2 i ii RIETI E-mail: tshibata@tmu.ac.jp E-mail: tetsuya.yamada@boj.or.jp / /2008.11 1
1. 2007 2 1 DCF DCF Leland [1994] Mella-Barral and Perraudin [1997] DCF DCF 2 /2008.11
1 1 3
2 Mella-Barral and Perraudin [1997] 2 i ii 2 3 Mella-Barral and Perraudin [1997] 4 2 5 6 7 2. 1 4 /2008.11
1990 2 15 2003 2 3 = = 1990 5 2004, 2006 1999 3 2005 3 39 2 1995 3 3 2005 4 1991 2002 2 2006 3 4 ROA 1990 ROA 3 2 5
5 468 6 2006 2005 2006 7 COO 5 5% 2 6 = = = 3 7 6 /2008.11
2006 2 1 2 1 2 Grenadier [1996] Weeds [2002] R&D 7
3. 1 2 1 Leland [1994] Mella-Barral and Perraudin [1997] MP Leland [1994] 8 8 Debt Equity Swap 8 /2008.11
MP 9 MP MP X t dx t D μx t dt C ffx t dz t ; X 0 D ; (1) z t w X t w M C C c D C =M 100% C» M 10 μ r r > μ 11 b b > r t X t X t F t fi b fi c F t F t 9 10 100% 11 r > μ R 0;1/ e rt.x 0 e μt / dt X 0 =.r μ/ r» μ 9
t T t F t E t. / D E. j F t / Z fib E.X t / D ma E t e r.s t /.X s w bm / ds fi b 2T t t ; (2) E./ (2) t < fi b fi b» t (2) fi Λ 2 T b t D.X t / D ma Z fi Λ b E t fi c 2T t t e r.s t / bm dsc Z fic fi Λ b e r.s t /.X s w/dsce r.fi c t / C fi Λ 2 T c t D./ (3) 1 t < fi Λ b bm 2 fi Λ b < t < fi c X s w 3 t D fi c C (3) ; 2 (2) E./ E./ D r w C bm C b μ r r C w C bm fl ; b < ; μ r b (4) b D fl w C bm.r μ/; (5) fl 1 r 2 fl (3) ff 2 =2 fl.fl 1/ C μfl D r fl D 1=2 μ=ff 2 10 /2008.11
p.μ=ff 2 1=2/ 2 C 2r=ff 2 < 0 (4) 1 12 μ ff 2 1 ff 13 b (5) b b fl r > μ (4) 1 Λ b ΛΛ Λ < ΛΛ < Λ b < < Λ 1 2 (4) 2.= b / fl b 14! 1.= b / fl! 0 D b.= b / fl D 1 E./! 1 1 D b E./ D b E 0./ D b 1 2 12 w C bm r r μ (1) 13 (4) ff de=dff D f.@e=@ b /.@ b =@fl / C @E=@fl g @fl =@ff D.@E=@fl /.@fl =@ff / @E=@ b D 0 @E=@fl D f b =.r μ/ C.w C bm /=r g.= b / fl log.= b / > 0.@fl =@ff / > 0 de=dff > 0 14 t; t C dt/ P.t» fi b < t C dt/ R 0;1/ e rtp.t» fi b < t Cdt/ R 0;1/ e rtp.t» fi b < t Cdt/ D E.ep. r fi b // D.= b / fl Diit and Pindyck [1994] 11
1 (3) b (5) c D./ D bm C Dj»b. b / bm fl ; b < ; (6) r r b Dj»b./ D c D r w C cm c μ r r C w μ r fl fl 1 cm C w r c fl ; (7).r μ/; (8) 3 (6) 1 2 D./! 1 1 b 2 D b (7) Dj»b./ 12 /2008.11
(7) 1 2 (4) 1 3 C (D cm).= c / fl Dj»b./ c D c C D 0. c / D 0 (6) (7) b < < b c 100% b > r c < b C (7) 3 c 1 4. 2 2 2 2 5 13
1 3 A B 2 2 2 M A M B M A C M B D M m A m B b 100% 15 2 L F fi Λ b D L i./ i D A ; B fi m 2 T t D L i.x t / D ma Z fi Λ b E t fi m 2T t t Z fim C fi Λ b e r.s t / m i bm ds e r.s t / m i.x s w/dsce r.fi m t / m i M ; (9) (9) 1 t < fi Λ b 2 fi Λ» b t < fi m 1 t fi Λ b 2 3 t D fi m m i M 15 M 6 14 /2008.11
