Financial Management Problem Set 6: Risk, Reward, and Project Evaluation, Assignments of Finance

Download Financial Management Problem Set 6: Risk, Reward, and Project Evaluation and more Assignments Finance in PDF only on Docsity! Financial Management Problem Set 6 Spring 2005 Prof. Kensinger page 1 Risk, Reward, and Project Evaluation 1. Calculate the expected return for a portfolio made up of equal proportions of investments with individual expected returns of 10%, 12%, and 14%, respectively. 2. Calculate the expected return for a portfolio with $200 invested in stock A, $300 in stock B, and $500 in stock C. Expected returns for the individual stocks are 10% for stock A, 12% for stock B, and 14% for stock C. 3. Suppose a portfolio is made up of equal proportions of investments whose returns distributions have standard deviation of 10%, 12%, and 14%, respectively. Which of the following could possibly be the standard deviation of the returns for the portfolio? a. 14% c. 9% b. 15% d. 20% 4. Suppose a portfolio includes $200 invested in stock A, $300 in stock B, and $500 in stock C. Standard deviations for the individual stocks are 10% for stock A, 12% for stock B, and 14% for stock C. Which of the following could possibly be the standard deviation of the returns for the portfolio? a. 14% c. 8% b. 13% d. 15% 5. Portfolio A has expected return of 12% with standard deviation 5%, portfolio B has expected return of 12% with standard deviation 7%, portfolio C has expected return of 14% with standard deviation 5%. Which of these portfolios is not dominated by any of the others? a. Porfolio A c. Porfolio C b. Portfolio B d. None of the above 6. Portfolio A has expected return of 15% with standard deviation 9%, portfolio B has expected return of 15% with standard deviation 7%, portfolio C has expected return of 14% with standard deviation 8%. Which of these portfolios is not dominated by any of the others? a. Porfolio A c. Porfolio C b. Portfolio B d. None of the above 7. In order to get the benefits of diversification, one needs to have a portfolio that includes equal proportions of how many securities? a. at least 100 c. at least 1000 b. at least 250 d. 12 to 15 8. Calculate the beta for a portfolio made up of equal proportions of investments with individual betas of .75, 1.0, and 1.25. 9. Calculate the beta for a portfolio with $200 invested in stock A, $300 in stock B, and $500 in stock C. Betas for the individual stocks are .75 for stock A, 1.0 for stock B, and 1.25 for stock C. 10. When the T-Bill rate is 9% and the expected return for the market portfolio is 12%, what is the opportunity cost of capital for an investment with beta of 1.5? Financial Management Problem Set 6 Spring 2005 Prof. Kensinger page 2 11. Assume the T-Bill rate is 10% and the expected return on the market portfolio is 18%. An investment is twice as risky as the market portfolio, in terms of its systematic risk. What is the opportunity cost of capital for this investment? 12. A project under analysis by Amalgamated Ajax management is in a relatively new technology, and much of its risk is considered to be unsystematic. The 95% confidence interval for its rate of return ranges from 4% to 40%, and the probability distribution is symmetric normal. Its beta is estimated to be 0.9. The expected return for the market portfolio is 15%, while the T-bill rate is 10%. Recommend whether to accept or reject the project. 13. A project under analysis by Molecular Compounds management is in an established technology, and much of its risk is considered to be systematic. The 95% confidence interval for its rate of return ranges from –5% to +35%, and the probability distribution is symmetric normal. Its beta is estimated to be 1.8. The expected return for the market portfolio is 15%, while the T-bill rate is 10%. Recommend whether to accept or reject the project. 14. Several years ago Molecular Compounds Corporation, a large multi-division chemical concern, installed a new capital budgeting system centered on the capital asset pricing model. Data for actual outcomes of several projects and accompanying market conditions during the project's life are given below. See if you can identify any possible problem areas in the decision process. 