P8?3 Risk preferences Sharon Smith, the financial manager for Barnett Corporation, wishes to evaluate three prospective investments: X, Y, and Z. Sharon will evaluate each of these investments to decide whether they are superior to investments that her company already has in place, which have an expected return of 12% and a standard deviation of 6%. The expected returns and standard deviations of the investments are as follows:

a. If Sharon were risk neutral, which investments would she select? Explain why.

b. If she were risk averse, which investments would she select? Why?

c. If she were risk seeking, which investments would she select? Why?

d. Given the traditional risk preference behavior exhibited by financial managers, which investment would be preferred? Why?

Investment Expected return Standard deviation

X 14% 7%

Y 12 8

Z 10 9

P8?4 Risk analysis Solar Designs is considering an investment in an expanded product line. Two possible types of expansion are being considered. After investigating the possible outcomes, the company made the estimates shown in the following table.

Expansion A Expansion B

Initial investment $12,000 $12,000

Annual rate of return

Pessimistic 16% 10%

Most likely 20% 20%

Optimistic 24% 30%

a. Determine the range of the rates of return for each of the two projects.

b. Which project is less risky? Why?

c. If you were making the investment decision, which one would you choose? Why? What does this decision imply about your feelings toward risk?

d. Assume that expansion B?s most likely outcome is 21% per year and that all other facts remain the same. Does your answer to part c now change? Why?

P8?9 Rate of return, standard deviation, and coefficient of variation Mike is searching for a stock to include in his current stock portfolio. He is interested in Hi-Tech, Inc.; he has been impressed with the company?s computer products and believes that Hi-Tech is an innovative market player. However, Mike realizes that any time you consider a technology stock, risk is a major concern. The rule he follows is to include only securities with a coefficient of variation of returns below 0.90.

Mike has obtained the following price information for the period 2012 through 2015. Hi-Tech stock, being growth-oriented, did not pay any dividends during these 4 years.

Stock price

Year Beginning End

2012 $14.36 $21.55

2013 21.55 64.78

2014 64.78 72.38

2015 72.38 91.80

a. Calculate the rate of return for each year, 2012 through 2015, for Hi-Tech stock.

b. Assume that each year?s return is equally probable, and calculate the average return over this time period.

c. Calculate the standard deviation of returns over the past 4 years. (Hint: Treat these data as a sample.)

d. Based on b and c, determine the coefficient of variation of returns for the security.

e. Given the calculation in d, what should be Mike?s decision regarding the inclusion of Hi-Tech stock in his portfolio?

P8?10 Assessing return and risk Swift Manufacturing must choose between two asset purchases. The annual rate of return and the related probabilities given in the following table summarize the firm?s analysis to this point.

Project 257 Project 432

Rate of return Probability Rate of return Probability

?10% 0.01 10% 0.05

10 0.04 15 0.10

20 0.05 20 0.10

30 0.10 25 0.15

40 0.15 30 0.20

45 0.30 35 0.15

50 0.15 40 0.10

60 0.10 45 0.10

70 0.05 50 0.05

80 0.04 100 0.01

a. For each project, compute: (1) The range of possible rates of return. (2) The expected return. (3) The standard deviation of the returns. (4) The coefficient of variation of the returns.

b. Construct a bar chart of each distribution of rates of return. c. Which project would you consider less risky? Why?

P8?13 Portfolio return and standard deviation Jamie Wong is considering building an investment portfolio containing two stocks, L and M. Stock L will represent 40% of the dollar value of the portfolio, and stock M will account for the other 60%. The expected returns over the next 6 years, 2015?2020, for each of these stocks are shown in the following table.

Expected return

Year Stock L Stock M

2015 14% 20%

2016 14 18

2017 16 16

2018 17 14

2019 17 12

2020 19 10

a. Calculate the expected portfolio return, rp, for each of the 6 years.

b. Calculate the expected value of portfolio returns, , over the 6-year period.

c. Calculate the standard deviation of expected portfolio returns, , over the 6-year period.

d. How would you characterize the correlation of returns of the two stocks L and M?

e. Discuss any benefits of diversification achieved by Jamie through creation of the portfolio.

P8?24 Capital asset pricing model (CAPM) For each of the cases shown in the following table, use the capital asset pricing model to find the required return.

Case Risk-free rate, RF Market return, rm Beta,?

