The board of directors of a company is concerned about cash flow. The board feels that the cash flow should be higher than it has been lately and fears that the company manager may be shirking. The board has decided to replace the current manager and to hire a new manager under a one-year contract, with compensation paid at the end of the year. You are hired to recommend a contract that will align the managers interests with those of the firm. Upon reviewing the firms history of past performance, you determine that if the manager works hard (a 1), cash flows of $1,000 are generated with probability 0.7 and $500 with probability 0.3. If the manager shirks (a2), the probability of $1,000 cash flow falls to 0.15, with the probability of $500 rising to 0.85. Your study of past financial statements reveals that the net income is a noisy predictor of cash flow. Specifically, if cash flow is $1,000, then net income for the year before any manager compensation is $850 with probability 0.75 and $350 with probability 0.25. If the cash flow is $350, net income for the year is $850 with probability 0.21 and $350 with probability 0.79. You interview a prospective manager and find that her reservation utility is 5. Also, she is risk- averse, with the utility of compensation equal to the square root of the dollar amount of compensation received. She is also effort-averse, with disutility of effort of 2.5 units of utility if she works hard and 1.5 units of utility if she shirks. Required a) What percentage of net income must the manager be offered, so that she will accept the contract and work hard? Show your calculations. (Round your answers to 2 decimal places.) b) Based on the percentage of net income that you recommended in point a), verify that the manager will work hard. Show your calculations. (Round your answers to 2 decimal places.) c) The sensitivity of a performance measure is the rate at which the expected value of the performance measure increases as the manager works harder. Using the information above, compute the sensitivity of the net income to the mangers efforts (work hard a1 and shirk a2). Show your calculations. d) Suppose that a new accounting standard reduces the noise in the net income. Under the new standard, if the cash flow is $1,000, the net income is $850 with probability 0.81 and $350 with probability 0.19. If cash flow is $500, the net income is $850 with probability 0.15 and $350 with probability 0.85. What percentage of net income must the manager be offered under the new standard? Show your calculations. e) What is the agency cost for the contract offered in point d)? Show your calculations