15. If you were certain that the market is going to rise, what sort of beta would you prefer for your portfolio? 16. If you were certain that the market is going to drop, what sort of beta would you prefer for your portfolio? 17. If you thought the market might be turning up, but still were frightened of a downturn, what sort of beta would you prefer for your portfolio? 18. The last questions are mini-cases for discussion in class. The Case of the Inventive Financial Analyst Blimps and Bags, Inc., is in the news. It seems that Tyrone Gasbag, the newly appointed chief financial officer, has created an innovative way to “put risk analysis back into risk analysis,” as he says. He has programmed a computer to create different combinations of cost and revenue streams using a random number generator, in order to produce what he calls a “synthetic history” of proposed new investment projects. The objective is to get an idea of the range of possible outcomes for a project. After generating several hundred possibilities, the computer calculates the mean return and standard deviation of return for the project from the simulated data. Division Project b j Rj RTbill Rmkt 1 A 0.4 12% 9% 14% 1 B 1.1 18% 10% 15% 2 C 0.8 13% 10% 15% 2 D 1.7 15% 9% 13% 3 E 0.5 13% 9% 14% 3 F 1.3 25% 10% 15% Financial Management Solutions: Problem Set 6 Spring 2005 Prof. Kensinger 1. Expected Return = 1/3 (10% + 12% + 14%) = 12% 2. Expected return = (.2 x 10%) + (.3 x 12%) + (.5 x 14%) = 12.6% 3. C. Since diversification reduces risk, the standard deviation for a portfolio is less than the weighted average of the standard deviations for the individual stocks in the portfolio. The weighted average for this portfolio is 12% (the numbers in this calculation are the same as problem 1). Choice C is the only one that could possibly be correct, because all the other choices exceed the weighted average. 4. C. Since diversification reduces risk, the standard deviation for a portfolio is less than the weighted average of the standard deviations for the individual stocks in the portfolio. The weighted average for this portfolio is 12.6% (the numbers in this calculation are the same as problem 2). Choice C is the only one that could possibly be correct, because all the other choices exceed the weighted average. 5. Portfolio C has higher return than any of the other portfolios, and no other portfolio has lower risk. There portfolio C dominates. 6. Portfolio B has lower risk than any of the other portfolios, and no other portfolio has higher return. There portfolio B dominates. 7. D 8. Beta = 1/3 (.75 + 1.0 + 1.25) = 1.0 9. Beta = (.2 x .75) + (.3 x 1.0) + (.5 x 1.25) = 1.075 10. OCC = 9% + 1.5 (12% – 9%) = 13.5% 11. OCC = 10% + 2 (18% – 10%) = 26.0% 12. The expected return is 22% (middle of the 95% confidence interval). Opportunity cost of capital is 10% + .9(15%–10%)=14.5%. Since the project has an expected return higher than the opportunity cost of capital, it is attractive. Also, the project’s expected return is higher than the market portfolio’s, with lower risk, so it clearly dominates the market. Accept it. 13. The expected return is 15% (middle of the 95% confidence interval). Opportunity cost of capital is 10% + 1.8(15%–10%)=19%. Since the project has an expected return lower than the opportunity cost of capital, it is not attractive. Also, the project has expected return the same as the market potfolio’s, with nearly twice the risk, so it is clearly dominated by the market. Reject it. Financial Management Solutions: Problem Set 6 Spring 2005 Prof. Kensinger 14. The results for the projects can be analyzed using the table below: Analysis:: Both of the Division 2 projects under-performed, while the other divisions’ projects all earned more than the opportunity cost of capital. Division 2 may have simply been a victim of external forces, or just bad luck. There is, however, the possibility that something may be wrong with the decision-making process in Division 2. 15. Very High. 16. Negative. 17. Low, perhaps less than 1. In the face of uncertainty, this choice is a matter of personal preference. 18. Cases are for class discussion. Division Project Rj Opportunity Cost of Capital 1 A 12% 11% 1 B 18% 15.5% 2 C 13% 14% 2 D 15% 15.8% 3 E 13% 11.5% 3 F 25% 16.5%