Investment Timing, Liquidity Constraints,
and Competition
Hsing-Hua Huang Pai-Ta Shih
Department of Information Management and Finance Department of Finance
National Chiao Tung University National Taiwan University
Mar16, 2015
(Prepared for the seminar at National Chung Cheng University)
From Financial Options to Real Options
Black and Scholes (1973, JPE), equity is a call option on asset value of firm.
Myers (1977, JFE), firm value depends on options to develop real asset.
Operational Flexibility
Brennan and Schwartz (1985, JB), evaluating natural resource projects.
Majd and Pindyck (1987, JFE), option to invest, defer option
Financial Flexibility (Structural Model in Credit Risk)
Leland (1994, 1998, JF), option to default and optimal capital structure.
Strategic Exercise of Real Options (Real Options Game)
Grenadier (1996, JF),the behaviorof a real estate market in duopoly.
Real Options Applied in Corporate Finance
Real Options Applied in Corporate FinMotivations (1/4)
Motivations (2/4)
Haushalter, Klasa, and Maxwell (2008, JFE)
When there isgreater interdependence ofinvestment opportunitieswithrivals, firms with larger cash holdings invest more.
Fresard (2010, JF)
Firmswith larger cash holdings gain at the expense of rivals,especially
when rivals face tighter financing constraints.
Relative financial constraints between a firm and its rivalshavea significant impactonfirms’investment decisions.
Motivations (3/4)
Morellec et al. (2013, WP)
Firms in more competitive industries hold more cash and the effects are stronger for smaller, financially more constrained firms
Lyandres and Palazzo (2014, WP)
Innovative firms’ optimal cash holdings increase in competition but only for relatively financially constrained firms by using NBER patent data.
The interdependent effectof financial constraints and competition significantly influencesfirms’ cash policies.
Motivations (4/4)
Munos (2009, Nature Reviews Drug Discovery)
The fraction of approved new drugs from small biotech firms rises up from 23% to nearly 70% partially due to growingfunds provided by venture capitalists.
Schroth and Szalay (2010, ROF)
Firms are more likely to win drugs and medical patent races when they hold more cash and assets than rivals.
Financial capacitiesare crucial for firms towin a patent race (aninvestment timing game).
What This Paper Does
We
extend Boyle and Guthrie (2003, JF) to a real optiongame model in a duopoly with a first-mover advantage.
investigate the interdependent effectsof asymmetric financing capacities and investment costs on an investment timing game.
Main Findings (1/3)
If the cost asymmetry between the two firms islarge,
1) the firm with a larger financing capacity tends to be the leader when the risk of future funding shortfalls is relatively high; and
2) thefirm with a cost advantage tends to be the leader
when the risk of future funding shortfalls is relatively low.
Main Findings (2/3)
If the cost asymmetry between the two firms is small,
1)a weaker firm that has a lower financing capacity and a small cost disadvantage can even be the leader when the risk of future funding shortfalls is median; and
2)asits financing capacity improves and closes to that of the rival, the weaker firm cannot be the leader anymore.
Main Findings (3/3)
Our model shows that higher project return volatility could make a firm’s investment timing earlier, later and unchanged.
Higher investment project return volatility can lead to the firm’s role change from a follower to a leader, thereby lowering the firm’s optimal investment trigger.
It can also make the firm’s optimal investment trigger unchanged due to its liquidity constraints.
Contributions to Literature (1/3)
This paper contributes to real options game literature which investigates the roles and decisions in an investment timing game. For example, Pawlina and Kort (2006), Manson and Weeds (2010), and Carlson et al. (2014).
This paper also contributes to theoretical literature which demonstrates the relation between a firm’s investment decision and its liquidity constraints. For example, Boyle and Guthrie (2003), Cleary et al. (2007), and Bolton et al. (2014).
Contributions to Literature (2/3)
This paper complements the recent findings showing that the interaction between financialconstraints and competition significantlyinfluencefirms’ decisions.
Strategic Cash Holding Policy
For example, Morellec et al. (2013), Hoberg et al. (2013),
Ma et al. (2014), and Lyandres and Palazzo (2014).
Strategic Investment Decision
For example, Haushalter et al. (2008) and Fresard (2010).
