2 002 , V ol. 13, N o.2 p p . 45～53
K alm an F ilt e r E s t im at ion o f a Com p an y 's In t an g ib le A s s e t s
K ih o Je on g1)・Chunky ung Le e2 )
A b s tra c t
A com pan y ' s m ark et v alu e - added , w hich equ als th e ex ces s of a com p any ' s m ark et capit alizat ion ov er it s b ook v alu e, is u s ed a s on e of t h e m ea su r es for int an gible a s set s v alu at ion in accoun t in g lit eratu r e. On e pr ob lem w it h t h e appr oa ch is th at t h e v alu ation r esu lt s ar e affect ed by sev ere flu ct u ation s in capit al m ark et s . In th is p aper , w e pr op os e an approach u sin g th e K alm an filt er for in t an gible a s set s v alu at ion . W e apply th is m et h od t o dat a of K or ean elect ronic com p anies .
K e y w o rd s : In t an g ible A s s et s , K alm an F ilt er , V alu at ion
1 . In tro du c ti on
A s in t an gible a s s et s h av e b ecom e m or e im p ort ant sour ces of v alu e - added in th is era of kn ow ledg e econ om y , sev er al v alu at ion m et h od s h av e b een dev elop ed . A m on g t h em , th e m ark et capit alization (M C ) m et h od , t h e r et urn on a s set s (ROA ) m et h od an d t h e dir ect int ellect u al capit al (DIC ) m eth od ar e com m on ex am ples . S ee W esph al ' s in t ern et sit e 3 ) for m or e dis cu s sion .
T h e M C m eth od b a sically a s su m es th at a com pany ' s m ark et v alu e - added (M VA ), t h e differ en ce b et w een it s m ark et v alu e an d b ook v alu e, is it s in t ellect u al capit al. T h e appr oach is in t uitiv e an d sim ple t o calculat e an d apply , but it is subj ect t o sev er e v olat ilit y du e t o flu ct u at ion s in capit al m ark et s . T h e ROA m et h od a s sum es t h at t h e ex ces s of a com p any ' s ROA ov er it s in du st ry av er ag e r eflect s it s ex ce s s in t an g ible a s set s . T h is m et h od is also int uitiv e an d ea sy t o apply , bu t it can on ly m ea su r e a com pan y ' s ex ces s int an gible a s set s ov er it s 1. A s s ociat e Pr ofes s or , School of Econom ics and T r ade, Kyungpook National Univ er sit y ,
T aegu , 702- 701, Kor ea, Em ail : khj eon g @knu .ac .kr .
2. Junior Officer , Cr edit Car d Risk M anagem ent T eam , Kor ea F ir st Bank, Gongpyung - Dong , J ongr o- Gu , Seoul, Kor ea
3. http :/ / w w w .icas it .or g/ km/ art icles .htm
in du st ry av er ag e , n ot t h e lev el of in t an g ible a s set s . T h e DIC m et h od is b a s ed on ident ify in g v ariou s com pon en t s of a com pan y ' s int an gible a s s et s an d t h en dir ect ly ev alu at in g ea ch com pon en t . It is com plex an d ex p en siv e t o im plem ent b ecau s e a lar g e n um b er of com p on ent s h av e t o b e ident ified an d in div idu ally m ea su r ed.
A ddit ion ally , it r equ ir es in side in form at ion on t arg et firm s for calcu lation .
A st at e space m odel, a g en er alizat ion of lat en t v ariable m odels t o a dy n am ic fr am ew ork , is th e only on e t o allow st atist ical in fer en ce on t im e series m odels w it h un ob s erv ed st at e v ariables . S in ce H arv ey (1981) in tr odu ced th e K alm an (1960) filt er t o econ om ist s a s t h e est im at ion t ool of st at e sp ace m odels , th e st at e space m odel an d th e K alm an filt er h av e foun d a w ide r an g e of applicat ion s in econ om et rics . F or ex am ple, th e K alm an filt er is u sed b y En gle an d W at s on (1981) for w ag e r at es , A n t on cic (1986 ) for ex an t e r eal in t er est r at es 4), Bu rm eist er an d W all (1982) an d Bu rn eist er , W all, an d H am ilt on (1986 ) for ex pect ed in flat ion , Kim an d N els on (1989 ) for a t im e - v ary in g m on et ary r eact ion of th e F eder al Re serv e, E n g el an d Kim (1999 ) for lon g - run r eal ex ch an g e r at e, an d Lu ginbu hl an d V os (1999 ) for GDP . F or m or e surv ey s , r efer t o En gle an d W at son (1987 ), H arv ey (1981,1989), T an izaki (1996 ), an d Kim an d N els on (1999 ), t h e la st b ein g a p articu larly ex cellen t s ou r ce of cla s sical an d Gib b s - sam plin g approach es for st at e - space m odels w ith M ark ov sw it chin g .
