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Numerical practice problems


Chapter 1 – Introduction

Answers to numerical problems
 Taxable Income
 Base Tax
 Plus this % over base
 0-10,000  $0  10%
 10,000-25,000  1,000  15
 25,000-100,000  3,250  25
 100,000-250,000  22,000  35
 250,000+  74,500  40
  1. An individual earns $125,000.00 of wages.
    1. Use the tax table to calculate the tax bill for this individual.
    2. What is this individual’s marginal tax rate?
    3. What is this individual’s average tax rate?
    4. If this individual receives an additional $1,000 of interest income, what is the additional tax on this investment income?
    5. If this individual sells shares of stock that result is $3,000 of capital gains, what is the additional tax on this income? 
    6. If this individual receives $500 of dividend income, what is the additional tax on this income?

Chapter 2 – Macroeconomics

  1. During the year, the price of a British stock went from £82 to £86 while paying a dividend of £5.  At the same time, the exchange rate went from $1.80/£ to $1.60/£.  What was the total dollar-denominated gain for this investment?  (Assume the dividend is exchanged for dollars at the end of the period).
  2. Over the last year, Nippon Industries shares went from ¥8,000 to ¥9,700 while paying a dividend of ¥80.  During this time, the exchange rate went from ¥125/$1 to ¥105/$1.  Find the dollar-denominated return for this investment.  (Assume the dividend is exchanged for dollars at the end of the period).

Chapter 3 – Individual security risk and return

  1. An investor buys a stock for $47 and gets an annual cash dividend of $2.25. Will he experience a capital gain or a capital loss if he sells the stock for $51.75 one year later? What is the investor’s dollar and percentage return?
  2. Another investor purchases a stock for $29.80 and gets an annual cash dividend of $1.60. This investor sells the stock three years later for $26.40 Will he experience a capital gain or a capital loss? What is this investor’s dollar and percentage return?
  3. Suppose you buy 400 shares of stock at the beginning of the year for $23/share and sell it in 6 months for $26/share. While you held the stock you received quarterly dividends of $0.25/share.
    1. Calculate your income and capital gains over the six months you held the stock. What is your total (dollar) return?
    2. Calculate your holding period return.
    3. What is your dividend yield and your capital gains yield over the six month period?
    4. Annualized your HPR using APR and EAR.
  4. Find the EAR for the following periodic returns.
    1. HPR =1% over 1 month.
    2. HPR=2.5% over 3 months.
    3. HPR=3% over 6 months.
    4. HPR=0.04% over one day.
  5. Imagine you buy a bond for $17,000, which pays $200 interest every 3 months. What are the total income, the amount of capital gain/loss, and the total dollar return you experience if you sell the bond for $15,500 nine months later? What is the HPR?
  6. For the following problems, determine (1) the current income, (2) the capital gain or loss, and (3) the total return in both dollars and as a percentage of the initial investment.
    1. An investor purchased a stock for $75 one year ago and received four dividend payments totaling $3.80. Today, the investor sells the share for $90.
    2. An investor sells his stock for $121. He bought the stock 18 months ago for $137 and received dividend payments of $8.10 every 6 months.
    3. An investor purchased a bond for $9,100 15 months ago. The bond paid $90 interest every 3 months and is now sold for $8,700.
  7. Bob is interested in a stock that is currently trading at $32 per share and that pays monthly dividends of $0.80 per share. His expectation is to sell the stock in four months for $35. Steve is interested in a different stock that is trading at $34 per share and that pays quarterly dividends of $0.95 per share. He expects to sell the stock in six months for $38. Which stock is more lucrative in terms of the annualized holding period return?
  8. You are buying a stock for $81 per share and are expecting to sell it in one year for $89. The Stock pays $1.27 per share in quarterly dividends. At the same time, your friend purchases a share of stock for $69. This stock is paying quarterly dividends of $1.09 per share and your friend is expecting to sell it in 3 months for $71. Will you or your friend have a better annualized holding period return?
  9. Imagine that an investment of $3,500 today is likely to return $6,000 in 8 years. Calculate the IRR on this investment. Decide whether it is worth doing this investment if a minimum rate of return of 6% is required. What is your decision if the required minimum rate of return is 8%?
  10. Another investment of $7,500 promises a return of $9,600 in 5 years. Estimate the IRR on this investment. Can you recommend this investment if a minimum rate of return of 6% is required? What if the required minimum rate of return is 7%?
  11. Imagine you purchased 250 shares of the investment described in the table at the beginning of 2004.
    1. Calculate the yearly total return in dollars.
    2. What is the aggregate (7-year) return in dollars and as a percentage of the initial investment if you sell the shares at the end of 2010?
    3. Calculate the IRR if income is received at the end of the year.
     Year  Income  Market Value Beginning
     Market Value Ending
     2004 $2.00
    $45.00
    $48.00
     2005  2.15  48.00  51.50
     2006  2.30  51.50  58.00
     2007  2.50  58.00  55.50
     2008  2.75  55.50  54.00
     2009  2.95  54.00  60.00
     2010  3.20  60.00  65.00

