Finance 100 Problem Set CAPM

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Bruce Turner
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1 Finance 100 Problem Set CAPM 1. Consider the following data for the companies Powergas and Supertech: Company Beta Standard Covariance with Deviation Market Powergas? 45% Supertech %? The expected return on the market index is 15% and the risk free rate of interest is 6% You can borrow and lend at the risk free rate. 1.a Suppose the standard deviation of the market portfolio is 15% What is the beta of Powergas and the covariance of Supertech with the market portfolio? 1.b What are the correlations between Powergas and the market (Supertech and the market)? 1.c How could you form a portfolio of Powergas and Supertech that has exactly the same expected rate of return as the market? 1.d How could you form a portfolio of Powergas and Supertech that has a expected rate of return of 24%? What is the risk of this portfolio if the correlation between Powergas and Supertech is 0.5? 1

2 1.e How could you form a portfolio that has the same expected return as the portfolio formed in part 1.d, but lower standard deviation? What is the lowest risk you have to assume for this expected return? 2. Company SmallCap is in the food processing business and has a market capitalization of $100 million and a market beta of 1.5. SmallCap considers a merger with LowCost, another company mainly producing computer software that has a market capitalization of $400 million and a market beta of 1.2. The CEO of SmallCap argues that this will reduce their cost of capital. The risk free rate of interest is 5% and the market risk premium is 8% Both companies and the merged company are 100% equity financed. 2.a What is the beta of the merged company? 2.b What is the required rate of return on equity of the merged company? 2.c What is the required return on a typical project in the software division of the merged company? Hence, comment on the reasoning of the CEO that merging has reduced SmallCap s cost of capital. 2.d The Index1000 fund holds shares in both SmallCap and LowCost exactly in proportion to their market capitalization. How is the risk of the fund affected by the merger if their holdings continue to be proportional to market capitalization. 3. You consider investing in two mutual funds with the following parameters: The funds are valued in a market where investors can borrow and lend, using T-bills, at the risk free rate of 5% and require a risk premium above this risk free rate of 8% for holding the market portfolio. 2

3 Fund 1 Fund 2 Beta Standard Deviation 20% 32% 3.a Suppose you can borrow and lend at the risk free rate of interest. Which of the two funds do you prefer? 3.b What is the lowest risk portfolio that gives you an expected return of 14.6% What is its standard deviation? Construct this portfolio using one of the funds and T-bills. 3.c Suppose you can invest at the risk free rate of 5% but you can only borrow at the higher rate of 7% What is the lowest risk portfolio with an expected return of 14.6% now? 4. Suppose the market risk premium is 9% and the risk free rate is 6% In a period where the market moved up by 30% during a single year, you observe the following risk and return data for mutual funds: Fund Return Beta A 30% 0.8 B 34% 1.2 C 33% 1.0 Which fund has offered the best risk adjusted return? 5. 5.a Suppose that the ABC company is expected to be worth $100 per share one year from today. How much are you willing to pay for one share today if the risk-free rate is 7%, the expected rate of return on the market is 15%, and the company s beta is 1.5? Assume that no dividends are paid. 3

4 5.b Suppose that the correlation coefficient between the rates of return on Knowlode Mutual Fund and the market portfolio is 0.7. The standard deviations of the rates of return are 0.20 for Knowlode and 0.15 for the market portfolio. How would you combine the Knowlode Fund and the riskless asset to obtain a portfolio with a beta of 1.5? 6. Consider two companies A and B operating in unrelated lines of business with the following data: Dividend Yield Market Fund Beta (Historic) σ Cap Company A 0.9 5% 25% $10 bn Company B 1.2 1% 30% $20 bn Market % 15% The coefficient of correlation of the two companies is 0.2. Both companies are 100% equity financed. The market risk premium is 8% and the risk free rate is 5% 6.a Calculate the required rate of return on equity for each of the two companies. 6.b Suppose companies A and B merge, and there are no synergies or disynergies between their operations. What is the beta and the required rate of return on equity for the merged company AB? What is the risk of the stock returns to the company as a whole? Comment briefly on the implications of conglomerate mergers for the cost of capital. 6.c Use the dividend growth model to determine the percentage appreciation in the stock price investors expect for each company. What is the dollar value each company pays out as a dividend today? Reconsider the merger in part II and assume the merged company pays out exactly the same dollar dividend 4

5 the two companies would have paid out had they remained separate. What is the dividend yield of the merged company AB? Hence, what is the expected appreciation in the merged company s stock price? 7. You are given the following information about possible investments: Asset Mean Market Standard Correlation Return Value Deviation with Market Real Estate 8% $5 trillion 15% 0.5 Growth Stocks 12% $2 trillion 22.5% 1.0 Antiques 15% $2.5 trillion 15% a What are the equal-weighted and value-weighted mean returns on portfolios, which include all three assets? 7.b If the market standard deviation is 15%, what are the CAPM betas of each of these assets? 7.c If real estate and growth stocks are correctly prices according to the CAPM, then show that the market expected return is 10% and the risk-free rate is 6%. 7.d Given the information in part 3, are Antiques priced correctly according to the CAPM? If Antiques are mispriced, how would you construct a portfolio to take advantage of this mispricing? 8. You are given the following information about possible investments: 5

6 Asset Mean Standard Correlation Return Deviation with Market Value Stocks 18% 30% 1.0 Growth Stocks??% 20% 0.5 Gold??% 20% -0.5 T-bills 6% 0% a If the market standard deviation is 20%, what are the CAPM betas of each of these assets? 8.b Assume all assets are priced correctly according to the CAPM. What are expected returns to the market, growth stocks and Gold? 8.c In addition to the assets described above you are told that the expected return on BadCo, Inc. equity shares is -14% and its beta is -2. Does the market correctly price this firm? If your answer is yes then proceed to the question, otherwise explain whether it is over or undervalued and how you would take advantage of this mispricing. 8.d Is the portfolio that you constructed in part (c) riskless? That is, do you stand to gain the 4% profit for sure next period? 6

Finance 100: Corporate Finance

Finance 100: Corporate Finance Professor Michael R. Roberts Quiz 3 November 16, 2005 Name: Section: Question Maximum Student Score 1 40 2 35 3 25 Total 100 Instructions: Please read each question carefully