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03-PS6-IR_sol

# 03-PS6-IR_sol - MIT Sloan School of Management J Wang...

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Unformatted text preview: MIT Sloan School of Management J. Wang 15.407 E52-456 Fall 2003 Problem Set 6: Interest Rates Solution 1. Sally Jameson should consider several issues when evaluating her compensation package: • Sally should consider the probability of her leaving Telstar before five years. If she leaves Telstar early, her options expire worthless. • Sally should also consider the implication of taxes on her income. If she takes the cash award, she will be taxed at marginal ordinary tax rate. If she uses the option and sell the stock at year 5, she will be taxed at ordinary tax, which will be likely to be the maximum rate. She will only be taxed at capital gains tax if she exercises the options but holds on to the stocks. However, that may or may not be desirable, depending on her risk preference. • Before applying the Black-Scholes formula, Sally should keep in mind that her option grant is illiquid and she is not able to trade it. Therefore, she should consider an illiquidity premia when evaluating her grant. • The grant gives Sally a Europena call on a non-dividend paying common stock, currently selling at \$18.75, with an exercise price of \$35.00, and a maturity of five years. The only unknown parameter in the Black Scholes formula is the volatility of Telstar Stock. The following table shows the implied volatilies of Telstar Stock from different call option prices. Expiration Strike Price Jun 1992 Jul 1992 Oct 1992 Jan 1994 12.5 36% 17.5 31% 40% 37% 35% 20.0 30% 34% 37% 38% 22.5 36% 35% The following table shows the historical volatility of Telstar stock. Recent 90-day annualized volatility 42% Maximum volatility 83% Minimum volatility 19% Average volatility 34% The various estimates of Telstar volatility demonstrates the complexity of pricing an...
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03-PS6-IR_sol - MIT Sloan School of Management J Wang...

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