 20% of the portfolio. Asset 4 has a beta of 1.6 and comprises the remaining 20% of the portfolio. If the riskless rate is expected to be 3% and the market risk premium is 6%, what is the beta of the portfolio? p = .3(.8) .3(1.1) .2(1.5) .2(1.6) = 1.19 1. The weighted average of the firm's costs of equity, preferred stock, and after tax debt is the: 2. If the CAPM is used to estimate the cost of equity capital, the expected excess market return is equal to the: 3. The best fit line of a pairwise plot of the returns of the security against the market index returns is called the: 4. The use of debt is called: 5. The weighted average cost of capital for a firm is the: 6. The WACC is used to _______ the expected cash flows when the firm has ____________. 7. Using the CAPM to calculate the cost of capital for a risky project assumes that: 8. The use of WACC to select investments is acceptable when the: 9. If the risk of an investment project is different than the firm's risk then: 10. If the project beta and IRR coordinates plot above the SML the project should be: 11. The beta of a security provides an: 12. Regression analysis can be used to estimate: 13. Beta measures depend highly on the: 14. The formula for calculating beta is given by the dividing the ___________ of the stock with the market portfolio by the ___________ of the market portfolio. 15. The slope of the characteristic line is the estimated: 16. Companies that have highly cyclical sales will have a: 17. Betas may vary substantially across an industry. The decision to use the industry or firm beta to estimate the cost of capital depends on: 18. Beta is useful in the calculation of the: 19. For a multi-product firm, if a project's beta is different from that of the overall firm, then the: 20. The problem of using the overall firm's beta in discounting projects of different risk is the: 21. The asset beta of a levered firm is generally: 22. Comparing two otherwise equal firms, the beta of the common stock of a levered firm is ____________ than the beta of the common stock of an unlevered firm. 23. The beta of a firm is determined by which of the following firm characteristics? 24. The beta of a firm is more likely to be high under what two conditions? 25. A firm with cyclical earnings is characterized by: 26. A firm with high operating leverage has: 27. If a firm has low fixed costs relative to all other firms in the same industry, a large change in sales volume (either up or down) would have: 28. A firm with high operating leverage is characterized by __________ while one with high financial leverage is characterized by __________. 29. Firms whose revenues are strongly cyclical and whose operating leverage is high are likely to have: 30. An industry is likely to have a low beta if the: 31. For the levered firm the equity beta is __________ the asset beta. 32. All else equal, a more liquid stock will have a lower ________. 33. Two stock market based costs of liquidity that affects the cost of capital are the: 34. When a specialist is caught in the middle of a trade between informed and uniformed traders, which effectively eliminates the spread or causes a loss, is subject to: 35. All else equal, new shareholders will ____ the capital gains of existing shareholders. 36. The following are methods to estimate the market risk premium: 37. Beta is the slope of the: 38. Two stocks that have the same beta ____ have the same correlation because _______: 39. When using the cost of debt, the relevant number is the: 40. Jack's Construction Co. has 80,000 bonds outstanding that are selling at par value. Bonds with similar characteristics are yielding 8.5%. The company also has 4 million shares of common stock outstanding. The stock has a beta of 1.1 and sells for $40 a share. The U.S. Treasury bill is yielding 4% and the market risk premium is 8%. Jack's tax rate is 35%. What is Jack's weighted average cost of capital? Re = .04 (1.1 .08) = .128 Debt: 80,000 $1,000 = $80m Common: 4m $40 = $160m Total = $80m $160m = $240m 41. Peter's Audio Shop has a cost of debt of 7%, a cost of equity of 11%, and a cost of preferred stock of 8%. The firm has 104,000 shares of common stock outstanding at a market price of $20 a share. There are 40,000 shares of preferred stock outstanding at a market price of $34 a share. The bond issue has a total face value of $500,000 