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Discuss how you would use CAPM to

(a) compute a required rate of return on an investment project; 

(b) value a risky cash flow;

(c) evaluate performance of an equity fund given information on its "alpha" and "beta" (draw a graph to illustrate youranswer).

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Related questions

Market portfolio has an expected return of 11% and volatility of 20%. Risk-free rate is 3%. Security X and Y have betas of 1.4 and 0.9 respectively.

a) According to CAPM, what are the expected return of X and Y?

E(rm)-rf = 11% - 3% = 8%

3% +1.4*8% = 14.2%

3% +1.4 *8% = 10.2%

b) What should be X worth today, if X pays a dividend of $1.2 one year from today and is priced at 30 one year from today? The required rate of return is the expected return using CAPM from part a).

c) If security X has expected return of 15%, is it underprice/overprice/fairly priced according to CAPM? What is its alpha?

d) Plot SML and label X, Y and Market portfolio on the line.

e) What is the beta of a portfolio with 50% in X and 50% in Y?

f)What is the beta of a portfolio with 55% in Market portfolio and 45% in risk-free asset?

g) You are investing in a complete portfolio. The complete portfolio is composed of risk-free asset and a risky portfolio, P, constructed with 20% in X and 80% in Y. It turns out that your complete portfolio has an expected rate of return of 9.4%. What is the beta of your complete portfolio? (hint: you may or may not use all information to solve this problem)

Q2. Stock A has a beta of 1 and standard deviation of 50%. Market portfolio has a standard deviation of 20%. What is the correlation of stock A with the market portfolio? How much of stock A’s total risk is due to market risk?

Q3. Assume the risk-free rate is 8% and the expected rate of return on the market is 18%. A stock has an expected return of 6%. What is its beta?

What are the betas listed for these companies?

Wells Fargo beta = 1.03

IBM beta = 0.87

1. If you made an equal dollar investment in each stocks what would be the beta of your portfolio?

2. If you made 70% of dollar investment in stock A, and 30% of dollar investment in stock B, what would be the beta of your portfolio? Please show your work.

3. Apply the Capital Asset Pricing Model (CAPM) Security Market Line to estimate the required return on these two stocks. Assumptions and Data: Note that you will need the risk-free rate and the market risk premium. Assume a 5% market risk premium. You will use the current 2.21 yield on 10-year Treasury securities as the risk-free rate to estimate the required rate of return on stocks.

4. Compare the required return on these stocks calculated using CAPM in question #3 against their historical return over the last 52 weeks (Wells Fargo 59.99) and IBM (182.79). Is there a difference between these returns? Is this a problem? Why is there a difference?

Assume CAPM holds and you have the following information regarding three investment opportunities:

Project 1 has a project beta of 2.0 and you have estimated that the project’s NPV using a cost of capital of 20% equals zero. Project 2 has a project beta of 1.5 and its NPV using a cost of capital of 10% equals zero. Lastly, project 3 has a project beta of 1.0 and its NPV equals zero using a cost of capital of 6%. None of these projects are ‘scale-enhancing’ for the firm, i.e. they are different than the regular operations the firm currently maintains. As the head of the capital budgeting department you are trying to decide which projects should be accepted. The company has a levered equity beta of 0.8 and a debt-to-equity ratio of 0.5, which the company is planning to maintain for the foreseeable future. The company currently faces a 40% tax rate. Given that the expected return on the market portfolio is 8% and the risk-free rate is 3%, which projects would you accept and why? (Assume there is no capital rationing and the projects are going to be financed with 100% equity.)

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