  12.  Assume an investor purchases shares of stock for $4.500 today and will sell them for $5,300 in 5 years. During those 5 years he receives $38, $40, $43, $39, and $41 in dividends. Calculate the internal rate of return on this investment.
  13. You invest $11,000 in a stock that pays $98, $105, $102, and $105 in dividends over the next 4 years. After the 4 years, you decide to sell the stock for $ $12,300. Determine the internal rate of return on your investment.
  14. Determine the IRR for the investments described in the following situations.
  15.  Situation     Initial investment
     Future value
     End of year
     1 $3,000
     $7,000  8
     2  900  4,000  25
     3  6,000  6,500  4

  16. The returns for two different investments are shown in the following table.
    1. Calculate the arithmetic and geometric average returns for each investment.
    2. Which of the two investments seems to be more risky? Explain why.
    3. What are the standard deviation of returns of each investment?
     Year Return on A
     Return on B
     2002  5% 10%
     2003  16  14
     2004  11  8
     2005  1  13
     2006  9  9
     2007  24  12
  17. The table below shows the returns for three alternative investments.
    1. Calculate the arithmetic and geometric average returns for each investment.
    2. What is the (average) risk premium of each investment?
    3. Determine which of the three investments seems to be most risky. Which appears to be the safest investment? 
    4. What are the standard deviations of returns of each investment?
     Year Return on A
     Return on B
     Return on C
     2003  8  16  24
     2004  8  5  16
     2005  8  9  10
     2006  8  14  3
     2007  8  1  7

Chapter 4 - Investing in stocks: the basics

  1. An investor purchases 150 shares of a certain stock at the following prices and margins. Calculate the loan for each transaction as well as the equity necessary to make these margin transactions.
  2.  Transaction Price/Share
     Margin Loan
    Equity
    a 45
    60%
       
    b  128  45%    
    c  22  73%    
    d  10  66%             
    e  84  57%    
    f  38  62%    
  3. Use the information from the previous question. Ignore any interest paid on loans.
    1. What is the investor’s new margin position if the stock price increases by $10 per share?
    2. What is the margin position if the share price decreases by $10?
  4. Bob purchased 150 shares of stock for $120 per share. The initial margin was 70% and the maintenance margin was 40%. At what price will Bob face a margin call?
  5. Kelly decides to buy 100 shares of a stock at a price of $62/share, using an initial margin of 60% and the maintenance margin being 30%. How far does the stock have to drop before Kelly faces a margin call?
  6. McDonald’s stock is currently selling at $48 per share. An investor purchases 100 shares of this stock using a margin of 70%. The annual dividends are $2 per share and the investor can obtain a margin loan at an annual interest cost of 6%. What is the return on invested capital that the investor can get if the stock price increases to $55 in 12 months?
  7. Steve bought 200 shares of UFO stock 12 months ago. The share price was $38 per share and the initial margin requirement used was 60%. Today, Steve decides to sell the shares. During the last 12 months, the stock paid $2 per share in cash dividends and the annual interest on the margin loan charged was 7%. There was a minimum maintenance margin of 35%.
    1. What is the initial value of the transaction? Determine the loan amount and the equity position on Steve’s transaction.
    2. Imagine the share price is i) $50, ii) $28, iii) $16, and iv) $45. What is the actual margin percentage for each situation? When would Steve be subject to a margin call?
    3. Imagine that after the 12-month holding period the sales prices are the following: i) $30, ii) $35, iii) $40, iv) $45, and v) $50. What is the rate of return for each situation?
  8. An investor has borrowed 300 shares of a stock from a broker. He decides to short sell them for $25 a share with the initial margin being 60%.
    1. Calculate the amount of money that will be in the investor’s account after the transaction.
    2. What is the margin if the stock falls to 22/share?
    3. What is the holding period return if the stock falls to $22 per share?
    4. If the maintenance margin is 35%, when will the investor receive a margin call? 
  9. An investor has borrowed 150 shares of stock from a broker. He decides to short sell them for $30 per share with an initial margin of 40% and the maintenance margin being 20%. Calculate the margin and indicate if there will be a margin call for each of the following situations.
    1. The stock price falls to $18 per share.
    2. The stock price falls to $25 per share.
    3. The stock price rises to $37 per share.
    4. The stock price rises to $42 per share. 
  10. Jimmy makes a cash purchase of 100 shares of a stock for $40 per share.  Louie buys the same stock but uses 50% margin and the loan has an 8% interest rate.  Each investor holds the stock for a year, receiving a $2 dividend.  Suppose they close their positions at the end of the year and all trades are charged a commission of $20.
    1. What is the return for each investor if the stock price is $50 per share at the end of the year?
    2. What is the return for each investor if the stock price is $30 per share at the end of the year?

