1. PhoneCo, a U.S. maker of smartphones and other consumer products, has $60 billion of cash and marketable securities on its balance sheet and revenues of $50 billion. Using the rule of thumb mentioned in the text, how much would you estimate as cash needed for operations and excess cash and marketable securities? Now suppose that you discover that of the $60 billion in cash, $40 billion of it is from profits earned overseas. Would your estimate of the value of excess cash and marketable securities change? How does this affect your valuation of PhoneCo? 2. MarineCo manufactures, markets, and distributes recreational motorboats. Using discounted-free-cash-flow analysis, you value the company's operations at $2,500 million. The company has a 20 percent stake in a nonconsolidated subsidiary valued at $500 million. The investment is recorded on MarineCo's balance sheet as an equity investment of $50 million. MarineCo is looking to increase its ownership. The company's marginal tax rate is 30 percent. Based on this information, what is MarineCo's enterprise value? If new management announced its plan to sell the company's stake in the subsidiary at its current value, how would that change your valuation? 3. MarineCo has no debt but does have unfunded pension liabilities valued at $200 million, recorded as a long-term other liability. MarineCo has detailed in its annual report a potential legal judgment of $100 million for defective engines. Since management estimates a 90 percent likelihood that the judgment will be enforced against the engine maker and not MarineCo, it has not reported a liability on the balance sheet. The company's marginal tax rate is 30 percent. Based on this information and information provided in Question 2 (assuming no sale of the subsidiary), what is MarineCo's equity value? 4. You are valuing a company that has $200 million in debt using probability-weighted-scenario analysis. You carefully model three scenarios, such that the resulting enterprise value equals $300 million in scenario 1, $200 million in scenario 2, and $100 million in scenario 3. The probabilities of the scenarios are 25 percent, 50 percent, and 25 percent, respectively. What is the expected enterprise value? What is the expected equity value? Management announces a new plan that eliminates the downside scenario (scenario 3), yielding a 75 percent probability of scenario 2. What happens to enterprise value and equity value? Why does enterprise value rise more than equity value? 5. You are valuing a technology company whose enterprise value is $800 million. The company has no debt but considerable employee options, 10 million in total. Based on option-pricing models, you value each option at $6.67 per option. Assume that the average strike price equals $15. If the company has 40 million shares outstanding, what is the company's equity value and value per share using (a) the option-pricing model and (b) the exercise value approach? Why is the option-pricing model the preferred method? 6. You are valuing an industrial firm whose enterprise value is $10 billion. The company has no straight debt but does have 100,000 convertible bonds outstanding. The market value of each bond is $1,150. If the company has 500 million shares outstanding, what is the company's equity value and value per share using (a) the market value approach and (b) the conversion value approach?

question 1

Assume the Black-Scholes-Merton framework. Consider a derivative se- curity of a stock. You are given: (a) The continuously compounded risk-free interest rate is 0.04. (b) The volatility of the stock is . (c) The stock does not pay dividends. (d) The derivative security also does not pay dividends. (e) S(t) denotes the time-t price of the stock. (f) The time-t price of the derivative security is [S(t)]/2, where k is a positive constant. Find k.