Investment Timing, Liquidity Constraints,
and Competition
Hsing-Hua Huang
Pai-Ta Shih
Department of Information Management and Finance
National Chiao Tung University
Department of Finance
National Taiwan University
Mar 16, 2015
(Prepared for the seminar at National Chung Cheng University)
Concept of Real Options
 Option
VS.
Commitment
Investment Timing
 NPV
 RO:
: Now or never
Wait and see
Waiting is valuable!
Resource:
http://itscertainlyuncertain.blogsp
ot.tw/2014/01/real-options-on-on
e-page.html
1/33
Concept of Investment Timing Game
The firm with large competitive advantage tends to be “Leader.”
If the first-mover advantage is large, then the “follower” tends to preempt.
For an investment timing game,
waiting is valuable, but should consider the preemptive investment by the rival.
2/33
Overview of Real Options
 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 behavior of a real estate market in duopoly.
3/33
Real Options Applied in Corporate Finance
 Financial Constraints (Boyle and Guthrie, 2003, JF)
 Capital Structure (Mauer and Sarkar, 2005, JBF)

 Macroeconomic Conditions (Hackbarth et al., 2006, JFE)

 M & A (Hackbarth and Morellec, 2008, JF)
RO   Credit Risk (Chen, 2010, JF)
 Managerial Compensation (He, 2011, JFE)

 Corporate Governance (Morellec et al., 2012, JF)
 Competition (Carlson et al., 2014, JFQA)

 Agency Conflicts and Cash (Nikolov and Whited, 2014, JF)
4/33
Motivations (1/4)
Investment
＋
Investment
＋
Financial Constraints
Competition
e.g. Boyle and Guthrie (2003, JF)
Almeida and Campello (2007, RFS)
Cleary et al. (2007, JFQA)
Denis and Sibilkov (2010, RFS)
Bolton et al. (2014, WP)
5/33
e.g. Akdoğu and MacKay (2008, JFQA)
Aguerrevere (2009, JF)
Akdoğu and MacKay (2012, JBF)
Carlson et al. (2014, JFQA)
Fresard and Valta (2014, WP)
Motivations (2/4)

Haushalter, Klasa, and Maxwell (2008, JFE)
When there is greater interdependence of investment opportunities with rivals,
firms with larger cash holdings invest more.

Fresard (2010, JF)
Firms with larger cash holdings gain at the expense of rivals, especially
when rivals face tighter financing constraints.

Relative financial constraints between a firm and its rivals have a
significant impact on firms’ investment decisions.
6/33
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 effect of financial constraints and
competition significantly influences firms’ cash policies.
7/33
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 growing funds 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 capacities are crucial for firms to win a patent race
(an investment timing game).
8/33
What This Paper Does
We

extend Boyle and Guthrie (2003, JF) to a real option game
model in a duopoly with a first-mover advantage.

investigate the interdependent effects of asymmetric
financing capacities and investment costs on an investment
timing game.
9/33
Main Findings (1/3)
If the cost asymmetry between the two firms is large,
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)
the firm with a cost advantage tends to be the leader
when the risk of future funding shortfalls is relatively low.
10/33
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)
as its financing capacity improves and closes to that of the
rival, the weaker firm cannot be the leader anymore.
11/33
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.
12/33
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).
13/33
Contributions to Literature (2/3)
 This paper complements the recent findings showing that the
interaction between financial constraints and competition
significantly influence firms’ 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).
14/33
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).
15/33
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.
16/33
Investment Environment
 Two risk-neutral firms, Firm 1 and Firm 2, both own perpetual rights to invest
in an irreversible project at asymmetric investment costs I i , i  1, 2 .
 The project value of investment follows the geometric Brownian motion as:
dV (t )
 (r   )dt   dW (t ) , given V (0)  V .
V (t )
 Before the follower invests, the leader’s post-investment payoff is V .
 When the follower has invested, the leader’s payoff becomes (1  qL )V and
the follower’s payoff is (1  qF )V , and further assume that 1  qF  qL  0.
17/33
 Investment is possible if and only if Ii  X  G  i (1  qk )V , i  1, 2 , k  L, F ,
where X and G respectively denote cash holdings and market values of
existing assets of the two firms, and i [0,1) shows the friction, capturing
Firm i ’s ability to extract the full project value for outside investors, limit the
amount of funding. Larger i means the firm with higher financing capacity.
 dX 
rXdt
investing cash in riskless securities

vdt   dB (t )
,
cash flows generated by G
 The firm with a smaller ( Ii  X  G) i , resulting from a lower investment cost
or/and a higher financing capacity, is the less (liquidity) constrained firm.
18/33
Review of Boyle and Guthrie (2003)
 Assume Firm 1 exclusively owns the right to invest this project.
 Firm 1 is liquidity constrained.
 The real option value of Firm 1, M 1c ( X ,V ) and optimal investment trigger
Vˆ1,cM ( X ) are solved simultaneously by using finite difference method.

c
ˆc (X )  I
lim
M
(
X
,
V
)

