Essays in Corporate Finance

Prior research has been divided regarding how firms respond to bankruptcy risk, largely revolving around two competing forces. On the one hand, asset substitution encourages firms to increase the riskiness of assets to extract value from creditors. On the other, firms want to minimize bankruptcy risk, either by reducing cash flow risk or through increasing the size of the firm. I test these two theories using a natural experiment of chemicals used in production processes being newly identified as carcinogenic to explore how firms may respond to potential negative cash flow resulting from litigation risk. I use plantlevel chemical data to study firm exposure to risk. I examine how responses between firms of differing levels of chemical exposure may vary within the industry, how firm financial distress affects firm response and whether public and private firms respond differently. In general, my research provides support for the asset substitution theory. My first paper studies how investment response varies based on level of carcinogenic exposure. I find that firms with moderate levels of exposure make efforts to mitigate their cash flow risk and reduce their exposure. At the same time, firms with high levels of exposure increase their exposure and riskiness of future cash flows. These findings are consistent with asset substitution theory. My second paper analyzes the interaction of financial distress and risk exposure. I find that firms in a stronger financial position are more likely to limit their exposure by reducing the number of exposed facilities. On the other hand, not only do firms in weaker financial position not decrease their exposure, I find that, in some instances, they increase their exposure to carcinogens. This work again supports the theory of asset substitution. Finally, in my third paper, I explore if public firms respond differently to a potential negative cash flow shock than do private firms. I test whether existing public firms are more likely to attempt to minimize their cash flow risk and thus reduce their carcinogen exposure than are private firms. I do not find evidence that public firms respond differently to this shock than do private firms.

Essays on Financial Constraints, R&D Investments, and Competition

This dissertation consists of two chapters of theoretical studies that investigate the effect of financial constraints and market competition on research and development (R&D) investments. In the first chapter, I explore the impact of financial constraints on two different types of R&D investments. In the second chapter, I examine the impact of market competition on the relationship between financial constraints and R&D investments. In the first chapter, I develop a dynamic monopoly model to study a firm’s R&D strategy. Contrary to intuition, I show that a financially constrained firm may invest more aggressively in R&D projects than an unconstrained firm. Financial constraints introduce a risk that a firm may run out of money before its project bears fruit, which leads to involuntary termination on an otherwise positive-NPV project. For a company that relies on cash flow from assets in place to keep its R&D project alive, early success can be relatively important. I find that when the discovery process can be expedited by heavier investment (“accelerable” projects), a financially constrained company may find it optimal to “over”-invest in order to raise the probability of project survival. The over-investment will not happen if the project is only “scalable” (investment scales up payoffs). The model generates several testable implications regarding over-investment and project values. In the second chapter, I study the effects of competition on R&D investments in a duopoly framework. Using a homogeneous duopoly model where two unconstrained firms compete head to head in an R&D race, I find that competition has no effect on R&D investment if the project is not accelerable, and the competing firms are not constrained. In a heterogeneous duopoly model where a financially constrained firm competes against an unconstrained firm, I discover interesting strategic interactions that lead to preemption by the constrained firm in equilibrium. The unconstrained competitor responds to its constrained rival’s investment in an inverted-U shape fashion. When the constrained competitor has high cash flow risk, it accelerates the innovation in equilibrium, while the unconstrained firm invests less aggressively and waits for its rival to quit the race due to shortage of funds.

