Corporate Finance: Capital structure and PMC. Yossi Spiegel Recanati School of Business

Transcription

1 Corporate Fnance: Captal structure and PMC Yoss Spegel ecanat School of Busness

2 Brander and Lews AE 986 Olgopoly and Fnancal Structure: The Lmted Lablty Effect

3 Cournot duopoly wth dfferentated products Two frms produce dfferentated products for whch the nverse demand functons are p γ reflects the degree of product dfferentaton γ the products are perfect substtutes < γ < the products are mperfect substtutes γ the products are unrelated γ < the products are complements Both frms have a constant margnal cost The proft functons: γ A 2 p2 A 2 p 2 p 2 2 π π Corporate Fnance 3 γ

4 The Nash eulbrum F.o.c for frm : π γ A 2 A 2 γ Margnal revenue The best-response functon of frm A γ 2 B 2 2 The best response functon of frm 2 s analogous Corporate Fnance 4

5 Ganng strategc advantage wth cost reducton from to 2 A-/γ A γ 2 2 A γ 2 ' 2 A-/2 A-/2+γ rect effect Indrect effect 2 A γ 2 A-/2+γ A-/2 A-/γ Corporate Fnance 5

6 The lmted lablty effect Margnal cost s c H wth prob. α or c L wth prob. -α ol prces fluctuate The frm chooses uantty before nowng f cost s hgh or low an arlne determnes ts flght schedule n advance and buys fuel on the spot maret Expected proft: Eπ αp c H Q + -αp c L Q The frm ssues debt wth face value that can be repad n full only f cost s c L : > p c H Q If cost s c H the frm goes banrupt; due to lmted lablty eutyholders get a payoff of The frm acts on behalf of eutyholders and therefore maxmes: -αp c L Q The frm behaves as f ts cost s c L rather than αc H + -αc L The frm gans a strategc advantage over rvals f strateges are strategc substtutes The strategy s costly: the frm goes banrupt wth probablty α Corporate Fnance 6

7 The general model The tmng: Perod Perod 2 Two rval frms ssue debt wth faces values and 2 The two frms choose output levels and 2 Profts are 2 and 2 2 has a unue maxmer < frm has a negatve externalty on frm > : s a postve shoc ether supply of demand shoc ~ [ accordng to f wth CF F Corporate Fnance 7

8 Examples Cost shocs: C C / C -C ~ [ ] emand shocs p p where p A- -γ p A- -γ Corporate Fnance 8

9 All-euty frm Frm chooses to maxme ts expected proft tang as gven Max df The best response of frm aganst s defned by The NE s defned mplctly by the system: df Corporate Fnance 9

10 Leveraged frm The frm s solvent ff: Comparatve statcs: Corporate Fnance

11 Corporate Fnance The problem of a leveraged frm Frm s problem: The best response of frm aganst s defned by The NE s defned mplctly by the system: df Max + df f

12 Corporate Fnance 2 The effect of leverage on the frm s strategy To fnd the effect of on fully dfferentate f.o.c.: The change n frm s best response functon depends on the sgn of by s.o.c } + f df

13 The sgn of Suppose that proft > the shoc boosts the margnal ecall that total area between the horontal axs and the graph of sums up to < Corporate Fnance 3

14 Effect of If > then wth frm becomes more aggressve when t ssues debt Why? ue to lmted lablty frm gnores low states of n whch t goes banrupt and hence behaves as f was on average hgh When > the frm produces more when s hgh In the Cournot model when frm s more aggressve frm s softer and frm enoys a strategc advantage vs-à-vs frm Corporate Fnance 4

15 The choce of The value of debt: B The value of euty: E The total value of the frm: + df Y df df df Corporate Fnance 5

16 Corporate Fnance 6 The optmal choce of by F.O.C for ' df df df df df df Y

17 The optmal choce of The f.o.c for : Y ' df df The second term s the postve strat. effect The frst term s the negatve drect effect: debt dstorts the frm s choce of uantty As the negatve drect effect vanshes Y > > Corporate Fnance 7

18 Spegel JEMS 996 The ole of ebt n Procurement Contracts

19 The model The tmng: Perod Perod 2 Perod 3 A frm nvests whch determnes the net surplus from tradng wth a buyer The frm ssues debt wth face value s realed the frm and the buyer bargan over a prce s due > > > and ~ U[ ] Corporate Fnance 9

20 The barganng stage The buyer and the frm trade ff o/w the prce the buyer pays s not enough to ensure solvency Let be such that If the buyer maes a TIOLI wth prob. γ and the frm maes an offer wth prob. -γ The frm s expected payoff when t ssues debt s Y γ d + d Euty 23 ebt Corporate Fnance 2

21 Corporate Fnance 2 The choce of debt The f.o.c for the frm s value: At Y > > { + + Y γ γ

22 Illustratng the model all euty. γ. Corporate Fnance 22

23 Illustratng the model. γ Corporate Fnance 23

24 Corporate Fnance 24 Investment The frm s value as a functon of : The f.o.c for : { + d d Y Y γ γ 4243 d d Y ebt Euty γ

25 Corporate Fnance 25 The effect of debt on nvestment The margnal beneft of : Snce : The effect of : d γ 2 γ <

26 The effect of debt on nvestment Suppose that 2 < The margnal beneft of ncreases wth The frm nvests more when t ssues debt Corporate Fnance 26