Th Firm s Valu and Timing of Adoping E-Commrc Using Ral Opions Analysis undr Uncrainy * David S. Shyu Dparmn of Financ, Naional Sun Ya-sn Univrsiy, Kaohsiung, Taiwan dshyu@cm.nsysu.du.w Kuo-Jung L Dparmn of Financ, Naional Sun Ya-sn Univrsiy, Kaohsiung, Taiwan d8843803@sudn.nsysu.du.w Absrac This papr applis ral opions analysis o analyz h opimal dcision of adoping -commrc whn a firm s oupu pric is uncrain. Th radiional discoun cash flow mhod ignors h valu of iming and opraional flxibiliy. Thrfor, i migh undrsima h valu of adoping -commrc. Th papr is h firs sudy o build a horical drivaion o dc h impac of adoping -commrc on a firm s valu and iming basd on h ral opions analysis. This sudy finds ha incrasing -commrc invsmn and incrasing pric volailiy will incras a firm s valu whil dlay h iming of adoping -commrc. By conras, dcrasing fficincy of -commrc will dcras a firm s valu and dlay h iming of adoping -commrc. Kywords: Timing, E-commrc, Ral opions. Inroducion E-commrc has bn dvloping vry fas rcnly. Inrn chnology improvs h flow fficincy of businss supply chain and dcrass producion cos. I provids cusomrs Inrn ordr and incrass sal prformanc. Efficincy improvmns and cos savings alrady achivd hrough businss-o-businss. E-commrc hav likly ld o highr produciviy growh, lowr coss and rducd pricing powr, which should allow a counry o grow fasr wihou inflaionary prssurs (Shim, 2000). On h ohr hand, i nds o invs rmndous amoun of mony in sofwar and hardwar. A company, hnc, has o considr h cos and bnfi bfor i implmns -commrc invsmn. Th impac of Informaion chnology (IT) on firm prformanc has long bn a subjc of inns rsarch, wih issus sudid ranging from masurmn of h impac, o h condiions ha ar ncssary o raliz hs impacs. Howvr, rsarchrs hav poind ou hs impacs ar nihr guarand upon implmnaion of h sysm nor ar hy uniform across h organizaion (Davrn and Kauffman, 2000; Will and Olson, 989). Ralizaion of h valu of h sysm is condiional upon inrnal and xrnal facors, som of which ar conrollabl by h organizaion (Will and Olson, 989). Shaw (2003), hus, hinks ha whn millions of dollars of invsmns ar bing pourd ino -businss sysm projcs in mos largr companis, i is naural for IT managrs o fac h challngs of quanifying h valu of -businss invsmns. I s a piy ha, up o now, hr is sill no mor good mhods o assss h valu of -commrc invsmns. * W ar graful for suppor from MOE Program for Promoing Acadmic Exclln of Univrsiis undr h gran numbr 9-H-FA08--4. 829
As w sudy -commrc and rlad opics in h financial fild, many liraurs ar srssd on h prformanc afr adoping -commrc, informaion chnology, and so on. Th vn sudy plays an imporan rol in h rlad liraur. I is an imporan mhodology in managmn rsarch ha nabls h assssmn of h valu crad by firm iniiaivs,.g. a firm s announcmn of is -commrc iniiaiv, basd on h rsponss of h capial mark o h announcmn (Subramani and Waldn, 200). Sinc h arly us of vn sudy mhod in h informaion sysm liraur (Sanos, Pffrs and Maur, 992), h us of his chniqu has rcnly surgd. Rsarchrs hav mployd i o invsiga h mark valu implicaions of IT invsmns (Im, Dow and Grovr, 200), -commrc iniiaivs (Subramani and Waldn, 200), craion of B2B -markplacs (Chn and Sims, 200), and -commrc sourcing (Agrawal, Kishor, and Rao, 2002). In h vn sudy, howvr, i s difficul o limina anohr facors impac on a firm s valu whn vn is happnd. Tha is, h fficin mark and clan daa ar askd in vn sudy (Subramani and Waldn, 200). Th sudis wih rgard o h subjc of valuaion and invsmn dcision in -commrc ar likly rar. Subramaniam and Shaw (2002) sudy wha is h