• The shareholders of Balloon Inc. are concerned about the operating cash flow. The shareholders feel that the cash flow should be higher than it has been lately and fear that the company manager may be shirking. They decided to replace the current manager and hire a new manager under a one-year contract, with compensation paid at the end of the year. As a consultant, you are tasked to propose a contract that aligns the manager’s interests with those of the firm. Upon reviewing the firm’s past performance, you determine that if the manager works hard (a1), cash flows of $1,000 are generated with probability 0.75, and cash flow of $500 with probability 0.25. If the manager shirks (a2), the probability of $1,000 cash flow falls to 0.2, with the probability of $500 cash flow rising to 0.8. Using the financial statements, you estimate that if cash flow is $1,000, then net income, before any manager’s compensation, is $961 with probability 0.73 and $361 with probability 0.27. If cash flow is $500, net income is $961 with probability 0.21 and $361 with probability 0.79. You interview a prospective manager and find that her reservation utility is 4. Also, she is risk and effort averse, with the following utility function: (where ???? captures the disutility of effort). Um=√???? െ ଵ ଶ ????ଶ Her disutility of effort is 3 units, if she works hard, and 2.5 unit if she shirks. The shareholders are assumed to be risk neutral. Required a) Assuming that you could observe the manager’s actions. What is the fixed salary that the manager will be willing to accept and work hard (i.e., the first best contract)? Show your computations. (Round your answers to 2 decimal places.) b) In practice, you cannot observe the manger’s actions, so, you propose a contract that includes a percentage of the net income as compensation. What percentage of net income must the manager be offered, so that she will accept the contract and work hard? Show your computations. (Round your answers to 3 decimal places.) c) What is the agency cost of the contract you proposed in point b)? Show your computations. (Round your answers to 2 decimal places.) d) The sensitivity of a performance measure is the rate at which the expected value of a performance measure increases as the manager works harder. Using the information above, compute the sensitivity of the net income to the manager’s efforts (work hard a1 and shirk a2). Show your computations. (Round your answers to 2 decimal places.) e) Suppose that the company updates its accounting policies; as a result, Nardo assesses that if the cash flow is $1,000, the net income is $961 with probability 0.70 and $361 with probability 0.3. If cash flow is $500, the net income is $961 with probability 0.24 and $361 with probability 0.76. You propose a new contract using the updated probabilities. What is the percentage of net income offered to the manager in this new contract? Explain why the new percentage differs from the one you computed in point b). What is the agency cost of this new contract? Show your computations for all requirements. (Round your answers to 2 decimal places.)