and sells at 102% of face value. The tax rate is 34%. What is the weighted average cost of capital for Peter's Audio Shop? Debt: $500,000 1.02 = $.51m Preferred: 40,000 $34 = $1.36m Common: 104,000 $20 = $2.08m Total = $.51m $1.36m $2.08m = $3.95m 42. Phil's Carvings, Inc. wants to have a weighted average cost of capital of 9%. The firm has an after-tax cost of debt of 5% and a cost of equity of 11%. What debt-equity ratio is needed for the firm to achieve its targeted weighted average cost of capital? .09 = [We .11] [(1 - We) .05) = .11We .05 - .05We; .04 = .06We; We = 66.67%; Wd = 1 - We = 100% - 66.67% = 33.33%; Debt - equity ratio = 33.33% 66.67% = .50 43. Jake's Sound Systems has 210,000 shares of common stock outstanding at a market price of $36 a share. Last month, Jake's paid an annual dividend in the amount of $1.593 per share. The dividend growth rate is 4%. Jake's also has 6,000 bonds outstanding with a face value of $1,000 per bond. The bonds carry a 7% coupon, pay interest annually, and mature in 4.89 years. The bonds are selling at 99% of face value. The company's tax rate is 34%. What is Jake's weighted average cost of capital? Debt: 6,000 $1,000 .99 = $5.94m Common: 210,000 $36 = $7.56m Total = $5.94m $7.56m = $13.50m Re = [($1.593 1.04) $36] .04 = .08602 44. The Consolidated Transfer Co. is an all-equity financed firm. The beta is .75, the market risk premium is 8% and the risk-free rate is 4%. What is the expected return of Consolidated? .04 0.75(.08) = .10 = 10% 45. Assuming the CAPM or one-factor model holds, what is the cost of equity for a firm if the firm's equity has a beta of 1.2, the risk-free rate of return is 2%, the expected return on the market is 9%, and the return to the company's debt is 7%? Rs = Rf (Rm - Rf) = .02 1.2(.09 - .02) = .104 = 10.4% 46. The cost of equity for Ryan Corporation is 8.4%. If the expected return on the market is 10% and the risk-free rate is 5%, then the equity beta is ___. Rs = Rf (Rm - Rf); .084 = .05 (.10 - .05); = .68 47. Suppose that the Simmons Corporation's common stock has a beta of 1.6. If the risk-free rate is 5% and the market risk premium is 4%, the expected return on Simmons' common stock is: Rs = Rf (Rm - Rf) = .05 1.6(.04) = .114 = 11.4% 48. Suppose the Barges Corporation's common stock has an expected return of 12%. Assume that the risk-free rate is 5%, and the market risk premium is 6%. If no unsystematic influence affected Barges' return, the beta for Barges is ______. Rs = Rf (Rm - Rf); .12 = .05 (.06); = .07/.06 = 1.17 49. Slippery Slope Roof Contracting has an equity beta of 1.2, capital structure with 2/3 debt, and a zero tax rate. What is its asset beta? A = (E/(D E.) E = (1/3)(1.2) = .40 50. The Template Corporation has an equity beta of 1.2 and a debt beta of .8. The firm's market value debt to equity ratio is .6. Template has a zero tax rate. What is the asset beta? .8(.6/1.6) 1.2(1/1.6) = 1.05 51. The NuPress Valet Co. has an improved version of its hotel stand. The investment cost is expected to be $72 million and will return $13.5 million for 5 years in net cash flows. The ratio of debt to equity is 1 to 1. The cost of equity is 13%, the cost of debt is 9%, and the tax rate is 34%. The appropriate discount rate, assuming average risk, is: WACC = .09(1 - .34)(.5) .13(.5) = .0297 .065 = .0947 = 9.47% 1. The book capital of a corporation is determined by: . 2. Retained earnings are: 3. The book value of the shareholders' ownership is represented by: 4. Shares of stock that have been repurchased by the corporation are called: . 5. The market value of the ownership of the firm equals: 6. A grant of authority allowing someone else to vote shares of stock that you own is called: 7. Unsecured corporate debt is called a(n): 8. A standard arrangement for the orderly retirement of long-term debt calls for the corporation to make regular payments into a(n): 9. Debt that may be extinguished before maturity is referred to as: 10. If a long-term debt instrument is perpetual, it is called a(n): 11. The amount of loan a person or firm borrows from a lender is the: 12. The written agreement between a corporation and its bondholders is called: 13. If cumulative voting is permitted: times the number of directors to be elected. 14. The market-to-book value ratio is implies growth and success when it is: . 