Chapter 5 - Market indices

  1. Consider the three stocks in the following table. P(t) Represents the price of each stock on day t and Q(t) represents the number of shares outstanding. Stock C splits two for one in the last period.
    1. Calculate the rate of return on a price weighted index of the three stocks for the first period (day 0 to day 1). Assume the original divisor is 3.0.
    2. Calculate the new divisor on day 2.
    3. Calculate the rate of return of the price-weighted index for the second period (day 1 to day 2).
     Stock      P(0)  Q(0)  P(1)  Q(1) P(2)
     Q(2)
     A  90 100
    95
    100
    96
    100
     B 50
     200 45
    200
     45 200
     C  100 200
    110
     200 59
     400
  2. Use the data from the previous problem to calculate the rate of return in the first period for a market value weighted index.
  3. Use the following data to answer the questions below. 
    1. Assume the day 0 value of the index is 100. Find the day 1 value of a market value weighted index and find the rate of return on the index. 
    2. Assume the day 0 value of the index is 161.56. Find the day 1 value of a market value weighted index and find the rate of return on the index.
     Stock  P(0)  Q(0)  P(1)  Q(1)
    X
     50  300  52 300
    Y  65 100
    67
    100
    Z  90 200
     44 400
  4. Use the following data to answer the following questions.
    1. If the divisor for the price-weighted index is 0.9, what is the index value?
    2. Suppose the market value of these three stocks was $10 million when a market value weighted index was created. When the index was created the base value of the index was 100. What is the current value of a market value weighted index?
     Stock  P(0)  Q(0)
    M 24
    300,000
     N  49 125,000
     O  17 550,000

Chapter 6 - Portfolio topics

  1. Calculate the average return of the following portfolio
  2.  Investment    Avg. Return   Amount invested
     Stocks  15% $100,000 
     Bonds  5%  50,000
     Real estate  10%  250,000

  3. Assume you are considering a portfolio containing two assets, A and B. Asset A will represent 45% of the dollar value of the portfolio, and asset B will account for the other 55%. The expected returns over next 6 years, 2009-2014, for each of these assets are summarized in the following table.
     Year Return on A 
     Return on B
    2009 
     13% 20% 
     2010  13  19
     2011  15  15
     2012  16  13
     2013  16  12
     2014  20  11

    1. Calculate the average return and standard deviation of returns for Assets A and B.
    2. Find the portfolio’s expected return for EACH of the 6 years.
    3. Calculate the (arithmetic) average expected portfolio return, over the 6-year period.
    4. Calculate the standard deviation of expected portfolio returns, over the 6-year period.
    5. How would you characterize the correlation of the returns of the two assets A and B (no calculations are necessary)?
    6. Discuss any benefits of diversification achieved through creation of the portfolio.

  4. You have been asked for your advice in selecting a portfolio of assets and have been supplied with the following future expected return data.
     Year Asset P 
    Asset Q 
     Asset R
    2009 
    10%
    14%
    9%
     2010  12  12  12
     2011  14  10  15

    You have been told that you can create 2 portfolios—one consisting of assets P and Q and the other consisting of assets P and R—by investing equal proportions (50%) in each of the 2 component assets. 
    1. What is the (arithmetic) average expected return for each asset over the 3-year period?
    2. What is the standard deviation of returns for each asset?
    3. What is the average for each of the two portfolios?
    4. What is the standard deviation of returns for each portfolio?
    5. How would you characterize the correlations of the 2 assets making up each of the 2 portfolios (no calculations are necessary)?
    6. Which portfolio do you recommend? Why?

  5. Referring to the above problem, what would happen of you constructed a portfolio consisting of assets P, Q, and R, equally weighted? Would this reduce risk or enhance return?
  6. Assume you wish to evaluate the risk and return behaviors associated with the various combinations of assets A and B under three assumed degrees of correlation: perfect positive, uncorrelated, and perfect negative. The following average return and risk values were calculated for these assets. 
     Asset Avg Return 
     Risk (Std Deviation)
     A

     B  12  10
    1. If the returns of assets A and B are perfectly positively correlated (correlation coefficient = +1), what is the range of return and risk for all possible portfolio combinations.
    2. If the returns of assets A and B are uncorrelated (correlation coefficient = 0),describe the approximate range of return and risk for all possible portfolio combinations.
    3. If the returns of assets A and B are perfectly negatively correlated (correlation coefficient = -1), describe the range of return and risk for all possible portfolio combinations.
  7. You are evaluating 2 possible stock investments, Sprinkles Co. and Jimmies Corp. Sprinkles Co. has an average return of 15%, and a beta of 1. Jimmies Corp. has an average return of 15%, and a beta of 1.3. Based only on this data, which stock should you buy and why?
  8. Referring to above problem, if you expected a significant market rally, would your decision be altered? Explain.
  9. Assume you have a portfolio of $25,000 invested in each of Investment P, Q, and R. What is your portfolio beta? Betas for securities P, Q, and R are as shown below:
  10.  Security    Beta 
     P 1.30 
     Q  0.50
     R  -0.80

  11. Calculate the beta of the following portfolio.
  12.  Stock Amt invested
    Beta
     ABC  $1,000  1.1
     JKL  3,000  0.6
     PQR  7,000  1.4
     XYZ  9,000  0.9

  13. Use the capital asset pricing model (CAPM) to find the required return for each of the following securities in light of the data given.
  14.  Security Risk-free rate 
    Return on market 
    Beta 
     P  6% 9% 
    1.20
     Q  9  12  0.85
     R  10  14  -0.30
     S  11  16  1.00
     T  8  13  0.70