fi Λ m D F j.x t / D ma fi c 2T E t Z fi Λ b t e r.s t / m j bm dsc e r.fi Λ m t / m i M C Z fic fi Λ m Z fi Λ m fi Λ b e r.s t / m j.x s w/ds e r.s t /.X s w/dsce r.fi c t / C (10) ; fi Λ m (10) (10) 1 t < fi Λ b 2 fi Λ» b t < fi Λ m 3 fi Λ m 4 fi Λ m < t < fi c 5 fi c C (10) 3 e r.fi Λ m t / m i M D D Z 1 e r.s t / r m i M ds fi Λ m Z fic fi Λ m e r.s t / r m i M ds e r.fi c t / m i M: (11) fi Λ m (11) fi Λ» m t < fi c (10) D F j.x t /D ma Z fi Λ b E t fi c 2T t t Z fic C e r.s t / m j bm dsc fi Λ m Z fi Λ m fi Λ b e r.s t / m j.x s w/ds e r.s t /.X s w r m i M / dsce r.fi c t /.C m i M / (12) ; 15
2 D L i./ D L i./ D m i bm C D Lj i» r b. b / m fl i bm ; b < ; (13) r b D L i j» b./ D m i m D fl fl 1 r μ w r M C w r C m i m M r C w μ r m fl ; (14).r μ/; (15) 4 (13) 1 2 (6) 2 D Lj i» b./ (14) 1 2 M m.= m / fl (15) m m D m D L i j» b./ (14) D L0 i j»b. m / D 0 (5) b (15) m b > r b > m 16 /2008.11
2 2 1 m 1 (13) 1 M (13) (6) 2 m 2 D F j./ b m D F j./ D m j bm C D Fj j» r b. b / m fl j bm ; b < ; (16) r b 17
D Fj j» b D m j r w μ r D Fj j» m D r w μ r m i M C C D Fj m j» m. m / m j r w ; μ r m fl (17) cm c r C w fl ; (18) μ r c 5 (16) D F j j» b./ (17) 2 D F j j» m./ (18) 1 2 cm c.= c / fl 100% c» m 100% c m 3 18 /2008.11
3 5. 16 1 A B A B 16 19
4 D F A./ DF B./ 4 80% 20% DA F./ DF B./ DB F./ 4 1 B P B P 17 17 20 /2008.11
DB F./ DA F./ P A < < P B A P < < P B o < o M B 4 1 o < b=r M B o 18 2 o A P < < P B o D A P» A P DF A./ A P 19 > A P DA F./ 1 2 D A P < A P DA F./ c c < < A P» c P 18 (15) 2 DB L./ DL B./ A P < < P B 19 2 15 D A 21
20 X t P fi P D minft j X t < P g 4 m P 4 2 A B 5 1 DAB L./ DF AB./ DAB F./ 1 P > P < P P 1 P pre-emption 21 Fudenberg and Tirole [1985] D P 2 22 Huisman and Kort [1999] 20 4 15 (10) 21 22 2 22 /2008.11
5 1 pre-emption 23 Kijima and Shibata [2005] n pre-emption 5 1 2 P m 5 2 b < P i D Fj i» b. b /» m i M 4 23 Huisman [2001] Weeds [2002] 1=2 23
5 2 3 P 4 2 4 2 A DA main./ B DB sub (10) fi Λ m./ fi P DA main./ fi P fi P DB sub./ (9) fi Λ m fi P (9) (10) fi b < fi Λ m fi b < fi P 24 /2008.11
fi P < fi b. fi b < fi P B DB main./ (9) D sub B Z fi Λ.X b t / D E t t Z fi P C fi Λ b e r.s t / m B bm ds e r.s t / m B.X s w/dsce r.fi P t / m B M ; (19) (9) C j» b. b / m BbM DB sub./ D m BbM r D sub B DB subj» b./ D m B r w μ r C m B M P r b fl ; b < ; r μ C w r P fl ; (20) 2 DB subj» b./ (21) 2 A DA main./ DA main.x t / D ma Z fi Λ b E t fi c 2T t t Z fi P C C e r.s t / m A bm ds fi Λ b Z fic fi P e r.s t / m A.X s w/ds e r.fi P t / m B M e r.s t /.X s w/ds C e r.fic t / cm (20) (21) ; (22) 25
(10) fi Λ m fi P fi c DA main./ D m AbM C DA mainj» r b. b / m fl AbM ; b < ; r b (23) DA mainj» b D m A w r μ r C D main A j» P.P / m A P r μ w r P fl ; (24) DA mainj» P D w r μ r m BM C cm c C w fl ; (25) r μ r c (25) DA mainj» P 2. fi P < fi b B DB main./ (9) D sub B Z fi P.X t / D E t t e r.s t / m B bm ds C e r.fi P t / m B M DB sub./ D m BbM r C m B M m BbM r ; (26) P fl ; P < ; (27) A DA main./ DA main.x t / D ma Z fi P E t fi c 2T t t e r.s t / m A bm ds e r.fi P t / m B M C C Z fic fi b Z fib fi P e r.s t / bm ds e r.s t /.X s w/ ds C e r.fic t / cm ; (28) 26 /2008.11
