Smeal College of Business Analytical Models: ACCTG 597EPennsylvania State University Professor HuddartTaxation of Stock OptionsYou are a middle level manager in a Fortune 500 company. Three yearsago, your employer initiated a non-qualified stock option program for itsemployees. When the program was initiated, you received the right, but notthe obligation, to buy 10,000 shares of your employer’s stock at $7.00 pershare. You may exercise this right on the third or fifth anniversary of thegrant, which was made three years ago today. The right expires on the dayafter the fifth anniversary. You can exercise this right only once.Today, your company’s stock is trading at $10 per share. You are unsurewhat the price of the stock will be on the fourth or fifth anniversary, butyou believe that every year, the stock price will either increase by a factorof 1.2 or fall by a factor of 1/1.2. For example, this means that next year youbelieve the stock price will either be $12.00 (10 × 1.2) or $8.33 (10/1.2). Theprobability that the stock price increases in any year is always .6, independentof the past evolution of the stock price. The probability that the stock pricedecreases is .4, independent of the past evolution of the stock price. Thus,you think there is a sixty percent chance the stock price will be $12.00 pershare on the fourth anniversary and a forty percent chance the stock pricewill be $8.33 on the fourth anniversary.Note 1 : For all parts to this problem, ignore the dilutive effect of your optionon the firm’s stock price. Assume the number of shares on which you holdoptions is trivial when compared to your employer’s outstanding equity.Note 2 : For all parts to this problem, assume that you are risk neutral. Inother words, you will select the course of action that provides the highestexpected payoff, regardless of the risk involved.a. On the fifth anniversary, what is the probability that the stock pricewill be $14.40 per share, given that the stock price today is $10.00 pershare? What is the probability it will be $10.00 per share? What is theprobability it will be $6.94 per share?Note 3 : If you exercise your option, you will sell the shares you acquireimmediately in order to buy a riskless bond that pays interest at the rateof six percent per year. Holding the bond is always better than holding thestock because the return on the bond is better than the expected returnfrom holding the stock. The stock has an expected annual return of 5.33%(.6 × 1.2 + .4/1.2 − 1).cSteven Huddart, 2001–2008. www.personal.psu.edu/sjh11ACCTG 597E Taxation of Stock Optionsb. Ignore all tax considerations (i.e., assume that your marginal rate of taxon capital gains and on income are both zero). Should you exercise theoption today?c. Assume that your marginal rate of tax on capital gains and on incomeare both twenty percent. Should you exercise the option today?d. Assume that your marginal rate of tax on capital gains and on incomeare both twenty percent this year. Next year, and for the foreseeablefuture, your marginal rate of tax will be forty percent. The pretax returnoffered by the bond and your beliefs about the stock price movements donot change as a result of the increase in tax rates. Should you exercisethe option today?e. Suppose the strike price for the options you hold is changed from $7.00per share to $9.50 per share. Tax rates are as in part d. Relative topart d, does your decision to exercise the option change? What reasonscan you offer for this?f. Suppose the strike price for the options you hold is $7.00 per share.Suppose your employer’s tax rate is ten percent this year, but is expectedto rise permanently to forty-five percent next year. When would youremployer prefer that you exercise your option? Why?g. Do your preferences (assuming the tax rate structure in part d) coincidewith those of your employer? If they do not, is there a way to modifythe option contract to make both you and your employer better off?h. In light of the intuitions provided by the analysis in parts a through g,comment on Mr. Eisner’s decision to exercise some of his stock optionsas described in the accompanying article, “Disney Officials Get $187Million From Stock sale,” (December 2, 1992) Wall Street Journal p. A3by David J. Jefferson.Page