Homework Lance
P 7–1: Solution to MRI (20 minutes)
[Choosing allocation base to maximize hospital reimbursement]
a. Memorial Hospital’s cost per image:
$885,000 ÷ 33,600 images = $26.34/image
b. Calculate Memorial Hospital’s cost per hour.
$885,000 ÷ 2,800 hours = $316.07/hour
c. The cost of 10 MRI images and one hour of MRI time based on cost per image.
10 images × $26.34 = $263.40
d. The cost of 10 MRI images and one hour of MRI time based on cost per hour.
1 hour × $316.07 = $316.07
e. If Memorial Hospital’s primary use of accounting costs is third-party reimbursement, then they should use cost per hour. This results in a larger reimbursement from the government ($316.07) than cost per image ($263.40).
P7-2: Solution to Fair Allocations (15 minutes)
[“Fairness” as a criterion for choosing alternative cost allocation methodologies]
“Fairness” is not an operational way to choose between cost-allocation methodologies. Cost allocations are equivalent to internal taxes, where the item being taxed is the allocation base used to allocate costs (direct labor, floor space, profits, etc.). And, like taxes, there is no way to determine “fairness.” Politicians discuss making the tax system “fair.” But what is fair to one group is likely unfair to another group. Each group wants to reduce the taxes it bears. However, reducing taxes on one group merely shifts the tax to another group. “Fairness” has not proven to be an operational way to choose among alternative tax regimes. Hence, “fairness” is unlikely to provide a workable criteria to choose among alternative cost allocation methodologies.
You could ask each party if the proposed allocation scheme is “fair,” and then select the allocation scheme that all parties agree is “fair.” But each party is likely to select as “fair” that allocation scheme that results in the lowest allocated cost it pays. Therefore, it is very likely that the parties will not agree on a single “fair” allocation scheme.
P 7-3: Solution to Slawson (20 minutes)
[Allocating costs using input measures versus noninsulating methods]
a. and b.
Argentina
United
States
Germany
Total
Number of employees
1,500
300
200
2,000
Net Income (loss) in pesos (millions)
(100)
400
500
800
Fraction of total employees
0.75
0.15
0.1
1.00
Fraction of total income
-0.125
0.5
0.625
1.00
Allocated corporate headquarter cost
Using employees
1.8
0.36
0.24
2.4
Using net income
-0.3
1.2
1.5
2.4
Notice that in part (b). Argentina is allocated a negative 300,000 pesos to offset their loss. This is like a tax refund.
c. Key issues to mention include:
Do corporate cost allocations affect income taxes paid by the operating divisions? This is the first question to address and is likely to drive the choice of allocation method if the answer is yes.
Allocating corporate headquarters cost based on number of employees is effectively a tax on employees and causes each operating company to have fewer employees. Slawson will want to use employees as an allocation base if hiring additional employees causes headquarters to bear additional costs. For example, does hiring additional employees in the United States generate externalities in other divisions or in headquarters for monitoring these employees?
A disadvantage of using employees as the allocation base is that it does not create as much incentive for the three operating divisions to cooperate as using net income.
Allocating based on net income is a noninsulating allocation method that provides incentives for the three divisions to cooperate.
Allocating based on net income also is a risk sharing device among the divisions. As long as the profits of the three operating companies are not perfectly correlated, then allocating corporate overhead results in risk diversification.
A disadvantage of using net income is that it distorts the performance of an operating company by having that operating company’s net income depend on the performance of the other two operating companies.
P 7–4: Solution to the Corporate Jet (20 minutes)
[Cost allocation as a transfer price is misallocating the resource]
This problem, which at first appears to be a cost allocation question, is really a transfer pricing problem. In fact, most cost allocation issues involve transfer pricing issues.
a. The formula being used consists of monthly expenditures for both fixed and variable costs divided by actual miles flown. In fact, the fixed costs such as depreciation and the pilot’s salary are rather significant.
b. As passenger miles increase, the average price charged falls. The proposed cost allocation scheme results in a downward-sloping supply curve for the jet.
c. Uncertainty regarding how much the plane will fly in the month will induce users to shy away from the plane in months of greatest uncertainty. In summer months there will be an excess demand for the jet because it is unlikely the jet will be grounded for weather-related reasons. Hence, the denominator in the formula will be large. In the winter, especially in the beginning of the month when total monthly usage is still uncertain, demand will be light until total passenger miles flown accumulates. Thus, in summer months, the price is low and in winter months it is high.
d. One way to smooth the price of the jet over the year is to base the charge per mile on normal (or average) passenger miles flown per month, not actual. That is, at the beginning of the year the cost per mile is estimated by dividing total annual operating cost by expected total miles to be flown in the year. This charge per mile does not fluctuate month-by-month with actual miles flown.
