Problems

1. Before paying employee bonuses and state and federal taxes, a company earns profits of $60,000. The company pays employees a bonus equal to 5 percent of after-tax profits. State tax is 5 percent of profits (after bonuses are paid). Federal tax is 40 percent of profits (after bonuses and state tax are paid). Determine the amount paid in bonuses, state tax, and federal tax.

2. On January 1, 2002, I have $500. At the end of each month I earn 2 percent interest. Each month’s interest is based on the average of the month’s beginning and ending balances. How much money will I have after 12 months?

3. My airplane is flying the following route: Houston-Los Angeles-Seattle-Minneapolis-Houston. On each leg of the journey, the plane’s fuel usage (expressed as miles per gallon) is 40–.02*(average fuel en route). Here, average fuel en route is equal to .5*(initial fuel en route+final fuel en route). We begin in Houston with 1000 gallons of fuel. The distance flown on each leg of the journey is as follows.

   Open table as spreadsheet

   Leg	Miles
   Houston to Los Angeles	1200
   Los Angeles to Seattle	1100
   Seattle to Minneapolis	1500
   Minneapolis to Houston	1400

4. How many gallons of fuel will remain when I return to Houston?

5. A common method used to allocate costs to support departments is the reciprocal cost allocation method. This method can easily be implemented by use of circular references. To illustrate, suppose Widgetco has two support departments: Accounting and Consulting. Widgetco also has two product divisions: Division 1 and Division 2. Widgetco has decided to allocate $600,000 of the cost of operating the Accounting department and $116,000 of the cost of operating the Consulting department to the two divisions. The fraction of accounting and consulting time used by each part of the company is as follows.

   Open table as spreadsheet

   	Accounting	Consulting	Division 1	Division 2
   Percentage of accounting work done for other parts of the company	0%	20%	30%	50%
   Percentage of consulting work done for other parts of the company	10%	0%	80%	10%

   How much of the accounting and consulting costs should be allocated to other parts of the company? We need to determine two quantities: total cost allocated to accounting and total cost allocated to consulting. Total cost allocated to accounting equals $600,000+.1*(total cost allocated to consulting) because 10 percent of all consulting work was done for the Accounting department. A similar equation can be written for the total cost allocated to consulting. You should now be able to calculate the correct allocation of both accounting and consulting costs to each other part of the company.