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Modigliani–Miller x43x5cx29x5cx20x41x25x25x27 MM x43x5cx20x4ex4fx70x9x47x37x3ax43x16x52x28x20x0
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? 3.1 Modigliani–Miller x43x5cx18x37x3ax43x16x52x28x29
? 3.2x27x53x77x78x2x79x20Modigliani–Miller x43x5cx29
? 3.3x27x53x48x2exex4ex20Modigliani–Miller x43x5cx29
3.1 1958x46x14x48 Modiglianix4Millerx5fx60x61x70x4cx5cx63x64x48x64x65xdx6e
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x4ax6x57x25xbx67xex33x3x78x13x27x62x3ex54x25xbx31x63x67x11xcx1Modigliani–Miller
x62x69(MMT)x48x51x6cx1x6ex66xax2x25x23x4fx4ex6bx62x61x40x41x78
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x77x77x6fx70x78x11x17x3ax3ex19x57x23x24x5dx33x6dx3cx61xdx3bx70x2bx62x4ax65x68x27x60x54x48
x25x67x23x24x53x76x1fx4ex1x28x5cx78x71x72x44x48 Modigliani–Millerx62x69x75x39x54x33x6d
x3cx61xdx4cx4cx2x1cx1dx62x4ax55xex78x58x25x70x55xex17x71x67x2Modiglianix4Miller
x54x65x63x54x6fx60x78x67x9x3fx70x48x62x3exdxex68x19x54x31x32x48x67x2x2a xdx50x27xfx4ax6
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xbxfx14x41x41x33 (x1ex6fx31x4dx9x9) x33x3x78x10x66x25x70x62x69x48x51x70x64xfx40x44x54
x70x55x1x2ax70x2bx71x72x54x4ex16x57x73x71x72x54x69x26x2x33x3x54x78
x49x25x70x51x2cx48x3ax3ex67x5dModigliani–Millerx62x69x2ex1x1cx1dx62x4ax55xex54
x15x28x6dx54x7x3bx27x4ex4fx65x63x78x22x23x49x62x63x44x48 Modigliani–Millerx62x69x17x71
x77x1ex37x62x4ax40x6fx62x69x4x68x3cx54x1cx1dx62x4ax55xex5x8x1a20x46x78
x1ax49x3ax3ex27x4ex1x68x4fx40x26x65x63x78x3ax3ex54x55x56x1cx7ax57x24xbx70x26x2x70
x2bx8x3ex55x56x48x4x51x17xbx4x50x27x78x2bx18x23x78x42x43x2cx44x58x54x3dx3ex1ex37x6fx50
x62xbx21x54x50x27x4ax6x2x28x29x2ax6cx48x58x10x3ex44x58x54x17xbx4ax6xex2x3cx62x54x48
x51x6cx50x27x4ax6x57x17xbx4ax6x75x76x54x3x4cx26x70x1cx1dx62x4ax65x68x27x44x62x78x26x66
x49x25x70x51x2cx48x3ax3ex47x48x54x10x44x2ex70x62x2x2cx68x6fx2cx68x14x25x54x4ax6x48x58x21
x2ex54x2x6ex66x54x4ax6x48x7bx7ex49x25x18x47x75x3bx70x2bx21x28x54x22x23x53x1ex27xcx73x10
x3ex78x25x70x53x1ex67x2x21x22xdx1ax3dx59 (cash flow)xfx78x1ax3dx59x6ax27x54x6ex7ax2x5d
59
x11x70x10x44x28x18x76x2ax5cx54x1ax3dx4ax6x78x1ax49x49x25x18xex2x5dx10x44x54x50x27x1ax3d
x4ax6x78x10x7bx17x66x3ax3exbx4bx21x70x54x50x62xbx21x54x50x27x4ax6x48x2x70x2bx28x29x2a
x6cx78x5ax67x2x70x48x28x29x2ax6cx1ax49x49x25x18x7fx2ex61x70x2bx19x2ex44x7bx10x54x53x1ex78x57
x24xbx70x26x48x26x31x2ex75x39xdx1ax3dx59xfx54x10x29x44x12x69x1ex10x49x25x18x54x6ex7ax78
x4dx70x69x4bx48x6fx51x54x55x56x2ex44x58x28x29x13x1ax7bx14x48x7bx7ex48x3ax3ex54x68x4fxe
x4cx23x4cx4cx61xdx1xdx1ax3dx59x28x29x2ax6cx7fx1fx4dx41x54x70x2bx1cx1dx72x76Cx24x58x17x44
x62x7ax54x1cx1dx62x4ax65x68p:C !Rx78 xfx10x18x48x3ax3ex5ax2ex70x62x61xdCx2cx51xdx33