Even making this proposed change does not overcome a remaining problem. The transfer price on the corporate jet does not take into account the demand curve for the jet. The existing system and the proposed change consider only costs. It is likely that the proposed change will still result in an excess demand for the jet. That is, the cost-based price is likely too low because of the extra convenience and prestige of flying on the jet. Price systems, including transfer pricing, should allocate scarce resources such that there is no excess supply or excess demand for the good or service. The proposed scheme does not ensure that there will be no excess demand for the jet. Because there is likely to be excess demand at least at certain times of the year, some other administrative device is required to ration seats. For example, only executives above a certain level in the firm have the right to make reservations. Or, seats are assigned on a first-come-first-served basis.
Some students may suggest a two-part price: allocate fixed costs to users based on expected usage, and charge per mile at the variable cost rate. This is a good way for the transportation office to capture more of the consumer surplus, although it does not necessarily result in a more efficient allocation of the scarce resources. The issue becomes monitoring what the transportation department claims are the fixed costs and preventing transportation from setting the “fixed costs” to maximize their profits by price discriminating.
P 7-5: Solution to Massey Electronics (20 minutes)
[Alternative allocation schemes]
a. The following table presents the allocation of the $9.5 million of shared manufacturing overhead using the four proposed schemes.
Texas
Mexico
Total
% Texas
Direct labor hours
3,000,000
4,000,000
7,000,000
43.0%
Direct labor dollars
$60,000,000
$40,000,000
$100,000,000
60.0%
Direct material dollars
$180,000,000
$200,000,000
$380,000,000
47.0%
Square footage
200,000
300,000
500,000
40.0%
Allocated overhead based on:
Direct labor hours
$4,085,000
$5,415,000
$9,500,000
Direct labor dollars
5,700,000
3,800,000
9,500,000
Direct material dollars
4,465,000
5,035,000
9,500,000
Square footage of plant
3,800,000
5,700,000
9,500,000
b. Questions involving how to allocate costs involve what input base to tax, and hence how the choice of the taxing scheme affects the firm’s cash flows. Since Massey has tax loss carry forwards, the allocation of the $9.5 million manufacturing overhead does not affect taxes, which is usually an important cash flow stream to consider.
The four allocation methods create significant differences in the dollars allocated to the two plants. In fact, the Texas and Mexico plants allocations vary by up to $1.9 million, depending on which method is used. Since the lines of business end up paying for these allocated costs through higher full cost-based transfer prices, the choice of allocation method could prove economically important if the lines of business change their prices of heat sinks to final customers based on the transfer prices that result from the four methods. Therefore, before selecting a particular allocation method, the product costs produced under each allocation scheme need to be examined in light of how the product cost impacts the pricing decision of the three lines of business.
Besides taxes and pricing, allocation methods can affect the choice of inputs used to produce the heat sinks and the amount of cooperation among managers.
Direct labor hours:
Taxes labor hours. Hence fewer labor hours and more material and machine hours will be used.
Since Mexico has more hours, it gets more of the shared overhead causing its products’ costs to rise relative to Texas products. This shifts production from Mexico to Texas.
Induces cooperation among lines of business and plants because it is a non-insulating method.
Direct labor dollars:
Taxes labor dollars. Hence fewer labor dollars and more material and machine hours will be used.
Having more expensive workers, Texas bears more overhead causing production to move from Texas to Mexico.
Induces cooperation among lines of business and plants because it is a non-insulating method.
Direct material dollars:
Taxes material dollars. Hence fewer material and more labor hours and machine hours will be used.
Induces cooperation among lines of business and plants because it is a non-insulating method.
Plant square footage:
Taxes square footage. But since square footage is hard to adjust in the short term, it is hard for managers to substitute away from plant.
Induces little cooperation among lines of business and plants because it is an insulating method.
Having the smaller plant causes Texas to bear less overhead. This shifts production from Mexico to Texas.
P 7-6: Solution to Avid Pharmaceuticals (20 minutes)
[Insulating vs. non-insulating cost allocations]
a. The following tables report the net incomes of Divisions A and B using the five alternative allocation bases:
Division A
Division B
Total
Number of employees
80
20
100
Plant square footage (000)
80
120
200
Revenues
$2,000
$1,000
$3,000
Operating expenses
600
500
1,100
Operating profits
$1,400
$500
$1,900
% of employees
80.00%
20.00%
100.00%
% plant square footage
40.00%
60.00%
100.00%
% revenue
66.67%
33.33%
100.00%
% op. expenses
54.55%
45.45%
100.00%
% operating profits
73.68%
26.32%
100.00%
Allocated corporate overhead based on:
% of employees
$720.00
$180.00
$900
% plant square footage
$360.00
$540.00
$900
% revenue
$600.00
$300.00
$900
% op. expenses
$490.91
$409.09
$900
% operating profits
$663.16
$236.84
$900
Net Profit after allocating corporate overhead:
% of employees
$680.00
$320.00
$1,000
% plant square footage
$1,040.00
($40.00)
$1,000
% revenue
$800.00
$200.00
$1,000
% op. expenses
$909.09
$90.91
$1,000
% operating profits
$736.84
$263.16
$1,000
b. Given the limited facts in the case, management should allocate corporate overhead using divisional operating profits for the following reasons:
Since Avid is privately held, it cannot give the two division managers stock in the company as a way to provide incentives for the division managers to cooperate.