Contributions to Literature (3/3)
This paper provides a theoretical foundation to explain why relative financing capacity plays an important role in winning a drug and medical patent race. For example, Munos (2009) and Schroth and Szalay (2010).
Theoretical Methodology
Boyle and Guthrie (2003)
Analyze optimal investment timing decision with liquidity constraints in a single-firm setup.
Our model
Two firms with asymmetric financing capacity and investment costs face an investment opportunity.
The roles (leader or follower) and optimal investment timing decisions are endogenously determined by a two-player investment timing game.
Investment Environment
Two risk-neutral firms, Firm 1 andFirm 2, both own perpetual rights to invest in an irreversible project at asymmetric investment costs , .
The project value of investment follows the geometric Brownian motion as:, given.
Before the follower invests, the leader’s post-investment payoff is .
When the follower has invested, the leader’s payoff becomes and the follower’s payoff is , and further assume that .
Investment is possible if and only if,,where and respectively denote cash holdings and market values ofexisting assets of the two firms, and shows the friction, capturing Firm ’s ability to extract the full project value for outside investors, limit the amount of funding. Larger means the firm with higher financing capacity.
The firm with a smaller , resulting from a lower investment cost or/and a higher financing capacity, is the less(liquidity) constrained firm.
Review of Boyle and Guthrie (2003)
Assume Firm 1exclusively owns the right to invest this project.
Firm 1isliquidity constrained.
The real option value of Firm 1, and optimal investment trigger are solved simultaneously by using finite difference method.
Given , , , , , and, optimal investment triggers are given by the following Figure 1.
Solve the Model Backward (1/3)
The follower’s value function and optimal investment trigger
After the leader has invested, the follower’s real option value and optimal investment trigger are solved together.
Just similar to the monopolistic case
Except that the post-investment payoff is
Solve the Model Backward (2/3)
The leader’s value function when the leader has invested but the follower has not.
Theleader’s post-investment value must be adjusted when the follower invests
The follower’s investment dilutes the value the leader enjoys.
Solve the Model Backward (3/3)
The leader’s value function and optimal investment trigger
When the leader has not invested, theleader’s real option value and optimal investment trigger are jointly solved.
Consider the above dilutioneffect on the leader’s investment decision.
Game Equilibria (1/2)
Define as the smallest solution of .
It denotes the earliest investment timing that Firm still has an incentive to preemptto be the leader given .
When the cash reserve is too low, the preemptive investment decision is not attainable.
Define, where .
(The leader must have sufficient funds to finance the investment project.)
Game Equilibria (2/2)
If or , Firm is the leader and Firm is the follower, where and .
Given the roles of the game, the leader Firm must consider the potential preemptive investment of the follower, thus choosing as its optimal investment timing decision, while the follower Firm chooses .
Results and Implications
EmployCrank-Nicolson finite difference method with parameters:,,, , , , and .
Firm 1 is fixed as the low-cost firm, i.e., , and with a greater value of Firm has alarger financing capacity.
We investigate how asymmetric financing capacitiesaffectthe two firms’roles and optimal investment timing decisions, when the cost asymmetry is large and small.
Fig. 2 Effects of asymmetricfinancing capacities when (large asymmetry)
Fig. 3 Effects of asymmetric financing capacities when (small asymmetry) Panel A:
Fig. 3 Effects of asymmetric financing capacities when (small asymmetry)
Panel B: Panel C:
Fig. 4 Investment timing decision and project return volatility
Concluding Remarks (1/2)
We extend Boyle and Guthrie (2003) to investigate the interdependent effects of asymmetric financing capacities and investment costs on investment timing decisions in a duopoly.
First, suffering a significant cost disadvantage the firm with larger financing capacity can still be the leaderwhen the risk of future funding shortfalls isrelatively high.
Second, a weaker firm that hasa lowerfinancing capacity and small cost disadvantage can even be the leader under some degree of the risk of future funding shortfalls.
Concluding Remarks (2/2)
In particular, as the financing capacity of the weaker firm improves and closes to that of the rival,the weaker firm cannot be the leader anymore.
Third, only when the risk of future funding shortfalls is low, small asymmetry of investment costs leads to preemption.
Finally, higher project return volatility can make the firm’s role change from a follower to a leader, thereby lowering the firm’s optimal investment trigger.
Thanks for your attention!
Comments and suggestions
arewelcome!
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