T h is pap er pr op os es an appr oach u sin g a st at e sp ace m odel an d th e K alm an filt er for in t an g ible a s set s v alu at ion t h at ov er com es th e w eakn es ses of th e v alu at ion m eth od s st at ed ab ov e. Ou r m odel follow s t h e lin e of t h e M C m eth od . H ow ev er , in st ead of dir ect ly estim atin g a com pan y ' s M V A for int an g ib le a s s et s v alu at ion , th e m odel s epar at es M V A in t o a perm an ent an d a t ran sit ory com p on ent an d ident ifies t h e com pon en t s in div idu ally u sin g th e K alm an filt er . Becau se capit al m ark et flu ct u at ion effect s ar e filt er ed ou t in t h e p erm an en t com pon en t , t h e latt er w ill allow m ore st able v alu ation s of int an g ib le a s set s . Be sides , lik e t h e M C m et h od , ou r appr oa ch is in t uitiv e an d sim ple t o calcu lat e an d apply . W e apply our m et h od t o dat a of K or ean elect r on ic com p anies . W e fin d t h at ou r appr oa ch r esu lt s in r eliab le v alu ation s of in t an g ible a s s et s .
In t h e n ex t sect ion , w e briefly des crib e t h e st at e space m odel for int an gible a s set s v alu ation . In S ect ion 3, w e dem on st rat e t h e appr oa ch by apply in g it t o dat a of K or ean elect ronic com p anies .
2 . M o del
A com pan y ' s M V A (m ark et v alu e - added ), qt, is a s su m ed t o con sist of a p erm an en t com pon en t , yt, an d a t r an sit ory com pon en t , xt :
4. An ex ant e r eal int er est r at e equals nominal int er est r at es minus an expect ed inflation r at e.
qt = yt + xt.
F or th e t w o com pon ent s , w e con sider t hr ee m odels :
M odel 1: {yxtt == tty t - 1+ t
M odel 2: {yxtt == t1ty t - 1+ 2 ty t - 2 + t M odel 3 : {yxtt == ttxy t - 1t - 1++ tt
in w hich t h e n oise t erm s , t an d t, follow t h e proces s
( )tt ~ i . i . d . N (( )00 , (02 02 )).
M odel 1 a s sum es A R (1) for a perm an en t com p on ent an d w h it e n oise pr oces s for a t r an sit ory com pon ent . M odel 2 a s sum es A R (2) an d w hit e n oise, re spectiv ely . M odel 3 a s sum es A R (1) for b ot h com p on ent s .
A st at e space m odel con sist s of t w o set of equ at ion s : m ea sur em en t equ at ion s , w h ich describ e h ow th e ob serv at ion s ar e r elat ed t o th e st at e v ariab les an d t r an sit ion equ at ion s , w hich describ e t h e ev olu t ion of t h e st at e v ariables . M odels 1, 2 an d 3 ar e sp ecified in t h e st at e sp ace form a s follow s :
M odel 1: {m ea s urem en t equat ion : qt = (1 0) (yyt - 1t )
+ t t ran s it ion equat ion : (yyt - 1t )
= (1 0t 0)(yy t - 1t - 2)
+ ( )01 t M odel 2: {m ea s urem en t equat ion : qt = (1 0) (yyt - 1t )
+ t t ran s it ion equat ion : (yyt - 1t )
= (11 t 02 t)(yy t - 1t - 2)
+ ( )01 t M odel 3 : {m ea s urem en t equat ion : qt = (1 1) ( )yxtt
t ran s it ion equat ion : ( )yxtt
= (0t 0t)(yx t - 1t - 1)
+ ( )0 11 0 ( )tt
.
In application , on e m odel w ill b e s elect ed for each com pany b a s ed on t h e log lik elih ood ratio.