x69x6ax1ax3dx59xfx48x4x7fx68 1 2 C. x17x47x75x61xdx18x48x3ax3ex53x22x23x2ex70x68x78x25
x18x48x3ax3ex7ex7fx61x62p(1) > 1. x3bx31x3ax3ex49x44x70x51x2cx21x5dx8x54x48 rf = 1=p(1)
x54x57x58x6ex7ax67x2x33x69x6ax3cx27x78xfx49x6fx51x2cx3ax3ex53x73x53x3bx44x49p(1),x58x2e
x3brf. x5ex66Hilbertx72x76x75x72x54x75x39x49x6fx51x2cxex2ex47x75x78
3.2 x3ax3ex79x65x63x33x68x67xex78x47x48x78x2bx49x17xbx51x10x26x54x6ax49x68nx3x58
x50x27x51x10x26x54x69x2x3x4fx1ex24x58x10x26x42x6x54x6ex66Ax4B. x3ax3ex54x5fx60x2x2a
x31x32x25x78x2bx6ex66x7ex47x2ex10x54x33x68x67xex48x33x34x10x3ex54x17xbx4ax6x2x35x4dx2e
x10x7ex1x7ex48xddA;dB 2Cx33x3fx1x10x3ex49x50x27x54x59x6ax54x33x68x6x78x10x3ex5bx2
xdx1ax3dx59x28x29x2ax6cxfx78 sA;sB 2 C x33x3fx1x10x3ex49x50x27x54x6ax73x4ax4bx78x10x3e
x5ax2xdx1ax3dx59x28x29x2ax6cxfx78x66x2x31x32x51x7dx49x50x27x1dx51Ax6fB x54x70x49x6a
x73x48x33x34x8x6ax73x49x50x27x54x4ax6x7x8x2dA + sA x6fdB + sB. x58Ax6fB x54
x6ax73x49x17xbx54x4ax4bxex7x2p(dA + sA)x4p(dB + sB). x26x66x33x68x67xex54x2e
x10x48x49x50x27x54x6ax49x68x4dx51x21x2ex10x78x3ax3exd ?nA x4 ?nB x33x3fx1x10x3ex49
x50x27x54x6ax49x2ax30x68x78x25x18x3ax3ex23x61xdx10x3ex5ax2x28x29x2ax6cx78xfx10x3ex51x43
x2xdx1ax3dx59x28x29x2ax6cxfx48x58x73x2x57xdx1ax3dx59x28x29x2ax6cxfx73x66x10x70x25x27x72
x76x54x28x29x2ax6cx78x3ax3ex54x31x63x31x56x2a
x36x3f 3.1 (Modigliani–Miller x36x3fx52x18) x7x20x61x74x64x75x39x3ax3bx3c
x75x76x44x45C x7fx60x61x75x76x62x63x64x65p. x57x58x76x77Ax71B x61x3x1bx73x25x5ex79
x78x62x79x7ax65n,x61x1ex1fx73x25x5ex79(x39x3a) x41x1cx6bx6c
(n+?nA)sA = (n+?nB)sB; (1)
x48x7bx73x14x49x7cx7dx7ex18x7fx79x25x5ex79x0x1x2x3x6x4x5x6bx6c
ndA ??nAsA = ndB ??nBsB; (2)
x5dx5eAx71B x61x3x1bx73x25x5ex79x79x6x63x7x6bx6c
p(dA +sA) = p(dB +sB): (3)
xdx27 x26(1)+(2)x4x68
n(dA +sA) = n(dB +sB):
60
x7bx7ex48 dA +sA = dB +sB. x39x58(3)x41x7dx78 2
x25x38x62x69x49x68x4fx44x73x47x3bx70xbx28x6dx54x4ex68x5x12x48x4x53x5dx50x27x54x2e
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x1fx27x69x1ex78 (1)x26x54x6ex7axfx7bx7cx48x17x78x14x67x2x6ex66x6ax49x42x6x54x62x7ax78x35
x1ex54x2(2)x26x48x1x37x34x10x79x41x42x78x2bx6ex66x51x7bx10x54x69x2x64x4fx1ex3fx8x78x2b
x71x44x48x9x26x54x78x14x23x3cx2ex6ex66x3fx2bx61x10x3ex54x35x33x68x24x19x54x69x2x4x21x51
x54x4fx1ex3fx8x24x13x54x40x4ax1ax3dx59x57x25xbx40x4ax53x3bx27x3fx2bx33x68x48x10x66x78x2bx6e
x66x27x70x48x4x33x3fx2ndA x4ndBx48x24x58x3fx2bx1bx17x6ax73x48x4x33x3fx2??nAsA
x4??nBsB (x67x4bx27x70x48x25x5bx2x5d?nA x4?nB x1x50x68x54x74x40x57x31x32x10
x3ex2x3bx68x48x7bx7x54x78x66x7x8x2x54x6ax68x19x54x18x38x3ex1ex54x7bx7ax6)x78x7bx7ex48
(2)x26x54x57x58x6ex7ax7x8x2x78x2bx6ex66x51x7bx10x54x69x2x64x4fx1ex3fx8x78x25x26x48x62
x693.1x70x68x54x2x2ax78x2bx6ex66x35x61x50x27(x2ex3cx62x54)x33x68x67xex4(x2ex3cx62x54)
x6ax4ax24x19x48x17x62x69x4bx7fx32x7bx10x78x31x63x2x78x2bx6ex66x17xbx54x6ax4ax2x7bx9x54x78
