Chapter 5 - Portfolio topics

1. Calculate the average return of the following portfolio

Investment	Avg. Return	Amount invested
Stocks	15%	$100,000
Bonds	5%	50,000
Real estate	10%	250,000



2. 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.

   
   
3. 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?

   
   
4. 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?
5. 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	8	6
   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.
6. 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?
7. Referring to above problem, if you expected a significant market rally, would your decision be altered? Explain.
8. 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:

Security	Beta
P	1.30
Q	0.50
R	-0.80



9. Calculate the beta of the following portfolio.

Stock	Amt invested	Beta
ABC	$1,000	1.1
JKL	3,000	0.6
PQR	7,000	1.4
XYZ	9,000	0.9



10. Use the capital asset pricing model (CAPM) to find the required return for each of the following securities in light of the data given.

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



11. 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?
12. 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?
    
    
13. 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  

(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  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 1  3  -4  2  4  12  4  5  -8  -1



14. 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?
    
    
15. 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%.
16. 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.

Topic 6 – Fundamental analysis

1. Assume you have given following abbreviated financial statements and calculate as many liquidity, asset management, debt management, and profitability 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.

Topic 7 - 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

Topic 8 - Technical Analysis

1.      Calculate TRIN for Day 1 using the Arms ratio, with the following data.

1. Day	# Advancing	Total Volume	# Declining	Total Volume
   1	500	15,300,000	300	4,500,000

2. 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

3. Use the data from question #2 to find market breadth each day and the cumulative advance/decline line.
4. 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

5. 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