valu of B2B -commrc o a buyr organizaion, how o masur his valu, and wha facors mos affc h ralizaion of h valu of B2B -commrc? Thy, howvr, ar no invsigaing hs issus undr mahmaical approachs. Th radiion DCF modl is asy o valu a firm wih -commrc and o mak a dcision of adoping -commrc. Bu h DCF mhod ignors h valu of iming and opraional flxibiliy (Dixi and Pindyck, 994 and Trigorgis, 996). Using h ral opions hory o accoun for h valu of fuur dvlopmn is now a sandard approach in financ among boh acadmics and praciionrs. Ral opions analysis is mor focusd on dscribing uncrainy and in paricular h managrial flxibiliy inhrid in many invsmns. Th ral opions approach was usd in h fild of naural rsourcs, vnur, and R&D invsmns. Rcnly, Billingon, Johnson, and Trianis (2003) hav xplaind som yps of opions in supply chain of high chnology. In addiion, Schwarz and Moon (2000) mploy ral opions hory and capial budging chniqus o h problm of valuing an Inrn company. Thy rpor ha h valu of an Inrn sock may b raional if growh ras in rvnus ar high nough. Tauds, Fursin, and Mild (2000) discuss h pracical advanags of ral opions approach for h slcion of a sofwar plaform. Th ral opion modl is usd for dciding whhr o coninu mploying SAP R/2 or o swich o SAP R/3. Bnaroch, and Kauffman (999, 2000) illusra h valu of applying ral opions analysis in h conx of a cas sudy involving h dploymn of poin-of-sal dbi srvics by h Yank 24 shard lcronic banking nwork of Nw England. d Jong, Ribbrs, and van dr Z (999) concrn h pracical applicabiliy of opion pricing in valuing IT invsmns and compard wih h NPV mhod. Kumar (997) uss ral opion valuaion o illusra h valu of improvd rsponsivnss (i.. flxibiliy) rsuling from IT invsmns. Th liraurs abov dmonsra h imporanc of ral opions analysis in IT or -commrc invsmn. Thy, howvr, don g crain soluion on h iming of h -commrc invsmn. Whn confrond wih h availabiliy of h invsmn of -commrc, h firm hav o choos no only if bu also whn o adop -commrc. Our modl ha invsigas a firm s valu and iming of adoping -commrc and g h closd form xprssion can hlp invsors o mak h opimal dcision whn confrond wih h invsmn of -commrc. By using ral opions modl, his sudy amps o find h impac of adoping -commrc on a firm s valu undr h assumpion of uncrainy in a 830
firm s oupu pric. Th papr is h firs sudy o build a horical drivaion o dc h impac of -commrc adopion on a company s valu and iming basd on h ral opions modl. Th srucur of h papr is as follows: Scion 2 xplains h assumpions and sablishs a modl abou a firm s valu of adoping -commrc undr h Cobb-Douglas producion funcion. In scion 3, his sudy uss h modl dvlopd in scion 2 o driv a closd form soluion for a firm s iming of adoping -commrc. Exnsion of h modl is invsigad in Scion 4. W sudy h impac of dprciaion of -commrc on a firm s valu and h iming of adoping -commrc. In scion 5, his sudy xplors h snsiiviy analysis of opimal -commrc invsmn, analyzs h simulaion rsuls and draws som infrncs by using numrical analysis. Scion 6 sums up his papr wih highlighs of imporan findings. 