Scott, Financial Accounting Theory, 7th Edition Instructor’s Solutions Manual Chapter 9
341
b. Your recommended profit share of .0291 yields Henry:
12
28235.63.00587.177.0
256.463.02917.0
2600,10291.3.0000,100291.7.0)( 1
≈
−×+×=
−−=
−
×+×=aEU
m
Note: Difference due to rounding.
If Henry shirks with this profit share, his expected utility is
8940.8
18940.9
17764.41176.5
18235.67.00587.173.0
156.467.02913.0
1600,10291.7.0000,100291.3.0)( 2
=
−=
−+=
−×+×=
−+=
−×+×=aEU m
Consequently, since this is less than EUm(a1) (and less than reservation utility of
12), Henry will work hard.
c. To compare sensitivities:
Sensitivity is the increase in the expected value of the performance measure as
the manager works harder.
Expected net income under mixed measurement
Increase in expected value of net income as manager works harder:
Scott, Financial Accounting Theory, 7th Edition Instructor’s Solutions Manual Chapter 9
342
Expected net income under fair value:
Increase in expected value of net income as manager works harder:
To compare precisions:
Precision is the reciprocal of the variance of the performance measure.
Variance of net income under mixed measurement:
Var(NI) given manager works hard:
0.7(10,000 – 7,480)2 + 0.3(1,600 – 7,480)2
Scott, Financial Accounting Theory, 7th Edition Instructor’s Solutions Manual Chapter 9
343
Reciprocal = 6.75
Variance of net income under fair value:
Var(NI) given manager works hard:
d. The fair value contract is more efficient than under mixed measurement, since a
14. a. The (net of amount loaned) payoff table is:
State Payoff
Scott, Financial Accounting Theory, 7th Edition Instructor’s Solutions Manual Chapter 9
344
b. If coverage ratio falls below 4, expected payoff is:
If coverage ratio does not fall below 4, expected payoff is:
Since the probability of the coverage ratio falling below 4 is 0.60, the
unconditional expected rate of return is:
345
15. The payoff table is:
a1 (8% interest) a2 (5% interest)
Payoff Probability Payoff Probability
Bankrupt 8,000 0.25 8,000 0.01
Not Bankrupt 10,800 0.75 10,500 0.99
a. Calculate the expected utility of each act:
b. It appears that the contract is incomplete, that is, no procedures are laid
348
17. The manager’s expected utility for a1 is:
[ ] [ ]
[ ] [ ]
.00.3
0001.3
26455.13546.3
21138.44.05910.56.0
23325.148462.00350.351538.04.03325.141538.00350.358462.06.0
2453185.8462.01103185.1538.04.0453185.1538.01103185.8462.06.0)(
1
approx
aEU
=
=
−+=
−×+×=
−+++=
−×+×+×+×=
Expected utility for a2 is:
9947.2
71.11138.46.05910.54.0)(
2
=
−×+×=aEU
The manager will work hard (a1) and receive reservation utility of 3.
The contract of Example 9.3 is more efficient than the contract of Example 9.2
because the manager attains reservation utility with a lower profit share.
18. A manager may not manage earnings, despite the temptation to do so, because
Scott, Financial Accounting Theory, 7th Edition Instructor’s Solutions Manual Chapter 9
349
Note: Two additional reasons can be suggested from material covered in
Chapter 10 (Section 10.2):
19. a. Let the percentage of net income be k. Then:
Scott, Financial Accounting Theory, 7th Edition Instructor’s Solutions Manual Chapter 9
350
12.
34.
29.20
7
7)81.348.16(
7]40.831.4[3.0]254.21[7.0
7]1084.093.2616.0[3.0]102.093.268.0[7.0
52]10084.072516.0[3.0]1002.07258.0[7.0)(
2/1
2/1
2/1
2/12/1
2/12/1
1
==
===
=+=
=+++=
=×+×+×+×=
=−+++=
k
k
k
kk
kk
kkkkaEU
m
Thus you recommend compensation of .12 times net income.
b. You require net income to be audited to reduce the likelihood of
opportunistic earnings management. The auditor will ensure that GAAP is
followed.
d. The percentage of net income will now be lower. This is because net
Scott, Financial Accounting Theory, 7th Edition Instructor’s Solutions Manual Chapter 9
351
20. First, calculate the expected value of reported net income under each effort
alternative:
If manager shirks, expected reported net income is:
If manager works hard, expected reported net income is:
The percentage increase in reported net income (i.e., sensitivity) is thus:
To calculate precision given work hard, first calculate the variance of reported net
income, given a1:
NI Prob. NI/a1 Calculation of Variance
352
21. a. If the manager works hard, his expected utility is:
5.219.12
5.2)65.354.8(
5.2)]12.94.0()24.146.0[(
5.2)]66.546.3(4.0)12.212.12(6.0[
5.2)]07.78.032.172.0(4.0)07.73.
032.177.0(6.0[
5.2)508.03002.0(4.0)503.03007.0(6.0)(
2/1
2/1
2/1
2/1
2/1
1
−×=
−+=
−×+×=
−+++=
−×+×+×+×=
−+++=
k
k
k
k
k
kkkkaEU
m
where k is the manager’s share of net income. If the manager is to accept the
contract, his expected utility must equal 4:
45.219.12
2/1
2/1
=−×
k
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353
8.1)74.38.017.92.0(8.0)74.33.017.97.0(2.0
8.1)148.0842.0(8.0)143.0847.0(2.0
8.1)28.508.028.3002.0(8.0)28.503.028.3007.0(2.0)(
2
−×+×+×+×=
−++×+=
−×+×+×+×=aEU
m
b. This is a case of moving support. If the owner observes net income of
$30, she will know that the manager chose a2. Consequently, a contract paying a
Then, the manager will be indifferent between working hard or shirking if
Scott, Financial Accounting Theory, 7th Edition Instructor’s Solutions Manual Chapter 9
354
c. The agency cost of the contract in a. is the difference between the
a1.
75.132
10.2365.109
75.574.075.1826.0
)25.42100(4.0)25.42225(6.0),( 1
=
+=
×+×=
−+−=firstbestaEUO
Under the contract in a., the manager receives 28% of net income. The owner’s
expected utility is
)28100(4.0)63225(6.0
)28.100100(4.0)28.225225(6.0),(
1
−+−=
×−+×−=aincontractaEU
O
22. a. The finding that earnout payments are larger the greater the riskiness of
Scott, Financial Accounting Theory, 7th Edition Instructor’s Solutions Manual Chapter 9
compensation. The higher is the risk averse manager’s compensation risk, the
higher the rate of incentive compensation required to attain reservation utility.
Note: Either a risk–based or an effort–based argument is acceptable.
The reason why the ratio of share value to market value (Tobin’s q) is
commonly used as a measure of a firm’s potential for future growth
b. This finding is consistent with agency theory concepts. In agency