Real Options, Debt Financing, and Competition

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Real Options, Debt Financing, and Competition
12th ANNUAL INTERNATIONAL CONFERENCE ON REAL
OPTIONS July 9-12, Rio de Janeiro

• Michi Nishihara Takashi Shibata
• Osaka University Tokyo Metropolitan
  University

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Outline

• Introduction
• Monopoly
• Duopolies (i), (ii), (iii)
• n Firms
• Numerical Examples
• Conclusion
• Future Work

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1 Introduction
Important Feature of Real Options Complex
Stakeholders
Firm A
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.
?This Paper? Equityholders(Owner
EntrepreneurManager), Bondholders, Several Firm
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Obtain Profit flow with Paying Coupon
Market Demand
Good

Time t
Bad
0
Default
Invest with Issuing Debt
Other Firms
Equityholders
Bondholders Equityholders (OwnerEntrepreneur)
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
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2. Monopoly
Unlevered McDonald, Siegel (1986)
Market Demand
Maximize Firm Value Equity (Owner) Value
Investment Time
Investment Trigger
Firm Value Equity Value
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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
Firm Value Equity Value Debt Value
cf. Leland(1994), Goldstein, Ju,
Leland(2001) Tradeoff between Tax Effects and
Default Costs
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Equityholders (owner) bondholders
Maximize Firm Value
Larger
Investment Time
Earlier
Investment Trigger
Coupon
Positive
Default Trigger
Positive
Leverage, Credit Spread (at time of investment)
Constants independent of
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3. Duopoly
Procedure (symmetric duopoly)

• Assuming that one of the firms (called Leader)
  has invested at , derive the best
  response of the other (called Follower).
• Derive Followers and Leaders expected payoff as
  functions of .
• 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 followers optimal response.

Benchmark Unlevered vs. Unlevered
Both try to invest at
Leader Follower No opportunity to invest Value
0
Preemptive
Levered
Action Set Investment Trigger
Coupon
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Prop. 1 Duopoly (i) Levered vs. Levered
Leader Follower Value Prop. 2 Duopoly
(ii) Levered vs. Levered (Only the leader can
issue debt) Leader Follower Value
Preemptive
Discount due to competition
Preemptive
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Prop. 3 Duopoly (iii) Levered vs. Unlevered
(exogenous reasons) Levered Leader Value Unle
vered Follower Value Levered
Leader Value Unlevered Follower Value Comparis
on of Duopoly (i), (ii), (iii)
Preemptive
Dominant leader-type
Same as Monopolist
cf. Kong, Kwok(2007)
(Value of Levered) gt (Value of Unlevered)
Investment Time (ii) lt (i), (iii) ? Monopolist
Value of Levered (ii) lt (i), (iii) ? Monopolist
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4. n Firms
n Unlevered firms Same Outcome as Duopoly,
zero-NPV timing

• n Levered firms (Every firm can issue debt)
• Procedure
• Solve the last firms problem
• Solve the problem of two firms remaining
  (Follower moves to ? , Prop. 1)
• Solve the problem of three firms remaining (Two
  Followers move to ?)
• 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
0 (Competitive Market) (n ?8)
cf. Lambrecht, Perraudin(2003)
Discount due to competition
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Table 1 Preemptive game
Monotone Decrease
Table2 Leader-Follower game
Monotone Increase
Social Loss
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5. Numerical Examples
Table 4 Comparison of a monopoly with Duopolies
(i), (ii), and (iii)
Crucial Point Whether a firm can optimize
capital structure.
Table 6 Loss(n) for various s.
Monotone Decrease
Active entry and default reduce the first
movers advantage.
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6. Conclusion

• The possibility of the leaders bankruptcy
  generates a positive firm value under preemptive
  competition among several firms.
• Firms investment trigger, coupon, and default
  trigger are larger with the order of 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.
• Firms Investment time goes to zero-NPV point and
  the firm value goes to 0 on letting the number
  of firms ?8.
• Social loss from preemption increase with the
  number of firms.
• Higher volatility moderates the preemptive
  competition and reduces the social loss.

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7.Future Work
1. Case of , i.e., two firms can be
active in the market.
Now Working
Second Movers Advantage When Follower enters
the market with Leader, Follower can choose
lower coupon than Leaders 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).

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Thank you very much!
Corresponding Author
Michi Nishihara Assistant Professor Center for
the Study of Finance and Insurance, Osaka
University nishihara_at_sigmath.es.osaka-u.ac.jp