  15. Mark is reviewing his portfolio of investments, which include certain stocks and bonds. He has large amount tied up in the risk free rate of 3%. He is considering moving some of his funds from the risk free rate into a stock. The stock has a beta of 1.20. If Mark expects a return of 12% from the stock (a little better than the current market return of 10%), should he buy the stocks or leave his funds in the risk free asset?
  16. Portfolios A through J, which are listed in the following table along with their returns [r(p)] and risk (measured by the standard deviation), represent all currently available portfolios in the feasible or attainable set.
     Portfolio Avg Return 
     Risk (Std Dev)
     A  9% 7% 
     B  4  9
     C  12  10
     D  15  14
     E  8  10
     F  12  8
     G  10  16
     H  7  12
     I  9  11
     J  10  12
    1. Plot the feasible or attainable set represented by these data on a set of portfolio risk (x-axis) and portfolio return (y-axis).
    2. Approximate the efficient frontier on the graph in part a.
    3. Which portfolios lie on the efficient frontier? Why do these portfolios dominate all others in the feasible or attainable set?
    4. How would an investor’s utility function or risk-indifference curves be used with the efficient frontier to find the optional portfolio?

  17. The following tables present returns on a pair of stocks for five periods. Without doing any calculations, can you characterize the correlation that would best describe the relationship between these pairs of stocks? Your choices are: (a) correlation is -1, (b) correlation is negative, (c) correlation is zero, (d) correlation is positive, and (e) correlation is +1  
  18.  (i)
     Period Stock A 
    Stock B 
     1 2% 
     4%
     2  6 12 
     3  -2  -4
     4  10  20
     5  5  10
     (ii)
     Period Stock C 
    Stock D 
     1 10% 

     2  2  2
     3  8  6
     4  4  6
     5  6  10

     (iii)
     Period Stock E 
    Stock F 
     1 10% 
    -10%
     2  6 -6 
     3  -5  5
     4  0  0
     5  -2  2
     (iv)
     Period Stock G 
    Stock H 
     1 10% 
     2%
     2  0
     3  -4  2
     4  12  4
     5  -8  -1

  19. A professional money manager is considering two investments. The first is a stock and the second is a bond. The average return and risk of the securities is shown below:
     Asset Avg return Std Dev
     Stock  15% 35% 
     Bond  8 20 
    1. Suppose the correlation between the securities is 0.7. Draw the investment opportunity set of the two securities. To do this, very the weights applied to the stock in the bond from zero to 100% in increments of 25%. Determine the average return and risk of each combination and plot the results on a graph.
    2. Repeat question a. assuming the correlation between the securities is -0.3.
    3. What is the impact of the difference in the correlation coefficient?

  20. Calculate the beta of a security if investors demand and return of 11%, the risk free rate is 5%, and the market risk premium is 3%.
  21. You are given that the beta of a stock is 0.6, the risk free rate is 7%, and the market risk premium is 5%.
    1. Draw the security market line for this situation.
    2. A stock analyst estimates that, based on the future prospects of the company, the stock is expected to earn 9%. Plot this stock on the graph and evaluate the attractiveness of this stock.

Chapter 7 – Fundamental analysis

  1. Assume you have given following abbreviated financial statements and calculate as many liquidity, asset management, debt management, and profitability ratios as you can.
    • Current assets $150
    • Fixed and other assets 300
    • Total assets $450
    • Current liabilities $150
    • Long-term debt 100
    • Stockholders’ equity 200
    • Liab & eq. $450
    • Total revenues $500
    • Total operating expenses 400
    • Interest expense 20
    • Income tax 30
    • Net profit 50 
  2. Krunchy Frosted Doughnuts Corporation has a net profit margin of 10% and a total asset turnover of 3.0 times.
    1. What is the company’s return on assets?
    2. If total assets are $3 billion and are financed with 50% debt, what is the company’s return on equity? 
  3. A firm has sales of $500,000 and an average inventory level of $250,000. The industry average for the inventory turnover ratio is 3.5. What would be the reduction in inventory if this firm achieves an inventory turnover comparable to the industry average?
  4. What is the debt to equity ratio and the equity multiplier for a company that has total debt of $700,000 and assets of $1 million.
  5. ABC has an equity multiplier of 4.0. What is the company’s debt ratio?
  6. DEF has a return on assets of 10%, a 2% profit margin, and a return on equity of 15%.
    1. What is the company’s total asset turnover?
    2. What is the company’s debt to equity ratio?
  7. XYZ reports profits of $400,000 and a tax rate of 40%. The company’s interest expense was $200,000. If XYZ can double their operating income while maintaining their tax rate and interest expense, what would be their net income?
  8. LMN has a TIE ratio of 6.0 and pretax earnings of $400. Calculate the company’s interest expense.
  9. You are given the following information about XYZ Corporation:
    • Cash $100
    • Fixed assets 275
    • Sales 1,000
    • Net income 50
    • Quick ratio 2.0
    • Current ratio 3.0
    • Days of sales outstanding 40.5 days
    • Return on equity 12%
    Determine the following (HINT: if you do the questions in order, you’ll begin to piece together the given financial ratios and information):
    1. Accounts receivable
    2. Current liabilities
    3. Current assets
    4. Total assets
    5. Return on assets
    6. Shareholder equity
    7. Long-term debt
  10. ABC expands its business by increasing sales by $1 million. In addition, cost of goods sold increase $700,000, depreciation expense rises by $50,000, and interest expense increases by $150,000. The company’s tax rate is 30%. How much will income increase or decrease as a result of the expansion?
  11. PDQ has total assets of $1 million and a debt ratio of 30%. The company has sales of $3 million and total operating expenses of $1,500,000. The interest rate on debt is 12% in the company’s tax rate is 40%. What is PDQ’s return on equity?
  12. JKL had $5 million in operating income, depreciation expense of $1 million, and interest expense of $1 million. The corporate tax rate was 40%. Calculate the company’s net income.

