20 C.Edwards,J.R.Graham,M.H.Lang,andD.Shackelford,
“EmployeeStockOptionsandTaxes,”workingpaper,SSRN,
2004.Inthispaper,theyestimatethetaxratesforfirmswith
substantialemployeeoptionsoutstandingand notethatthey
arewellbelowthemarginaltaxrate.ForDell,theyestimatea
tax rate of 20 percent as a resultof option expensing, as
opposed to the marginal tax rate of 35 percent.
21 J. Bulow and J. B. Shoven, “Accounting for Stock
Options,” working paper, SSRN, 2004.
22 J. Hull and A.White, “Howto ValueEmployee Stock
Options,” Financial Analysts Journal 60, no. 1 (2004):
114–119.
23 M. Ammann and R. Seiz, “Does the Model Matter? A
Valuation Analysis of Employee Stock Options,” working
paper, SSRN, 2003.
24 Thevarianceestimateisactuallyonthenaturallogofthe
stockprices.Thisallowsustoclingtoatleastthepossibility
ofanormaldistribution.Neitherstockpricesnorstockreturns
canbe normally distributed sinceprices cannotfall below
zero and returns cannot be lower than −100 percent.
25 AlloftheinputstotheBlack-Scholesmodelhavetobein
annualterms.Toannualizeaweeklyvariance,wemultiplyby
52.
26 Harkingbacktothelastsection,thevalueofoptionsused
shouldbecalculatedbasedonthecurrentstockprice(rather
than an estimated value) and on a pretax basis.