x25x67x2x52x53x54 Modigliani–Miller x62x69x54x70x2bx31x63x78x2ex1fx10x8x1ax49
Modigliani–Miller 1961x46x54x63x64[10]x2cx78x3ax3ex7x8x1fx79x19x25x18x10x62x69x54
x41x7dx51x2dx2ex38x3dx78x31x32x25xbx38x3dx57x1ax71x74x75x8x1x2ex4ex48x33x34x3ax3ex67x7
x8x49x1ax71x4cx5bx2cx76x4fx19x74x6ex66x54x33x68x67xex2x7bx17x28x79x54x78x7ax58x48x49x1a
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x3ex33x3fx27x65x63(1)x4(2)x2ex41x7dx54x6ax7bx78
(1) x71x72x44x79x41x42x33x68x67xex2ex13x14x6ex66x54x42x6x48x16x17x2x2ex13x14x6a
x4ax78x58x25x2x57x2bx71x2ex4ex54x78x25x2x7bx1x49x6ax42x44x48x7cx6ax51x2ex7ex7fx5dx68x78x66
x2x17x33x68x20x71x18x48x7dx3ex4dx24x1x25x2x3cx28x34x6ax48x58x42x53x7dx3ex1x3ex6ax4ax44
x8x48x24x5ex1x3ex6ex66x54x42x6x44x8x78x17x15x52x31x32x74x7ax2x1x3ex33x68x28x54x6ex66
x17xbx54x6ax4ax75x71x78x67x9x3fx70x48 (1)x54x41x7dx47x75x7cx6ax7ex7fx5dx68x48x4x2ex66x49
x21x22xdx7cx6ax2ex10xcxfx54x1ax44x78x49x3dx3ex57x58x4fx54x57x4fx65x63x2cx48x7cx6ax54x2ex3b
xfx5fx4ex1x69x63xex4cx78x58x25x18x2ex44x58x7cx6ax54x2ex3bx2x68x2ex19x4ex70x57x54x31x32
x54x78x7bx7ex48x75x17x4e(1)x67xcx2cx49x4ex70x57x54x69x63xex4cx2cx4ex4fx78x25x66x8x61x3a
x3ex54x51x7ax54x5ax1ax78
(2)x2ex41x7dx54x6ax7bx75x70x2x17x2cx36x51x47x48x2bx7dx21x68x23x5fx60x78x31x32x3ax3e
x47x48x33x68x21x68x54x23x27x57x1ex6fx54x21x21x68x54x23x27x51x21x2ex10x48x33x34x31x63x5ax67
x4dx51x2ax5cx78x25x2x49x3ax3ex54xex4cx2cx23x24x65x63x54x5fx60x78
x1ax49x61x62x21x51x4fx1ex31x4bx2fx10x26x54x23x27x48x33x68x21x68x23x27x1?d,x1ex6fx54
61
x21x21x68x23x27x1?c,x6cx10x3ex9xa
0 6 ?c < ?d < 1: (4)
x49x25x64x74x75x56x48x10x66x6ex66Ax54x70x49x6ax73x27x70x48x10x49x50x27x54x23xbx1ax3dx59
x28x29x2ax6cx1dA +sA;x58x17x23x13x1ax3dx59x28x29x2ax6cyA x53x9xax69x6a
yA = dA(1??d)+[sA ?p(yA)](1??c)+p(yA); (5)
x17x2cp(yA)x2Ax6ex66x54x17xbx6ax4a(x1fx79x3ax3exbx4bx20x19x54x3x66x33x69x6ax1ax3d
x59x57x7fx68x2ex0x48x3fx54x70x68x48x25x18 p(yA) x17x71x2x70x66x33x69x6axbx21)x78x10x66
B x5ax51x72xdx54x69x6ax78x66x2x3ax3ex7fx51x56x5cx62x69x2a
x36x3f 3.2 x61x62x93.1x79x7x20x21x6bx57x58x49x7cx47x5xax13x1d?d,x6x7xb
x12x47x5xax13x1d?c, x2x15x5axaxb (4), dA > dB (x15x16x2cx2ddA 6 DB x79x3dx13
x1dx23x6bx2e dA > dB x79x3dx13x3ex6ex23)x6bx1x2x18x19x1ax74x64x751 2 C,x7ex3x1bx63
x1c p(1) 6 1. x63x7x62 p x67x68x75x76x64x65x6bx6cx3 dA > dB x4, p(dA) > p(dB).
x5dx5eAx71B x61x3x1bx79x79x6x63x7p(yA)x71p(yB)xaxb
p(yA) < p(yB): (6)
x6cx1ex1fx49x7cxcxdx79x76x77x3x1bx79x79x63xcxex0
xdx27 x2bx71x44x48x26(5)x23x68
p(yA) = p(dA(1??d)+[sA ?p(yA)](1??c)+p(yA))
= p[(1??c)(dA +sA)?(?d ??c)dA]+?cp(yA)p(1);
x17x2cx3bx19p(p(yA)) = p(yA)p(1). x26x7ex23x1ex68
p(yA) = p[(1??c)(dA +sA)?(?d ??c)dA]1??
cp(1)
:
x10x69x48
p(yB) = p[(1??c)(dB +sB)?(?d ??c)dB]1??
cp(1)
:
x26x7ex23x68x48
p(yB)?p(yA) = (?d ??c)p(dA ?dB)1??
