# Blog

**FINANCE FOR EXECUTIVES**

**Problem Set**

Please answer the problems in Excel and submit the Excel spreadsheet. A template Excel file “Finance for Executives”.

These cells have been formatted to display the correct number of decimal places. No rounding should be necessary. You can add additional calculations elsewhere in the spreadsheet, but please put your answers in the highlighted cells.

Assume the risk-free rate is 1% (rf = 1%), the expected return on the market portfolio is 5% (E[rM] = 5%) and the standard deviation of the return on the market portfolio is 15% (σM = 15%). (All numbers are annual.) Assume the CAPM holds.

a. What are the expected returns on securities with the following betas:

(i) β = 1.4

(ii) β = 0.6

(iii) β = -0.2

b. What are the betas of securities with the following expect returns:

(i) 10%

(ii) 5%

(iii) -1%

c. What are the portfolio weights (in the risk-free asset and the market portfolio) for efficient portfolios (portfolios on the efficient frontier/CML) with expected returns of

(i) 4%

(ii) 5%

(iii) 7%

d. What are the portfolio weights (in the risk-free asset and the market portfolio) for efficient portfolios (portfolios on the efficient frontier/CML) with standard deviations of

(i) 6%

(ii) 15%

(iii) 21%

e. For a moment (but just a moment) assume that the CAPM may not hold. A non-dividendpaying stock has a current price of $50/share and an expected price in 1 year of 2 $53/share (based on your personal analysis of the company’s prospects).

(i) If the stock has a beta of 1 (β = 1.0), what is its alpha (α)?

(ii) What is the alpha (α) if the beta is 2 (β = 2.0)?

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2. Assume that there are 3 firms in an industry for which you wish to compute an industry beta. The betas of these 3 firms are 1.1, 1.2, and 1.4.

a. What is the beta of an equal-weighted portfolio of the 3 firms?

b. If the market capitalizations of the 3 firms are $100 million (beta 1.1), $200 million (beta 1.2), $300 million (beta 1.4), what is the beta of a market capitalization value-weighted industry portfolio.

3. Consider a firm with two equally sized divisions (in terms of their value) that engage in completely different lines of business with different risks.

a. If these 2 divisions have betas of 0.8 and 1.3, what is the beta of the firm?

b. If one division has a beta of 0.8, and the beta of the firm is 1.0, what is the beta of the second division?

c. For the firm in part (b), what beta should be used to compute the cost of capital for the low risk division, i.e., should it be the firm beta or the divisional beta?

4. XYZ Inc. has expected earnings over the next year of $2/share (E[E1] = 2). The company is expected to maintain an earnings retention rate of 40% (b = 0.4), i.e., 60% of earnings are expected to be paid out as dividends every year. The company has a beta of 2, the risk-free rate is 1% (rf = 1%), and the market risk premium is 4% (E[rM]-rf = 4%).

a. If the growth rate in earnings is expected to be 3% in perpetuity

(i) What is the value of the stock?

(ii) What is the expected return over the next year?

b. If the current price of the stock is $16/share, what is the implied growth rate of earnings (and dividends)?

XYZ Inc. is expected to pay no dividends for the next 5 years. However, at the end of the sixth year (at time 6), the company is expected to pay a dividend of $1/share. Dividends are expected to grow at 10% per year for the following 9 years (through the end of the 15th year, i.e., time 1

5), then to grow at 3% every year thereafter (forever). Assume the appropriate discount rate (required return) is 6%.

a. What is the expected value of the stock at time 15 (not including the time 15 dividend)?

b. What is the expected value of the stock at time 5?

c. What is the value of the stock today?

6. Assume the risk-free rate is 1% (rf = 1%), the expected return on the market portfolio is 5% (E[rM] = 5%) and the standard deviation of the return on the market portfolio is 15% (σM = 15%). Assume the CAPM holds. A stock with a beta of 1 has a return standard deviation (volatility) of 30%.

a. What is the standard deviation (volatility) of the systematic component of the stock’s return?

b. What is the standard deviation (volatility) of the idiosyncratic component of the stock’s return?

c. What fraction of the stock’s return variance is systematic?

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