Valuation of stocks

1. Suppose Busted Bank (BB) will pay a dividend of USD 1.25 per share at the end of this year.

After the dividend payment you expect BB’s share price to be USD 25.75. BB’s cost of capital

is 8%.

a. What price would you be willing to pay for a share of BB’s stock today?

b. Compute BB’s dividend yield, and assume that it remains constant for the

foreseeable future. What is then the expected rate of growth in BB’s dividends

beyond next year?

c. What is the expected growth rate of BB’s share price?

2. At the beginning of this year, a press release from Exodus Exploration (EE) revealed that an

oil discovery had been made, which would increase the free cash‐flow of the company by

USD 50M at the end of next year, and by USD 30 M in subsequent years (in perpetuity).

a. With 120M shares outstanding and a weighted average capital cost of 11%, how

would the announcement affect the share price of Exodus Exploration?

b. Would you expect to be able to make a profit on this announcement? Explain.

Risk, returns, and optimal portfolio choice

3. The last four years of returns for a stock are as follows:

a. What is the average annual return?

b. Compute the return of a USD100 investment in the above stock, assuming that you

were invested through the entire 4‐year period. What would be your compound

average annual return?

c. What is the variance of the stock’s returns?

d. What is the standard deviation of the stock’s returns?

4. Assume a risk‐free interest rate of 3.3%, and a stock market that will have an annual return

of either 33.3% or −13.3% each year, with equal probabilities. Compare two investment

strategies:

1: Invest for one year in the risk‐free investment, and one year in the market

2: Invest for both years in the market.

a. Which strategy has the highest expected final payoff?

b. Which strategy has the highest standard deviation for the final payoff?

c. Compute the Sharpe‐ratio (SR) for the two strategies? Which strategy offers the best

risk‐adjusted excess returns?

2

5. Suppose Busted Bank (BB) and Exodus Exploration (EE) have expected returns and volatilities

shown below, with a correlation of 27%.

a. Calculate the expected return and the volatility (standard deviation) of a portfolio

that is equally invested in BB and EE stock.

b. How would the expected return and volatility of the above portfolio be influenced by

an increase in the correlation between the two stocks?

6. You are a financial advisor, and must choose one of the funds below to recommend to a

client of yours. Whichever fund you recommend, your client will then combine it with riskfree

borrowing and lending depending on their desired level of risk. Assume the risk‐free rate

is 3%.

a. Which fund would you recommend without knowing your client’s risk preference?

b. Is your answer the same if the risk‐free rate of interest is 6% instead of 3%?

The CAPM Model

7. Suppose Busted Bank has a beta of 0.89 and Exodus Exploration has a beta of 1.92. Assuming

a risk‐free interest rate of 3% and a return of the market portfolio of 12%, use the CAPM to

compute the expected return of a portfolio that consists of 57% BB stock and 43% EE stock.

8. Exodus Exploration (EE) considers an investment in a new drilling rig. Development Drilling

(DD) is an all‐equity firm that is fully specialized in this line of the oil and gas business.

Suppose DD’s equity beta is 2.1, the risk‐free rate of interest is 3%, and the market riskpremium

is 6%. If EE is also all equity financed, what would be the cost of capital for this

investment.

Corporate finance

9. Now assume that Exodus Exploration (EE) has EBIT of USD 735M in 2013. In addition, EE has

interest expenses of USD 237M and a corporate tax rate of 78%.

a. What is EE’s 2013 net income?

b. What is the total of EE’s 2013 net income and interest payments?

c. If Exodus Exploration had no interest expenses, what would its 2013 net income be?

How does the answer compare to your answer in part b?

d. What is the amount of EE’s interest tax shield in 2013?

3

10. Exodus Exploration (EE) is currently an all‐equity firm with an expected return of 11%. It is

considering a leveraged recapitalization in which it would borrow and repurchase existing

shares.

a. Suppose EE borrows to the point that its debt‐equity ratio is 0.40. With this amount

of debt, the debt cost of capital is 5.5%. What will the expected return of equity be

after this transaction?

b. Suppose instead that Exodus Exploration borrows to the point that its debt‐equity

ratio is 2.00. With this amount of debt, EE’s debt will be much riskier. As a result, the

debt cost of capital will be 7.8%. What will the expected return of equity be in this

case?

c. A senior manager argues that it is in the best interest of the shareholders to choose

the capital structure that leads to the highest expected return for the stock. How

would you respond to this argument?

d. Based on the assumptions and results from question b, compute EE’s pre‐tax

weighted average capital cost.

e. If the tax rate is 78%, what is the EE’s effective after‐tax WACC?

Subject | Mathematics |

Due By (Pacific Time) | 10/31/2014 03:00 pm |

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