DA main./ D m AbM r DA mainj» P D bm r C D main A m B M C j» P.P / m AbM r D main A DA mainj» b D r w μ r m BM C cm P fl ; P < ; (29) b fl ; j» b. b / bm C m B M r (30) c r C w fl ; (31) μ r c 2 6 1 P P P 27
6 28 /2008.11
6. P X t μ 0% X t ff 10% 0.5 1.5 w 1 b 5% r 2% M 10 M A 7 C 6 60% 1 C 7 c c D 60% 24 i P 6 P 6 P ii c 24 7 c c c 29
7 iii b c 7 c D 80 100% 2 5 1 7 2 2 30 /2008.11
2 2 6 3 P 2 b P 8 i P ii 6% P iii 2002, 2006 25 25 2007a, b 2005 31
8 3 ff P 9 i 9 P ii P iii 2 Shibata [2005] Kijima and Shibata [2005] i i 32 /2008.11
9 (15) (17) D C C 9 ff 25% P ff 25% 33
μ ff c 26 μ ff ff 9 P 27 7. 2 i ii iii 26 27 34 /2008.11
1 2 2 2 2 2 μ ff μ μ w μ 35
1. 1 A B A M A M B M c b p r A-1 A 00.p/ B 00.p/ 1 1 p M A.1 C b/ p M A c 1 M A..1 p/.1 C b/ C pc/ M A A 00.p/ A 00.p/ D M A..1 p/.1 C b/ C pc/=.1 C r / M A ; B 00.p/ D M B..1 p/.1 C b/ C pc/=.1 C r / M B ; (A-1) B A A B M A M A 00.p/ M B A-1.A 00.p/; B 00.p//.A 01.p/; B 01.p//.A 10.p/; B 10.p//.A 11.p/; B 11.p// 36 /2008.11
A 01.p/ D M..1 p/.1 C b/ C pc/=.1 C r / M ; B 01.p/ D 0: (A-2) A B A 10 D 0; B 10.p/ D M..1 p/.1 C b/ C pc/=.1 C r / M; (A-3) cm A M A A 11.p/ D cm A M A ; B 11.p/ D cm B M B : (A-4) 2 p p 3 P 0 P 1 P 2 0 < M B < M A P 0 < P 1 < P 2 P 0 b r 1 c C b ; (A-5) P 1 P 2 b r 1 c C C M B b M b r 1 c C C M A b M.1 C r /.1 c/ ; (A-6) 1 c C b.1 C r /.1 c/ : (A-7) 1 c C b. p < P 0 A 00 > A 10 A 01 > A 11 B 00 > B 10 B 01 > B 11 A B. ; /. P 0 < p < P 1 A 00 < A 10 A 01 > A 11 B 00 < B 10 B 01 > B 11 A B. ; /. ; / 37
. P 1 < p < P 2 A 00 < A 10 A 01 > A 11 B 00 < B 10 B 01 < B 11 B A B A A B. ; /. P 2 < p A 00 < A 10 A 01 < A 11 B 00 < B 10 B 01 < B 11 A B. ; / 38 /2008.11
2. (2) E.X t / E.X tcdt / E.X t / D e rdt maf.x t w bm / dt C E t E.X tcdt / ; 0g: (A-8) E./ re./ D w bm C 1 2 ff 2 2 E 00./ C μe 0./; 8 < : E.! 1/! =.r μ/.w C b/=r; E. b / D 0; E 0. b / D 0; (A-9) (A-10) (A-10) 1 2 3 b b b (A-10) E./ D 8 < : r w C bm μ r C b r C w C bm fl ; b < ; μ r b 0;» b ; b D fl w C bm fl 1 r (A-11).r μ/: (A-12) fl (6) p ff 2 =2 fl.fl 1/ C μfl D r fl D 1=2 μ=ff 2.μ=ff 2 1=2/ C 2r=ff 2 39
3. 2 b 1 (3) D.X t / D ( e rdt.bm dt C E t D.X tcdt / /; t < fi Λ b ; e rdt ma f.x t w/ dt C E t D.X tcdt / ; C g; fi Λ b» t; (A-13) D./ rd./ D bm C 1 2 ff 2 2 D 00./ C μd 0./; b < ; (A-14) ( D.! 1/! 0; D. b / D Dj»b. b /; (A-15) rd./ D. w/ C 1 2 ff 2 2 D 00./ C μd 0./;» b ; (A-16) 8 < : D.! 1/! =.r μ/ w=r; D. c / D C; D 0. c / D 0; (A-17) (A-16) (A-14) c (A-17) 8 bm C Dj»b. b / bm fl ; b < ; r r b D./ D < : c D fl fl 1 r w C C c μ r r C w μ r c fl ; c <» b ; C;» c ; (A-18) cm C w.r μ/: (A-19) r 40 /2008.11
