Corporate Finance: Asymmetric information and capital structure signaling. Yossi Spiegel Recanati School of Business

Transcription

1 Corporate Finance: Asymmetric information and capital structure signaling Yossi Spiegel Recanati School of Business

2 Ross, BJE 1977 he etermination of Financial Structure: he Incentive-Signalling Approach

3 he model he timing: Stage 0 Stage 1 Stage he firm issues debt with face value he capital market observes and updates the belief about the firm s type Cash flow is realized Cash flow is x ~ U[0,], where {,H}, < H is private info. to the firm he capital market believes that H with prob. γ In case of bankruptcy, the manager bears a personal loss C he manager s utility: U V C x Prob. of bankruptcy Corporate Finance 3

4 he full information case he value of the firm when is common knowledge: V xdf( x) + df( x) + 0 ( x ) df( x) xˆ With uniform dist.: xˆ / he manager s utility: U xˆ C F( ) xˆ he manager will not issue debt C Corporate Finance 4

5 Asymmetric information is the debt level of type B is the prob. that the capital market assigns to the firm being of type Perfect Bayesian Equilibrium (PBE), ( H,,B): H and are optimal given B B is consistent with the Bayes rule Corporate Finance 5

6 Bayes rule P ( A B) P ( B A) P( B) P( A) In our case, two levels of are chosen. Suppose the probability that each type plays them is as follows: ype H (γ) ype (1 γ) 1 h 1 l 1 h l Having observed 1 the capital market believes that the firm is type H with prob.: P ( H ) 1 P ( 1 H) P( H ) h1γ P( ) hγ + l (1 γ ) In a sep. equil., h 1 1 and l 1 0. In a pooling equil., h 1 l Corporate Finance 6

7 Corporate Finance 7 Separating equilibria: H he belief function: In a separating equil., 0 because type cannot boost V by issuing debt 0 B(0) 0 V(0) / w o B H / ' 0 1 γ

8 Separating equilibrium he IC of H: V C 1443 H Payoff of H when it issues { Payoff of H when 0 he IC of : V C { Payoff of when 0 Payoff of when it issues Indifference of type between V and : V C V + C { 1443 Payoff if 0 Payoff when issuing if it induces value V Corporate Finance 8

9 he set of separating equilibria V V + C V + C H sep. equil. V V H is defined by /+Cx/ H/ (H-)/C Corporate Finance 9

10 he OM criterion is a dominated strategy for type : 0 always guarantees a higher payoff no matter what the capital market believes he OM criterion: B γ ' H o / w he idea: type will never play while type H might. Hence, if, then the firm s type must be H he OM criterion still does not determine the beliefs for < and 0 Under the OM criterion: 0, H Corporate Finance 10

11 Separating equilibria under the OM criterion V V + C V + C H V H 0, H V Corporate Finance 11

12 Pooling equilibria: H p he belief function: B γ γ ' o / w p In a pooling equil., the choice of p is uninformative; hence ˆ H V γ + ( 1 γ) Corporate Finance 1

13 he set of pooling equilibria V V + C V + C H pooling equil. V H V Vˆ V Corporate Finance 13

14 he OM criterion he OM criterion: B γ 1 γ ' p o / w he OM criterion eliminates some pooling equilibria but not all Corporate Finance 14

15 he set of pooling equilibria V V + C V + C H pooling equil. V H V Vˆ V Corporate Finance 15

16 he intuitive criterion ue to Cho and Kreps, QJE 1987 Fix a equilibrium (, H ) and consider a deviation from this equilibrium to. If the deviation never benefits type x (even if it induces the most favorable beliefs by the capital market) but can benefit type y, then the deviation was played by type y he intuitive criterion: B γ 1 is dominated γ ' o / w p by p he intuitive criterion still does not determine the beliefs everywhere Corporate Finance 16

17 he set of pooling equilibria under the intuitive criterion V V + C V + C H pooling equil. V V H V Vˆ he intuitive criterion eliminates all pooling equil. Corporate Finance 17

18 Conclusions he only equilibrium which survives the intuitive criterion is 0 and H his equilibrium is the Pareto undominated separating equilibrium and it is called the Riley outcome ebt can be used as a signal of high cash flow he debt of type H: + C H ( H ) C when, H-, and C, is independent of γ! Corporate Finance 18

19 eland and Pyle, JF 1977 Informational asymmetries, financial structure, and financial intermediation

20 he model he timing: Stage 0 Stage 1 Stage An entrepreneur sell a fraction 1-α of the firm to outside equityholders he capital market observes 1-α and updates the belief about the firm s type Cash flow is realized Cash flow is x ~ [0, ), with Ex x and Var(x)σ, where {,H}, x < x H is private info. to the firm he capital market believes that H with prob. γ he entrepreneur s expected utility: EU b ( W ) EW Var( W ) W αx+ ( 1 α)v Corporate Finance 0

21 he full information case he variance of W : Var he entrepreneur s expected utility: Under full info., V x : ( W) E( αx+ ( 1 α) V EW) E( α( x x )) α σ EU W α 0 he entrepreneur will sell the entire firm Why? Because the entrepreneur is risk-averse and the capital market is risk-neutral ( ) α x + ( 1 α) V 1 α 3 σ EU EW b b ( W ) x α σ Var ( x) Corporate Finance 1

22 Asymmetric information α is the equity participation of type B is the prob. that the capital market assigns to the firm being of type Perfect Bayesian Equilibrium (PBE), (α H, α,b): α H and α are optimal given B B is consistent with the Bayes rule Corporate Finance

23 Corporate Finance 3 Separating equilibria: α H α he belief function: In a separating equil., α 0 because type cannot boost V by keeping equity α 0 B(0) 0 V(0) x w o B H / ' 0 1 γ α α α α

24 Separating equilibrium he IC of H: b αxh ( 1 α) V α σ { x Payoff of H when he keeps a fraction α of the firm Payoff of H when α 0 he IC of : b V α σ ( ) { x αx+ 1 α Payoff of when α 0 Payoff of when he keeps a fraction α of the firm Indifference of type between V and α: b x αx α ( α) α σ { x x + 1 V V α if Payoff α 0 Payoff when keeping a fraction α of the firm if it induces a value V + bσ α 1 α Corporate Finance 4

25 Corporate Finance 5 he set of separating equilibria α α α σ + 1 b x V x H V x V V α α sep. equil. α α σ α α b x x V H ( ) σ α b x x Z Z Z Z H + +

26 he Riley outcome Using s IC, the ownership share of type H is: b ( ) { x αx+ 1 α xh α σ α Z{ + Z( Z+ ) Payoff of when α 0 Payoff of when he keeps a fraction α of the firm and the market believes that his type is H x H x bσ α increases with Z which increases with the extent of asymmetric info., x H -x decreases with risk aversion, b decreases with the variance of cash flows, σ Using H s IC: ( ) { x αxh + 1 α Payoff of H when α 0 b xh α σ Payoff of H when he keeps a fraction α of the firm and the market believes that his type is H α ( x x ) H bσ α < 1 iff (x H x )< bσ ; otherwise, type H prefers every α > 0 over α 0 provided that he convinces outsiders that the firm s type is H Corporate Finance 6