2013 3 25 ( 4 ) Modigliani-Miller(1963) 1 1 1 IRR ( ) NPV IRR NPV IRR NPV IRR 100 EBIT 20 20% τ (1 τ) 20% CC tax = S V ρ S + B V (1 τ)ρ B (1) S B V ρ S CAPM 1
ρ B *1 (1) MM *2 ( ) MM MM ( ) MM (1 τ) 20% (1) CC tax CC tax CC tax 1 CC tax 1 500 *1 Brealey-Myers-Allen(2011) Ross-Westerfield-Jaffe(2011) *2 Modigliani-Miller(1958) Modigliani-Miller(1963) Modigliani-Miller(1963) MM MM Arditti-evy(1977) Ben-Horim(1979) Boudreaux-ong(1979) evy-sarnat(1990) 2
CC tax 2 CC tax 2 *3 1 1 1 1 *3 Myers(1984) Myers-Majluf(1984) ( ) ShyamSunder-Myers(1999) Fama-French(2002) Frank-Goyal(2003) 3
( ) 2 Hayashi(1982) Dixit-Pindyck(1994) Bolton-Chen-Wang(2011) eland(1998) Morellec(2004) 1 Giat-Hackman-Subramanian(2010) DeMarzo-Fishman-He-Wang(2012) Hackbarth-Mauer(2012) 1 2 3 4 5 6 4
2 2.1 *4 1 2 1 1 EBIT S B S B V V senior debt EBIT EBIT µ σ Φ(µ,σ ) *5 K K= kv ( ) τ 1 V V ( B) B V + B τ[ V ( B)] V + B Q S τ( V [ B]) Q S = 0 (> ) ( V + B ) (V + B> ) Q S V + B (2) *4 Tsuji(2012) *5 N(µ,σ 2 ) 5
3 S > 0 V B( S )>0 V + B (2) 1 ( ) 2 3 Q B Q B K >K Q (>K) B = ( ) K (> K ) 0 (K> ) >K 1 2 K 3 K Q (K ) ( ) B = (4) 0 (> ) 2 S B CAPM 1 S B [ E( Q (>K) B B= [ E( Q (K ) B S = E( Q S ) λ cov( R M, Q S ) (5) 1+R F ]/ ) λ cov( R M, Q (>K) (1+R F ) (>K ) B ) ) λ cov( R M, Q (K ) B ) ]/ (1+R F ) (K ) R F R M (3) (6) λ= E( R M ) R F σ( R M ) 2 (5) (6) partial moment f ( ) Φ(µ,σ ) 6
F( ) E( Q S )=µ [1 τ+τf(v + B) F()]+σ 2 [ f () τ f (V + B)] [1 F()]+τ(V + B)[1 F(V + B)] cov( R M, Q S )=cov( R M, )[1 τ+τf(v + B) F()] E( Q (>K) B )=[1 F()] K[F() F(K)] +µ [F() F(K)] σ 2 [ f () f (K)] cov( R M, Q (>K) B )=cov( R M, )[F() F(K)+ K f ()] E( Q (K ) B )=[1 F()] cov( R M, Q (K ) B )=cov( R M, ) f () 2.2 CAPM ( ) eland(1998) Morellec(2004) CAPM ( ) µ σ cov( R M, ) Q S Q B ( ) (2) (3) ( (4) ) (5) (6) (5) (6) S B µ σ k λ R F cov( R M, ) τ µ σ 3 *6 3 *6 k cov( R M, ) 7
S = S (,µ,σ ) B= B(,µ,σ ) V = V (,µ,σ )=S (,µ,σ )+ B(,µ,σ ) µ σ µ σ µ σ µ σ µ σ µ σ *7 µ σ 2 EBIT EBIT EBIT EBIT EBIT ω EBIT ( ) ( ) µ *7 Hart(1995) 8
ω µ ω µ 1 µ =ω α α>0 (7) α 1 µ ω α *8 = arg max V (,µ,σ ) (8) ( ) σ S σ = arg max σ S (,µ,σ ) (9) (7) (8) (9) 3 µ σ µ σ µ =ω α (10) V (,µ,σ )=0 (11) S (,µ σ,σ )=0 (12) µ σ ω α 2 S B *8 Jensen-Meckling(1976) Myers(1977) EBIT Tsuji(2012) Appendix ((7) EBIT (7) 1 2 9
ω α S = S (ω,α;,µ,σ ) B= B(ω,α;,µ,σ ) V = V (ω,α;,µ,σ ) 2.3 1 10 1 10 EBIT 1 ω ( ) 10 EBIT 50 1 α 0.2 k 0.4 τ 0.45 1 E( R M )=0.11 σ( R M )=0.18 R F =0.06 corr( R M, ) 0.2 E( R M ) 11% 1 1 1 10 (1.11) 10 1 1.839 1 10 E( R M )=1.839 1 10 10 λ 3.236 1 1 µ =47.41 σ =23.66 =12.93 (10) (11) (12) 3 S B V DR B/V ROA R ROA = ω V V (13) ω (50.0) 1 10 10 (10 ) ROA R ROA 1 *9 11.44% *9 ROA (13) R ROA (1+R ROA ) 10 1 1 10
