# Calculate the beta of a portfolio that includes the following stocks

In a Word document complete the following problems.

- You may solve the problems algebraically, or you may use a financial calculator.
- If you choose to solve the problems algebraically, be sure to show your computations.
- If you use a financial calculator, show your input values.

In addition to your solution to each computational problem, you must show the supporting work leading to your solution to receive credit for your answer.

Unless otherwise directed, assume annual compounding periods in the computational problems.

1.

- If you deposited $250 in your savings account today, and the bank pays 4 percent interest per year, how much would you have in your savings account after 9 years?
- Recalculate the account balance using a 6 percent interest rate and a 7 percent interest rate.

- A $450 deposit earns 6 percent interest in the first year, 3 percent interest in the second year, and 7 percent interest in the third year. What is the future value at the end of the third year?
- What is the annual rate of return for an $8,000 investment if in five years it grows to $12,500?
- Assuming the growth occurred in six years and then eight years, recalculate the rate of return for these two scenarios.

2.

- If interest rates are 8 percent, what is the future value of a $400 annuity payment over six years? Unless otherwise directed, assume annual compounding periods.
- Recalculate the future value at 6 percent interest and 9 percent interest.

- If interest rates are 5 percent, what is the present value of a $900 annuity payment over three years? Unless otherwise directed, assume annual compounding periods.
- Recalculate the present value at 10 percent interest and 13 percent interest.

- What is the present value of a series of $1150 payments made every year for 14 years when the discount rate is 9 percent?
- Recalculate the present value using discount rate of 11 percent and 12 percent.

3

- Imagine that on June 4, the Dow Jones Industrial Average closed at 13,598.14, which was up 148.86 points from the previous day’s close of 13,449.28. Calculate the return, in percent to four decimal places, of the stock market for June 4.
- The cost per stock at a brokerage firm is $0.10. Calculate how much money you would need to buy 150 shares of HiTech, Inc., which trades at $18.22.
- HiTech, Inc.’s growth for the future is forecasted to be a constant 10 percent. HiTech’s next dividend is expected to be $1.18. Calculate the value of HiTech stock when the required return is 12 percent.
- Preferred stock from HiTech, Inc. pays $1.20 in annual dividend. Calculate the value of the stock if the required return on the preferred stock is 4.5 percent.
- HiTech, Inc. has earnings per share of $1.82 and a P/E ratio of 31.54. Calculate the stock price.

4

- Assuming semi-annual compounding, what is the price of a zero coupon bond that matures in 3 years if the market interest rate is 5.5 percent? Assume par value is $1000.
- Using semi-annual compounding, what is the price of a 5 percent coupon bond with 10 years left to maturity and a market interest rate of 7.2 percent? Assume that interest payments are paid semi-annually and that par value is $1000.
- Using semi-annual compounding, what is the yield to maturity on a 4.65 percent coupon bond with 18 years left to maturity that is offered for sale at $1,025.95? Assume par value is $1000.

5.

- Two years ago, Conglomco stock ended at $73.02 per share. Last year, the stock paid a $0.34 per share dividend. Conglomco stock ended last year at $77.24. If you owned 200 shares of Conglomco stock, what were your dollar return and percent return last year?
- Calculate the coefficient of variation for the following three stocks. Then rank them by their level of total risk, from highest to lowest:
- Conglomco has an average return of 11 percent and standard deviation of 24 percent.
- Supercorp has an average return of 16 percent and standard deviation of 37 percent.
- Megaorg has an average return of 10 percent and standard deviation of 29 percent.

- Year-to-date, Conglomco has earned a −1.64 percent return, Supercorp has earned a 5.69 percent return, and Megaorg has earned a 0.23 percent return. If your portfolio is made up of 40 percent Conglomco stock, 30 percent Supercorp stock, and 30 percent Megaorg stock, what is your portfolio return?

6

- Based on the probability and percentage of return for the three economic states in the table below, compute the expected return.

Economic StateProbabilityPercentage of ReturnFast Growth0.1060Slow Growth0.5030Recession0.40-23

- If the risk-free rate is 7 percent and the risk premium is 4 percent, what is the required return?
- Suppose that the average annual return on the Standard and Poor’s 500 Index from 1969 to 2005 was 14.8 percent. The average annual T-bill yield during the same period was 5.6 percent. What was the market risk premium during these 10 years?
- Conglomco has a beta of 0.32. If the market return is expected to be 12 percent and the risk-free rate is 5 percent, what is Conglomco’s required return? Use the capital asset pricing model (CAPM) to calculate Conglomco’s required return.
- Calculate the beta of a portfolio that includes the following stocks:
- Conglomco stock, which has a beta of 3.9 and comprises 35 percent of the portfolio.
- Supercorp stock, which has a beta of 1.7 and comprises 25 percent of the portfolio.
- Megaorg stock, which has a beta of 0.3 and comprises 40 percent of the portfolio.

7

- Based on the cash flows shown in the chart below, compute the NPV for Project Huron. Suppose that the appropriate cost of capital is 12 percent. Advise the organization about whether it should accept or reject the project.

Project Huron

Time01234Cash Flow$12,000$2,360$4,390$1,520$3,300

- Based on the cash flows shown in the chart below, compute the IRR and MIRR for Project Erie. Suppose that the appropriate cost of capital is 12 percent. Advise the organization about whether it should accept or reject the project.

Project Erie

Time012345Cash Flow$12,000$2,360$4,390$1,520$980$1,250