A 5% 8% 1.30

B 8 13 0.90

C 9 12 ?0.20

D 10 15 1.00

E 6 10 0.60

P8?25 Beta coefficients and the capital asset pricing model Katherine Wilson is wondering how much risk she must undertake to generate an acceptable return on her portfolio. The risk-free return currently is 5%. The return on the overall stock market is 16%. Use the CAPM to calculate how high the beta coefficient of Katherine?s portfolio would have to be to achieve each of the following expected portfolio returns.

a. 10%

b. 15%

c. 18%

d. 20%

e. Katherine is risk averse. What is the highest return she can expect if she is unwilling to take more than an average risk?

P8?26 Manipulating CAPM Use the basic equation for the capital asset pricing model (CAPM) to work each of the following problems.

a. Find the required return for an asset with a beta of 0.90 when the risk-free rate and market return are 8% and 12%, respectively.

b. Find the risk-free rate for a firm with a required return of 15% and a beta of 1.25 when the market return is 14%.

c. Find the market return for an asset with a required return of 16% and a beta of 1.10 when the risk-free rate is 9%.

d. Find the beta for an asset with a required return of 15% when the risk-free rate and market return are 10% and 12.5%, respectively.

P5?1 Using a time line The financial manager at Starbuck Industries is considering an investment that requires an initial outlay of $25,000 and is expected to result in cash inflows of $3,000 at the end of year 1, $6,000 at the end of years 2 and 3, $10,000 at the end of year 4, $8,000 at the end of year 5, and $7,000 at the end of year 6.

a. Draw and label a time line depicting the cash flows associated with Starbuck Industries? proposed investment.

b. Use arrows to demonstrate, on the time line in part a, how compounding to find future value can be used to measure all cash flows at the end of year 6.

c. Use arrows to demonstrate, on the time line in part b, how discounting to find present value can be used to measure all cash flows at time zero.

d. Which of the approaches?future value or present value?do financial managers rely on most often for decision making? Why?

P5?4 Future values For each of the cases shown in the following table, calculate the future value of the single cash flow deposited today at the end of the deposit period if the interest is compounded annually at the rate specified.

Case Single cash flow Interest rate Deposit period (years)

A $ ?200 5% 20

B 4,500 8 7

C 10,000 9 10

D 25,000 10 12

E 37,000 11 5

F 40,000 12 9

P5?5 Time value You have $1,500 to invest today at 7% interest compounded annually.

a. Find how much you will have accumulated in the account at the end of (1) 3 years, (2) 6 years, and (3) 9 years.

b. Use your findings in part a to calculate the amount of interest earned in (1) the first 3 years (years 1 to 3), (2) the second 3 years (years 4 to 6), and (3) the third 3 years (years 7 to 9).

c. Compare and contrast your findings in part b. Explain why the amount of interest earned increases in each succeeding 3-year period.

P5?8 Time value Misty needs to have $15,000 at the end of 5 years to fulfill her goal of purchasing a small sailboat. She is willing to invest a lump sum today and leave the money untouched for 5 years until it grows to $15,000, but she wonders what sort of investment return she will need to earn to reach her goal. Use your calculator or spreadsheet to figure out the approximate annually compounded rate of return needed in each of these cases:

a. Misty can invest $10,200 today.

b. Misty can invest $8,150 today.

c. Misty can invest $7,150 today.

P5?10 Present value calculation Without referring to the preprogrammed function on your financial calculator, use the basic formula for present value, along with the given opportunity cost, r, and the number of periods, n, to calculate the present value of $1 in each of the cases shown in the following table.

Case Opportunity cost, r Number of periods, n

A 2% 4

B 10 2

C 5 3

D 13 2

P5?17 Cash flow investment decision Tom Alexander has an opportunity to purchase any of the investments shown in the following table. The purchase price, the amount of the single cash inflow, and its year of receipt are given for each investment. Which purchase recommendations would you make, assuming that Tom can earn 10% on his investments?

Investment Price Single cash inflow Year of receipt

A $18,000 $30,000 5

B 600 3,000 20

C 3,500 10,000 10

D 1,000 15,000 40

P5?21 Time value: Annuities Marian Kirk wishes to select the better of two 10-year annuities, C and D. Annuity C is an ordinary annuity of $2,500 per year for 10 years. Annuity D is an annuity due of $2,200 per year for 10 years.

a. Find the future value of both annuities at the end of year 10 assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.

b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 10 for both the (1) 10% and (2) 20% interest rates.

c. Find the present value of both annuities, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest.

d. Use your findings in part c to indicate which annuity has the greater present value for both (1) 10% and (2) 20% interest rates.

e. Briefly compare, contrast, and explain any differences between your findings using the 10% and 20% interest rates in parts b and d.

