sharesoutstandingandbringsfreshcashintothefirm;both
will affect the stock price.
21 Theexpectednegativeimpact(dilution) ofexercisewill
decreasethevalueofwarrantscomparedtootherwisesimilar
calloptions.TheadjustmentintheBlack-Scholesfordilution
tothestockpriceisfairlysimple.Thestockpriceisadjusted
fortheexpecteddilutionfromtheexerciseoftheoptions.In
the case of warrants, for instance:
whereS= Current value of the stock
ns= Number of shares outstanding
W= Value of warrants outstanding
nw= Number of warrants outstanding
When the warrants are exercised, the number of shares
outstanding will increase, reducing the stock price. The
numeratorreflectsthemarketvalueofequity,includingboth
stocks and warrants outstanding. The reduction in S will
reduce the value of the call option.
Thereisanelementofcircularityinthisanalysis,sincethe
value of the warrant is needed to estimate the
dilution-adjustedS,andthedilution-adjustedSisneededto
estimate the value of the warrant. This problem can be
resolvedbystartingtheprocessoffwithanassumedvaluefor
the warrant(say, the exercise value or thecurrent market
priceofthewarrant).Thiswillyieldavalueforthewarrant,