Strategic Investment with Debt Financing

Transcription

1 Strategic Investment with Debt Financing Workshop on Finance and Related Mathematical and Statistical Issues September 3-6, Kyoto *Michi Nishihara Takashi Shibata Osaka University Tokyo Metropolitan University

2 Outline 1. Introduction 2. Monopoly 3. Duopolies (i), (ii), (iii) 4. n Firms 5. Numerical Examples 6. Conclusion 7. Future Work

3 1 Introduction Important Feature of Real Options Complex Stakeholders Firm AFirm A Firm B Firm C Managers Conflict Competition, Conflict Firm D Equityholders Bondholders Real Options (ex. opportunity to invest some project) Stochastic Models Competition among Firms + Concept of Preemptive Game Grenadier(1996), Weeds(2002), Lambrecht, Perraudin(2003), etc. Conflict in a Firm + Mechanism Design Grenadier, Wang(2005), Nishihara, Shibata(2008), etc. Influence Consume r This Paper Equityholders(=Owner = Entrepreneur=Manager), Bondholders, Several Firm

4 Market Demand Good Bad Other Firms 0 Invest with Issuing Debt Bondholders + Equityholders (=Owner=Entrepreneur) Default Obtain Profit flow with Paying Coupon Equityholders Time t Other Firms Sundaresan, Wang (2007), Mauer, Sarkar (2005): Combine investment timing decision (McDonald, Siegel(1986), etc.) with capital structure and endogenous bankruptcy decision (Leland (1994), etc.) This Paper: Extend analysis in Sundaresan, Wang (2007) to the case allowing Preemptive Competition among Several Firms

5 2. Monopoly Unlevered McDonald, Siegel (1986) Market Demand Maximize Firm Value= Equity (Owner) Value Small Investment Time Risk-free Rate Profit Rate Tax Rate Sunk Cost Investment Trigger Positive Root(>1) Firm Value = Equity Value

6 Levered Sundaresan, Wang (2007) Assume that the firm has already invested at along with issuing debt with coupon. Equityholders (owner) have an incentive to default. Equityholders (owner) Maximize Equity Value Default Time Default Trigger Debt Value Negative Root Default Cost Firm Value = Equity Value + Debt Value cf. Leland(1994), Goldstein, Ju, Leland(2001) Tradeoff between Tax Effects and Default Costs

7 Equityholders (owner) + bondholders Maximize Firm Value Investment Time Larger Investment Trigger Earlier Coupon Default Trigger Constant(<1) Positive Constant(>1) Positive Leverage, Credit Spread (at time of investment): Constants independent of

8 3. Duopoly Procedure (symmetric duopoly) 1. Assuming that one of the firms (called Leader) has invested at, derive the best response of the other (called Follower). 2. Derive Follower s and Leader s expected payoff as functions of. 3. Find the preemptive trigger where the two values are equivalent. Assumption The profit rate when two firms are active in the market. One of the firms is fairly chosen as a leader when the firms try to invest at the same trigger. The others take the follower s optimal response. Benchmark Unlevered vs. Unlevered Both try to invest at Leader: Follower: No opportunity to invest Value: 0 Levered Action Set = Investment Trigger + Coupon Preemptive

9 Prop. 1 Duopoly (i) Levered vs. Levered Leader Preemptive Follower Value Point where Leader s Value = Follower s Value in Discount due to competition Prop. 2 Duopoly (ii) Levered vs. Levered (Only the leader can issue debt) Preemptive Leader Follower Value

10 Prop. 3 Duopoly (iii) Levered vs. Unlevered (exogenous reasons) Levered: Leader Preemptive Value Unlevered: Follower Value Point where Leader s Value = Follower s Value for Unlevered firm in Levered: Leader Value Unlevered: Follower Value Dominant leader-type Same as Monopolist cf. Kong, Kwok(2007) (Value of Levered) > (Value of Unlevered) Comparison of Duopoly (i), (ii), (iii) Investment Time: (ii) < (i), (iii) Monopolist Value of Levered: (ii) < (i), (iii) Monopolist

11 4. n Firms n Unlevered firms Same as Duopoly, zero-npv timing, no profit n Levered firms (Every firm can issue debt) Procedure 1 Solve the last firm s problem 2 Solve the problem of two firms remaining (Follower moves to 1, Prop. 1) 3 Solve the problem of three firms remaining (Two Followers move to 2) Solve the problem of n firms remaining (n-1 Followers move to ) Prop. 4 n Levered firms Firm n that invests first Firm 1 that invests last Value Discount due to competition 0 (Competitive Market) (n ) cf. Lambrecht, Perraudin(2003)

12 Table 1: Preemptive game Table2: Leader-Follower game Monotone Decrease Social Loss Monotone Increase

13 5. Numerical Examples Table 4: Comparison of a monopoly with Duopolies (i), (ii), and (iii) Table 6: Loss(n) for various σ. Crucial Point: Whether a firm can optimize capital structure. Monotone Decrease Active entry and default reduce the first mover s advantage.

14 6. Conclusion The possibility of the leader s bankruptcy generates a positive firm value under preemptive competition among several firms. Firm s investment trigger, coupon, and default trigger are larger for later investment. The order of difficulty of the preemptive competition is Duopoly (ii), (i), (iii). In Duopoly (iii), the levered firm always invests first and overwhelms the unlevered firm. Firm s Investment time goes to zero-npv point and the firm value goes to 0 when the number of firms goes to infinity. Social loss from preemption increases with the number of firms. Higher volatility moderates the preemptive competition and reduces the social loss.

15 7.Future Work 1. Case of, i.e., two firms can be active in the market. Second Mover s Advantage: Now Working When Follower enters the market with Leader, Follower can choose lower coupon than Leader s coupon so that Follower can win the exit game. 2. Effects of the Financial Constraint where a part of the investment cost must be financed by debt. Almost Finished Second best Capital Structure, Leverage, Credit Spread Competition affects Capital Structure, Leverage, Credit Spread. 3. Mean Reversion Process, Regime Switching Process Not Yet More appropriate to the model because we consider both investment (upper boundary) and default (lower boundary).

16 Thank you very much! Corresponding Author Michi Nishihara Assistant Professor Center for the Study of Finance and Insurance, Osaka University