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1、Chapter23:OptionsandCorporateFinance:ExtensionsandApplications23.1a.TheinputstotheBlack-Scholesmodelarethecurrentpriceoftheunderlyingasset(S),thestrikepriceoftheoption(K),thetimetoexpirationoftheoptioninfractionsofayear(t),thevarianceoftheunderlyingasset(q2),andthecontin
2、uously-compoundedrisk-freeinterestrate(「)・Mr.Levinhasbeengranted20,00()EuropeancalloptionsonMountainbrook^sstockwith4yearsuntilexpiration.Sincetheseoptionsweregrantedat-the-money,thestrikepriceofeachoptionisequaltothecurrentvalueofoneshare,or$50・Therefore,theBlack-Schole
3、sinputsare:S=$50cj2=0.25K二$50r=0.06t=4Afteridentifyingtheinputs,solveford
4、andd2:山=
5、ln(S/K)+(r+I6o2)(t)
6、/(o2t),/2=[ln(5O/5O)+{0.06+力(0.25)}(4)]/(0.25*4严=0.7400d2=d
7、-(o2t)'2=0.7400・(0.25*4严=-0.2600FindN(d])andN(d2),theareaunderthenormalcurvefromnegativeinfinitytod]andnegat
8、iveinfinitytod2,respectively・N(dJ二N(0.7400)=0.7704N(d2)=N(-0.2600)=0.3974AccordingtotheBlack-Scholesformula,thepriceofaEuropeancalloption(C)onanon-dividendpayingcommonstockis:C=SN(dj)-KertN(d2)=(50)(0.力04)-(50)e(006X4)(0.3974)=$22.89TheBlack-ScholesPriceofonecalloptionis
9、$22.89.SinceMr.Levinwasgranted20,000options,thecurrentvalueofhisoptionspackageis$457,794(=20,000*$22.89).b・BecauseMr.Levinisrisk-neutral,youshouldrecommendthealternativewiththehighestnetpresentvalue.Sincetheexpectedvalueofthestockoptionpackageisworthmorethan$450,000,Mr・L
10、evinwouldprefertobecompensatedwiththeoptionsratherthanwiththeimmediatebonus・c.IfMr.Levinisrisk-averse,hemayormaynotpreferthestockoptionpackagetotheimmediatebonus.Eventhoughthestockoptionpackagehasahighernetpresevalue,hemaynotpreferitbecauseitisundiversified.Thefactthathe
11、cannotsellhisoptionsprematurelymakesitmuchmoreriskythantheimmediatebonus・Therefore,wecannotsaywhichalternativehewouldprefer.23.2Jared'stotalcompensationpackageconsistsofanannualsalaryofS500,000for3yearsinadditionto10,000at-the-moneystockoptions.First,findthepresentvalueo
12、fthesalarypayments.Sincethepaymentsoccurattheendoftheyear,thepaymentscanbevaluedasathree-yearannuity,di