DIRECT NUMERICAL SIMULATION OF INCOMPRESSIBLE MULTIPHASE FLOW WITH PHASE CHANGE

Phase change problems arise in many practical applications such as air-conditioning and refrigeration, thermal energy storage systems and thermal management of electronic devices. The physical phenomenon in such applications are complex and are often difficult to be studied in detail with the help of only experimental techniques. The efforts to improve computational techniques for analyzing two-phase flow problems with phase change are therefore gaining momentum. The development of numerical methods for multiphase flow has been motivated generally by the need to account more accurately for (a) large topological changes such as phase breakup and merging, (b) sharp representation of the interface and its discontinuous properties and (c) accurate and mass conserving motion of the interface. In addition to these considerations, numerical simulation of multiphase flow with phase change introduces additional challenges related to discontinuities in the velocity and the temperature fields. Moreover, the velocity field is no longer divergence free. For phase change problems, the focus of developmental efforts has thus been on numerically attaining a proper conservation of energy across the interface in addition to the accurate treatment of fluxes of mass and momentum conservation as well as the associated interface advection. Among the initial efforts related to the simulation of bubble growth in film boiling applications the work in \cite{Welch1995} was based on the interface tracking method using a moving unstructured mesh. That study considered moderate interfacial deformations. A similar problem was subsequently studied using moving, boundary fitted grids \cite{Son1997}, again for regimes of relatively small topological changes. A hybrid interface tracking method with a moving interface grid overlapping a static Eulerian grid was developed \cite{Juric1998} for the computation of a range of phase change problems including, three-dimensional film boiling \cite{esmaeeli2004computations}, multimode two-dimensional pool boiling \cite{Esmaeeli2004} and film boiling on horizontal cylinders \cite{Esmaeeli2004a}. The handling of interface merging and pinch off however remains a challenge with methods that explicitly track the interface. As large topological changes are crucial for phase change problems, attention has turned in recent years to front capturing methods utilizing implicit interfaces that are more effective in treating complex interface deformations. The VOF (Volume of Fluid) method was adopted in \cite{Welch2000} to simulate the one-dimensional Stefan problem and the two-dimensional film boiling problem. The approach employed a specific model for mass transfer across the interface involving a mass source term within cells containing the interface. This VOF based approach was further coupled with the level set method in \cite{Son1998}, employing a smeared-out Heaviside function to avoid the numerical instability related to the source term. The coupled level set, volume of fluid method and the diffused interface approach was used for film boiling with water and R134a at the near critical pressure condition \cite{Tomar2005}. The effect of superheat and saturation pressure on the frequency of bubble formation were analyzed with this approach. The work in \cite{Gibou2007} used the ghost fluid and the level set methods for phase change simulations. A similar approach was adopted in \cite{Son2008} to study various boiling problems including three-dimensional film boiling on a horizontal cylinder, nucleate boiling in microcavity \cite{lee2010numerical} and flow boiling in a finned microchannel \cite{lee2012direct}. The work in \cite{tanguy2007level} also used the ghost fluid method and proposed an improved algorithm based on enforcing continuity and divergence-free condition for the extended velocity field. The work in \cite{sato2013sharp} employed a multiphase model based on volume fraction with interface sharpening scheme and derived a phase change model based on local interface area and mass flux. Among the front capturing methods, sharp interface methods have been found to be particularly effective both for implementing sharp jumps and for resolving the interfacial velocity field. However, sharp velocity jumps render the solution susceptible to erroneous oscillations in pressure and also lead to spurious interface velocities. To implement phase change, the work in \cite{Hardt2008} employed point mass source terms derived from a physical basis for the evaporating mass flux. To avoid numerical instability, the authors smeared the mass source by solving a pseudo time-step diffusion equation. This measure however led to mass conservation issues due to non-symmetric integration over the distributed mass source region. The problem of spurious pressure oscillations related to point mass sources was also investigated by \cite{Schlottke2008}. Although their method is based on the VOF, the large pressure peaks associated with sharp mass source was observed to be similar to that for the interface tracking method. Such spurious fluctuation in pressure are essentially undesirable because the effect is globally transmitted in incompressible flow. Hence, the pressure field formation due to phase change need to be implemented with greater accuracy than is reported in current literature. The accuracy of interface advection in the presence of interfacial mass flux (mass flux conservation) has been discussed in \cite{tanguy2007level,tanguy2014benchmarks}. The authors found that the method of extending one phase velocity to entire domain suggested by Nguyen et al. in \cite{nguyen2001boundary} suffers from a lack of mass flux conservation when the density difference is high. To improve the solution, the authors impose a divergence-free condition for the extended velocity field by solving a constant coefficient Poisson equation. The approach has shown good results with enclosed bubble or droplet but is not general for more complex flow and requires additional solution of the linear system of equations. In current thesis, an improved approach that addresses both the numerical oscillation of pressure and the spurious interface velocity field is presented by featuring (i) continuous velocity and density fields within a thin interfacial region and (ii) temporal velocity correction steps to avoid unphysical pressure source term. Also I propose a general (iii) mass flux projection correction for improved mass flux conservation. The pressure and the temperature gradient jump condition are treated sharply. A series of one-dimensional and two-dimensional problems are solved to verify the performance of the new algorithm. Two-dimensional and cylindrical film boiling problems are also demonstrated and show good qualitative agreement with the experimental observations and heat transfer correlations. Finally, a study on Taylor bubble flow with heat transfer and phase change in a small vertical tube in axisymmetric coordinates is carried out using the new multiphase, phase change method.