Three essays on corporate finance modelling

Abstract

In this thesis I use mathematical modelling techniques to further our understanding of three outstanding corporate finance problems. In each case, I derive a novel model of agent behaviour, calculate an efficient numerical solution, then explore how the model informs theory and practice. I present my contributions to each problem as separate self-contained essays. In my first essay I build a novel equity valuation model, based on the fundamental accounting equation and observable book values, that determines a firm's optimal voluntary liquidation policy. Voluntary liquidation allows equityholders of a poorly performing firm to liquidate its assets, repay any creditors, and keep any remaining value. Empirical evidence suggests that investors react favourably to voluntary liquidation announcements, suggesting that the liquidation of inefficient firms improves economic resource allocation. I find that the firm's voluntary liquidation policy is primarily sensitive to earnings risk, expected asset depreciation, liquidation expenses, leverage, expected earnings yield, and expected cost-of-debt. My model successfully replicates empirically observed voluntary liquidation behaviour and suggests that voluntary liquidation aligns manager and equityholder behaviour with respect to leverage and debt maturity choice and increased earning volatility. Manager and equityholder incentives conflict with respect to asset liquidation costs. As a supplement to my first essay, I provide a detailed derivation of my model and the numerical solution of my model's governing partial differential equation. I also provide a highly optimized implementation of the projected successive overrelaxation algorithm that I use to solve my model. This implementation exploits CPU cache locality to greatly accelerate solving two-dimensional stochastic differential equations with early exercise conditions. In my second essay I develop a formal economic model of company director decision making under Australia's past and present insolvent trading laws. A director of an Australian company who incurs debts while their company is insolvent can be chased by creditors for compensation if their company fails. I provide the first tractable model that can determine if this threat of insolvent trading affects director's decisions in a way that is always advantages creditors. I explore director's decision making and subsequent creditor outcomes when directors are threatened by insolvent trading, as well as when directors tactically use Australia's voluntary administration insolvency procedure to avoid insolvent trading litigation. I show that neither a combination of insolvent trading or voluntary administration can simultaneously ensure creditors-best outcomes, eliminate insolvent trading, and reduce director underinvestment. In my third essay I derive a global asset pricing model with endogenous home preference that contains a small open economy with a dividend imputation tax system; Dividend imputation eliminates double taxation by attaching tax credits to distributed dividends for already paid company tax. Domestic investors can use these credits to reduce their personal taxes, while credits are useless to foreign investors. The interplay between imputation eligible domestic investors and ineligible foreign investors makes it difficult to value imputation credits. My model assumes that home bias arises endogenously from the status quo and endowment effect behavioural biases. I find that these biases interact with dividend imputation to drive domestic investors to hold highly concentrated domestic portfolios. I also find that risk-averse domestic investors cannot fully capture the value of imputation credits because concentrating their holdings in the domestic market reduces their diversification.