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 manager’s interests with those of the firm. Upon reviewing the firm’s history of past performance, you determine that if the manager works hard (a1), cash flows of $1,100 are generated with probability 0.88 and $450 with probability 0.12. If the manager shirks (a2), the probability of $1,100 cash flow falls to 0.25, with the probability of $450 rising to 0.75. Your study of past financial statements reveals that the net income is a noisy predictor of cash flows. Specifically, if cash flows will be $1,100, then net income for the year, before any manager compensation, is $1,024 with probability 0.80 and $400 with probability 0.20. If cash flows will be $450, net income for the year is $1,024 with probability 0.16 and $400 with probability 0.84. You interview a prospective manager and find that her reservation utility is 6. Also, she is risk- averse, with utility of compensation equal to the square root of the dollar amount of compensation received (ඥ$). She is also effort-averse, with disutility of effort of 2 units of utility if she works hard and 1 unit 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 (namely, show that the expected utility from a1 is higher than the expected utility from a2). 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 manger’s efforts (a1 and a2) and briefly comment on the results. Show your calculations. d) Suppose that a new accounting policy decreases the noise in the net income. Under the new policy, if the cash flow will be $1,100, the net income is $1,024 with probability 0.9 and $450 with probability 0.1. If cash flow will be $450, the net income is $1,024 with probability 0.15 and $400 with probability 0.85. Without resorting to any calculations, if you were to rewrite the contract, do you expect the percentage of the net income offered to the manger to work hard (a1) to be higher or lower than the percentage you computed in point a)? Explain why.