4. D L i./ (17) D L i.x t / D L i.x tcdt/ D L i.x t / D ( e rdt.m i bm dt CE t D L i.x tcdt/ /; t < fi Λ b ; e rdt mafm i.x t w/dt CE t D L i.x tcdt/ ; m i M g; fi Λ b» t: (A-20) D L i./ rd L i./ D m i bm C 1 2 ff 2 2 D L i 0./ C μd L00 i./; b < ; (A-21) ( D L i.! 1/! 0; D L i. b/ D D Lj i» b. b /; (A-22) rd L i./ D m i. w/ C 1 2 ff 2 2 D L i 8 < : D L i.! 1/! m i.=.r μ/ w=r /; D L i. m/ D m i M; D L i 0.m / D 0; 00./ C μd L0 i./;» b ; (A-23) (A-24) i m (A-24) D L i./ D 8 < : m D fl fl 1 m i bm C D Lj i m <» r b. b / m i bm r m i r w Cm i M m μ r r C w μ r b fl ; b < ; m fl ; m <» b ; m i M;» m ; M C w r (A-25).r μ/: (A-26) 41
5. D F j./ (18) D F j.x t / D 8 < : e rdt.m i bm dtce t D F j.x tcdt/ /; t < fi Λ b ; e rdt.m j.x t w/dtce t D F j.x tcdt/ /; fi Λ b» t < fi Λ m ; e rdt maf.x t w r m i M / dtce t D F j.x tcdt/ ; C m i M g; fi Λ m» t: (A-27) D F j./ rd F j./ D m j bm C 1 2 ff 2 2 D F j 00./ C μd F0 j./; b < ; (A-28) ( D F j.! 1/! 0; D F j. b/ D D Fj j» b. b /; (A-29) rd F j./ D m j. w/ C 1 2 ff 2 2 D F j 00./ C μd F0 j./; m <» b ; ( D F j.! 1/! m j.=.r μ/ w=r /; D F j. m/ D D Fj j» m. m /; rd F j./ D. w r m i M / C 1 2 ff 2 2 D F j 8 < : (A-30) (A-31) 00./ C μd F0 j./;» m ; D F j.! 1/!.=.r μ/ w=r / m i M; D F j. c/ D cm m i M; D F j 0.c / D 0; (A-32) (A-33) j c (A-33) 42 /2008.11
D F j./ D 8 < : c D fl fl 1 m i bm r m w j r μ r C D Fj j m <» b. b / m i bm r C r w μ r m i M C D F j j c <» m. m / m j m c cm r C w μ r fl ; b < ; b r μ w r m fl, m <» b ; m fl ; c <» m ; cm m i M;» c ; cm C w r (A-34).r μ/: (A-35) 43
24 1 2005 56 2 2005 VaR 26 2 2007 a VaR VaR 26 2 2007 b 2005 2006 2006 15 2003 2002 2006 70 2 2004 CARF CARF-J-022 2006 2007 Diit, A., and R. Pindyck, Investment under Uncertainty, Princeton University Press, 1994. Fudenberg, D., and J. Tirole, Pre-emption and Rent Equalisation in the Adoption of New Technology, Review of Economic Studies, 55, 1985, pp. 383 401. Grenadier, R., The Strategic Eercise of Options: Development Cascades and Overbuilding in Real Estate Markets, Journal of Finance, 51, 1996, pp. 1653 1679. Huisman, K., and P. Kort, Effect of strategic interactions of the option value of waiting, CentER Discussion Paper 9922, 1999., Technology Investment: The game theoretic Real Option Approach, Kluwer Academic Publishers, 2001. Kijima, M., and T. Shibata, Real Options in An Oligopoly Market, Kyoto Economic Review, 74, 2005, pp. 47 64. Leland, H., Corporate Debt Value, Bond Covenants, and Optimal Capital Structure, Journal of Finance, 49, 1994, pp. 1213 1252. 44 /2008.11
Mella-Barral, P., and W. Perraudin, Strategic Debt Services, Journal of Finance, 52, 1997, pp. 531 556. Shibata, T., On the Value-Volatility Relationship in a Real Options Model, Kyoto Economic Review, 74, 2005, pp. 205 213. Weeds, H., Strategic Delay in a Real Options Model of R&D Competition, Review of Economic Studies, 69, 2002, pp. 729 747. 45
46 /2008.11