Response to the following :
ECRI Corporation is a holding company with four main subsidiaries. The percentage of its capital invested in each of the subsidiaries (and their respective betas) are as follows:
Subsidiary Percentage of Capital Beta
Electric utility 60% 0.70
Cable company 25 0.90
Real estate development 10 130
International/special projects 5 1.50
1. What is the holding company's beta?
2. If the risk-free rate is 4% and the market risk premium is 5%, what is the holding company's required rate of return?
3. ECRI is considering a change in its strategic focus; it will reduce its reliance on the electric utility subsidiary, so the percentage of its capital in this subsidiary will be reduced to 50%. At the same time, it will increase its reliance on the international/special projects division, so the percentage of its capital in that subsidiary will rise to 20%. What will the company's required rate of return be after these changes?
4. A stock's returns have the following distribution:
Demand for the Company's Products Probability of This Demand Occurring Rate of Return If This Demand Occurs
Weak 0.1 (50%)
Below average 0.2 (5)
Average 0.4 16
Above average 0.2 25
Strong 0.1 60
1.0
Calculate the stock's expected return, standard deviation, and coefficient of variation.
5. An individual has $35,000 invested in a stock with a beta of 0.7 and another $40,000 invested in a stock with a beta of 1.5. If these are the only two investments in her portfolio, what is her portfolio's beta?
6. Assume that the risk-free rate is 5% and the expected return on the market is 13%. What is the required rate of return on a stock with a beta of 0.8?
7. Assume that the risk-free rate is 5% and the market risk premium is 6%. What is the expected return for the overall stock market? What is the required rate of return on a stock with a beta of 1.4?
8. A stock has a required return of 11%, the risk-free rate is 6%, and the market risk premium is 4%.
a. What is the stock's beta?
b. If the market risk premium increased to 5%, what would happen to the stock's required rate of return? Assume that the risk-free rate and the beta remain unchanged.
9. Stock R has a beta of 1.6, Stock S has a beta of 0.65, the expected rate of return on an average stock is 13%, and the risk-free rate of return is 7%. By how much does the required return on the riskier stock exceed the required return on the less risky stock?
10. Calculate the required rate of return for Manning Enterprises assuming that investors expect a 3% rate of inflation in the future. The real risk-free rate is 2.5%, and the market risk premium is 6.5%. Manning has a beta of 1.6, and its realized rate of return has averaged 13.5% over the past 5 years.