2. Firm s Valu of Adoping E-Commrc W assum a firm s valu, V(p ), is drmind by a sochasic oupu pric p. Th -commrc invsmn is irrvrsibl, which implis ha h firm s valu prior o h adopion of -commrc includs an opion o adop -commrc, whras h firm s valu afr adoping -commrc dos no. Th firm s valu n of h opion of adoping -commrc is calld h sand-alon valu and is dnod by V s (p ). Hnc, V ( p ) = Vs ( p ) + O( p ), whr O(p ) dnos h ndognously drmind valu of h opion o adoping -commrc. Th oupu pric p is assumd o follow h gomric Brownian moion: dp = α p d + σp dz, () for consansα < r, σ > 0. Z is a sandard Brownian moion and r dnos h riskfr ra of inrs. A firm s insananous profi funcion is givn by: a p L K b w L F, (2) L whr L dnos h variabl producion inpu (i.. labor), whras K is fixd (i.. capial). Th cos includs variabl and fixd cos ha is dnod by w L L and F rspcivly. Th cos pr uni of inpu in L is dnod by. Th oupu is drmind by a Cobb-Douglas w L producion funcion, L a K b. Th producion funcion displays dcrasing rurns o scal wih rspc o h inpu (i.. a, b < ). Thn, h profi flow whn h variabl inpu, L, is chosn opimally is givn by: a b a a p a a a a w a p a = π ( ) L K F, b Π( w, a) p K F, (3) L whr = a dnos lasiciy (or powr) of h pric. Bcaus a <, i follows ha Π > 0 and >. Thrfor, h profis ar a convx incrasing funcion of h oupu pric, p. Th sand-alon valu of h firm, V s, can b sn as h discound valu of all fuur profis, and Dixi and Pindyck (994) show ha h sand-alon valu of h firm is givn by: 83
b Π p K F F Vs ( p ) = ψp, (4) r g( ) r r 2 whr g ( ) = ( r δ ) + 2 σ ( ). For all his o mak conomic sns w nd o assum r > g( ). W can rcogniz h xprssion for r g( ) as jus h ngaiv of our fundamnal quadraic valuad a. Thrfor by rquiring ha r > g( ), w ar rquiring Q ( ) < 0. Thn mus li bwn h wo roos of h quadraic, spcifically < β. By aking accoun of producion funcion of adoping -commrc, h Cobb-Douglas producion funcion (Goo and Suzuki, 989) can b xpandd as: h a~ ~ b c ( L, E) = L( E) K E, (5) whr E dno -commrc invsmn and E > 0 undr h siuaion of adoping -commrc. W assum h ffc of adoping -commrc will spillovr o h producion dparmn, so h producion lasiciy, a and b, will bcom a ~ and b ~ rspcivly. Sinc d h -commrc will also affc labor inpu, w assum L ( E) = L / E. I is naural o assum ha a ~ ~ a and b b bcaus adoping -commrc usually incrass sals by Inrn. On would probably xpc adoping -commrc o lad o a dcras in uni coss, bu w don impos h rsricions on d, which has o biggr han 0. This is bcaus h labor inpu will incras o suppor -commrc adopion in h bginning. As im gos on, h labor inpu will b savd whn h fficincy of -commrc dvlopd. In addiion, h influnc of -commrc on producion funcion dpnds upon paramr c. W assum 0 c <, and quaion (5) convrgs o original Cobb-Douglas producion funcion whn c and d is zro. d Variabl cos funcion of adoping -commrc is c ( L, E) = wll / E. Similarly, h profi flow, π ( p ), of adoping -commrc whn h variabl inpu is chosn opimally is hn givn by: ~ b ~ π ( p ) = Π( w, a~ ) p K E F, (6) L a~ a~ a a whr w a L a~ ~ ~ ) Π (, = a a w ~ L, ~ a~ ( a~ ) d + c = a ~, and = a~ sam mhod w can driv h firm s valu of adoping -commrc blow:. By using h Proposiion : Assuming ha invsors ar risk nural and ha hr xiss a risk fr ass yilding a consan inrs ra, r, a which invsors may borrow or lnd frly, hn h valu of a firm o adop -commrc is givn by: F V ( p ) = ψ p ~ E. (7) r From h quaion (7), w can find ha h firm valu is affcd by h -commrc invsmn hrough h paramr. Th following diffrnial rsuls mak i asir o undrsand: β is posiiv roo of quadraic quaion and on can s Dixi and Pindyck, 994 for furhr dails. 832
