W. TERRY DANCER

 PROFESSOR OF ACCOUNTING

ARKANSAS STATE UNIVERSITY

P 7–7:                    Solution to Wasley  (20 minutes)

[Cost allocations create incentives to drop profitable products]

a.

b.

c.             Yes, Shirley Chen increased her divisional income from –$40 ($190 – $230) to +$58.

d.             No, corporate income decreases by dropping a product with positive contribution.

*Note that the Contribution margin for A = $550; B = $250, C = $585; D = $850.

e.             This is an example of the beginnings of a death spiral.  Cost allocations can distort relative profitability and lead to incorrect operating decisions.

Source:  Charles Kile

P 7-15:   Solution to Fuentes Systems (30 minutes)

                                [Cost allocations as a proxy for hard to observe opportunity cost]

a.             $2,184,000/70 = $31,200

b.             Including the corporate overhead allocation, the total cost of a sales person is $151,200 ($120,000 + $31,200).  Hiring one sales person generates a net expected increase in the western region’s profits of $33,800 ($185,000 - $151,200), whereas hiring two sales people will generate net expected profits of $20,600 ($323,000 – 2 × $151,200).  To maximize profits in your region, you will hire one sales person.

c.             The incremental administrative cost per sales person of going from 70 to 80 sales people is $45,600 ([$2,640,000 - $2,184,000] / 10).  This is an estimate of the marginal administrative cost of hiring an additional sales person.  The allocated administrative cost currently is only $31,200 and this is expected to rise to $33,000 ($2,640,000 / 80).  Thus, while the current cost allocation mechanism does not “tax” the regions enough for adding sales people, it is still better to tax them $33,000 rather than zero.  Ideally, Fuentes should charge the regions’ the marginal cost (approximately $45,600).  But marginal cost is only known after special studies and even the $45,600 does not include the delay costs and other externalities imposed on corporate administrative functions when additional sales people are hired.

d.             The incremental administrative cost per sales person of going from 70 to 80 sales people is only $1,600 ([$2,200,000 - $2,184,000] / 10).  This is an estimate of the marginal administrative cost of hiring an additional sales person.  The allocated administrative cost currently is $31,200 and this is expected to fall to $27,500 ($2,200,000 / 80).  Thus, the current cost allocation mechanism “over taxes” the regions for adding sales people.  Take the case of the western region.  The actual marginal cost of adding a sales person is $121,600 ($120,000 + $1,600).  Adding one sales person yields total profits of $63,400 ($185,000 - $121,600), whereas adding two sales people yields total profits of $97,800 ($323,000 – 2 × $112,600).  Clearly, Fuentes would like the western region to hire two sales people.  But the current cost allocation system causes the western region to add only one sales person.  In this case, it would be better if Fuentes did not allocate administrative overhead to the regions.

P 7–17:  Solution to World Imports (35 minutes)

                                [Overhead as a tax that affects pricing and quantity decisions]

a.             Using the data provided in the table, the profit-maximizing price is determined to be $5.00.  This yields total profits for the district of $45,000.

b.             If corporate overhead is allocated to the sales districts, this is a tax on sales commissions.  The table below calculates the net profit from various pricing alternatives after including the corporate overhead allocation. 

As can be seen from the table, the district’s profit-maximizing price (if corporate overhead is included in district profits) is now $5.50 per T-shirt.  The district manager views the allocation as an increase in marginal costs.  When marginal cost schedules shift up, the profit-maximizing price tends to increase and the profit-maximizing quantity decreases.

                When corporate overhead is allocated to the districts, Krupsak views this as an increase in marginal costs and raises price and lowers quantity sold.

c.             The argument for allocating overhead must be that the current system of measuring costs is not capturing the true costs district managers impose on corporate headquarters by their pricing decisions.  The arguments given in the case by the corporate controller cannot be complete.

                If by deciding to sell the T-shirts, Krupsak imposes costs on corporate headquarters, then Krupsak should take account of these costs in his pricing decision.  If the T-shirts generate additional legal or payroll costs or if they consume scarce corporate resources, then an externality is generated that Krupsak should bear.  Allocating corporate overhead is one way to do this.  But it should be recognized that the overhead rate of 30% of commissions is an average rate, not a marginal rate.  Therefore, it might be too high a tax on commissions.

                If the headquarters expenses are truly fixed with respect to the number of T-shirts Krupsak sells, then allocating these expenses causes too high a price to be set and too few T-shirts will be ordered. 

P 7-19:   Solution to Scanners Plus (35 minutes)

                                [Non-insulating allocations as a risk sharing mechanism]

a.             The possible total revenues for the Home model are:

b.             The possible total revenues for the Pro model are:

c.             The table below (in 000s) calculates the possible levels of profits for the two profit centers:

d.             There can be four different sets of allocations of marketing costs depending on the particular revenues of the Home and Pro models (in 000s):

e.             The table below calculates the various profit numbers that can result from using relative revenues to allocate marketing costs (all amounts in $000).