Chapter 8 - Stock Valuation

  1. XYZ has $600,500,000 in total assets and total liabilities of $200,000,000. There are 100,000,000 shares of common stock outstanding.
    1. What is the book value per share?
    2. If the stock is selling for $6.00 per share. What is the price-to-book ratio?
  2. ACE common stock is selling at a P/E of 18 times trailing earnings. The stock price is $30. What were the firm’s earnings per share?
  3. JKL Inc. had sales of $60 million in 2006, and is expected to have sales of $80,000,000 for 2008. The company’s net profit margin was 5% in 2006 which is expected to increase to 9% by 2008. Estimate the company’s net profit for 2008.
  4. Strong Garbage Cans, Inc., is expected to pay a dividend of $2 in the coming year. The required rate of return is 15%, and dividends are expected to grow at 6% per year. Find the intrinsic value of the company’s common shares.
  5. An investor estimates that next year’s sales for RST Products should amount to about $80 million. The company has 2.2 million shares outstanding, has a net profit margin of 6%, and a payout ratio of 50%. Compute the following.
    1. Estimated net earnings for next year.
    2. Next year’s dividend per share.
    3. The expected price of the stock (assuming P/E ratio is 24).
    4. The expected holding period return (latest stock price $27 per share).
  6. Ben Daredunthat is thinking about buying some shares of Loops Inc., at $65 per share. He expects the price of the stock to rise to $80 over the next 3 years. During that time he also expects to receive annual dividend of $8 per share.
    1. What is the intrinsic worth of the stock, given a 12% required rate of return?
    2. What is its expected return?
  7. Lucas is considering a stock purchase. The stock pays constant annual dividend of $3 per share, and is currently trading at $32. Lucas’s required rate of return for this stock is 10%. Should he buy this stock?
  8. Assume you have generated following information about the stock of Nice Pants: The company’s latest dividend of $5 per share is expected to grow to $5.40 next year, to $5.95 the year after that, and to $6.45 in year 3. In addition, the price of the stock is expected to rise from $60 (its current price) to $97.77 in 3 years.
    1. Use the dividends-and-earnings model and a required rate of return of 15% to find the value of stock.
    2. Use IRR procedure to find the stock’s expected return.
    3. If dividends are expected to grow indefinitely at 8% (starting at time 0), use a 15% required rate of return to find the value of stock.
    4. Go back to the original dividends. If the dividend received in year 3 is $6.45 and then the dividend growth rate stays at 8%, find the stock price at end of year 3 if the required rate of return is 15%.
  9. ABC Manufacturing pays annual dividend of $3 a share (and that’s not expected to change within the next few years). The stock trades at a P/E of 20 times earnings and has a beta 1.16. The risk free rate is 7%, along with a market risk premium 6%. You would like to hold the stock for 3 years, at the end of which time think EPS will peak at about $8 a share.
    1. Given that the stock currently trades at $80, use the IRR approach to find this security’s expected return.
    2. Now find intrinsic value of this stock. Does this look a good investment to you?
  10. You estimate that Texarkana Corporation’s earnings next year should come in at about $5 a share. In addition, although the stock normally trades at a relative P/E of 1.5 times of the market, you believe that the relative P/E will rise to 1.65, where the market P/E should be around 19 times earnings. Given this information, what is the maximum price you should be willing to pay for this stock? If you buy this stock today at $88, what rate of return will you earn over the next 12 months if the price of the stock rises to $110 by the end of the year?(Assume that the stock doesn’t pay any dividends and the required rate of return is 18%.)
  11. Nile.com Books is an online retailer of used books and finally turned a profit last year so you’ve decided to take a closer look. Nile.com is expected to generate $45 million in sales next year and have 15 million shares outstanding, use the average Price to sales ratio to put a value on the stock. You have collected Price to sales multiples on the following Internet retailer stocks:
    • YourBooks.com = 5
    • MyBooks.com 4.3
    • TheirBooks.com 3.8
  12. TWZ Airlines just paid a dividend of a dollar per share is expected to grow at 40% for the next two years as they expand into new markets. After two years the company’s growth rate is expected to fall to 5% per year. Assume shareholders require a 10% return
    1. What is the intrinsic value of the stock today?
    2. What is the expected stock price in one year?
    3. Based on your answers for parts a. and b., what are the capital gains yield and dividend yield earned in the first year?
    4. What are the capital gains yield and dividend yield earned in the third year?
  13. You are given the required return on an investment is 14%. You estimate the firm’s dividends per share over the next four years as follows:
    1. 0.50
    2. 1.00
    3. 2.25
    4. 3.25
    5. In subsequent years you expect the dividend to grow at 6% annually. What is the maximum price that you should pay for the stock?
  14. If the dividend of GHI Corp. was 33¢ in 1996, and $1.20 in 2006, calculate the historical growth rate in dividends over the ten year period.
  15. Use the following data to project Davidson’s stock price at the beginning of 2008. Assume the risk free rate is 5%, the market risk premium is 10%, and the beta of Davidson is 1.2. In addition, Assume the P/E ratio stays constant at 22. There are 40,000 shares outstanding.
    Year
     Sales  Earnings
     Dividends Paid 
     2005 $2,000,000
     190,000 76,000 
     2006  2,500,000  250,000  112,500
     2007  3,125,000  328,125  114,844

