MODI
GLI
ANI
-MI
LLERTHEORY
TheM&M Theorem, ort
heModi gli
ani
-Mil
lerTheorem, i
soneofthemost
i
mportanttheor
emsi ncorporat
ef i
nance.Thet heorem wasdevel
oped
byeconomistsFrancoModi gli
aniandMer tonMi l
lerin1958.Themain
i
deaoft heM&M t heoryisthatthecapi
talstr
uctureofacompanydoes
notaf
fectit
soverallval
ue.
Thefir
stv er
sionoft heM&M t heor
ywasf ul
lofl i
mit
ati
onsasi twas
devel
opedundert heassumpt i
onofper f
ectlyeffi
cientmarkets,inwhich
thecompaniesdonotpayt axes,whil
et herearenobankr uptcycosts
orasymmet r
ic infor
mat i
on. Subsequent ly, Mill
er and Modi gli
ani
devel
oped the second v er
sion oft hei
rt heor
y by including t
axes,
bankr
uptcycosts,andasymmet rici
nfor
mat ion.
TheM&M Theor
em i
nPer
fect
lyEf
fi
cientMar
ket
s
Thisist hef i
rstversi
onoft heM&M Theor em witht heassumptionof
perf
ectlyef fi
cientmar ket
s.The assumption i
mpl i
est hatcompanies
operat
ingi ntheworldofper f
ect
lyeff
ici
entmarketsdonotpayanyt axes,
the trading of secur i
ti
es is executed without any t r
ansacti
on
costs,
liquidati
onispossi bl
ebutt hereareno bankr uptcycosts,and
i
nformat i
oni sperf
ectl
ysy mmetri
cal.
Pr
oposi
ti
on1(
M&M I
):
Wher
e:
VU=Valueoft
heunl
everedfi
rm( f
inanci
ngonlyt
hroughequit
y)
VL=Valueoft
helev
eredfir
m( f
inancingthr
oughami xofdebtand
equi
ty)
Pr
oposi
ti
on2(
M&M I
):
, Wher
e:
rE=Costofl
everedequi
ty
ra=Costofunl
everedequi
ty
rD=Costofdebt
D/E=Debt-t
o-equi
tyrat
io
The second pr oposit
ion of the M&M Theor em states t
hat the
company’scostofequi tyi
s dir
ectly propor
ti
onalt othe company ’
s
l
ev er
age l
evel
.An i ncrease i
nl ever
age levelinduces hi
gherdefaul
t
probabi
l
ityt
oacompany .Ther
efore,i
nv est
orstendtodemandahi gher
costofequi
ty(r
eturn)tobecompensat edf ort
headditi
onalri
sk.
M&M Theor
em i
ntheReal
Wor
ld
Conversel
y,thesecondv er
sionoft heM&M Theorem wasdevel
opedto
bett
ersuitreal
-worl
dconditions.Theassumpt
ionsofthenewerversi
on
i
mpl ythatcompani espaytaxes;ther
earetr
ansacti
on,bankr
upt
cy,and
agencycosts;andinfor
mationisnotsymmetri
cal
.
Pr
oposi
ti
on1(
M&M I
I)
:
Wher
e:
t
c=Taxrat
e
D=Debt
Thef i
rstpropositi
onstatest hatt axshieldst hatresultfrom thet ax-
deducti
blei nter
estpayment smaket hev alueofal ever
ed company
hi
ghert hant hev alueofanunl ev er
edcompany .Themai nrati
onal e
behi
ndt het heorem isthattax-deductibl
ei nter
estpay ment sposit
ively
aff
ectacompany ’
scashf l
ows.Si nceacompany ’
sv alueisdetermined
asthepr esentv alueofthef uturecashf l
ows,t hev alueofal evered
companyi ncreases.
GLI
ANI
-MI
LLERTHEORY
TheM&M Theorem, ort
heModi gli
ani
-Mil
lerTheorem, i
soneofthemost
i
mportanttheor
emsi ncorporat
ef i
nance.Thet heorem wasdevel
oped
byeconomistsFrancoModi gli
aniandMer tonMi l
lerin1958.Themain
i
deaoft heM&M t heoryisthatthecapi
talstr
uctureofacompanydoes
notaf
fectit
soverallval
ue.
Thefir
stv er
sionoft heM&M t heor
ywasf ul
lofl i
mit
ati
onsasi twas
devel
opedundert heassumpt i
onofper f
ectlyeffi
cientmarkets,inwhich
thecompaniesdonotpayt axes,whil
et herearenobankr uptcycosts
orasymmet r
ic infor
mat i
on. Subsequent ly, Mill
er and Modi gli
ani
devel
oped the second v er
sion oft hei
rt heor
y by including t
axes,
bankr
uptcycosts,andasymmet rici
nfor
mat ion.
TheM&M Theor
em i
nPer
fect
lyEf
fi
cientMar
ket
s
Thisist hef i
rstversi
onoft heM&M Theor em witht heassumptionof
perf
ectlyef fi
cientmar ket
s.The assumption i
mpl i
est hatcompanies
operat
ingi ntheworldofper f
ect
lyeff
ici
entmarketsdonotpayanyt axes,
the trading of secur i
ti
es is executed without any t r
ansacti
on
costs,
liquidati
onispossi bl
ebutt hereareno bankr uptcycosts,and
i
nformat i
oni sperf
ectl
ysy mmetri
cal.
Pr
oposi
ti
on1(
M&M I
):
Wher
e:
VU=Valueoft
heunl
everedfi
rm( f
inanci
ngonlyt
hroughequit
y)
VL=Valueoft
helev
eredfir
m( f
inancingthr
oughami xofdebtand
equi
ty)
Pr
oposi
ti
on2(
M&M I
):
, Wher
e:
rE=Costofl
everedequi
ty
ra=Costofunl
everedequi
ty
rD=Costofdebt
D/E=Debt-t
o-equi
tyrat
io
The second pr oposit
ion of the M&M Theor em states t
hat the
company’scostofequi tyi
s dir
ectly propor
ti
onalt othe company ’
s
l
ev er
age l
evel
.An i ncrease i
nl ever
age levelinduces hi
gherdefaul
t
probabi
l
ityt
oacompany .Ther
efore,i
nv est
orstendtodemandahi gher
costofequi
ty(r
eturn)tobecompensat edf ort
headditi
onalri
sk.
M&M Theor
em i
ntheReal
Wor
ld
Conversel
y,thesecondv er
sionoft heM&M Theorem wasdevel
opedto
bett
ersuitreal
-worl
dconditions.Theassumpt
ionsofthenewerversi
on
i
mpl ythatcompani espaytaxes;ther
earetr
ansacti
on,bankr
upt
cy,and
agencycosts;andinfor
mationisnotsymmetri
cal
.
Pr
oposi
ti
on1(
M&M I
I)
:
Wher
e:
t
c=Taxrat
e
D=Debt
Thef i
rstpropositi
onstatest hatt axshieldst hatresultfrom thet ax-
deducti
blei nter
estpayment smaket hev alueofal ever
ed company
hi
ghert hant hev alueofanunl ev er
edcompany .Themai nrati
onal e
behi
ndt het heorem isthattax-deductibl
ei nter
estpay ment sposit
ively
aff
ectacompany ’
scashf l
ows.Si nceacompany ’
sv alueisdetermined
asthepr esentv alueofthef uturecashf l
ows,t hev alueofal evered
companyi ncreases.