cp(1)
> 0:
2
x25x70x62x69x70x68x48x1x49x21x68x23x44xfx77x66x45x4x10x71x17xbx54x6ax4ax48x49p(1) 6
1x54x61xdx56(x25x70x61xdx74x7ax5ax14x42x3x1dx2ex3b)x48x33x68x7x8x4bx5fx4bx28x48x15x28
62
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x71xfx19x19x2x26x6ax42x21x69x0x14x54x48x10xdx15x7x8x66x66x4fx1x3dx3ex4fxcxdx5ax52x78
x2ex66x66x25x18x54xcxdxex4cx78xfx2x4x53x2ex47x48x25x70x7bx46x48x1cx7ax23x24x5fx1ax48x25
x10x26x57x71x72x2ex4ex78x51x7dx5dx10x1ex4dx1x48x30x16x19x8x48x21x51x6ex66x4bx2fx10x26x54
x23x27x25x70x61x62x57x71x72x2ex4ex78 Miller x4 Scholes x49x64x67 [8] x2cx10x33x68x57x23
x20x75x76x54x3x4cx4ex4fx61x22x23x54xcxdx78x62x3ex54x31x63x2x6ex66x4dx7ex47x64x64x12x2a
x53x68x33x68x2ex55x21x68x23x48x24x5ex71x72x44 ?d … ?c. x25x26x7fx53x1fx5ex57x71x72x2ex4e
x54x6ax4ax57x33x68x67xex33x3x54x31x63x78x25x70x68x55x56x1cx7ax51x2ex7ex6ex75x73x78x23x25
x15x16x6fx54x58x2x78x2bx74x69x4bx7ex7fx70x26x54x6ex66x2x2ex66x49x54x78x5x75x48x25x69x4b
x54xcxdxcxdx49x25x70xex6dx44x2x7fx7fx2ex63x54x78
3.3 x4dx70x38Modigliani–Millerx62x69x2x70x6ex66x54x4ax6x57x6ex66x54x1ex6fx31
x4dx33x3x78x70x71x74x75x56x48x20x19Modigliani–Millerx62x69x6fx4x60x48x5bx2x5dx25x70
x38x62x69x78x25x18x54x1ex6fx31x4dx2x5dx6ex66x54x69xbx57x6axbx75x76x54x77x45x78x49x62x3e
x54xcxdx24xbx48x4bx57x51x70xbx57x58x4fx59x0x1x48x7x8x66x49x70x2bx15x13x54x69xb/x6a
xbx77x48x53x68x6ex66x54x4ax6x15x71x78x58Modiglianix4Millerxex7ex1fx33x6dx3cx61xd
x1fx8x54x1cx1dx62x4ax55xex2cx68x61x6ex66x54x4ax6x2x57x7ex33x3x54x78x10x7ex48x3ax3ex1c
x23x7ex1fxbx4bx54x55x56x27x65x63x78
x61x62x51x6ex66Ax4B, x6ex66Ax47x5fx4fx6ax73x48x7fx5fx4fx69x68x57x58x6ex66B
xex73x5fx4fx6ax73x48x2ex5fx4fx69x68x78x25x78x2bx6ex66x49x50x27x54x4ax6xA;xB 2Cx2x70
x26x54x48x4 xA = xB. x25x18x75x1fx79x48x25x2bx9x26x79x41x42x78x2bx28x29x2ax6cx7bx9x78
xfx2
xA = nAxeA +mAxbA; xB = nBxeB; (7)
x17x2cxeA 2 C x2Ax6ex66x50x27x54x6ax4ax48x10x2x1ax3dx59x28x29x2ax6cx57 nA x2Ax6e
x66x54x3cx62x6ax49x68x57 xbA 2Cx2Ax6ex66x50x27x54x69x68x4ax78x26x66x6ex66x51x23x25x3b
x37x48x69x68x4ax4bx51x18x5ax23x25x2x28x29x2ax6cx48x7bx58x10x5ax2Cx54x38x46x57 mA x2x6e
x66Ax5fx4fx54x3cx62x69x68x68x57 xeB 2 Cx4nB x2x10x66x6ex66B x54x50x27x54(x28x29)
x6ax4ax4(x3cx62)x6ax49x68x78
x36x3f 3.3 (Modigliani–Miller x36x3f 1) x7x20x61x74x64x75x39x3ax3bx3cx75
x76x44x45C x7fx60x61x75x76x62x63x64x65 p. x57x58x76x77 A x71 B x79x1ex1fx63x1cx25x26x6b
x6c xA = xB, x14x15x5ax79x6x7x15x7bx49xfxaxb (7), x5dx5ex15x5ax79x3x1bx63x1c VA
x71VB x10x25x26x0
xdx27 x2bx71x44x48x26x62x4ax65x68px54x1cx1dx1dx48x3ax3ex51
VA = nAp(xeA)+mAp(xbA)
= p(nAxeA +mAxbA)
= p(xA) = p(xB) = p(nBxeB) = nBp(xeB) = VB:
63
2
x12rx1x69x68x54(x5)x20x21x27x78x49x1cx1dx62x4ax55xex56x48 Ax4B x78x2bx6ex66
x5fx4fx54x69x68x54x20x21x27 (x61x62x78x64x69x68x5bx33x69x6a) x7x8x2x70x26x54x78x7bx7ex48
r = xbA=p(xbA) = xbB=p(xbB). x4dx70x69x4bx48x26x62x69 3.3 x23x1bx48x78x2bx6ex66x54x5
x4ax6x54(x5)x20x21x27 ‰x5ax2x70x26x54x48x4‰ = xA=p(xA) = xB=p(xB). x25x26x48
x10x66x6ex66Ax54x6ax73x54(x5)x20x21x27 iA = xeA=p(xeA)x7x8x51x56x5cx76x63x41x7dx2a
x59x40(Modigliani–Miller x36x3f 2) x61x62x93.3x79x7x20x21x6bx57x58x76
x77Ax71B x79x1ex1fx63x1cx25x26x6bx6cxA = xB,x5dx5ex76x77Ax79x79x6x11x12x13iA
x1dx7ex0x43/x79x43x16x79x75x76x64x65x6bx6c
iA = ‰+(‰?r)DAS
A
; (8)
x7ex7fSA = nAp(xeA), DA = mAp(xbA).