3 . E s tim ation
T h e m odel describ ed in S ect ion 2 is applied t o y early dat a of K or ean elect r on ic com pan ie s . Com pan ie s th at h av e b een list ed on t h e S eou l S t ock Ex ch an g e for 10 or m or e y ear s w er e s elect ed for application . T h e n um b er of select ed com p anies is fift een . E ach com pan y ' s dat a period is fr om t h e list ed y ear t o 1996. A com pan y ' s m ark et v alu e is defin ed a s th e st ock price t im es t h e n um b er of is su ed st ock s plu s debt . Book v alu e is defin ed a s t h e t ot al v alu e of a s set s list ed in t h e com p any ' s a ccou nt b ook . T h e st ock prices u sed in th e calcu lation w er e b a s ed on t h e closin g prices at s ett lin g day .
T able 1 pre sen t s th e r esu lt s of t h e e st im at ion s , w h er e t h e b est m odel is select ed b a sed on t h e log of lik elih ood . F or alm ost all com panies , M odel 1 is t h e b est m odel am on g t h e t hr ee. M odel 3 is t h e b est m odel for t w o com p anies 5 ).
T o dem on str at e th e re sult s of int an gible a s set s v alu at ion of t h e M C m et h od an d our appr oa ch , w e plot t ed b ot h v alu ation r esu lt s for t hr ee com pan ie s : D aew oo E lect r on ic s ; M ax on T elecom ; an d S am w h a E lect ric . F igu r es 1, 2 an d 3 sh ow t h e r esult s 6 ). In ea ch fig ur e, qt den ot es t h e M C m eth od ' s r esult s an d y t den ot es our r esult s . F or all t hr ee com pan ies , t h e e st im at ed v alu es of int an g ib le a s set s sh ow sm ooth er m ov em en t s in our appr oach th an in t h e M C m eth od . T h e s am e b eh av ior is ob s erv ed in t h e ot h er com p anies ' v alu ation s a s w ell.
F r om t h e r esult s st at ed ab ov e, a qu estion m ay b e r ais ed t h at ou r appr oach r eally sep ar at es t h e perm an ent com pon en t an d th e t r an sit ory com pon en t of t h e M V A . In oth er w or d s , does ou r appr oach r eally filt er ou t th e effect s of capit al m ark et flu ct u ation , n ot ju st sm oot h th e r esu lt of t h e M C m eth od ? U nfort un at ely , it is n ot pos sible t o g et a defin it iv e an sw er t o th is qu estion b ecau se w e do n ot h av e ob serv ation s of com pan ie s ' in t an gible a s set s v alu es t o com p ar e. H ow ev er , w e sh all pr esen t som e ev iden ce t h at ou r appr oach is , at lea st , plau sible. T o inv estig at e t h e qu est ion , w e set u p a r egr es sion m odel
Pt = o+ 1 T A t + 2 yt+ 3 ( qt - 1 - yt - 1) + et, (1)
w h er e Pt = Pt - Pt - 1= ch an g e in st ock price, T A t = ch an g e in t an g ible a s set s , yt = ch an g e in int an gible a s set s estim at ed by our approach an d
( qt - 1 - yt - 1) = th e differ en ce b et w een lag g ed v alu es of in t an g ible a s set s
e st im at ed by t h e M C m et h od an d our appr oach . If ou r appr oach r eally filt er s ou t 5. T he thr ee m odels show ed alm ost the s am e r esult s for int angible as s et s v aluation for all
analyzed companies .
6. T he r esult s for the r em aining companies ar e av ailable at ht tp :/ / bh .knu .ac.kr/ ~khj eong/ int angible.hw p
t h e effect s of capit al m ark et flu ctu at ion , t h en th e la st regr es s or of equ at ion (1) w ill m ea sur e ex ces s m ark et v alu at ion of int an gible a s set s in t im e t - 1, t h at is t h e b ubble, im ply in g th at t h e coefficien t 3 is n eg at iv e. T hu s , n eg ativ en es s of th e coefficient 3 in dir ect ly v alidat es ou r appr oach . T able 2 pr esent s t h e estim at ion r esult s of t h e r eg re s sion equ at ion (1). T h e t able report s ar e th e t v alu e of t h e coefficient 3 an d R2. W e n ot e t h at t h e coefficient 3 is st at istically sign ificant for eig ht com p anies out of fift een an d is est im at ed t o b e n eg at iv e for alm ost all ex cept t w o. T h is in directly v alidat es our appr oach a s a w ort hy v alu at ion pr oce s s of int an gible a s set s .