P8-3 Risk preferences Sharon Smith, the financial manager for Barnett Corporation, wishes to evaluate three prospective investments: X, Y, and Z. Sharon will evaluate each of these investments to decide whether they are superior to investments that her company already has in place, which have an expected return of 12% and a standard deviation of 6%. The expected returns and standard deviations of the investments are as follows: a. If Sharon were risk neutral, which investments would she select? Explain why. b. If she were risk averse, which investments would she select? Why? c. If she were risk seeking, which investments would she select? Why? d. Given the traditional risk preference behavior exhibited by financial managers, which investment would be preferred? Why? Investment X Y Z Expected return 14% 12 10 Standard deviation 7% 8 9 P8-4 Risk analysis Solar Designs is considering an investment in an expanded product line. Two possible types of expansion are being considered. After investigating the possible outcomes, the company made the estimates shown in the following table. Expansion A Expansion B Initial investment $12,000 $12,000 Annual rate of return Pessimistic 16% 10% Most likely 20% 20% Optimistic 24% 30% a. Determine the range of the rates of return for each of the two projects. b. Which project is less risky? Why? c. If you were making the investment decision, which one would you choose? Why? What does this decision imply about your feelings toward risk? d. Assume that expansion B's most likely outcome is 21% per year and that all other facts remain the same. Does your answer to part c now change? Why? P8-9 Rate of return, standard deviation, and coefficient of variation Mike is searching for a stock to include in his current stock portfolio. He is interested in Hi-Tech, Inc.; he has been impressed with the company's computer products and believes that Hi-Tech is an innovative market player. However, Mike realizes that any time you consider a technology stock, risk is a major concern. The rule he follows is to include only securities with a coefficient of variation of returns below 0.90. Mike has obtained the following price information for the period 2012 through 2015. Hi-Tech stock, being growth-oriented, did not pay any dividends during these 4 years. Stock price Year 2012 2013 2014 2015 Beginning $14.36 21.55 64.78 72.38 $21.55 64.78 72.38 91.80 End a. Calculate the rate of return for each year, 2012 through 2015, for Hi-Tech stock. b. Assume that each year's return is equally probable, and calculate the average return over this time period. c. Calculate the standard deviation of returns over the past 4 years. (Hint: Treat these data as a sample.) d. Based on b and c, determine the coefficient of variation of returns for the security. e. Given the calculation in d, what should be Mike's decision regarding the inclusion of Hi-Tech stock in his portfolio? P8-10 Assessing return and risk Swift Manufacturing must choose between two asset purchases. The annual rate of return and the related probabilities given in the following table summarize the firm's analysis to this point. Project 257 Rate of return 10% 10 20 30 40 45 50 60 Project 432 Probability 0.01 0.04 0.05 0.10 0.15 0.30 0.15 0.10 10% 15 20 25 30 35 40 45 Rate of return 0.05 0.10 0.10 0.15 0.20 0.15 0.10 0.10 Probability 70 80 0.05 0.04 50 100 0.05 0.01 a. For each project, compute: (1) The range of possible rates of return. (2) The expected return. (3) The standard deviation of the returns. (4) The coefficient of variation of the returns. b. Construct a bar chart of each distribution of rates of return. c. Which project would you consider less risky? Why? P8-13 Portfolio return and standard deviation Jamie Wong is considering building an investment portfolio containing two stocks, L and M. Stock L will represent 40% of the dollar value of the portfolio, and stock M will account for the other 60%. The expected returns over the next 6 years, 2015-2020, for each of these stocks are shown in the following table. Expected return Year Stock L Stock M 2015 2016 2017 2018 2019 2020 14% 14 16 17 17 19 20% 18 16 14 12 10 a. Calculate the expected portfolio return, rp, for each of the 6 years. b. Calculate the expected value of portfolio returns, , over the 6-year period. c. Calculate the standard deviation of expected portfolio returns, , over the 6-year period. d. How would you characterize the correlation of returns of the two stocks L and M? e. Discuss any benefits of diversification achieved by Jamie through creation of the portfolio. P8-24 Capital asset pricing model (CAPM) For each of the cases shown in the following table, use the capital asset pricing model to find the required return. Case Risk-free rate, RF Market return, rm Beta, A B C D E 5% 8 9 10 6 8% 13 12 15 10 1.30 0.90 0.20 1.00 0.60 P8-25 Beta coefficients and the capital asset pricing model Katherine Wilson is wondering how much risk she must undertake to generate an acceptable return on her portfolio. The risk-free return