1 ω α k τ E( R M ) σ( R M ) R F λ corr( R M, ) 50.0 0.2 0.4 0.45 0.11 0.18 0.06 3.236 0.2 µ σ S B V DR ROA 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 ( )E( R M ) σ( R M ) R F 1 1 λ 1 10 ω µ σ 1 10 DR B/V ROA ( ) (13) R ROA 1 2 ω ω µ σ S B V DR ROA 40.0 37.93 18.92 10.35 8.41 5.13 13.54 0.379 0.1144 45.0 42.67 21.28 11.64 9.46 5.78 15.23 0.379 0.1144 50.0 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 55.0 52.15 26.02 14.23 11.56 7.06 18.62 0.379 0.1144 60.0 56.90 28.38 15.52 12.61 7.70 20.31 0.379 0.1144 ( )ω 1 1 1 2 ω ω 50 60 1.2 µ σ S B V 1.2 DB ROA 1 (10) ω µ 2 1 1 3 3.1 11
1 *10 I I I B I S I= I S + I B I I I S I B (0) α (0) µ (0) σ (0) V ( ω (0) ( S ω (0) σ µ (0) =,α ; (0),µ (0) α (0) (10),α ; (0),µ (0),σ (0),σ (0) ) = 0 (11) ) = 0 (12) Φ ( ) µ (0),σ (0) (0) S (0) B(0) S (0) = S ( ω (0),α ; (0),µ (0) B (0) = B (,α ; (0),µ (0),σ (0),σ (0) ) ) *10 1 1 10 1 1 10 1 12
Φ ( ) µ (1), (1) S (1) B(1) (1) µ (1) (1) σ S ( ) = arg max S (1),µ (1) σ,σ (10) (14) µ (1) µ (1) = α (1) (15) α α (1) *11 B(1) S (1) S (1) = S ( ω (1),α ; (1),µ (1) B (1) = B (,α ; (1),µ (1),, I I B ) (1 (0) B (1) = I B (16) (1) I B (1) ( ) (1) B (1) 1 (0) ( ) (1) (0) I (1) B 1 (0) B (1) (1) I B I B (0) B (1) B (0) (1) ) ) *11 (15) α α α ( ) 13
I S 1 S P(0) 1 P (1) n (0) S S (0) = n(0) S S S n(1) S S I S /P (1) S S (1) S (1) = n(1) S P(1) S = n(0) S + I S P(1) S P (1) S P (1) P (0) = S (0) + I S+ n (0) S (P(1) S P (0) S ) (17) I S S (1) ( 3 ) P (1) S (17) P (1) S P (0) S S (1) S (0) + I S P (1) S = P (0) S ( ) S (1) = S (0) + I S ( = arg max S ω (1) σ,α ; ) (1),µ (1),σ (14) (1 (0) (1) ( S ω (1),α ; (1),µ (1) µ (1) = ) B (,α ; (1),µ (1), S (0) P (0) S α (1) (15) ) S ( ω (0),,α ; (0),µ (0) ) = IB (16) ),σ (0) = IS (18) (14) σ (15) (16) (18) (16) (18) 4 (0) I S I B µ (1) µ (1) 4 (1) (14) (15) 14
(16) (18) 2 (1) µ (1) (1) R q ω(1) ω(0) I I (1 ) (I B I S ) I I B I S R q I B R q R q R q (I B ) R q (19) min R q 0 I B I I S = I I B (20) I B I B R q 3.2 1 ROA (19) R q 1 (13) R ROA 2 1 S (1) S (0) = I S I S = S (0) I B B (1) S (0)= B (1) 15
I B (1) B (0) = I B (16) (0) (1) B(1) = B (0) (21) (21) 1 I B B (0) (21) B (0) 1 ω c c = cω(0) = cσ (0) = ω(1) σ (0) (22) 2 I( ) B (0) /V (0) I B /I I B I S I B I S B (,α ; (1),µ (1) ( S ω (1),α ; (1),µ (1) = ω(1) σ (0) (22) µ (1) = α (1) (15) ) (, B ω (0),α ; ) (0),µ (0),σ (0) = IB (23), ) S ( ω (0),α ; (0),µ (0),σ (0) ) = IS (18) (18) (15) (23) (22) (23) 16
