as shown in files

Economics 203, Fall 2001

The actions: Nature

o Chooses the type of the manager: 80% of the time he is a bad manager and 20% of the time he is a good manager.

The manager needs to choose if he wants to issue debt or equity. o If he issues debt he needs to choose the face value (the amount that

investor will receive next period) of the bonds he will issue. o Ifheissuesequityheneedstodecidetheshare????ofthefirmthathewill

sell to the investor (the investor will receive a share ???? of the future cash

flows generated by the firm). The investor needs to choose if he wants to spend $40 to buy the equity or the

bonds that the manager issued.

The payoffs:

• The manager is trying to finance an investment project that cost $40. That project will produce cash flows of $100 in the good state and $20 in the bad state.
• The probability of the good state of the world is given by the type of manager. If the manager is bad the probability that the good state is realized is 50%. If the manager is good the probability that the good state is realized is 80%.
• The manager receives the payoff of the shareholders (since there are no moral hazard problem between shareholders and manager in this case). The investor receives the payment for his bond/equity minus the $40 financing if he accepted the contract and $0 otherwise (this is implied by the required return of 0%).

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Furthermore, there is a cost of bankruptcy in this case. If the firm goes bankrupt (it cannot pay the face value of outstanding bonds) the investor needs to pay $10 bankruptcy fee.

Pooling and separating equilibria in this case. For an equilibrium to be a pooling equilibrium in which both managers issue debt in this case the bad manager and the good managers need to issue debt with the same value (or if they issue equity they have to offer the same share of the firm). For the same reason, a separating equilibrium could have both manager issue debt but issue debt of a different face value (note this is unlikely since the bad manager has incentive to pretend he is a good manager).

1. 1) Suppose that the good manager decides to issue bonds (debt) with a face value of $x. Assuming that $x>20, what is the payoff of the investor and manager if the investor accepts the contract? (2 marks)

