ANEXOS, CUADROS A LOS ESTADOS FINANCIEROS

Managers are generally given stock because they are believed to have the ability to positively influence the value of the firm. Work relating to the optimal incentive level that shareholders should give managers to motivate them to exert effort has shown that the optimal incentive level decreases with firm risk.39 _{These models generally focus on a manager who can directly}

affect the stock price of the firm he works for by exerting effort, but the

stock price is subject to significant noise. As the level of noise increases, the manager’s optimal level of effort decreases because the firm’s stock price performance depends less on his level of effort. It is therefore not surprising that as the level of noise increases, the optimal incentive decreases in this context. As will become clear later, a key distinction between my thesis and this work is that there is no “noise” in my model. That is, the manager’s effort is fully reflected in the shareholder’s payoff.

The majority of this work however does not make any attempt to separate the impact of the firm’s systematic and idiosyncratic risk on the optimal in- centive level. The exception to this is a paper by Jin (2002), who examines the optimal incentive given to the manager when he cannot trade the stock of his own firm but can trade the market portfolio. He finds that idiosyn- cratic risk decreases the optimal incentive for the same reasons as in the standard model, while systematic risk has no effect on the optimal incentive level. The reason that systematic risk has no effect is that the manager can simply adjust his holding of the market portfolio to eliminate any changes in the systematic component of the firm’s risk. This analysis however doesn’t take into account how changes in the level of both systematic and idiosyn- cratic risk can affect the manager’s valuation of the firm. This is likely to affect the manager’s optimal level of effort, and thus the contract provided to the manager. In this thesis I will model a slightly different problem that incorporates the manager’s valuation problem as well as his effort decision. I do this by allowing effort to affect the investment cost of the firm’s project. Once the manager’s optimal level of effort is determined, we can then model the shareholder’s problem of how much stock to give the manager.

A related problem that has not been discussed is what impact effort has in a real options setting. The real options papers that have examined the difference between shareholders and managers and how to contract to correct for these differences have generally focused on inducing optimal timing from a manager who has private information. Wonder (2006) presents a model

of private information where the manager can divert the firm’s assets to his own use and shows that the optimal contract is a call option on the project payoff. Grenadier and Wang (2005) take a different approach and allow the manager to exert effort to alter the probability distribution of the private portion of the payoff. In their model effort alters the chance of getting a “good” project instead of a “bad” project. In this setting, since the manager also receives private information by waiting, his option is more valuable than the shareholders’ and thus the manager will delay investment more than a shareholder would. Finally, Hugonnier and Morellec (2007a) present a model where the manager is undiversified and thus values the project differently to the shareholders but faces the possibility of a control challenge if his behaviour deviates too far from value maximising behaviour. They find that risk aversion and idiosyncratic risk significantly speed up investment, but this is mitigated by the threat of a control challenge. This model however has a very ad-hoc link between the manager’s wealth and the project in that his wealth is simply scaled up or down by a constant at the time of investment. This constant depends on whether he is replaced and if the project has a negative NPV.

Chapter

3

General Setup

3.1

Introduction

The purpose of this chapter is to set out the modelling framework we will be using in the rest of this thesis. This serves the purpose of consolidating any common assumptions in a single point of reference. We begin this chapter in Section 3.3 by setting out the principal agent problem between the manager and shareholder. Following this we describe the specific assumptions made concerning the shareholder’s problem in Section 3.3 and the manager’s prob- lem (including possible utility functions) in Section 3.4. We next set out the assumed stochastic structures for the market asset and the firm’s cashflow in Section 3.5. The final part of the framework we need to lay out is the man- ager’s inter-temporal wealth equations, which we do in Section 3.6. These equations set out the dynamics of the manager’s financial wealth before and after investment.

The next step is to combine these different assumptions to derive the man- ager’s general Hamilton-Jacobi-Bellman (HJB) equation. This is done in Sec- tion 3.7 and serves as the basis for the various models we will solve throughout

Chapter 1: Introduction

Part 2: The “clean path” Chapter 4: CARA valuation

of SBM cashflow

Chapter 5: Managerial Effort

Chapter 6: The Shareholder's Static Hiring Decision

Chapter 7: Effort and the timing option

Chapter 8: The Shareholder's Dynamic Problem Chapter 9: CRRA valuation

of GBM cashflow

Chapter 10: Conclusion Chapter 2: Literature Review

Chapter 3: General Setup

Part 1: Introduction/ Motivation Part 3: Direct wealth effects Appendices Part 4: Conclusion & appendices

out this thesis.

The final section of this chapter (Section 3.8) sets out a special case of the general model, corresponding to the manager’s value function when there is no project/cashflow. This is the well known model from Merton (1969). The solution to this model is important as it represents the manager’s outside option, i.e. the payoff he gets from investing/not accepting the job.1