15. There are 3 directors' seats up for election. If you own 1,000 shares of stock and you can cast 3,000 votes for a particular director, this is illustrative of: 16. If you own 1,000 shares of stock and you can cast only 1,000 votes for a particular director, then the stock features: 17. If a group other than management solicits the authority to vote shares to replace management, a _____ is said to occur. 18. Shareholders usually have which of the following right(s)? . 19. Different classes of stock usually are issued to: . 20. Which of the following statements is false? . 21. Corporations try to create hybrid securities that look like equity but are called debt because: 22. Technically speaking, a long-term corporate debt offering that features a specific attachment to corporate property is generally called: 23. If a firm retires or extinguishes a debt issue before maturity, the specific amount they pay is: 24. If a debenture is subordinated, it: 25. Not paying the dividends on a cumulative preferred issue may result in: 26. Preferred stock has both a tax advantage and a tax disadvantage. These two are: 27. Preferred stock may be desirable to issue for which of the following reason(s)? 28. Preferred stock may exist because: 29. The written agreement between a corporation and its bondholders might contain a prohibition against paying dividends in excess of current earnings. This prohibition is an example of a(n): 30. What percentage of the dividends received by one corporation from another is taxable? 31. Which of the following statements about preferred stock is true? 32. If a debt issue is callable, the call price is generally ____ par. 33. There was an upward trend in the ratio of the book value of debt to the book value of debt and equity throughout the 1990s. Some of this was due to the repurchasing of stock. The market value ratio of debt to debt and equity exhibited no upward trend. This can be explained by: 34. Based on historical experience, which of the following best describes the "pecking order" of long-term financing strategy in the U.S.? 35. Financial deficits are created when: 36. Financial economists prefer to use market values when measuring debt ratios because: 37. Corporate financial officers prefer to use book values when measuring debt ratios because: 38. Rockwell Corporation had net income of $150,000 for the year ending 2008. The company decided to payout 40% of earnings per share as a dividend. Rockwell has 120,000 shares issued and outstanding. What are the retained earnings for 2008? RE = NI (1 - payout ratio) = $150,000 (1 - .4) = $90,000. 39. Nelson Company had equity accounts in 2008 as follows: Projected income is $150,000 and 40% of this amount will be paid out immediately as dividends. What will the ending retained earnings account be? RE0 = NI (1 - payout ratio) = $150,000 (.6) = $90,000. RE1 = RE-1 RE0 = $32,000 $90,000 = $122,000. 40. Holden Bicycles has 1,000 shares outstanding each with a par value of $0.10. If they are sold to shareholders at $10 each, what would the capital surplus be? Capital Surplus: ($10.00 - $0.10) * 1,000 = $9,900. 41. The Lory Bookstore used internal financing as a source of long-term financing for 80% of its total needs in 2008. The company borrowed an additional 27% of its total needs in the long-term debt markets in 2008. What were Lory's net new stock issues in that year? Net new issues = - 7%, as more stock was repurchased than issued. (100% - (80 27)) = (100 - 107) = -7%. 42. David's Building Equipment (DBE) had net income of $200,000 for the year ending 2008. The company decided to payout 30% of earnings per share as a dividend. DBE has 50,000 shares issued and outstanding. What are the retained earnings for 2008? RE = NI (1 - payout ratio) = $200,000 (1 - .3) = $140,000. 43. Alexandra Investments had equity accounts in 2008 as follows: Projected income is $200,000 and 20% of this amount will be paid out immediately as dividends. What will the ending retained earnings account be? RE0 = NI (1 - payout ratio) = $200,000 (.8) = $160,000. RE1 = RE-1 RE0 = $250,000 $160,000 = $410,000. 44. Michael's Motor Scooters has 1,000 shares outstanding each with a par value of $0.05. If they are sold to shareholders at $5 each, what would the capital surplus be? Capital Surplus: ($5.00 - $0.05) * 1,000 = $4,950. 