Accounting for Decision Making and Control 6th Edition by Jerold Zimmerman

Exercise 38

The local sales manager of Kink Sales receives a fixed salary plus a bonus based on sales. Only the local sales manager knows the probability distribution over possible sales levels for the next year in her sales district, which is as follows:

The manager's bonus is $100 for every unit above the budgeted sales figure she forecasts at the beginning of the year, with the bonus being nonnegative. That is,
Bonus = $100 X (Actual sales - Budgeted sales), Bonus 0 (1)
Senior management is considering changing the bonus scheme to the following:
Bonus = $100 X Actual sales - $20 X | Budgeted sales - Actual sales | (2)
In this scheme, the local manager would receive $100 per unit sold but be penalized $20 for every unit sold that differs from budget. (Note: The symbol |... | denotes absolute value.)
If senior management changes the bonus, it will adjust the fixed component of salary to offset any gain or loss in the expected level of total compensation.
Required:
a. Graph the two bonus schemes.
b. Using the first bonus scheme, what budgeted sales figure will the local manager report
c. Using the proposed bonus scheme, what budgeted sales figure will the local manager report
d. Which method do you prefer Why