Economics 454 Theory of Corporate Finance Instructor: Francis Michaud Assignment 3 Due Date: Wednesday December 2nd Student Name: Student Number: Instruction: Print this document and write your answers on it. No copies will be accepted unless you used this document to answer the questions. Space was provided for your answers. MAKE SURE YOUR COPY IS CLEAN. YOUR COPY CAN BE REFUSED IF YOU ERASED MANY TIMES (FOR EXAMPLE). MAKE SURE YOU WORK ON THE PROBLEM ON A DIFFERENT SHEET OF PAPER AND ONLY WRITE HERE ONCE YOU KNOW YOUR ANSWER IS RIGHT. For the whole assignment you can assume a required rate of return of 0% (unless otherwise noted) and risk neutrality. Question 1) Suppose that we have the following game. The players: Nature, a manager and a prospective investor (hereafter \"the investor\"). The actions: Nature o Chooses the type of the manager: 80% of the time he is a bad manager and 20% of the time he is a good manager. The manager needs to choose if he wants to issue debt or equity. o If he issues debt he needs to choose the face value (the amount that investor will receive next period) of the bonds he will issue. o If he issues equity he needs to decide the share of the firm that he will sell to the investor (the investor will receive a share of the future cash flows generated by the firm). The investor needs to choose if he wants to spend $40 to buy the equity or the bonds that the manager issued. The payoffs: The manager is trying to finance an investment project that cost $40. That project will produce cash flows of $100 in the good state and $20 in the bad state. The probability of the good state of the world is given by the type of manager. If the manager is bad the probability that the good state is realized is 50%. If the manager is good the probability that the good state is realized is 80%. The manager receives the payoff of the shareholders (since there are no moral hazard problem between shareholders and manager in this case). The investor receives the payment for his bond/equity minus the $40 financing if he accepted the contract and $0 otherwise (this is implied by the required return of 0%). 1 Furthermore, there is a cost of bankruptcy in this case. If the firm goes bankrupt (it cannot pay the face value of outstanding bonds) the investor needs to pay $10 bankruptcy fee. Pooling and separating equilibria in this case. For an equilibrium to be a pooling equilibrium in which both managers issue debt in this case the bad manager and the good managers need to issue debt with the same value (or if they issue equity they have to offer the same share of the firm). For the same reason, a separating equilibrium could have both manager issue debt but issue debt of a different face value (note this is unlikely since the bad manager has incentive to pretend he is a good manager). 1) Suppose that the good manager decides to issue bonds (debt) with a face value of $x. Assuming that $x>20, what is the payoff of the investor and manager if the investor accepts the contract? (2 marks) 2) Suppose that the bad manager decides to issue bonds with a face value of $x. Assuming that $x>20, what is the payoff of the investor and manager if the investor accepts the contract? (2 marks) 3) Suppose that the good manager decides to issue enough equity so that the investor will have a share of the firm. What is the payoff of the investor and manager if the investor accepts the contract? (2 marks) 4) Suppose that the bad manager decides to issue enough equity so that the investor will have a share of the firm. What is the payoff of the investor and manager if the investor accepts the contract? (2 marks) 2 5) This question will make you look for a pooling equilibrium where both managers pool on choosing to issue debt. To make the question easier it is divided in smaller questions that lead you through the steps. For question 5 always assume that what you did in a previous sub question still holds. a) Suppose that both the bad manager and the good manager pool on a debt issue by issuing debt with a face value of $x. What will be the investor's belief that he is dealing with a good manager if he observe that the manager issued debt with a face value of $x? (2 marks) b) Would you say that the signal (issuing debt with a face value of $x) is informative in this case? Why? (Restated question: Does it help the investor have better beliefs?) (2 marks) c) Given your answer to a), what is the face value of the debt that the managers (both good and bad since they are pooling) must issue if they want the investor to buy the bonds (debt)? (4 marks) d) If managers issue bonds with the face value found in c), what is the payoff that the good manager and bad manager will receive? (4 marks) 3 e) What is the lowest payoff that the good manager and bad manager could receive if they decided to issue shares (if they deviated from the pooling strategy)? (Notice that to answer this question you first have to think about the off equilibrium beliefs of the investor which are not fixed by Bayes rule: any belief is acceptable off equilibrium in this case. What would be the off equilibrium belief by the investor that would make both the good and bad manager worst off? Given these beliefs, what share of the firm would the manager have to give the investor in exchange for his investment? Given this share, what would be the payoff of the bad and good manager?) (8 marks) f) Given your previous answers to question 5, is it an equilibrium when both type of managers are pooling on issuing debt? Explain why. (2 marks) 4 6) This question will make you look for a separating (and semi-separating) equilibrium. To make the question easier it is divided in smaller questions that lead you through the steps. For question 6 always assume that what you did in a previous sub question still holds. a) Suppose that the good manager decides to issue debt and the bad manager decides to issue equity. What will be the investor's belief that he is dealing with a good manager if he sees a debt issue? What will be the investor's belief that he is dealing with a good manager if he sees an equity issue? (2 marks) b) Given your answer to a, what should be the face value of bonds issued by the good manager if he wants the investor to buy the bonds? What should be the share of the firm that the bad manager offers to the investor if he wants him to buy the equity? (2 marks) c) What would the payoff of the good and bad managers be given your answer to b? (4 marks) 5 d) Show that the bad manager would always want to deviate given your answer to the previous question, this separating equilibrium thus can't be an equilibrium. (What would the bad manager get off equilibrium) (4 marks) e) There is a semi-separating equilibrium where the good manager only issues debt and the bad manager sometimes issues debt (with the same face value as the good manager) and sometimes issues equity. What should be the bad manager's payoff from issuing debt in such an equilibrium (and what should the face value of the debt that he issues be)? (Use mostly your previous answers, you don't have to do a lot of calculations). (4 marks) f) What should be the investor's belief that he is dealing with a good manager in the semi-separating equilibrium found in f? (Note: Only one such belief is consistent for the face value found in f). (4 marks) 6 g) Given your answer to g, how often will the bad manager decide to issue debt in the semi-separating equilibrium found in f? (2 marks) h) Would you say that in the semi-separating equilibrium described in questions f, g and h the signal that the manager sends is informative? (2 marks) 7