V ( p) ~ = ψp E. (8) E Th rsul is posiiv if > 0. This implis ha h adopion of -commrc dos no always nhanc firm s valu. Th firm s valu may dcrass spcially whn labor inpus incras and fficincy of -commrc dosn b dvlopd in h iniial sag. Th bnfi of -commrc is h diffrnc of valu bfor and afr -commrc adopion: V ~ ( p ) V ( p ) = ψ p E ψ p. (9) I is inrsing o considr h spcial cas whr h producion lasiciy don chang afr adoping -commrc, and hnc a ~ ~ = a and b = b. In his cas h rsul of bnfi is showd mor simply by: b Π p K ( E ) V ( p ) V ( p ) = = ψ p ( E ). (0) r g( ) From h spcial cas abov, on can raliz h characr of bnfi from adoping -commrc mor asily. Th bnfi from adoping -commrc is posiiv if > 0 or consqunly if a ~ ( a~ ) d + c > 0. Sinc h bnfi from adoping -commrc is a convx incrasing funcion of h oupu pric, p, i is procyclical: i riss a an incrasing ra in conomic booms and falls in conomic buss. In considring -commrc invsmn, a firm maks a radoff bwn h sochasic bnfi and h cos of adoping -commrc. As a firm has h opion bu no h obligaion o adop -commrc, on will do so only whn i is in on s inrs. This implis ha h bnfi from adoping -commrc has call opion characrisics, which is discussd in h nx scion. 3. Th Timing of Adoping E-Commrc Whn h valu of h opion which dpnds on h oupu pric is larg nough, h opion will b xrcisd. Tha is, h firm s dcision o adop -commrc is coningn upon h oupu pric. Th firm s valu wihou adoping -commrc, V(p ), quals h sum of h sand-alon valu plus h valu of h opion o adop -commrc. Thus, F V ( p ) = ψ p + O( p ). () r Th opion valu of -commrc invsmn is dnod as follow: O( p ) = max[ V ( p ) V ( p ) E,0], (2) s Th opion valu is worh o invs in h -commrc only if h firm s valu wih -commrc is grar han ha wihou -commrc. W follow h sps of coningn claims valuaion (Dixi and Pindyck, 994 and McDonald and Sigl 986), and h opion, O(p), o invs in h -commrc mus saisfy h following diffrnial quaion: 2 2 '' ' 2 σ p O ( p) + µ po ( p) ro = 0, (3) subjc o h boundary condiions: O( p) = V ( p) V ( p) E, s ' ' ' O ( p) = V ( p) Vs ( p), O(0) = 0. (4) Th firs quaion is h valu-maching condiion and i mans ha h valu of h opion mus qual h n valu obaind by xrcising i. Th scond quaion is h smooh-pasing 833
condiion and ha is, h graphs of O(p) and V (p) - V(p) E should m angnially a p. Essnially, his condiion nsurs ha p is h riggr ha maximizs h valu of h opion. Th opion valu of -commrc invsmn is gaind in closd form xprssion blow: Proposiion 2: Adoping -commrc aks plac h firs whn h sa variabl p his h hrshold 2 p from blow. Th valu of firm s opion o adop -commrc is givn by: ~ ( ψ p E ψp E) p O( p, p) = for p p. (5) p Th opimal hrshold, p, of adop -commrc is h soluion whr β β V ( p) β E ~ + ~ =. (6) β V ( p) β V ( p) In ordr o find som characrs of adoping -commrc, i is ncssary o considr h spcial cas whr h producion lasiciy don chang afr adoping -commrc, and hnc a ~ ~ = a and b = b. In his cas w g h firm s opion valu in closd form xprssion blow: Proposiion 3: Adoping -commrc aks plac h firs whn h sa variabl p his h hrshold p from blow. In h Spcial Cas, i.. a ~ = a and ~ b = b, h valu of firm s opion o adop -commrc is givn by: ( ψp ( E E) β p O( p, p) = ) for p p. (7) p Th opimal hrshold, p, of adop -commrc is givn by: βe p =, (8) ( β ) ψ ( E ) Th opimal sragy is o bgin adoping -commrc h firs momn ha p() quals or xcds h riggr valu p, as dfind in quaion (8). Tha is, h opimal iming o adop -commrc, T E, can b wrin as: β E T E = inf 0 : p( ). ( β ) ψ ( E ) Undr h dynamic siuaion ha oupu pric is sochasic, h highr h pric h highr a firm profi is. Th p is h opimal hrshold o adoping -commrc. In ohr words, whn h oupu pric rachs h hrshold p from lowr pric, i s h opimal iming o adop -commrc. Bsids, w furhr xprss h pric hrshold quivalnly in rms of a valu hrshold, β 2 Sinc h facor β xcds uniy h pric hrshold xcds h Marshallian brak-vn hrshold. Th firm s n prsn valu is hrfor sricly posiiv. On can s Dixi and Pindyck, 994 for furhr dails. 834