45. Calhoun Computech used internal financing as a source of long-term financing for 80% of its total needs in 2008. The company borrowed an additional 15% of its total needs in the long-term debt markets in 2008. What were Calhoun's net new stock issues, in percentage terms, for 2008? C. 5% Net new issues = 5%, as 100% - (80% 15%) = 5%. 1. The use of personal borrowing to change the overall amount of financial leverage to which an individual is exposed is called: 2. The proposition that the value of the firm is independent of its capital structure is called: 3. The proposition that the cost of equity is a positive linear function of capital structure is called: 4. The tax savings of the firm derived from the deductibility of interest expense is called the: 5. The unlevered cost of capital is: 6. The cost of capital for a firm, rWACC, in a zero tax environment is: 7. The difference between a market value balance sheet and a book value balance sheet is that a market value balance sheet: 8. The firm's capital structure refers to: 9. A general rule for managers to follow is to set the firm's capital structure such that: 10. A levered firm is a company that has: 11. A manager should attempt to maximize the value of the firm by: 12. The effect of financial leverage depends on the operating earnings of the company. Which of the following is not true? . 13. The Modigliani-Miller Proposition I without taxes states: 14. MM Proposition I without taxes is used to illustrate: 15. A key assumption of MM's Proposition I without taxes is: . 16. In an EPS-EBI graphical relationship, the slope of the debt ray is steeper than the equity ray. The debt ray has a lower intercept because: 17. In an EPS-EBI graphical relationship, the debt ray and equity ray cross. At this point the equity and debt are: 18. When comparing levered vs. unlevered capital structures, leverage works to increase EPS for high levels of EBIT because: 19. Financial leverage impacts the performance of the firm by: 20. The increase in risk to equityholders when financial leverage is introduced is evidenced by: 21. The reason that MM Proposition I does not hold in the presence of corporate taxation is because: 22. MM Proposition I with corporate taxes states that: 23. The change in firm value in the presence of corporate taxes only is: 24. A firm should select the capital structure which: 25. In a world of no corporate taxes if the use of leverage does not change the value of the levered firm relative to the unlevered firm is known as: 26. Bryan invested in Bryco, Inc. stock when the firm was financed solely with equity. The firm is now utilizing debt in its capital structure. To unlever his position, Bryan needs to: 27. The capital structure chosen by a firm doesn't really matter because of: 28. MM Proposition I with no tax supports the argument that: . 29. The proposition that the value of a levered firm is equal to the value of an unlevered firm is known as: 30. The concept of homemade leverage is most associated with: 31. Which of the following statements are correct in relation to MM Proposition II with no taxes? I. The required return on assets is equal to the weighted average cost of capital. II. Financial risk is determined by the debt-equity ratio. III. Financial risk determines the return on assets. IV. The cost of equity declines when the amount of leverage used by a firm rises. 32. MM Proposition I with taxes supports the theory that: 33. MM Proposition I with taxes is based on the concept that: . 34. MM Proposition II with taxes: as MM Proposition II without taxes. 35. MM Proposition II is the proposition that: cost of equity capital is a positive linear function of the firm's capital structure. 36. The interest tax shield has no value for a firm when: I. the tax rate is equal to zero. II. the debt-equity ratio is exactly equal to 1. III. the firm is unlevered. IV. a firm elects 100% equity as its capital structure. IV only 37. The interest tax shield is a key reason why: debt to a firm is generally less than the cost of equity. 