3 µ (0) σ (0) (0) S (0) B (0) V (0) DR ROA 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 µ (1) (1) S (1) B (1) V (1) I B I B /I RRI 55.91 53.02 26.45 14.46 11.75 7.18 18.93 0.758 0.379 0.1144 ( )ω µ σ 1 10 (0) (1) DR B/V ROA ( ) (13) R ROA 1 RRI ( ) (19) R q 1 (22) 4 µ (1) (1) 4 ω(0) (19) I= 2 3 I= 2 0.379 I B 0.758 1.242 I S B (0) ) 10.51 6.42 B(1) ) 11.75 7.18 (S (1) (S (0) I S I B (1) =14.46 µ (1) =53.02 55.91 I=2 =50 ω(1) =55.91 R q 1 11.44% ( 3 RRI ) RRI R q 1 RRI ROA B (0) /V (0) I I B I S 1 I=2 I B 0 2 ( I S = I I B ) ((22) (15) (23) (18) 4 ) R q R q R q R q R q 1 R q I B I S B (0) S (0) 17
0.1151 RRI 0.115 0.1149 0.1148 0.1147 0.1146 0.1145 0.1144 0.1143 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 I B 1 (I B ) ( ) I B I S R q ( ) (I B ) R q I B I I B 1 I I B R q I B 1 I I B R q I B 3.3 R q R q I B I S R q (20) 4 I B = 2 I= 2 R q 18
0.119 RRI 0.118 0.117 0.116 0.115 0.114 0.113 0.112 0.111 0.11 0.109 0.108 0.107 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 I B 2 (I B ) ( ) 4 ( ) µ (0) σ (0) (0) S (0) B (0) V (0) DR ROA 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 µ (1) (1) S (1) B (1) V (1) I B RRI 55.55 52.14 26.28 17.05 10.51 8.28 18.79 2.0 0.1075 ( ) 3 I B 0 2 R q 2 I B R q 6.42 2 6.28 ( B (1) 8.28 I B 2 ) 1 S (0) σ (1) S (1) σ (1) σ (0) = 0 [σ,σ ] S (1) 19
σ σ = ω(1) σ σ (0) 1.3 σ (0) ω σ σ 30% 4 σ σ 4 1 R ROA R q R q R ROA σ (0) 20
4 I α k τ λ corr( R M, ) 1 1 5 11 1 I B /I 1.0 ( ) B (0) OldB OldB OldB B (0) DR (0) DR (1) 1 [σ,σ ] σ ω(0) σ (0) RRI ROA 5 ( (0) ) 2 DR(0) ROA RRI 6 50 I RRI 5 7 α α DR (0) α=0.16 α=0.24 50% 20% 7 α RRI 8 9 k ( 8) τ ( 9) 21
k τ DR (0) k τ RRI k RRI 8 9 τ RRI 10 11 10 λ 11 corr( R M, ) λ corr( R M, λ corr( R M, ) RRI λ corr( R M, ) 1 (1) RRI 5 11 CC tax RRI tax *12 10% 15% 5 CC tax RRI tax CC tax 2 α (0) µ (0) σ (0) α 1 ( ) α (0) µ (0) σ (0) *12 RRI tax = (1 τ)rri 10 1 CC tax RRI tax 22
µ (0) µ (1) 5 σ (0) (0) S (0) B (0) V (0) DR (0) ROA CC tax (1) B (1) DR (1) OldB I B /I RRI RRI tax 40.00 37.93 18.92 10.35 8.41 5.13 13.54 0.379 0.1144 0.0659 45.56 42.67 21.56 14.48 7.00 0.454 5.00 1.000 0.1077 0.0592 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 0.0659 55.55 52.14 26.28 17.05 8.29 0.441 6.29 1.000 0.1075 0.0591 60.00 56.90 28.38 15.52 12.61 7.70 20.31 0.379 0.1144 0.0659 65.54 61.62 31.00 19.62 9.57 0.431 7.57 1.000 0.1073 0.0590 ( ) DR (0) DR (1) B (0) /V (0) B(1) /V (1) ROA (13) R ROA RRI (19) R q 1 CC tax (1) OldB B (1) I B I B /I 1.0 RRI tax (1 τ)rri α=0.2 k=0.4 τ=0.45 I=2.0 λ=3.24 corr( R M, )=0.2 I 1.0 2.0 5.0 µ (0) µ (1) 6 I σ (0) (0) S (0) B (0) V (0) DR (0) ROA CC tax (1) B (1) DR (1) OldB I B /I RRI RRI tax 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 0.0659 52.76 49.77 24.96 14.97 7.35 0.412 6.35 1.000 0.1070 0.0589 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 0.0659 55.55 52.14 26.28 17.05 8.29 0.441 6.29 1.000 0.1075 0.0591 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 0.0659 64.04 59.33 30.30 23.52 11.11 0.514 6.11 1.000 0.1087 0.0598 ( ) α=0.2 k=0.4 τ=0.45 λ=3.24 corr( R M, )=0.2 5 α 0.16 0.20 0.24 µ (0) µ (1) 7 α σ (0) (0) S (0) B (0) V (0) DR (0) ROA CC tax (1) B (1) DR (1) OldB I B /I RRI RRI tax 50.00 47.00 20.89 18.73 8.49 9.27 17.76 0.522 0.1091 0.0599 55.20 51.54 23.07 22.84 11.11 0.567 9.11 1.000 0.1002 0.0551 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 0.0659 55.55 52.14 26.28 17.05 8.29 0.441 6.29 1.000 0.1075 0.0591 50.00 48.41 24.84 6.62 13.16 3.39 16.55 0.205 0.1169 0.0717 55.83 53.29 27.74 10.62 5.31 0.288 3.31 1.000 0.1130 0.0622 ( ) k=0.4 τ=0.45 I=2 λ=3.24 corr( R M, )=0.2 5 23
k 0.2 0.4 0.5 µ (0) µ (1) 8 k σ (0) (0) S (0) B (0) V (0) DR (0) ROA CC tax (1) B (1) DR (1) OldB I B /I RRI RRI tax 50.00 45.78 19.18 21.12 7.33 10.68 18.01 0.593 0.1075 0.0565 55.15 50.12 21.15 25.13 12.53 0.631 10.53 1.000 0.0992 0.0546 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 0.0659 55.55 52.14 26.28 17.05 8.29 0.441 6.29 1.000 0.1075 0.0591 50.00 48.02 25.69 9.89 11.67 4.88 16.55 0.295 0.1169 0.0698 55.70 52.89 28.62 14.06 6.75 0.367 4.75 1.000 0.1105 0.0608 ( ) α=0.2 τ=0.45 I=2 λ=3.24 corr( R M, )=0.2 5 τ 0.40 0.45 0.50 µ (0) µ (1) 9 τ σ (0) (0) S (0) B (0) V (0) DR (0) ROA CC tax (1) B (1) DR (1) OldB I B /I RRI RRI tax 50.00 48.79 23.84 6.03 14.45 3.15 17.59 0.179 0.1101 0.0726 55.55 53.56 26.48 9.95 5.08 0.260 3.08 1.000 0.1074 0.0644 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 0.0659 55.55 52.14 26.28 17.05 8.29 0.441 6.29 1.000 0.1075 0.0591 50.00 46.04 19.63 19.81 7.35 9.84 17.20 0.572 0.1126 0.0553 55.34 50.56 21.73 23.91 11.67 0.613 9.67 1.000 0.1032 0.0516 ( ) α=0.2 k=0.4 I=2 λ=3.24 corr( R M, )=0.2 5 λ 1.62 3.24 4.85 1.62 µ (0) µ (1) 10 λ σ (0) (0) S (0) B (0) V (0) DR (0) ROA CC tax (1) B (1) DR (1) OldB I B /I RRI RRI tax 50.00 47.29 26.82 13.53 11.81 6.60 18.41 0.358 0.1051 0.0592 55.01 51.39 38.37 18.13 7.88 0.400 5.88 1.000 0.0963 0.0529 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 0.0659 55.55 52.14 26.28 17.05 8.29 0.441 6.29 1.000 0.1075 0.0591 50.00 47.38 21.14 13.12 9.20 6.61 15.81 0.418 0.1221 0.0707 55.96 52.52 23.66 17.16 8.48 0.480 6.48 1.000 0.1153 0.0634 50.00 46.34 41.61 18.28 15.15 8.39 23.55 0.356 0.0782 0.0393 ( ) α=0.2 k=0.4 τ=0.45 I=2 corr( R M, )=0.2 5 24