xdx27 x2bx71x44x48
iA = nAx
e
A
nAp(xeA) =
xA ?mAxbA
SA
= ‰(DA +SA)?rDAS
A
:
x7bx7ex48 (8)x41x7dx78 2
x62x693.3x58x17x76x63(x10x3ex3bx2x15x1bx54x78x38Modigliani–Millerx62x69)x10
x26x49x68x4fx44x2x36x65x54x48x51x6cx3ax3ex39x2cx68x2cx23x24x3cx8x48x17x2cx17x71x51x2ex44
x58x6ax73x3x69x68x54x37x1fx1dx60x78x31x32x70x2bx6ex66x54x4ax6x23x24x60x1ax1x40x41x64x2c
x68x54x2ex10x14x25x48x33x34x62x69x54x31x63x1cx7ax41x7dx78x39x25x2bx3ax3bx27x3cx48x25x38x62
x69x33x43x2x70x48x78x2bx2cx68x14x25x49x50x27x54x6x7bx10x48x33x34x10x3ex49x17xbx54x6x5a
x7bx10x78x58x25x3bx2x3ax3ex49x6fx51x54x70x6fx7cx67x70x1fx54x2bx48x4x10x2x1cx1dx62x4ax55
xex54x31x32x78x2ex1fx17x46Modiglianix4Millerx51x50x5dx62x3ex54x2cx68x1ex68x31x7ex40
x26x5cx48x58x2x18x38x39 VA 6= VB x27x1fx8x70x2bx6dx3cx29x4dx78x17x76x29x36x7ax75x77x44
x4bx2ax52x78x39x25x18x5ax23x24x3cx8x68x4fx40x26x5cx54x28x73x78
x7ax58x48x31x44x76x29x54Modigliani–Millerx62x69x5ax57x2bx71x2ex4ex48x4x1ax71x57
x58x2cx54x6ex66x54x69xb/x6axbx77x51x17x70x62x33x3x78x25x67x47x75x17x4ex44x29x62x69x78x17
x4ex39x78x69x4bx27x47x48x78x70x2x39x6ex66x21x68x23x69x4bx27x47x48x57x70x2x39x2bx7dx21x68
x23x69x4bx27x47x48x78
xdx6ex66Ax5fx4fx54x69x68x54x17xbx4ax4bx1D = p(xbA),x69x68x33x62x54(x22)x3c
x27x1i, x4x31x32x6ex66x2ex3bx37x48x10x53x10x59x49x69x68x3fx2b(1 + i)D. iD x53x2x59
64
x49x69x68x54x3cx6ax78x47x48x6ex66x4bx2fx54x2x72xdx6bx56x21x73x54x74x75x2ax69x68x3cx6ax3f
x8x23x24x17x23x48x4x53x6ex66x4bx2fx3bx37x5ax2x31x7ex78x31x32x6ex66x23x27x1?c,x33x34x6e
x66Ax54x17x23x4ax1i?cmAD. x66x2x3ax3ex7fx51x56x5cx62x69x2a
x36x3f 3.4 x61x62x93.3x79x7x20x21x6bx57x58x0x76x77xax18x79x74x64x75x49xfx1d
xA(1??c)+i?cmAD; xB(1??c);
x7ex7fi, ?c, Dx57x7cx47x17x6bx1x2x18x19x1ax74x64x751 2C,x7ex3x1bx63x1cp(1) 6 1,
x5dx5ex0x76x77x79x3x1bx63x1cVA x71VB xaxbx21x7fx26x7cx7d
VA = VB +i?cmADp(1): (9)
xdx27 x2bx71x44x48
VA = p(xA(1??c)+i?cmAD)
= p(xA)(1??c)+(i?cmAD)p(1)
= p(xB)(1??c)+(i?cmAD)p(1)
= p(xB(1??c))+(i?cmAD)p(1)
= VB +(i?cmAD)p(1):
2
x25x38x62x69x39x69x68x3cx6ax23x17x23x54x3ax3bx27x47x4fx78x2bx50x27x4ax6x70x26x54x6e
x66x49x17xbx54x4ax6x7bx7dx78x31x63x40x2x5fx4fx69x68x4bx2ex54x6ex66x54x17xbx4ax6x4bx4ex78
x25x70x31x63xdx15x2x70x48x49x6bx56x33x26x54x23x20x67xex56x48x18x38x3ex1ex2ex31x76x38x3e
x1ex78x25x10x26x2x57x2bx71x2ex4ex54x78x5fx60x49x66xcx69x7ex2ex48x6ex66x1ex2ex17x69x18x67
x75x3bx37x78x58x3bx37x2x75x2bx8x4ex4ax54x78x31x32x4ex70x57x47x48x3bx37x35x3bx48x33x34x17
x4ex13x54x62x69x67x4dx2ax68x77x77x25x69x78
x1x7ex48x3ax3ex47x75x62x7axdx3bx37x35x3bxfx78x25x2x70x66x50x62xbx21x48x49x2ex3bx37
x18x10x1x7dx48x58x49x3bx37x18x10x4ex66x7dx48x51x6cx2x69x68x17xbx4ax4bDx54x49x54x65x68x78
x37x1fx1ex70x48 Ax6ex66x54x3bx37x35x3bx2x70x66x49x45x66Ax54x1ax3dx59x54x65x68x78x10x3e
x75x76x54x3x4cx67x5ex6ax36x2cx68x57x1ax36x2cx68x75x76x54x3x4cx78x3bx37x67x2x5fx36x61x1e