+ βe V ( p) =. (9) ( β )( E ) I mans ha i s no h iming o adop -commrc unlss h firm s valu has rachd h hrshold from h lowr firm valu. Th comparaiv saic wih rspc o h mrgr hrshold is vry much in lin wih h prdicions of ral opions hory. Namly, incrasing uncrainy (σ ) will lowr β and hrfor incras h (hysrsis) facor β /( β ) and hnc h hrshold, p. Consqunly, highr volailiy dlays invsmn, a wll-known rsul from h ral opions liraur (Dixi and Pindyck, 994 and Trigorgis, 996). In addiion, incrasing volailiy also raiss h growh ra, g ( ), which in is urn spds up invsmn. Th ohr ffc rsuls from h convxiy of profi in h oupu pric and has bn rmd h Jnsn s Inqualiy ffc on invsmn. For conomically maningful paramrs, h formr ffc usually dominas. An incras in volailiy hrfor dlays mrgrs. Th largr -commrc coss usually dlay h iming o adop -commrc. Diffrnial hrshold, p, by -commrc invsmn, w can mor undrsand h ffc of -commrc: p E = β ( β )( E ) ψ E ( ) E ( E) is posiiv if > 0 and E ( ) >. Bcaus = ( a( a) d + c) /( a), h ffc of -commrc invsmn on hrshold, p, dpnds on lasiciy paramrs of -commrc, c and d. Whn d is ngaiv and c is small, h ffc of -commrc invsmn on p is ngaiv. This siuaion usually happnd in h iniial sag of adoping -commrc. In h mos im, h ffc of -commrc invsmn on p is posiiv. I mans ha h highr invsmn of -commrc will dlay h iming of adoping -commrc. 4. Dprciaion Effc of E-Commrc W hav assumd hus far ha h invsmn of -commrc lass forvr. In raliy, physical dcay or chnological obsolscnc limis h dvlopmn of -commrc. Capial hrby dprcias hrough ag, or us, or advanc of comping chnologis. On would xpc ha opporuniy invs in a dprciaing projc of -commrc would b lss valuabl. W assum h form of dprciaion according o h modl of Dixi and Pindyck (994). Exponnial dcay a any im T, if h projc of -commrc has lasd ha long, hr is probabiliy λdt ha i will di during h nx shor inrval of im dt. Now, from h iniial prspciv, h probabiliy ha h projc dis bfor T, or h cumulaiv probabiliy disribuion funcion of h random lifim T, is λt. Th corrsponding probabiliy dnsiy funcion of T is λ λt. Th bnfi of -commrc on cash flow can b dnod by π ( p ) π ( p ). If h projc of -commrc lass T yars, h xpcd prsn valu of is profi flows is T ' µ E [ π ( p ) π ( p )] d 0 835
Π p = K b ( E )( r g( ) [ r g( )] T ). (20) By us h probabiliy dnsiy of h lifim for a Poisson procss, w can obain h xpcd valu of a firm wih dprciabl -commrc ( p) : b [ r T Π p K ( E )( V ( p) = λ λ λ 0 r g( ) V λ g( )] T ) dt + V ( p) b Π p K ( E ) = + Vs ( P) λ + r g( ) F ψ λ p ( E ) + ψ p, (2) r ΠK whr ψ λ = b λ+ r g( ). Th firm s valu wih dprciabl -commrc compard wih ha in quaion (7), h discoun ra of firm valu is incrasd by λ. Tha is, h rsul of quaion (7) is h cas of λ = 0. By using h sam mhod, w can g h opimal iming of adoping -commrc undr h cas of dprciaion: Proposiion 4: Adoping -commrc aks plac h firs whn h sa variabl p his h hrshold p λ from blow. In h Spcial Cas, i.. a ~ ~ = a and b = b, h valu of firm s opion o adop -commrc undr h cas of dprciaion is givn by: Th opimal hrshold, ( p ( E E) λ ψ λ λ, p ) = ) pλ β p O( p for p pλ. (22) p, of adop -commrc undr h cas of dprciaion is givn by: λ βe λ ( β ) ψ λ ( ) p =. (23) E Th hrshold wih dprciabl cas abov is similar wih ha in quaion (8). 