Chapter 9 - Technical Analysis

  1. Calculate TRIN for Day 1 using the Arms ratio, with the following data.
     Day  # Advancing
     Total Volume
     # Declining
     Total Volume
     1     500  15,300,000  300  4,500,000
  2. Calculate TRIN for Day 1 using Arms ratio, with the following data.
     Day  # Advancing
     Total Volume
     # Declining
     Total Volume

    800 
     19,000,000  200  5,000,000
  3. Compute the Arms index (trin) over the following 3 days. Which of the 3 days would be considered the most bullish?
     Day  # Adv
     # Decl
     Vol Adv (million)
     Vol Decl (million)
     1 385 
    154 
     750 400 
     2  250  200  300  800
     3  280  275  900  350
  4. Use the data from question #2 to find market breadth each day and the cumulative advance/decline line.
  5. Compute the level of on balance volume (OBV) for the following 3-day period for a stock, if the beginning level of OBV is 60,000 and the stock closed yesterday at $30. Does the movement in OBV appear to confirm the rising trend in prices?
     Day  Closing Price
     Volume
     1 $27 
     80,000
     2  22  30,000
     3  30  100,000
  6. You find a closing price for a stock you own. You want to use a 10-day moving average to monitor the stock. Calculate the 10-day moving average for 11 days through 20. Based on the data in the table below, are there any signals you should act on? Explain.
     Day  Closing Price
     Day  Closing Price
     1  $25.00  11 $29.00 
     2  26.00  12 29.00 
     3  27.50  13  31.50
     4  28.50  14 32.00
     5  28.00  15 31.00 
     6  29.00  16  33.00
     7  28.00  17  28.00
     8  30.00  18  28.00
     9  26.00  19  26.50
     10  27.50  20  26.00
    7. Calculate the TRIN using the arms ratio.
            
 Day  # Adv
 # Decl
 Vol Adv (million)
 Vol Decl (million)
 1 275 
650 3.5 4

    8. Calculate the TRIN using the arms ratio, then find the market breadth for each day and the cumulative advance/decline line.
        
 Day  # Adv
 # Decl
 Vol Adv
 Vol Decl 
 1 300 479 
 2,500,000 2,200,000
 2  285  425  2,700,000  2,500,000
 3  375  450  2,750,000  2,450,000