V
1
1, M
1
ˆc
V V1,M ( X )
 Given I1  G  100 ,   0.3 , r    0.03 ,   0.5 ,   80 , and 1  0.8 ,
optimal investment triggers are given by the following Figure 1.
19/33
Fig. 1
Optimal investment triggers when the firm is liquidity constrained
Vˆ1,cm
M ( X )  ( I1  G  X )  1
Vˆ1,uM
Vˆ1,cM ( X )
20/33
The risk of future funding
shortfalls is high
The risk of future funding
shortfalls is low
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
Fi c ( X ,V ) and optimal investment trigger Vˆi ,cF ( X ) are solved together.
 Just similar to the monopolistic case
 Except that the post-investment payoff is
c
ˆc (X )  I
lim
F
(
X
,
V
)

(
1

q
)
V
i
F
i ,F
i
ˆc
V Vi , F ( X )
21/33
Solve the Model Backward (2/3)
 The leader’s value function when the leader has invested
but the follower has not.

The leader’s post-investment value L ic ( X ,V ) must be adjusted when the
follower invests

c
ˆc (X )
lim
L
(
X
,
V
)

(1

q
)
V
i
L
j ,F
ˆc
V V j , F ( X )
 The follower’s investment dilutes the value the leader enjoys.
22/33
Solve the Model Backward (3/3)
 The leader’s value function and optimal investment trigger
 When the leader has not invested, the leader’s real option value
Lci ( X ,V ) and optimal investment trigger Vˆi ,cL ( X ) are jointly solved.
 Consider the above dilution effect on the leader’s investment decision.

23/33
c
c
ˆ c ( X ))  I
lim
L
(
X
,
V
)

L
(
X
,
V
i
i
i ,L
i
ˆc
V Vi , L ( X )
Game Equilibria (1/2)




 Define Vˆi ,cP ( X ) as the smallest solution of Fi c X ,Vˆi ,cP ( X )  L ic X ,Vˆi ,cP ( X )  I i .
 It denotes the earliest investment timing that Firm i still has an incentive to
preempt to be the leader given X .
 When the cash reserve is too low, the preemptive investment decision is
not attainable.


ˆ c ( X ),Vˆ cm ( X ) , where Vˆ cm ( X )  ( I  G  X )  (1  q ) .
(
X
)

max
V
 Define Vˆi ,cm
P
i,P
i,L
i ,L
i
i
L
(The leader must have sufficient funds to finance the investment project.)
24/33
Game Equilibria (2/2)



ˆ cm
ˆc
ˆ cm
If min Vˆ1,cL ( X ),Vˆ2,cL ( X ),Vˆ1,cm
P ( X ),V2, P ( X )  Vi , L ( X ) or Vi , P ( X ) , Firm i
is the leader and Firm j is the follower, where i, j  1, 2 and i  j .

Given the roles of the game, the leader Firm i must consider the
potential preemptive investment of the follower, thus choosing


as its optimal investment timing decision, while
min Vˆi ,cL ( X ),Vˆjcm
,P ( X )
the follower Firm j chooses Vˆjc,F ( X ) .
25/33
Results and Implications

Employ Crank-Nicolson finite difference method with parameters: I1  100 ,
G  100 ,   0.3 , r    0.03,   0.5 ,   80 , qL  0.45 and qF  0.55 .

Firm 1 is fixed as the low-cost firm, i.e., I1  I 2 , and with a greater value
of i Firm i has a larger financing capacity.

We investigate how asymmetric financing capacities affect the two firms’
roles and optimal investment timing decisions, when the cost asymmetry is
large and small.
26/33
Fig. 2 Effects of asymmetric financing capacities when I 2  150 (large asymmetry)
Panel A: Firm 1 has a higher financing
capacity (1  0.8   2  0.5 )
27/33
Panel B: Firm 2 as a higher financing
capacity (1  0.8   2  1)
Fig. 3 Effects of asymmetric financing capacities when I 2  103 (small asymmetry)
Panel A: 1  0.8   2  0.5
 Firm 2, the weaker firm, which has a
lower financing capacity and small
cost disadvantage can even be the
leader.
 Firm 1 starts to enjoy waiting flexibility
and delays its investment timing.
Vˆ2,cmP ( X )  The risk of delaying investment for
Firm 2 is still so high that its optimal
investment decision is to invest as
soon as possible.
28/33
Fig. 3 Effects of asymmetric financing capacities when I 2  103 (small asymmetry)
Panel B: 1   2  0.8
Panel C: 1  0.8   2  1
Vˆ2,cmP ( X )
29/33
Vˆ2,cmP ( X )
Fig. 4 Investment timing decision and project return volatility
 Firm 1 changes its role from
a follower to a leader as
project value volatility rises
from 0.2 to 0.4.
30/33
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 leader when the risk of future
funding shortfalls is relatively high.
 Second, a weaker firm that has a lower financing capacity and
small cost disadvantage can even be the leader under some
degree of the risk of future funding shortfalls.
31/33
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.
32/33
Thanks for your attention!
Comments and suggestions
are welcome!
33/33