x2ex17x69x54x70x75x78 Ax6ex66x54xdx1exfx2x10x54x23x13x1ax3dx59x48x31x44x21x29x48x10x9x66
xA(1??c) + i?cmAD; A x6ex66x54xdx69xfxex2 mAD(1 + i). x66x2x3bx37x35x3b c
x7x62x7ax1
c =
‰ 0; x3x
A(1??c)+i?cmAD > mAD(1+i);
c(D): x3xA(1??c)+i?cmAD < mAD(1+i); (10)
65
x17x2cc(D)x60x27x10x2x69x68x17xbx4ax4bDx54x49x54x65x68x78x3bx37x35x3bc 2Cx54x17
xbx4ax6x36x7ax67x2p(c). x49x25x26x54x61x62x56x48x3ax3ex51x56x5cx62x69x2a
x36x3f 3.5 x61x62x93.3x79x7x20x21x6bx57x58Ax76x77x79x19x8x1ax6cx1dx57(10)
x47x62x59x6bx5dx5ex76x77Ax71B x79x3x1bx63x1cVA x71VB xaxbx21x7fx26x7cx7d
VA = VB +i?cmADp(1)?p(c); (11)
p(c)x1dx19x8x1ax6ccx79x3x1bx63x1cx0
x25x70x62x69x54x76x69x35x61Ax6ex66x54x4ax6x2cx2ex61x70x66x19x48x57x44x4bx3x15x7e
x7fx70x26x78x17x5ex2fx76x1fx2ex40x39x0x78x62x69x70x68x6ex66Axcx2cx49x5fx4fx69x68x3fx23
x21x68x57x3bx37x35x3bx75x76x2ex8xbx73x48x58x51x43x2x69x4bx2ex4bx28x78x25x67x57x71x72x74
x75x77x77x38x5dx78
x1ax49x3ax3ex47x48x39x2bx7dx21x68x23x69x4bx27x17x4eModigliani–Millerx62x693.3.
x61xdx78x2bx6ex66x54x4fx1ex31x5bx4bx2fx10x26x54x2bx7dx21x68x23x27?b x4?e,x17x2c?b x2
x69xbx21x68x54x21x68x23x27x48 ?ex2x6axbx21x68x54x21x68x23x27x57x10x3ex5bx2x16x661x54x3b
x68x78x10x18x61xdx6ex66Ax54x69x68x2x33x69x6ax54x48x4Ax9xax56x5cx2ex3bx37x38x3dx2a
xA(1??c)+i?cmAD > mAD(1+i):
x49x25x64x74x75x56x48x6ex66Ax4x6ex66Bx54x23x13x1ax3dx59yA x4yB x7x8x33x3fx9xa
x56x5cx69x6ax2a
yA = (xA ?imAD)(1??c)(1??e)+imAD(1??b)+?ep(yA); (12)
yB = (xB)(1??c)(1??e)+?ep(yB): (13)
x1x5dx8x25x78x2bx69x6ax48x10Ax6ex66x33x3fx47x48x6axbx21x51x31x7fx1fx4x69xbx21x51x31
x7fx1fx54x3cx21x78x10x66x6axbx21x51x31x54x23x13x1ax3dx59x9xax56x5cx69x6ax2a
nAZeA = [(xA ?imAD)(1??c)?mAD?nAp(ZeA)](1??e)+nAp(ZeA);
x25x18xbx70x66x1x23x13x54x1ex6fx54x21x20x1x48x58x13x70x66x2x6ax6fx6x78x69xbx21x51x31
x54x23x13x1ax3dx59x1
mAZbA = mAD +imAD(1??b):
x5dx78x26x7bx0x48x51x1fx79x19 D = p(ZbA), yA = mAZbA + nAZeA x4 p(yA) =
mAp(ZbA) + nAp(ZeA),x4x68(12). (13)x10x69x23x68x78x51x61x25xbx65x63x24x13x48x3a
x3ex67x51x56x5cx62x69x2a
x36x3f 3.6 x61x62x93.3x79x7x20x21x6bx57x58x0xcx76x77x79x3x6x1bx24x1cx1dx5e
x78x79xcx1ex47x5xax13?b x71?e,x7ex7f?b x67x0x43x47x5x79x47x5xax13x6b ?e x67x79x43
66
x47x5x79x47x5xax13x6bx5dx5ex76x77 A x71 B x79x3x1bx63x1c VA x71 VB xaxbx21x7fx26
x7cx7d
VA = VB +imADp(1)[(1??b)?(1??c)(1??e)]=(1??ep(1)): (14)
xdx27 x2bx71x44x48
VA = p(yA) = p((xA ?imAD)(1??c)(1??e)+imAD(1??b)+?ep(yA))
= p(xA)(1??c)(1??e)+imAD[(1??b)?(1??c)(1??e)]p(1)
+?ep(yA)p(1):
x26x7ex23x1ex68
VA = p(yA)
= fp(xA)(1??c)(1??e)+imAD[(1??b)?(1??c)(1??e)]p(1)g
=(1??ep(1)):
x10x69x23x68
VB = p(yB)
= p(xB)(1??c)(1??e)=(1??ep(1)):
xfx2xA = xB,x7bx7e(14)x41x7dx78 2
x25x70x62x69x5dVA x4VB x75x76x54x4ex16x5fx60x30x31x1x23x27x75x76x54x3x4cx78x17
(1 ? ?b) > (1 ? ?c)(1 ? ?e) x18x48x4x69xbx21x68x54x2bx7dx21x68x23x27x7bx77x66x6axb