Chapter 11 – Bond valuation

  1. Calculate the prices of the following T-bonds:
    1. $10,000 face value, 8% coupon, quote = 97:25
    2. $1,000 face value, 6 % coupon, quote = 101:07
    3. $5,000 face value, 12% coupon, quote = 103:20 
  2. Identify the cash flows of the following bonds:
    1. $1,000 face value, 4 year maturity, 10% coupon
    2. $10,000 face value, 2 year maturity, 6% coupon
    3. $1,000 face value, 6-year maturity, 8% annual coupon
    4. $6,000 face value, 10-year maturity, 4% quarterly coupon 
  3. Suppose a municipal bond has a yield of 6.5% and a corporate bond has a yield of 9%.
    1. If your marginal tax rate is 20%, what is the equivalent tax-exempt yield of the corporate bond?  Which bond would you prefer if all other features were similar (e.g., default risk)?
    2. If your marginal tax rate is 45%, what is the equivalent tax-exempt yield of the corporate bond?  Which bond would you prefer if all other features were similar (e.g., default risk)?
  4. A 15%, 15-year bond is currently trading at $1,200. What is its current yield?
  5. Joe buys a 12% corporate bond with a current yield of 5%. How much did he pay for the bond?
  6. Find the price of a semiannual coupon bond given that the coupon rate = 9%, the face value = $1000, the required return = 10%, and there are 27 years remaining until maturity.
  7. A 5% coupon bond with semi-annual payments, maturing in 4 years, is purchased for $951.90. What is its yield to maturity? 
  8. An investor purchases an 8% coupon bond, annual payments, 10 years to maturity for $982.63. He sells the the bond 3 years later for $1,000. What is his yield on this bond?
  9. A 6% coupon bond, $10,000 par value, with semi-annual payments is purchased 3 years ago when it still has 14 years to maturity for a price of $10,172.15. The investor sells the bond today for $9,995.15. What is the realized yield on the bond?
  10. What is the price of a $10,000 par value bond, 6% coupon paid semi-annually, 10 years to maturity, when the required rate of return in the market is 4.5%?
  11. The $1,000 face value bond has a coupon rate of 6%, with interest paid semi-annually, and matures in 5 years. If the bond is priced to yield 8%, what is the bond's value today?
  12. Which of the following three bonds offers the highest current yield? Assume that the face value of all of the bonds is $1,000.
    1. A 9%, 18-year bond quoted at 908.
    2. An 18%, 12-year bond quoted at 1980.
    3. A 4%, 20-year bond quoted at 500.
  13. Using semiannual compounding, find the prices of the following bonds. Assume the face value is $1000 for each:
    1.  A 10%, 12-year bond priced to yield 9%
    2. A 6%, 8-year bond priced to yield 9.5%
    3. A 15%, 19-year bond priced to yield 10%
  14. Two bonds have face values of $1,000. One is a 6%, 12-year bond priced to yield 8%. The other is an 8%, 16-year bond priced to yield 4%. Which of these two has the lower price?
  15.  A 15-year bond has a coupon of 10% and is priced to yield 9%. Calculate the price per $1000 face value.
  16. A 12-year bond has an ANNUAL pay coupon of 7% and is priced to yield 10%. Calculate the price per $1,000 face value.
  17. A bond is currently selling in the market for $1,050. It has a coupon of 10% and a 20-year maturity. Calculate the promised yield on this bond.
  18. A bond is currently selling in the market for $1,750. It has a coupon of 8% and a 22-year maturity. Calculate the yield to maturity on this bond. Assume the face value is $1000.
  19. A zero-coupon bond that matures in 10 years is currently sells of $527.47 per $1,000 par value. Calculate the promised yield on this bond.
  20. A zero-coupon bond that matures in 14 years is currently selling for $256 per $1,000 par value. What is the promised yield?
  21. Assuming annual coupons, find the yield-to-maturity for each of the following bonds.
    1. An 8.5%, 20-year bond priced at $984.50.
    2. A 15%, 17-year bond priced at $1432.50.
    3. A 7%, 14-year bond priced at $379.80.
  22. You have an 8%, 20-year bond that is currently priced in the market at $900.
    1. Find the current yield
    2. What is the yield to maturity?
  23. Complete the table below for zero-coupon bonds, all of which have face value of $1,000.
  24. Maturity  Price  YTM
     20 years
     400  
     15 years
      8% 
       310.07  10%
  25. A 10%, 23-year bond has a face value of $1,200 and a call price of $1,250. (The bond’s first call date is in 5 years.)
    1. Find the current yield, YTM, and YTC on this issue, given that it is currently being priced in the market at $1,500. Which of these three yields is the highest? Which is the lowest? Which yield would you use to value this bond? Why?
    2. Repeat the 3 calculations above, given that the bond is being priced at $900. Now which yield is the highest? Which is the lowest? Which yield would you use to value this bond? Why?
  26. Find the yield to maturity on a semiannual coupon bond given that the bond price = $1024, the coupon rate = 13%, the face value = $1000, and there are 19 years remaining until maturity.
  27. Find the yield to maturity on a semiannual coupon bond given that the bond price = $790, the coupon rate = 14%, the face value = $1000, and there are 4 years remaining until maturity.
  28. Find the yield to call on a semiannual coupon bond with a face value of $1000, a 10% coupon rate, 15 years remaining until maturity given that the bond price is $1175 and it can be called 5 years from now at a call price of $1100.
  29. A 30 year bond has an 8% coupon is callable in five years at a call price of $1,100. Today, the bond sells to yield 7%. Assume the face value is 1000.
    1. What is the yield-to call?
    2. What is the yield to call if the call price is only $1,050?
    3. What is the yield to call if the call price is $1,100, but the bond can be called in two years instead of five years?
  30. Assume that you pay $900 for a long-term bond that carries a 8% coupon. Over the course of the next 12 months, interest rates drop sharply. As a result, you sell the bond at a price of $1,200.
    1. Find the current yield that existed on this bond at the beginning of the year. What was it by the end of the 1-year holding period?
    2. Determine the holding period return on this investment.
  31. An investor is considering the purchase of a 10%, 20-year corporate bond that’s being priced to yield 10%. He thinks that in a year, this same bond will be priced in the market to yield 9%. Assume the face value is $1,000.
    1. Find the price of the bond today and in 1 year.
    2. Find the realized yield on this investment, assuming that the investor’s expectations hold true.
  32. A 30-year bond has a face value of $1,000 and has a call price of  $1,375 in 7 years.  The coupon rate is 13% and it is currently being priced in the market at $1,450.
    1. Find the current yield.
    2. Find the YTM.
    3. Find the YTC.  
    4. Which of these three yields is the highest? Which is the lowest? 
  33. A 17%, 32 year bond is currently trading at $2,200.  What is its current yield?
  34. A 13 year bond has a coupon of 8% and its priced to yield 7%.  Calculate the price per 1000 face value.
  35. A 11 year bond has an ANNUAL coupon of 12% and its prices to yield 10%.  Calculate the price per 1000 face value.
  36. A zero coupon bond that matures in 13 years is currently selling for $874.36 per 1000 par value.  What is its promised yield?
  37. A bond is currently selling in the market for $914.76.  It has a coupon of 12% and 18 year maturity.  Calculate the promised yield on this bond.