5. Numrical Rsuls Alhough w driv h closd form soluions of firm valu and hrshold of adoping -commrc, snsiiviy analysis maks i asy o undrsand h infrnc of paramr o firm valu and hrshold undr complica calculaions. In his scion w prform som snsiiviy analysis o xploir h impac of paramr o a firm valu and hrsholds of adoping -commrc. W s paramrs as following: r = 0.05, rurn shorfall δ = 0.045, σ = 0., a = 0.4, b = 0.55, c = 0.003, d = 0.00, w = 300, F = 5000, K = 000000, and currn oupu pric p = 0. Among sings of paramrs, h sing valu of c and d ar much small han valu of a and b. This is bcaus a and b ar lasiciy paramr of labor and capial rspcivly and labor and capial ar ssnial facors of a firm. On h conrary, c and d ar rlad lasiciy paramrs of -commrc, and -commrc isn ssnial facors of a firm alhough i bcoms mor and mor imporan for a company. W hus s h valu of a and b ar much s 836
largr han valu of c and d. On of cours may s h valu of c and d largr spcially whn fficincy of -commrc has dvlopd. Tha h ffcs of -commrc invsmns on hrsholds ar prsnd in figur. W can find h incrasing -commrc invsmns (E) incras h hrshold and Pric hrshold 30 25 20 5 0 5 0 λ= 0 λ= 0.0 λ= 0.03 5 0 5 20 25 30 E-commrc invsmn (0 housand) Figur Th ffc of -commrc invsmn on hrshold dlay h iming of adoping -commrc undr boh siuaions, considring ( λ 0 ) and no considring ( λ = 0 ) dprciaion. For gnral cas ( λ = 0 ), if -commrc invsmn is 50 housand dollars, i s hrshold o adop -commrc is 7.32. I hus mans ha now is h opimal iming o adop -commrc undr h currn pric, 0. If h fficincy of -commrc is no affcd by h siz of -commrc invsmn, i isn suiabl o adop -commrc immdialy unlss h -commrc invsmn is undr 68 housand dollars (hrshold is 0.02) for dprciabl cas wih λ = 0. 0 and h -commrc invsmn is undr abou 45 housand dollars (hrshold is 9.94) for dprciabl cas wih λ = 0. 03 rspcivly. Tha h ffcs of -commrc invsmns on firm s valu ar prsnd in figur 2. W can find h incrasing -commrc invsmn incras a firm s valu slowly undr boh gnral ( λ = 0 ) and dprciaion siuaions. Bsids, dprciaion lowrs a firm s valu sriously and dcrass a firm s valu as λ incrasing. Firm valu (0 housand) 30 305 300 295 290 λ= 0 λ= 0.0 λ= 0.03 5 0 5 20 25 30 E-commrc invsmn (0 housand) Figur 2 Th ffc of -commrc invsmn on a firm's valu W can find h ffcs of pric uncrainy (σ ) on hrshold in figur 3. Th plo illusras ha incrasing pric uncrainy will incras h hrshold and dlay h iming of adoping -commrc spcially for dprciabl cas wih λ = 0. 03. Th pric hrshold will incras rapidly whn σ bcoms biggr. In h cas of λ = 0, h adoping hrshold, for insanc, is 837
9.28 whn σ = 0. 05 and h hrshold is 3.77 whnσ = 0. 2. This is consisn wih h rsuls of ral opion horm (Dixi and Pindyck, 994; McDonald and Sigl, 986). Pric hrshold 40 30 20 0 λ= 0 λ= 0.0 λ= 0.03 0 0.0 0.05 0.09 0.3 0.7 0.2 0.25 σ Figur 3 Th ffc of σ on hrsholds of adoping -commrc Figur 4 plos h join ffc of -commrc lasiciy c and d on h hrsholds. Th lasiciy c dnos h fficincy of -commrc in h producion oupu and d dnos h fficincy of -commrc in labor inpu. Th largr h lasiciy c, h fficin h -commrc is, and hrfor h hrshold is ging lowr whn lasiciy d is givn. Bu, whn c is larg nough (.g. c = 0.005), a firm can adop -commrc immdialy in h rang of 0.003 < d < 0.003. This is bcaus adoping hrshold is smallr han currn pric, 0 in h rang of 0.003 < d < 0.003. Bsids, h small h lasiciy d, h highr h hrshold of adoping -commrc is spcially whn d is ngaiv and c is small (i.. c = 0.00). Pric hrshold 50 c = 0.00 40 c = 0.003 c = 0.005 30 20 0 0-0.003-0.002-0.00 0 0.00 0.002 0.003 d Figur 4 Th ffc of -commrc lasiciy c and d on hrsholds 6. Conclusions This papr applis a ral opions approach o analyz h impac of adoping -commrc on a firm s valu and iming whn h oupu pric is uncrain. By using a ral opion approach, his papr shds som ligh on no only if bu also whn for