复制下来有点乱码，可以直接二楼的pdf

• Consider a firm which is initially 100 percent owned by a manager. The manager’swealth, [size=11.000000pt]W , consists only of the market value of the firm’s equity. The total amount ofthe firm’s resources is $1 million. The manager will use some of the firm’s resourcesfor his/her own perquisite consumption, [size=11.000000pt]F, which is completely unproductive. Thatis, $1 perquisite consumption by the manager would result in $1 reduction in the firmvalue. The manager has a utility function, [size=11.000000pt]U ([size=11.000000pt]F, W ), which is increasing and concavein both [size=11.000000pt]F and [size=11.000000pt]W. The manager’s utility function is publicly known, but his/herperquisite consumption is unobservable by others.
  (a)Show graphically and explain in words how the owner-manager optimally chooseshis/her perquisite consumption.
  (b)Now, the owner-manager wants to reduce his/her ownership of the firm from100% to 51%. The manager thus sells 49% of the firm’s shares to new sharehold-ers who are willing to purchase the shares as long as they expect to break-even atthe zero riskless rate of interest. Show that if the new shareholders naively con-jecture that the owner-manager remains to consume the same amount of perksas that characterized in part (a) and price the shares accordingly, they will suffera loss.
  (c)Who would bear the agency costs of outside equity? Why？
  
  
  2.Suppose that a firm has assets in place which generate $100 million in good stateand $50 million in bad state, where either state is equally likely to occur. The firmhas outstanding debt with promised payments of $50 million. An investment project,which requires $10 million and yields a risky cash flow of $11 million in the good stateand zero in the bad state, is now available to the firm. Suppose that the existing debthas no covenant restricting the firm to issue senior debt to raise additional funds.Assume zero riskless rate of interest and universal risk neutrality.
  (a)If the firm has to issue equity to existing shareholders, would the firm optimallychoose to undertake the project given that its objective is to maximize share-holders’ wealth? Why?
  (b)If the firm has to issue debt junior than the existing debt, would the firm op-timally choose to undertake the project given that its objective is to maximizeshareholders’ wealth? Why?
  
  (c) If the firm has to issue debt with the same seniority as the existing debt, wouldthe firm optimally choose to undertake the project given that its objective is tomaximize shareholders’ wealth? Why?
  (d) If the firm has to issue debt senior than the existing debt, would the firm op-timally choose to undertake the project given that its objective is to maximizeshareholders’ wealth? Why?
  
  
  3. Consider a firm that investors believe is one of two types, good or bad, with equalprobability. Information is asymmetric in that managers of the firm know with cer-tainty the true type of the firm. The firm has access to a project which requires animmediate investment of $1 million. The objective of the managers is to maximizethe intrinsic value of the existing shareholders’ claims. The cash flow distribution ofthe firm, contingent on its investment decision and type, are presented below:
  
  
  Good Bad
  Asset-in-place $1.25 million $1 million
  Project $1.2 million $1.1 million
  
  
  
  
  Suppose that all agents are risk neutral (i.e., they only care about expected value)and the riskless rate of interest is 5%. If the firm is limited to equity financing, shouldit go ahead with the project? Why?