x21x68x54x2bx7dx21x68x23x27x75x6fx68x2ex18x48x3cx27x5fx4fx69x68x54x6ex66x77x2ex5fx4fx69x68
x54x6ex66x54x4ax6x75x71x78x7ax75x48x17x25x2bx2ex9x26x7bx7ax18x48x31x63x5ax7bx7ax78x58x17
(1??b) = (1??c)(1??e)x18x48x6ex66x54x4ax6x7fx57x69xb/x6axbx77x33x3x78
x3ax42x72xdx54x5ex7ex3ax3ex58x23x2ex21x22x1x54x33x14x78x2ex1fx21x51x25xbx5bx2x2a
x7dx49x69x55x54x42x43x70x71x56x78x25x70x42x43x6cx79x2x7ex7fx5dx68x54x48x4x10x59x70x4fx1e
x31x27x70x48x5bx25x6dx6ex42x43x54x21x51x7cx6ax78x71x72x74x75x17x7ax51x43x31x7ex48x16x17x2x6e
x66x54x69xb/x6axbx77x21x2x10x32x7cx6ax48x19x7dx19x19x33x55x68x1bx78x25x26x48x31x32x75x47
x48x7cx6ax44x54x2ex5dx68x1dx48x6fx31x70x7cx6ax54x2ex10xcx1dx48x33x34x44x29x65x63x67x21x74
x68xfx2exax78x70x64x28x6dx54x47x48x67x2x5dx69xb/x6axbx77x2ex1x70x2bx13x14x1ax3dx59x4
x6x54x7bx46x48x66x2x67x51x23x25x7ex1fx70x64xdx72x73xfx33x14x48x27x3cx62x15x6dx54x69xb/x6a
xbx77x78x57x7ex51x3x54xcxdx23x46x3cRoss [11]x78x25x69x4bx58x49x4x0x0x14x2dx2ex21x51
x70x12x43x54xcxdx48x53x6ex66xax2x25x2bx4fx4ex2ex73x22x1x5fx3fx78
67
x39x44x4bx54x27x28x2cx3ax3ex23x24x3cx19x48x21x22Modigliani–Millerx62x69x48x30x16
x19x8x73x2x1cx1dx62x4ax55xex54x28x6dx7x3bx78x7bx58x48x3x66x10x54x51x3x65x63x2x35x4ex25
x71x72x54x5fx60x5ax67x2x6ex66x4ax6x2x35x9xax1cx1dx62x4ax55xex54x5fx60x78x58x13x70x5f
x60x33x43x67x2x6ex66x54x5x4ax6x2x35x67x9x66x10x54x1bx32x4ax6x54x5x4x78x25x70x5fx60
x54x1cx6cx17x7ax49x70x62x6ax3bx44x7x8x2x10x54x48xfx2x7bx7ax54x74x75x10x26x19x73x23x4fx78
x2fx5ex7dx3ex23x24x70x48x3bx74x64x20x2ax3ex1ex27x7bx2ax70x2bx6ex66x54x30x43x67x49x66x75x53
x17x5x1fx4ax6x4ex66x17x1bx32x4ax6x75x4x78x16x17x2x6ex66x75x76x4ex6cx54x20x17x51x17x1a
x44x3bx2x70x68x1cx1dx62x4ax55xex49x25x72x74x75x56x70x62x2ex41x7dx78x15x5dx54x70x66x3x66
x6ex66xax2x69x63x5fx3fx54x18x29 [13] x5dx8x48x39x69x63x44x27x70x48 Modigliani–Miller
x62x69x2x35x41x7dx49x66x32x26x27x69x1ex70x2bx6ex66x78x31x32x5dx6ex66x69x1ex1x70x2bxdx68x3c
x54x25x65x54x7fx38(a nexus of explicit contracts)xfx48x33x34Modigliani–Millerx62
x69x69x21x17x7ax1ex7x8x41x7dx78xfx2x1ax71x70x68x2dx2ex6ex66x5bx36x51x33x34x28x6dx78x4
x53x28x6dx1ex10x6ex66x47x48x17xdx7ax6ex25x65(implicit contract)xf (x45x31x48x69xbx4x6a
xbx67x51x2ex10x54xdx7ax6ex25x65xf)x54x66x49x48 Modigliani–Millerx62x69x67x19x57x47x75
x27x3bx78x21x1fx75x10x66x1ax4exdx3x27x70x48x58x51x2dx2ex45x75x54x44x62x1dx54x7bx46(x45x31
x7dx43x1ex6fx3x6ex66x21x69x31x4dx9)x47x75x47x48x78x22x23x31x7ex48 Modigliani–Millerx62
x69x2ex1x6ex66xax2x69x63x54x6bx40x1dxcxdx48x17x45x75x1dx1cx7ax2x2ex23x30x50x54x78
x2fx6a Modigliani–Miller x43x5c (MMT) x47x3e Modigliani x34 Miller x53 1958
x2x6xex1ax20x58x1cx4fx2e [9] x7x42x7dx2ex2cx20x29x6x31x4x51x7cx20x2ex4ax7x5x25x12x4ex33x28x1ax37
Modigliani–Miller x6x30 (MM Proposition, MMP)x29x1cx19x15x19x1ax20x43x5c 3.3x20 x10x4x6b
x16x13x18x48x2exex4ex70x27x13x33x37MMT 1x7cMMP 1x5 x56 MMT 2x7cMMP 2x47x21x10x4x6b