Chapter 12 – Investment companies

  1. A year ago Big Growth Fund was being quoted at a NAV of $20 and an offer price of $22.5. Today, it’s being quoted at $22.10 (NAV) and $24.10 (offer). What is the holding period return on this load fund, given that it was purchased a year ago and that its dividend and capital gains distributions over the year have totaled $1.06 per share?
  2. You have uncovered the following per-share information about a certain mutual fund. On the basis of this information, find the fund’s holding period return for 2006, 2007, and 2008. (In all 3 cases you buy the fund at the beginning of the each year and sell it at the end of each year.)
       2006      2007  2008
     Ending share prices:
         
     Offer  44.10  61.28  58.46
     NAV  42.00  58.36  55.68
     Dividend income
     2.15  2.86 2.54 
     Capital gains distribution
     1.56  5.23 4.11 
     Beginning share prices:
         
     Offer  54.44 44.10 
    61.28 
     NAV  51.85 42.00 
     58.36
  3. You invested in the no-load Best Mutual Fund one year ago by purchasing 1,400 shares of the fund at an NAV of $22.00 per share. The fund distributed dividends of $1.80 and capital gains of $2.00. Today, the NAV is $25.
    1. What was your HPR?
    2. If The Best was a load fund with 3% front end load, what would be the HPR?
  4. One year ago, High Return Closed-End Fund had a NAV of $11 and was selling at a 19% discount. Today, its NAV is $11.90 and it is priced at a 5% premium. During the year, High Return paid dividends of $0.50 and had a capital gains distribution of $0.90. On the basis of the above information, calculate each of the following.
    1. High Return’s NAV-based holding period return for the year.
    2. High Return’s market-based holding period return for the year. Did the market premium/discount hurt or add value to the investor’s return? Explain.
    3. Repeat the market-based holding period return calculation, except this time assume the fund started the year at a 20% premium and ended it at a 5% discount. (Assume NAVs remain the same.) Is there any change in return? Why?
  5. What is the net asset value of an investment company with $20 million in assets, $950,000 in liabilities, and 1,500,000 shares outstanding?
  6. A mutual fund has net asset value of $26.60 and the fund sells it shares at an offer price of $27.42. What is the front and load?
  7. You are considering investing in the Ahlgrim high value, low risk mutual fund. The fund has two classes of shares. Use the following load and expense information to evaluate the best fund depending on your investment horizon. Assume the underlying portfolio earns 15% and that you invest $1,000.
    1. Which class of shares provides the highest return if your investment horizon is two years?
    2. Which class of shares is best if your horizon is 25 years?
    Load/fee  Class A
     Class Z
     Front-end 6% 
     0%
     Back-end  0% 4% CDSC 
     12b-1  0.2% 1.1% 
     Mgmt fee
    0.6% 
     0.6%
    Operating expense 
     0.3%  0.3%

  8. The opportunity for you to invest in a high value, low risk mutual fund has presented itself.  The fund has two classes of shares.  Refer to the load and expense data in the table below to determine which fund is the best.
  9. Load/Fee  Class Ahlgrim 
     Class Jagmin
     Front-end  8.25%  0%
     Back-end  0%  6%
     12b-1(annual)  0.34%  1.3%
     Management Fee
     0.55%  0.70%
     Operation/Administration Fee
     0.25%  0.35%
    Assume the portfolio earns 12% and the amount you invest is $1,000.
    1. Which class of shares, either Ahlgrim or Jagmin, provides the greatest return if your investment horizon is three years?
    2. If the investment horizon was expanded which class of shares would be best in 20 years?
    3. After making these calculations, determine which class of shares is better in the short-term (3 years) AND long-term (20 years).
  10. Last year ISU Fund was being quoted at a NAV of $12 and an offer price of $16.  Today it is quoted at $18 (NAV) and $20.75 (offer).  What is the HPR on this fund given it was purchased a year ago and its capital gain distributions and dividend total $3.95/share?
  11. What is the net asset value of an investment of an investment company with assets of $50 million, $4,750,000 in liabilities, and 3 million shares outstanding?
  12. You invest in a no-load ISU mutual fund 1 year ago by purchasing 3,000 shares of the fund at an NAV of $8 per share.  The fund distributed dividends and capital gains of $1.75.  Today the NAV is $11.25.
    1. What is the HPR?
    2. If ISU was a load fund, what is the HPR if it had 4% front end load?
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