Corporate Governance; Executive Compensation Fifteen years ago, in fiscal year 2002, Microsoft granted 254,000,000 stock options to its employees as part of their compensation. The options had an expiration of 10 years and an exercise price of $ 24.27. Assume that Microsoft's dividend rate was 0%, its stock volatility was 0.39, the risk-free rate was 5.4%, the Microsoft stock price on the date of grant was $ 24.27, and the number of outstanding shares was 10,700,000,000. 1. What was the fair market value of all these 2002 executive stock options on their date of grant, according to the Black-Scholes formula? 2. Suppose that Microsoft used a different compensation policy and decided to grant shares of stock to its employees instead of stock options. How many shares would the company have to issue the same amount of economic value as calculated in the answer to question 1 above? Assume the stock price is $ 24.27 per share. 3. If the stock's volatility was 0.39, then Microsoft's shares had a two-thirds probability of rising or falling by 39% or less over the next year. If the stock had risen 39% over the next year, what would have been the value of the options granted in question 1, and what would have been the value of the shares granted in question 2? If the stock had dropped 39% over the next year, what would have been the value of these shares and options? Assume that volatility, dividends, and the riskfree rate are unchanged. 4. Based on your answer to question 3, which would have been the best compensation policy for Microsoft: delivering an equal amount of economic value through shares or through options? In reaching your conclusion, what goals and assumptions would you consider most important to you? Are you surprised that in the years since 2002, Microsoft and many other firms have shifted their equity compensation away from options and largely towards shares? Credit Derivatives Suppose you are structuring CDO consisting of three bonds. Each of the bonds has a probability of 8% over the next seven years and a recovery rate of 0.35. The coupon payment on each of the three bonds is 5% per year, compounded annually, but paid at the end of six years. (Assume that the recovery rates apply to the amounts received at the end of six years for the principal and the compounded coupon. ) Suppose also that the underlying assets of the CDO consist of equal amount invested in the three bonds, ie, for a notional amount of $ 390 million, with equal investment of $ 130 million in each bond. The CDO is split into two tranches, a senior tranche and an equity tranche. The interest rate during the 6-year period is constant at 6% per annum. 1. Assuming that the default events of the three bonds are uncorrelated, draw the tree illustrating the various outcomes and the associated probabilities. (1 point) 2. Draw the cumulative probability distribution of the cash flows at the end of six years from the portfolio underlying the CDO. (1 point) 3. Suppose the credit rating agency requires the senior tranche to have a probability of less than 2% at the end of the maturity of six years to be given an AA rating. What is the maximum and minimum size of the senior tranche in terms of cash flows at the end of six years? If AA bonds with a six-year maturity are yielding 4% today, what is the present value of the senior tranche? (2 points) 4. Compute the maximum and minimum payoffs at maturity to the equity tranche, as well as its value today, if there is in arbitrage. (1 point) 5. Suppose that the three bonds are correlated in the following manner. Bond 1 and Bond 2 are correlated such that, if Bond 1 defaults, the probability of Bond 2 defaulting is 0.6. However, if Bond 1 does not default, the probability of Bond 2 not defaulting is also 0.9. Bond 3 is uncorrelated with Bonds 1 and 2. Redo your calculations for questions 1 to 4 above. (2 points) 6. Go back to the zero correlation case. Suppose a CDS contract is available on one of the issuers of one of the three bonds, Bond 1. Suppose the price of the CDS is 300 basis points per year for six years, payable on a compounded basis at the end of the six years. What is the maximum size of the AAA tranche now, if this one-third of the total portfolio is fully protected against default and the probability of it being tightened to 1%? (2 points) 7. Discuss, without calculations, how your answer might change if the credit rating agency used the expected loss percentage rather than the probability of loss as the criterion for the AAA rating. (1 point) 8. (Bonus) What would happen to the maximum size of the senior tranche in part (6) if the investments in the three bonds are $ 100 million, $ 130 million and $ 160 million, respectively? (Please provide simple calculations if needed.) (2 points)