4 . Co n c lu s io n s
W e h av e in t rodu ced a n ew v alu at ion appr oach for a com pan y ' s int an gible a s set s . Our appr oach is b a sed on a st at e space m odel an d t h e K alm an filt er , in w hich a com pan y ' s m ark et v alu e - added (M VA ) is sp ecified t o con sist of a perm an ent an d a tr an sit ory com p on ent . T h e fir st com pon ent , iden tified u sin g t h e K alm an filt er , is em ploy ed a s th e est im at ed v alu e of int an g ib le a s set s .
Com p ar ed w it h ex ist in g m eth od s , our appr oach h a s st r en g t h s in t h at it requ ir es only inform at ion r eadily av ailable, t h e v alu at ion pr ocedur e is int uitiv e an d th e effect s of capit al m ark et flu ct u ation s ar e sm ooth . T o in dir ect ly v alidat e ou r appr oach , w e est im at e a st ock price ch an g e r eg r es sion m odel, w h er e th e differ en ce b et w een t h e v alu e s of th e in t an g ible a s s et s est im at ed by th e M C m et h od an d our appr oach is on e of r egr es sor s . F or t h e r egr es sor , w e fin d t h at t h e coefficien t is sig nifican tly n eg at iv e , im ply in g th e plau sibility of our appr oach .
< F igu r e 1> Daew oo Elect r on ics ' Int an gible A s set s (un it : t h ou san d w on )
qt : a com p any ' s M VA (m ark et v alu e - added )
yt : a com p any ' s in t an g ible a s s et s est im at ed by ou r appr oa ch
< F ig ur e 2> M ax on T elecom ' s Int an gible A s set s (un it : t h ou san d w on )
qt : a com p any ' s M VA (m ark et v alu e - added )
yt : a com p any ' s in t an g ible a s s et s est im at ed by ou r appr oa ch
< F igu r e 3> S am w h a Elect ric ' s Int an gible A s set s (un it : t h ou san d w on )
qt : a com p any ' s M VA (m ark et v alu e - added )
yt : a com p any ' s in t an g ible a s s et s est im at ed by ou r appr oa ch
< T ab le 1> M odel S election Result s
Com p any Nu m b er of
Ob serv at ion s
S elect ed M odel
Log Lik elih ood Rat io
Daew oo Elect ronics 13 1 - 268.681
Daew oo T elecom 10 1 - 195.975
M ax on T elecom 13 1 - 231.437
S am sun g Elect r o- M ech anics 17 3 - 339.842
S am su n g S DI 17 1 - 344.910
S am su n g Electr onics 17 1 - 389.411
S am y oun g Elect r on ics 17 1 - 340.496
S am w h a Elect ric 11 1 - 190.426
S am w h a E lect r on ic s 10 1 - 171.738
S u nn y E lect r on ic s 10 1 - 169.273
LG Electr onics 17 1 - 369.725
Orion Electric 17 1 - 329.426
E z.com 10 1 - 167.345
KE C 17 3 - 309.185
Et r on ics 11 1 - 94.734
< T able 2> T est Re sult s of 3 in E qu at ion (1)
Com pan y t v alu e p v a l ue
degr ee of f r eedom
R2
Daew oo Elect r on ics - 2 . 116 0 . 032 9 . 875
Da ew oo T elecom - 1. 393 0 . 107 6 .483
M ax on T elecom - 0 . 4 15 0 . 346 9 . 63 1
S am su n g E lect r o- M ech an ics - 2 . 126 0 . 039 13 . 639
S am sun g S DI - 0 . 784 0 . 23 1 13 . 694
S am su n g Electr onics 0 . 116 0 . 545 13 . 984 S am y ou n g E lect r on ic s - 2 . 57 1 0 . 02 1 13 .42 1
S am w h a Elect ric - 5 . 77 0 . 00 1 7 . 983
S am w h a Electr onics - 14 . 998 0 . 000 6 . 996
S u nn y Electr onics - 2 . 364 0 . 028 6 . 963
LG Electr onics - 1. 856 0 . 056 13 . 883
Orion Electric - 0 . 559 0 . 298 13 .306
E z.com - 3 . 037 0 . 0 11 6 . 929
KE C - 1. 360 0 . 111 13 .357
E tr onics 1 . 632 0 . 93 1 7 .337
n ot e : R2 is coefficient of det erm in at ion .
R e f e re n c e s
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[ 2002년 5월 접수, 2002년 8월 채택]