corr( R M, ) 0.2 0.4 0.8 0.1 µ (0) µ (1) 11 corr( R M, ) σ (0) (0) S (0) B (0) V (0) DR (0) ROA CC tax (1) B (1) DR (1) OldB I B /I RRI RRI tax 50.00 47.41 23.66 12.93 10.51 6.42 16.93 0.379 0.1144 0.0659 55.55 52.14 26.28 17.05 8.29 0.441 6.29 1.000 0.1075 0.0591 50.00 47.22 18.95 13.90 7.89 7.11 15.00 0.474 0.1279 0.0735 56.29 52.72 21.34 17.87 8.99 0.533 6.99 1.000 0.1214 0.0668 50.00 45.87 11.36 20.67 3.47 11.18 14.65 0.763 0.1306 0.0644 56.60 51.72 12.86 24.39 13.11 0.791 11.11 1.000 0.1268 0.0697 50.00 46.34 41.61 18.28 15.15 8.39 23.55 0.356 0.0782 0.0393 ( ) α=0.2 k=0.4 τ=0.45 I=2 λ=3.24 5 I 15% 1 2 1 1974 1983 10 [1](period[1]) 1 1984 1993 10 [2](period[2]) 10 1 S (0) B(0) E( R M ) σ( R M ) R F λ 1 10 corr( R M, ) k τ k=0.3 τ 0.45 12 [1] 515 [2] 592 α 471 578 ( ) 3.1 [1] 442 [2] 576 ( =σ ) [1] 284 [2] 572 σ [2] [1] 3 [1] 3 [2] σ [1] 253 [2] 455 25
12 period[1] period[2] 1 (A) 515 592 (B) 471 578 (B)/(A) 91.5% 97.6% (C) 442 576 (C)/(B) 93.8% 99.7% 158 4 284 572 253 455 31 117 ( ) period[1] 1974 1983 10 ( [1]) period[2] 1984 1993 10 ( [2]) α σ (0) (0) µ (0) 3.1 [1] 1 31 [2] 2 117 σ σ σ σ 13 RRI tax CC tax *13 CC tax RRI tax (s.d.) CC tax RRI tax 2 CC tax RRI tax di f f di f f CC tax RRI tax di f f [1] [2] [1] 0.78% [2] 18.54% [1] di f f 130 [2] di f f 6 CC tax RRI tax [1] [2] CC tax 13 RRI tax CC tax 3 t-test *13 4 CC tax 5 CC tax CC tax 26
13 CC tax RRI tax CC tax RRI tax di f f period[1] period[2] period[1] period[2] period[1] period[2] mean 0.0832 0.0763 0.0822 0.0648 0.0078 0.1774 s.d. 0.0151 0.0091 0.0085 0.0046 0.1140 0.0982 min 0.0549 0.0557 0.0615 0.0550 0.1988 0.1049 max 0.1236 0.1092 0.1069 0.0791 0.3625 0.5874 difference: test statistics correlation firms di f f > 0 t-test di f f - Wilcoxon Pearson Spearman Kendall period[1] 284 130 1.832 1.155 0.856 0.816 0.809 0.624 period[2] 572 566 41.71 43.22 20.68 0.727 0.732 0.541 ( ) RRI tax CC tax di f f di f f = (CC tax RRI tax )/RRI tax t-test RRI tax CC tax t diff- f f = 0 Wilcoxon Pearson Spearman Kendall 5% 1% t- di f f - di f f - 3 Wilcoxon [1] RRI tax CC tax [2] 1% RRI tax CC tax 13 3 (Pearson) [1] 0.816 [2] 0.727 Spearman Kendall 3 [2] [1] 3 2 1% 14 [1] [2] RRI tax CC tax RRI tax 13 2 278 [1] [2] RRI tax CC tax 183 65% RRI tax CC tax 27
14 CC tax RRI tax total 278 same movement 183 (percentage) (65.8%) ( ) total RRI tax [1] [2] RRI tax same movement CC tax ( ) 1% 18% CC tax RRI tax 6 MM 1 1 1 28
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