38. Which of the following will tend to diminish the benefit of the interest tax shield given a progressive tax rate structure? I. a reduction in tax rates II. a large tax loss carryforward III. a large depreciation tax deduction IV. a sizeable increase in taxable income 39. Thompson & Thomson is an all equity firm that has 500,000 shares of stock outstanding. The company is in the process of borrowing $8 million at 9% interest to repurchase 200,000 shares of the outstanding stock. What is the value of this firm if you ignore taxes? Price per share = $8m 200k = $40; [(500,000 - 200,000) $40] $8m = 500,000 $40 = $20m; Value of the firm is $20m 40. Uptown Interior Designs is an all equity firm that has 40,000 shares of stock outstanding. The company has decided to borrow $1 million to buy out the shares of a deceased stockholder who holds 2,500 shares. What is the total value of this firm if you ignore taxes? Price per share = $1m 2,500 = $400; [(40,000 - 2,500) $400] $1m = 40,000 $400 = $16m 41. You own 25% of Unique Vacations, Inc. You have decided to retire and want to sell your shares in this closely held, all equity firm. The other shareholders have agreed to have the firm borrow $1.5 million to purchase your 1,000 shares of stock. What is the total value of this firm today if you ignore taxes? Price per share = $1.5m 1,000 = $1,500; Current number of shares = 1,000 .25 = 4,000; [(4,000 -1,000) $1,500] $1.5m = 4,000 $1,500 = $6m 42. Your firm has a debt-equity ratio of .75. Your pre-tax cost of debt is 8.5% and your required return on assets is 15%. What is your cost of equity if you ignore taxes? Re = .15 (.15 - .085) .75 = .19875 = 19.88% 43. Bigelow, Inc. has a cost of equity of 13.56% and a pre-tax cost of debt of 7%. The required return on the assets is 11%. What is the firm's debt-equity ratio based on MM Proposition II with no taxes? .1356 = .11 (.11 - .07) D/E; D/E = .64 44. The Backwoods Lumber Co. has a debt-equity ratio of .80. The firm's required return on assets is 12% and its cost of equity is 15.68%. What is the pre-tax cost of debt based on MM Proposition II with no taxes? .1568 = .12 (.12 - Rd) .80; Rd = .074 = 7.40% 45. The Winter Wear Company has expected earnings before interest and taxes of $2,100, an unlevered cost of capital of 14% and a tax rate of 34%. The company also has $2,800 of debt that carries a 7% coupon. The debt is selling at par value. What is the value of this firm? VU = [$2,100 (1 - .34)] .14 = $9,900; VL = $9,900 (.34 $2,800) = $10,852 46. Gail's Dance Studio is currently an all equity firm that has 80,000 shares of stock outstanding with a market price of $42 a share. The current cost of equity is 12% and the tax rate is 34%. Gail is considering adding $1 million of debt with a coupon rate of 8% to her capital structure. The debt will be sold at par value. What is the levered value of the equity? VL = (80,000 $42) (.34 $1m) = $3.36m .34m = $3.7m; VE = $3.7m - $1m = $2.7m 47. The Montana Hills Co. has expected earnings before interest and taxes of $8,100, an unlevered cost of capital of 11%, and debt with both a book and face value of $12,000. The debt has an annual 8% coupon. The tax rate is 34%. What is the value of the firm? VU = [$8,100 (1 - .34) ] .11 = $48,600; VL = $48,600 (.34 $12,000) = $52,680 48. Scott's Leisure Time Sports is an unlevered firm with an after-tax net income of $86,000. The unlevered cost of capital is 10% and the tax rate is 34%. What is the value of this firm? VU = $86,000 .10 = $860,000 49. An unlevered firm has a cost of capital of 14% and earnings before interest and taxes of $150,000. A levered firm with the same operations and assets has both a book value and a face value of debt of $700,000 with a 7% annual coupon. The applicable tax rate is 35%. What is the value of the levered firm? VU = [$150,000 (1 - .35)] .14 = $696,428.57; VL = $696,428.57 (.35 $700k) = $941,428.57 = $941,429 50. The Spartan Co. has an unlevered cost of capital of 11%, a cost of debt of 8%, and a tax rate of 35%. What is the target debt-equity ratio if the targeted cost of equity is 12%? .12 = .11 (.11 - .08) D/E (1 - .35); .01 = .0195D/E; D/E = .51 51. Hey Guys!, Inc. has debt with both a face and a market value of $3,000. This debt has a coupon rate of 7% and pays interest annually. The expected earnings before interest and taxes is $1,200, the tax rate is 34%, and the unlevered cost of capital is 12%. What is the firm's cost of % VU = [EBIT (1 - Tc)] RU = [$1,200 (1- .34)] .12 = $6,600 VL = VU (Tc D) = $6,600 (.34 $3,000) = $7,620 VL - VD = VE = $7,620 - $3,000 = $4,620 RE = RU (RU - RD) D/E (1 - TC) = .12 [(.12 - .07) ($3,000 $4,620) (1 - .34)] = .12 .02143 = .14143 = 14.14% 52. Anderson's Furniture Outlet has an unlevered