Several Problems Of Corporate Finance With Time-inconsistent Preferences

The 2002 Nobel Prize in economics was awarded to Daniel kahneman,a pioneer in behavioral economics,and Vernon Smith,a pioneer in experimental economics and since thenthe behavioral finance has attracted a great attention from the financial community.The main advantage of behavioral finance is that it is able to reasonably explain many financial phenomena that traditional finance cannot explain.The inconsistency of time preference is one of the main topics in the study of behavioral finance,which deeply affects the traditional theory of asset pricing and financial decision-making.This article considers a series of corporate finance problems where agents might be time-inconsistent.We develop rigorous mathematical financial models,utilize stochastic control method,numerical calculation technique and economic analysis to examine the capital structure,investment and principle-agent problems.We derive an interesting set of results,which is a meaningful supplement and further improvement to the existing corporate finance theory.Our contributions are summarized as follows:First,we assume that entrepreneur is time-inconsistent and sophisticated,and the cash flow generated by the enterprise follows a double exponential jump diffusion process.According to the asset pricing theory,we explicitly derive the equity value,debt value and optimal default threshold.We examine the impact of time-inconsistent preferences on sophisticated entrepreneur's capital structure,default policy,risk-shifting motive and the inefficiencies arising from debt overhang.By numerical analysis,we find that compared to the time-consistent benchmark,sophisticated entrepreneur often chooses the smaller coupon and the higher default threshold.Time-inconsistent preferences mitigate the sophisticated entrepreneur's risk-shifting incentives,reducing the sophisticated entrepreneur's moral hazard and adverse selection.However,it makes debt-overhang problem more serious.Second,we assume that entrepreneur is time-inconsistent and sophisticated and the holder of convertible debt is time-consistent.The investment costs are raised by equity and convertible debt.According to the real options approach,stochastic optimal control and game theory,we explicitly derive the equity value,convertible debt value and option value.We examine the impact of time-inconsistent preferences on sophisticated entrepreneur's investment policy,default policy,conversion policy ofholder of convertible debt and agency costs between entrepreneur and holder of convertible debt.Our results show that compared to the time-consistent benchmark,time-inconsistent preferences results in entrepreneur's incentive to underinvestment and reduces the option value.The entrepreneur chooses the higher default level,while,the holder of convertible debt chooses the lower conversion level.We find that entrepreneur's interested behavior with time-inconsistent preferences can mitigate the debt overhang problem and the asset substitution problem.Most of all,the appropriate level of the time-inconsistent preferences can eliminate the agency costs between entrepreneur and holder of convertible debt.Third,we assume that the entrepreneur is time-inconsistent,according to the real options approach and stochastic optimal control,we derive the sophisticated entrepreneur's and naive entrepreneur's the value of growth option,investment level and default level,respectively.We examine that the impact of time-inconsistent preferences on entrepreneur's policies.Our results show that the time-inconsistent preferences lead to the underinvestment problem,and compared to sophisticated entrepreneur,naive entrepreneur's underinvestment problem is more severe.What's more,the time-inconsistent preferences eliminate optimistic and confident entrepreneurs' overinvestment problem.We also find that compared to naive entrepreneur,sophisticated entrepreneur prefers to speed up default.Specially,sophisticated entrepreneur is benchmark,the time-inconsistent preferences have larger impact on the degree of the distortion of naive entrepreneur's pre-investment default level,and have small impact on the degree of the distortion of naive entrepreneur's post-investment default level.Fourth,we investigate strategic real investment under uncertainty with time-inconsistent preferences resulting from quasi-hyperbolic discounting in a duopoly market using a game-theoretical real options approach.We demonstrate that time-consistent agents become leaders when facing time-inconsistent rivals.If rivals' time-inconsistent degrees are low,the leaders accelerate investment and investment thresholds are their rivals' preemptive thresholds.In the opposite situations,the leaders invest optimally as competition disappears.Time inconsistency mitigates and even eliminates inefficient investment from preemptive competition.Our model provides behavioral explanation for why preemption occurs in some markets but disappears in others.Fifth,we consider a game model between shareholders and a time-inconsistent manager under the stock-based incentive compensation in a real options framework.We explicitly derive the Nash equilibrium.We show that optimal compensation increases with the time-inconsistent degree and the compensation for a naive manager is higher than that for a sophisticated one.The shareholders' value managed by a time-inconsistent manager is smaller than that by a time-consistent one.Shareholders must choose among time-inconsistent managers in general while they prefer a sophisticated manger to a naive one.Sixth,we explicitly derive the optimal intertemporal consumption and investment with stochastic hyperbolic discounting for a constant absolute risk aversion investor.After that,we explicitly present the utility-based indifference price of cash flows received by the investor.We find that the optimal investment and indifference price do not depend on the discount factor but during the low discounting period,the optimal consumption is more than that under Merton model.The shorter the low discounting period or the bigger the difference between the high and low discount factor,the more obvious the distinction between the two optimal consumption.Last,we consider a firm's investment and financing decisions made by a group of which each member may utilize different discount rates to price cash flow generated by the investment project.We show that a higher degree of decreasing impatience or a greater group diversity increases the project value,accelerates investment and postpones default.Both the value of the investment option and the optimal leverage increase with the degree of the decreasing impatience and the group diversity.The inefficiency from asset substitution increases but it from debt overhang decreases with the degree of the decreasing impatience and the group diversity.Most of our predictions are documented by empirical evidences.