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# Finance problems: Beta, required rate of return

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Sample Exam problems July 09.

1. How much do you have to invest today at an annual rate of 8%, if you need to have \$5,000 six years from today?

2. Bavarian Sausage, Inc. has preferred stock outstanding. This stock pays a semiannual dividend of \$1.25. If the next dividend is paid six months from now and the annual required return is 10%, what should be the value of the preferred stock?

3. A share of preferred stock pays a \$2 annual dividend, but pays the dividend in four equal quarterly installments. Investors seek a 12% annual percentage return on the investment. What price should the preferred stock trade?

4. Security I has a beta of 1.3, the risk-free rate is 4%, and the expected market risk premium is 11%. What is the expected return for Security I?

5. As a result of a company's 15% increase in sales their EBIT increased by 25%. What is the company's operating leverage?

#### Solution Summary

The problems deal with issues in finance including required rate of return, EBIT, and operating leverage etc.

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## Finance Problems: Required Rate of Return

2. Required Rate of Return
AA Industries stock has a beta of 0.8. The risk-free rate is 4% and the expected return on the market is 12%. What is the required rate of return on AA's stock?

10. Portfolio Required Return
Suppose you manage a \$4 million fund that consists of four stocks with the following investments:
Stock Investment Beta______________
A \$ 400,000 1.50
B 600,000 -0.50
C 1,000,000 1.25
D 2,000,000 0.75
If the market's required rate of return is 14% and the risk-free rate is 6%, what is the fund's required rate of return?

13. Historical Realized Rates of Return
You are considering an investment in either individual stocks or a portfolio of stocks. The two stocks you are researching, stock A and B, have the following historical returns:

Year rA rB_________
2009 -20.00% -5.00%
2010 42.00% 15.00%
2011 20.00% -13.00%
2012 -8.00% 50.00%
2013 25.00% 12.00%
a. Calculate the average rate of return for each stock during the 5-year period.
b. Suppose you had held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would have been the realized rate of return on the portfolio in each year? What would have been the average return o the portfolio during this period?
c. Calculate the standard deviation of returns for each stock and for the portfolio.
d. If you are a risk-averse investor, then, assuming these are your only choices, would you prefer to hold Stock A, Stock B, or the portfolio? Why?

14. Historical Returns: Expected and Required Rates of Return
You have observed the following returns over time:

Year Stock X Stock Y Market_____
2009 14% 13% 12%
2010 19 7 10
2011 -16 -5 -12
2012 3 1 1
2013 20 11 15
Assume that the risk-free rate is 6% and the market risk premium is 5%.
a. What are the betas of Stocks X and Y?
b. What are the required rates of return on Stock X and Y?
c. What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?

3. Two-Asset Portfolio
Stock A has an expected return of 12% and a standard deviation of 40%. Stock B has an expected return of 18% and a standard deviation of 60%. The correlation coefficient between Stock A and B is 0.2. What are the expected return and standard deviation of a portfolio invested 30% in Stock A and 70% in Stock B?

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