Brander and Lewis (1986) Link the relationship between financial and product sides of a firm.

Transcription

1 Brander and Lews (1986) Lnk the relatonshp between fnanal and produt sdes of a frm. The way a frm fnanes ts nvestment: (1) Debt: Borrowng from banks, n bond market, et. Debt holders have prorty over a frm s nome. (2) Equty: Stok market. Stokholders are resdual lamers. That s, they reeve devdend only after debts are pad. However, they have ontrol rght. 1

2 Ths has two effets on a frm s nvestment behavor: (1) As a frm takes on more debt, t has nentve to pursue output strateges that rase returns n good states but lower return n bad. (2) Any frm s suseptblty to fnanal dstress depends on ts fnanal struture. Compettors an mprove proftablty by drvng ts rvals nto fnanal dstress. Frms mght make produt market deson that rase the hane of drvng rvals nto nsolveny. Ths paper onentrates on the frst. 2

3 Two man ponts of the paper: (1) Produt market behavor s nfluened by fnanal struture. (2) Reversely, sne frms foresee (1), produt market ondtons wll nfluene fnanal struture. 3

4 Model: (1) Duopoly market. (2) Two stages: Frst the two frms dede ther fnanal strutures. Then they selet output level. (3) Output desons are made before realzaton of a r.v refletng varatons n demands and osts. (4) After profts realze, frms need to pay debt lams out of profts. If proft < debt, the frm goes bankrupt. Lmted lablty mples that shareholders nomes are zero (not negatve). 4

5 Detals: (1) q : output of frm. (2) R ( q q j, z ), : proft of frm. z [ z, z ] s a r.v. wth densty f ( z ). z and z j are IID. (3) R < 0, R j < 0, Rj < 0, Rz > 0. R z an be ether postve or negatve. (4) D : Debt level of frm. Solves for equlbrum behavor by bakward nduton. 5

6 The seond stage equlbrum: The proft of shareholders s V z ( q, q ) ( R ( q, q, z ) D ) f ( z ) dz ; j = zˆ j where R ( q, q j, z ) = D. ˆ Assume z < z ˆ < z. 6

7 The frms hoose q 1 and q 2 to maxmze own V. It an be shown that d zˆ / dd > 0, d zˆ / dd j = 0, d zˆ / dq = R ( zˆ )/ R ( zˆ ), z ( zˆ )/ R ( zˆ ) 0. j = j z d zˆ / dq R > FOC: V zˆ ( q, q, z ) f ( z ) dz = 0 z = R j. SOC: V < 0. 7

8 j j Assume V < 0, V V jj Vj V j > 0. Assume symmetry ( q = q, D D for all ). It an be shown that = q / D > 0 f R z > 0 and q / D < 0 f R z < 0. A neessary and suffent ondton that fnanal struture has no effet on output s R z = 0. If R z > 0, then dq / dd > 0 and dq j / dd < 0. If R z < 0 dq / dd < 0 and dq j / dd > 0., then 8

9 Fgure 2 Note that f the frm s ontrolled by debt holders, then t maxmzes W ( ) zˆ = R z j. ( q, q, z ) f ( z ) d z + D 1 F ( zˆ ) It an be shown that output s hgher n shareholder-ontrolled frm f z R > 0, and lower f R z < 0. Ths shows a onflt of nterest between shareholders and bondholders. 9

10 Frst stage: Seleton of debt level. Suppose the objetve of frm s to maxmze the value of the frm,.e., sum of Wrte V and W, all t q D. q as ( ) (, D ) Υ q ( D ), q j ( D ) zˆ = R ( q ( D ), q ( D ), D ) f ( z ) z + z zˆ R ( q ( D ), q ( D ), D ) f ( z ) j j Υ. whh s exatly the expeted proft over all states. dz dz, 10

11 Issung debt s only a break-even transaton exept that t affet output level. If output s, for some exogenous reason, fxed, then debt s neutral. Υ D = [ z zˆ R ( z ) f ( z ) dz dq ] dd + [ z ( z ) f ( z ) dz R ( z ) f ( z ) zˆ R z j + z ˆ j dz dq ] dd. 11

12 R for z zˆ f R z > ( < )0, we know that Sne ( z ) < ( > )0 zˆ z R ( z ) f ( z ) dz < 0( > 0) ff R z > ( < ) 0 But d / dd > ( <0) f R z > ( < ) 0, we know the frst term s negatve. If R z < 0, then dq / dd > 0. As a result, the seond term s negatve, and Υ D < 0. That s, the frm wll entrely be equty fnaned. 12

13 Ths also mples that monopolst wll take no debt. If R z > 0, then q j / dd < 0 and the seond term s postve. However, f D = 0, then the 1 st term s 0 and seond remans postve. Ths mples that Υ D > 0 for suffently low level of debt. In summary, f R z > 0, then debt level s strtly postve. If frm holds any debt, t wll produe more output than the tradtonal olgopoly level. 13

14 An nrease n debt has two effets. The frst s that t exaerbates the onflt of nterests between debt- and equty-holders, and thus redues frm value. The seond s the strateg effet n nfluenng rval s output. If R z > 0, more debt onfers strateg advantage. The frm wll takes debt to balane the two effets. If R z < 0, debt has only dsadvantage. Thus D =0. 14

15 Maksmov (1988) Debt struture an hange the ablty of frms n olgopoly to ollude. There s an upper bound whh lmts the possble level of debt a frm an take f at the same tme t ntends to sustan olluson. Model (1) n dental frms ompete repeatedly n Cournot fashon. (2) Eah perod ontans two subperods. Frst produton takes plae. Then output s marketed, ash flow realzed, and fator of produton pad. (3) γ : dsount rate. 15

16 The frms an use trgger strategy to ollude. Let N q j be Cournot output for frm j, q j be the olluson output for frm j whh attans jont monopoly proft. A trgger strategy desgnates that frm j produes q j n eah perod. If n any stage ant frm devates from forever. q, then every frm j produes N q j 16

17 Colluson an be sustaned ff where π, and d N π + π / r π + π,.e., ( N ) ( d π π π π ) γ < / ; N π are per perod proft under olluson and Cournot d output, and π s the maxmum devaton payoff of a frm when others are produng output orrespondng to π. Suppose frms ssue debts so that they reeve a lump-sum payment now but have to pay $1 bak n eah of the followng perods. Suppose frm ssues b debt nstruments, so that t pays b n eah perod. 17

18 Obvously, debt level an t be more than π / γ, and b annot be more than π n eah perod; otherwse the frm goes bankrupt. N If b [0, π ], then bankrupty wll not our, and there s no dfferene n ollusve power between a frm wth no debt and one wth debt b. N If b [ π, π ], then a devaton of a frm an drve frm nto bankrupty. Shareholders gve out ontrol to debtor, and reeve a payoff of zero. 18

19 The payoff of devaton for frm s shareholder s devates f π d b. Thus he d ( π b ) γ π b > π b + /. ( ) ( d ).e., γ π b π π > /. Let π b Δ = arg max b γ d π π d. I.e., Δ = π γ [ π π ]. In summary, the maxmum possble debt oupon for frm n order to ( N ) sustan olluson s, π max Δ. 19

20 Example of lnear demand: P ( ) = a m q. : margnal ost. ( 2 ) N 2 = ( a )/ 4mn, π = ( a ) / m( n+ 1) d = ( a ) ( n + 1) /16mn π, π. Can be shown that ( Δ / π )/ γ < 0 and ( Δ / )/ n < 0 π. That s, maxmum leverage at whh equlbrum an be sustaned delnes as nterest nreases, and as number of frms nreases. See fgure 1 20