x20x6fx71x48x2ex75x4ax47x70x71/x6fx71x37x20x37x3ax5ex3cx7ax32x13x29 x13x43x5c 3.3 x20x73x4fx29xbx9x14xex44
x60x2cx2ax6[9]x7x29x7dx53x19x1axbx53x20x43x5c3.1x5x2cx2ax6Modiglianix34Millerx61961x2
x24x29x20x4fx2e [10] x7x29x28x25x12x46x33x37 MMT 3x29x3bx67x5x79x25x47x30 6 x20x5bxdx25x12x4ex33x37
MMT 4x29x25x27x38x2bx20x4ex4fx28x5bx2cx4dx45Miller [8]x29
x1cx3fxbx53x20x2bx2cx5x19x1ax0x47x4ex44xe MM x43x5cx47x6x7x66x3cx4dx5cx50xex20x29x19x1axb
x53x24x25x16x5fx26x7x64x2fx7xbx2cx10x48x2ex5cx5dx21x58x72x2x5 x40x41x3bx7dx13x23x24x20x2dx42x3ax20x3cx43x5
x2bx37x41x2ex2cx20x32x33x7fx18x7x35x7ex6ex58x3dx42x7dxex61x10xbx18x3cx43x29xax35x47x6x53x55x20x2ex4ax7x5
x72x73x5cx5dx20x36x6cx47x1cx3fx16x3bx14x3dx30x24x20x4x6bx2x40x26x4dx70x2ax20x29x2ax6x19x1ax64x3x72x73x5c
x5dx20x36x6cx2bx74x1cx3fx4x6bx24x4dx70x2ax29xbx3bx1x1cx51x3eStiglitz [12] x7fx44xex29xex2ex2cx5 x48x4a
Arrow–Debreu x72x71x27x2cx6x20x10Arrow–Debreu x5cx5dx13x4dx2fx11x3dx30x24x4x6bx20x36x6cx29xe
xdx7dx6x7ex53x6ex2ex2cx48x35x43x16x60x2ex43x5cx20x3x69x29 x1ex56x5x19x1ax4ex0x47x12x12x7fx44xex32x33x32
x71x52x53x7ex61x7fx25x59x7x66x29 MM x43x5cx20x7ex61x6ex7ex47x3dx5fx5bx20x5x2bx37x3dx5bx5dxex9x14x25x16
x17x2bxcx20x4x6bx29xbx4fx3cx50x28x2ax16x47x3bxax3bx56x5ex11x71xcx52x4x6bx1x5x20x25x5ex15x29
MMx43x5cx47x4x6bx1x5x5cx4fx20x60x1bx29x2bx3bx5x6x3x4x6bx1x5x36x37x5bx2cx31x19x20Coperand–
Weston [1] x7x5x70x4fx6x5cx4fxfx79x47x6x7ex72xfx5x52x3bx60x36x47x1cx5x4ex4f (x12 13–16 x6b)x29
x35x7xax35x47x6x5cx4fxfx5x28x15MM x43x5cx18CAPMx34x55x71x43x16x5cx4fx52x5cx28x20x4ex4fx13x50
x3bx7fx29 x3cx6x3bx56x20x11x12x58x59x33x7x64x2fx7x5x52 MM x43x5cx32x32x2bx36x21x1x2bx2cx29 Huang–
Litzenberger [4]x7x1x6128x74x2bx1cx7bxex2exex28x29 Ingersoll [5]x28x46x52x28x6x10x3dx61x11x12
68
x33x13x20xbx69x5cx7bx7cx4ex4fx29x19x1ax20x2bx2cx60x2exfx4dx45Jarrow [6]x20x25x27x6bx1(x124x5 10x34
11x6b)x29 x35x7ex5x36x37x37x3ax43x16x52x28x20x3ex3fx0x4ax5 MM x43x5cx47x9x19x4dx25 x4ex9x19x25x4ax20x30
x64x29 MM x43x5cx6Duffie [3]x7x46x2cx2ax648x74x20x3bx20x53x29x6Duffie [2]x20122–124x74
x7x5x25x2ex6bxfx18xbx53x4ex4fx3bx7dx20MM x43x5cx5 x3cx28x47x6x5ex11x71xcx7x4ex4fx20x5x23x44x35x29
x43x3fx77x32x33x15x29
x44x30x23x41x45x23
1. x37x34x2x51x3x33x68x67xex54 Modigliani–Miller x62x69x7ex61x4cx3ax56x6ax42x54
x71x72x74x75x48x25x70x62x69x51x37x34x76x27x7e
2. x37x34x2Modigliani–Millerx62x69(x62x693.3)x7ex10x2x49x37x34x38x3dx56x68x19
x54x7ex10x54x71x72x79x7ax1fx49x7e
3. Modigliani–Millerx62x69x54x2cx68x2x32x26x5fx60x61x4cx1cx1dx62x4ax55xex54x7ex46
x16x51xbx6ex66xax2x54x52x2ex48x3ax25x49x8x3bx70x2bx28x6dx54x70x71x60 (x50x27x73
x51x51x2ax64x70x71)x27x47x29Modigliani–Millerx62x69x2x7e
4. x32x26x49Modigliani–Millerx62x69x54xex4cx2cx47x48x23x20x3x3bx37x9x7bx46x7e
5. x49x8x62x693.5x54x5ex2fx2cx68x78
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