Question: Mary is the owner operator of a growing business Until

Mary is the owner– operator of a growing business. Until recently, she has worked hard ( a1), in which case annual net income ( before manager compensation) was $ 10,000, 70% of the time and $ 1,600 30% of the time. More recently, Mary has found it difficult to work hard due to the increasing time devoted to her growing family. As a result, she has shirked on effort, and annual net income has been $ 10,000 only 30% of the time and $ 1,600 70% of the time. Mary decides to hire a manager on a trial basis for one year while she takes the year off. She expects the manager to work hard, thereby restoring net income probabilities to their earlier levels. Mary’s utility of money is equal to her firm’s annual net income after manager compensation.
Mary is negotiating with Henry for the manager job. She ascertains that Henry is risk averse, with utility for money equal to the square root of the dollar compensation received.
Henry is willing to work for Mary providing he receives expected utility of at least 12. Henry advises Mary that he is effort averse, with disutility of effort of 2 if he works hard, and 1 if he does not work hard.

a. Mary realizes that if Henry is to work hard, his compensation must depend on his effort. She decides to offer him compensation based on net income. What proportion of net income must Mary offer Henry if he accepts a one- year contract and works hard? Show calculations.
b. Verify that Henry will work hard based on the net income share you calculated in part a.
c. Net income for Mary’s company has always been prepared based on a mixed measurement model. However, Mary hears that net income based on fair value accounting for certain assets and liabilities will better motivate a manager than net income based on a mixed measurement model. She consults Bill, an accounting theorist, who advises her that under fair value accounting and hard work by the manager, net income would be $ 11,025 70% of the time and $ 900 30% of the time. If the manager shirks, net income will be $ 11,025 30% of the time, and $ 900 70% of the time. Mary wonders why net income is both higher and lower under fair value accounting. Bill replies that, under fair value accounting, net income is volatile since more unrealized gains and losses are included in net income than is the case under the mixed measurement model. Verify that net income is more sensitive and less precise under full fair value accounting than under the mixed measurement model.
d. After some calculation, Bill advises Mary that if she adopts full fair value accounting, a .0288 share of net income will motivate Henry to work hard. Is this contract more or less efficient than the contract under mixed measurement calculated in part a (no calculations required). Explain your answer, using the concepts of performance measure sensitivity and precision.

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