a firm o adop -commrc. Undr h condiion of Cobb-Douglas producion funcion, w driv a closd form soluion for a firm s valu and h iming whn -commrc is adopd. By using numrical analysis o xplor h snsiiv analysis of opimal -commrc invsmn, h rsuls of simulaion ar as follows: () Th largr h -commrc invsmn, h highr h hrshold of adoping -commrc, and h grar a firm valu is. (2) W find ha incrasing pric volailiy will incras h hrshold, dlay h iming of adoping -commrc. This is consisn wih h rsuls of ral opion horm. (3) Dprciaion of -commrc will mak a firm s valu lss valuabl, incras h hrshold, and dlay h iming of adoping -commrc. 838
Rfrncs Agrawal, M., Kishor, R., and Rao, H. R. "E-Commrc Sourcing: Examinaion of Mark Racions and an Evn Sudy Analysis," SUNY Buffallo Working Papr, 2002. Bnaroch, M., and Kauffman, R. Jusifying Elcronic Banking Nwork Expansion Using Ral Opions Analysis, MIS Quarrly (24:2), 2000, pp. 97-226. Bnaroch, M., and Kauffman, R. A Cas for Using Ral Opions Pricing Analysis o Evalua Informaion Tchnology Projc Invsmns, Informaion Sysms Rsarch (0:), 999, pp. 70-86. Billingon, C., Johnson, B., and Trianis, A. A Ral Opions Prspciv on Supply Chain Managmn in High Tchnology, Journal of Applid Corpora Financ (Winhr), 2003, pp. 32-43. Chn, A. H., and Sims, T. F. "B2B Emarkplac Announcmns and Sharholdr Walh," Economic and Financial Rviw, 200, pp. 2-22. Davrn, M.J. and Kauffman, R.J. Discovring Ponial and Ralizing Valu from Informaion Tchnology Invsmns, Journal of Managmn Informaion Sysms (6:4), 2000, pp. 2-43. d Jong, B., Ribbrs, P., and van dr Z, H. Opion Pricing for IT Valuaion: A Dad End, Th Elcronic Journal of Informaion Sysms Evaluaion (2:), 999. Dixi, A. K. and Pindyck, R. S. Invsmn Undr Uncrainy, Princon Univrsiy Prss, NJ, 994. Dos Sanos, B. L., Pffrs, K. G., and Maur, D. C., Th impac of informaion chnology invsmn announcmns on h mark valu of h firm, Informaion Sysms Rsarch (4:), 993, pp. -23. Goo, A. and Suzuki, K., R&D Capial, Ra of Rurn on R&D Invsmn and Spillovr of R&D in Japans Manufacuring Indusris, Th Rviw of Economics and Saisics (7:4), 989, pp. 555-564. Im, K. S., Dow, K. E., and Grovr, V. "Rsarch Rpor. A Rxaminaion of IT Invsmn and h Mark Valu of h Firm: An Evn Sudy Mhodology," Informaion Sysm Rsarch (2:), 200, pp. 03-7. Kumar, R. Undrsanding h Valu of Informaion Tchnology Enabld Rsponsivnss, Th Elcronic Journal of Informaion Sysms Evaluaion (:), 997. McDonald, R., and Sigl, D. Th Valu of Waiing o Invs, Th Quarrly Journal of Economics (0), 986, pp. 707-727. Schwarz, E. S., and Moon, M. Raional Pricing of Inrn Companis, Financial Analyss Journal (56:3), 2000, pp. 62-75. Shaw, M. J., E-Businss Managmn: A Primr, E-businss Managmn : Ingraion of Wb Tchnologis Wih Businss Modls, Boson Kluwr Acadmic Publishrs, 2003. Shim, J. K. Th Inrnaional Handbook of Elcronic Commrc, Chicago, Nw York AMACOM Books, 2000. Sims, T. F. B2B E-Commrc: Why h Nw Economy Livs, Souhws Economy (4), 200, pp.-5. Subramaniam, C. and Shaw, M. J. A Sudy of h Valu and Impac of B2B -Commrc: Th Cas of Wb-Basd Procurmn, Inrnaional Journal of Elcronic Commrc (6:4), 2002. Subramani, M., and Waldn, E. Th Impac of E-commrc Announcmns on h Mark Valu of Firms, Informaion Sysms Rsarch (2), 200, pp. 35-54. Tauds, A., Fursin, M., and Mild, A. Opion Analysis of Sofwar Plaform Dcisions: A Cas Sudy, MIS Quarrly (24:2), 2000, pp. 227-243. Trigorgis, L. Ral Opions, Th MIT Prss, 996. 839
Will, P. and Olson, M. H. Managing invsmn in informaion chnology: Mini cas xampls and implicaions, MIS Quarrly (3:), 989, pp. 3-7. 840