The Firm s Value and Timing of Adopting E-Commerce Using Real Options Analysis under Uncertainty *

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1 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 d @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-FA

2 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

3 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

4 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

5 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

6 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

7 + 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

8 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 = , 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

9 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 λ= 0 λ= 0.0 λ= 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 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 = 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) λ= 0 λ= 0.0 λ= 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 = Th pric hrshold will incras rapidly whn σ bcoms biggr. In h cas of λ = 0, h adoping hrshold, for insanc, is 837

10 9.28 whn σ = and h hrshold is 3.77 whnσ = This is consisn wih h rsuls of ral opion horm (Dixi and Pindyck, 994; McDonald and Sigl, 986). Pric hrshold λ= 0 λ= 0.0 λ= 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 < d < This is bcaus adoping hrshold is smallr han currn pric, 0 in h rang of < d < 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 = c = c = 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

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