cost of capital of 10%, a tax rate of 34%, and expected earnings before interest and taxes of $1,600. The company has $3,000 in bonds outstanding that have an 8% coupon and pay interest annually. The bonds are selling at par value. What is the cost of equity? VU = [EBIT (1 - Tc)] RU = [$1,600 (1- .34)] .10 = $10,560 VL = VU (Tc D) = $10,560 (.34 $3,000) = $11,580 VL - VD = VE = $11,580 - $3,000 = $8,580 RE = RU (RU - RD) D/E (1 - TC) = .10 [(.10 - .08) ($3,000 $8,580) (1 - .34)] = .10 .00462 = .10462 = 10.46% 53. Walter's Distributors has a cost of equity of 13.84% and an unlevered cost of capital of 12%. The company has $5,000 in debt that is selling at par value. The levered value of the firm is $12,000 and the tax rate is 34%. What is the pre-tax cost of debt? VE = $12,000 - $5,000 = $7,000; .1384 = .12 (.12 - RD) ($5,000 $7,000) (1 - .34); .0184 = . - .RD; RD = .08097 = 8.10% 54. Rosita's has a cost of equity of 13.8% and a pre-tax cost of debt of 8.5%. The debt-equity ratio is .60 and the tax rate is .34. What is Rosita's unlevered cost of capital? .138 = RU (RU - .085) .60 (1 - .34); .17166 = 1.396RU; RU = .12297 = 12.30% 55. Your firm has a pre-tax cost of debt of 7% and an unlevered cost of capital of 13%. Your tax rate is 35% and your cost of equity is 15.26%. What is your debt-equity ratio? .1526 = .13 (.13 - .07) D/E (1 - .35); .0226 = .039D/E; D/E = .579 = .58 56. Wild Flowers Express has a debt-equity ratio of .60. The pre-tax cost of debt is 9% while the unlevered cost of capital is 14%. What is the cost of equity if the tax rate is 34%? RE = .14 (.14 - .09) .60 (1 - .34) = .14 .0198 = .1598 = 15.98% 57. Your firm has a $250,000 bond issue outstanding. These bonds have a 7% coupon, pay interest semiannually, and have a current market price equal to 103% of face value. What is the amount of Annual interest tax shield = $250,000 .07 .35 = $6,125 58. Bertha's Boutique has 2,000 bonds outstanding with a face value of $1,000 each and a coupon rate of 9%. The interest is paid semi-annually. What is the amount of the annual interest tax shield if the tax rate is 34%? Annual interest tax shield = 2,000 $1,000 .09 .34 = $61,200 59. Juanita's Steak House has $12,000 of debt outstanding that is selling at par and has a coupon rate of 8%. The tax rate is 34%. What is the present value of the tax shield? Present value of the tax shield = .34 $12,000 = $4,080 60. A firm has debt of $5,000, equity of $16,000, a leveraged value of $8,900, a cost of debt of 8%, a cost of equity of 12%, and a tax rate of 34%. What is the firm's weighted average cost of capital? WACC = [($16k $21k) .12] [($5k $21k) .08 (1 - .34) = . . = .1040 = 10.40% 61. A firm has zero debt in its capital structure. Its overall cost of capital is 10%. The firm is considering a new capital structure with 60% debt. The interest rate on the debt would be 8%. Assuming there are no taxes or other imperfections, its cost of equity capital with the new capital structure would be _____. Rs = .10 .60/.40(.10 - .08) = .10 .03 = .013 = 13% 62. A firm has a debt-to-equity ratio of .60. Its cost of debt is 8%. Its overall cost of capital is 12%. What is its cost of equity if there are no taxes or other imperfections? C. 14.4% Rwacc = .12 = (.6/1.6)(.08) (1/1.6)X .12 = .375(.08) .625(X) .09 = .625x X = .144 = 14.4% 63. A firm has a debt-to-equity ratio of 1. Its cost of equity is 16%, and its cost of debt is 8%. If there are no taxes or other imperfections, what would be its cost of equity if the debt-to-equity ratio were 0? Rs = 16 = r0 1(r0 -.08) .16 = 2r0 - .08 .24 = 2r0 r0 = .12 = 12% WACC = rd wd rd we = .08(.5) .16(.5) = .12 = 12% 64. A firm has a debt-to-equity ratio of 1.20. If it had no debt, its cost of equity would be 15%. Its cost of debt is 10%. What is its cost of equity if there are no taxes or other imperfections? Rs = .15 1.2.15 - .10) = 21% 65. If a firm is unlevered and has a cost of equity capital of 12%, what would its cost of equity be if its debt-equity ratio became 2? The expected cost of debt is 8%. Rs = Rsu (B/S)(Rsu - Ru) Rs = .12 2(.12 - .08) = .0200 = 20% 66. A firm has zero debt in its capital structure. Its overall cost of capital is 9%. The firm is considering a new capital structure with 40% debt. The interest rate on the debt would be 4%. Assuming that the corporate tax rate is 34%, what would its cost of equity