currently is 5%. The return on the overall stock market is 16%. Use the CAPM to calculate how high the beta coefficient of Katherine's portfolio would have to be to achieve each of the following expected portfolio returns. a. 10% b. 15% c. 18% d. 20% e. Katherine is risk averse. What is the highest return she can expect if she is unwilling to take more than an average risk? P8-26 Manipulating CAPM Use the basic equation for the capital asset pricing model (CAPM) to work each of the following problems. a. Find the required return for an asset with a beta of 0.90 when the risk-free rate and market return are 8% and 12%, respectively. b. Find the risk-free rate for a firm with a required return of 15% and a beta of 1.25 when the market return is 14%. c. Find the market return for an asset with a required return of 16% and a beta of 1.10 when the risk-free rate is 9%. d. Find the beta for an asset with a required return of 15% when the risk-free rate and market return are 10% and 12.5%, respectively. P5-1 Using a time line The financial manager at Starbuck Industries is considering an investment that requires an initial outlay of $25,000 and is expected to result in cash inflows of $3,000 at the end of year 1, $6,000 at the end of years 2 and 3, $10,000 at the end of year 4, $8,000 at the end of year 5, and $7,000 at the end of year 6. a. Draw and label a time line depicting the cash flows associated with Starbuck Industries' proposed investment. b. Use arrows to demonstrate, on the time line in part a, how compounding to find future value can be used to measure all cash flows at the end of year 6. c. Use arrows to demonstrate, on the time line in part b, how discounting to find present value can be used to measure all cash flows at time zero. d. Which of the approachesfuture value or present valuedo financial managers rely on most often for decision making? Why? P5-4 Future values For each of the cases shown in the following table, calculate the future value of the single cash flow deposited today at the end of the deposit period if the interest is compounded annually at the rate specified. Case A B C D E F Single cash flow $ 200 4,500 10,000 25,000 37,000 40,000 Interest rate 5% 8 9 10 11 12 Deposit period (years) 20 7 10 12 5 9 P5-5 Time value You have $1,500 to invest today at 7% interest compounded annually. a. Find how much you will have accumulated in the account at the end of (1) 3 years, (2) 6 years, and (3) 9 years. b. Use your findings in part a to calculate the amount of interest earned in (1) the first 3 years (years 1 to 3), (2) the second 3 years (years 4 to 6), and (3) the third 3 years (years 7 to 9). c. Compare and contrast your findings in part b. Explain why the amount of interest earned increases in each succeeding 3year period. P5-8 Time value Misty needs to have $15,000 at the end of 5 years to fulfill her goal of purchasing a small sailboat. She is willing to invest a lump sum today and leave the money untouched for 5 years until it grows to $15,000, but she wonders what sort of investment return she will need to earn to reach her goal. Use your calculator or spreadsheet to figure out the approximate annually compounded rate of return needed in each of these cases: a. Misty can invest $10,200 today. b. Misty can invest $8,150 today. c. Misty can invest $7,150 today. P5-10 Present value calculation Without referring to the preprogrammed function on your financial calculator, use the basic formula for present value, along with the given opportunity cost, r, and the number of periods, n, to calculate the present value of $1 in each of the cases shown in the following table. Case A B C D Opportunity cost, r 2% 10 5 13 4 2 3 2 Number of periods, n P5-17 Cash flow investment decision Tom Alexander has an opportunity to purchase any of the investments shown in the following table. The purchase price, the amount of the single cash inflow, and its year of receipt are given for each investment. Which purchase recommendations would you make, assuming that Tom can earn 10% on his investments? Investment A B C D $18,000 600 3,500 1,000 Price $30,000 3,000 10,000 15,000 Single cash inflow 5 20 10 40 Year of receipt P5-21 Time value: Annuities Marian Kirk wishes to select the better of two 10-year annuities, C and D. Annuity C is an ordinary annuity of $2,500 per year for 10 years. Annuity D is an annuity due of $2,200 per year for 10 years. a. Find the future value of both annuities at the end of year 10 assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest. b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 10 for both the (1) 10% and (2) 20% interest rates. c. Find the present value of both annuities, assuming that Marian can earn (1) 10% annual interest and (2) 20% annual interest. d. Use your findings in part c to indicate which annuity has the greater present value for both (1) 10% and (2) 20% interest rates. e. Briefly compare, contrast, and explain any differences between your findings using the 10% and 20% interest rates in parts b and d