All five methods are non-insulating to varying degrees and hence give the two divisions incentives to cooperate. Since synergies exist between the two divisions, managers should have incentives to cooperate. Non-insulating cost allocations provide such incentives.
Number of employees and square footage probably, being sticky, vary less with division performance than the other three allocation bases. Hence, these two bases create less incentive to cooperate than revenues, or operating profits.
Using revenue to allocate corporate overhead creates incentives to cooperate on revenue. If Division A’s manager helps lower B’s operating costs, this does not directly affect B’s revenue, nor A’s allocated cost. Hence, revenue as an allocation base provides no incentives to cooperate to reduce costs.
Allocating corporate overhead using operating costs actually creates perverse incentives. If Division B asks A for help to lower B’s costs, A is actually harmed. By Division A helping to lower B’s costs, B is allocated less overhead and A receives more overhead. So allocating corporate overhead using operating costs as the allocation base creates disincentives for the divisions to cooperate to reduce the other division’s costs.
Operating profits as the allocation base provides incentives for both managers to cooperate to raise the other division’s revenues and/or lower the other division’s costs. Either higher revenues or lower costs in the other division increases that division’s profits, and hence the amount of overhead they absorb. The more overhead the other division is allocated, the less overhead is allocated to the other division.
All five methods help to diversify the risk each division manager bears. If one division does well, it absorbs more overhead and the other division less. But basing each division manager’s bonus on operating profits less corporate overhead, diversifies the risk in both revenues and operating costs, and better protects the division manager than just diversifying revenue. In a sense, using operating profits as the allocation base provides a “bigger market basket” to help reduce the risk than just using revenues. So again, operating profits is likely the better choice as an allocation base than any of the other four.
P 7–7: Solution to Wasley (20 minutes)
[Cost allocations create incentives to drop profitable products]
a.
Income Statement
Product A
Product B
Product C
Product D
TotalNet Sales
$1,250
$850
$1,250
$1,650
$5,000
Direct Labor
(450)
(600)
(540)
(640)
(2,230)
Direct Materials
(250)
0
(125)
(160)
(535)
Corporate Overhead*
(360)
(480)
(432)
(512)
(1,784)
Operating Income
$ 190
$(230)
$ 153
$ 338
$ 451
*OH Rate = $1,784 ÷ $2,230 = 80% of direct labor dollars
b.
Income Statement
Product A
Product B
Product C
Product D
TotalNet Sales
$1,250
$0
$1,250
$1,650
$4,150
Direct Labor
(450)
0
(540)
(640)
(1,630)
Direct Materials
(250)
0
(125)
(160)
(535)
Corporate Overhead
(492)
0
(592)
(700)
(1,784)
Operating Income
$ 58
$0
$ (7)
$ 150
$ 201
*OH Rate = $1,784 ÷ $1.630 = 109% of direct labor dollars
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 7-8: Solution to Hallsite Imaging (20 minutes)
[Non-insulating allocations create cooperation incentives but distort profitability]
Allocated Marketing Division expenses to the Hardware and Software Divisions: (all figures are in millions of dollars).
Last Quarter
This Quarter
Hardware Division
Software Division
Total
Hardware Division
Software Division
Total
Revenue
$500
$700
$1,200
$510
$400
$910
Percent of total sales
41.67%
58.33%
100%
56.04%
43.96%
100%
Allocated marketing division costs
$133.33
$186.67
$320.00
$207.36
$162.64
$370.00
Hardware and Software Divisions’ profits after allocating Marketing Division’s expenses (all figures are in millions of dollars):
Last Quarter
This Quarter
Hardware Division
Software Division
Total
Hardware Division
Software Division
Total
Revenue
$500.00
$700.00
$1,200.00
$510.00
$400.00
$910.00
Division expenses
315.00
308.00
623.00
321.30
176.00
497.30
Allocated marketing costs
133.33
186.67
320.00
207.36
162.64
370.00
Profits
$51.67
$205.33
$257.00
-$18.66
$61.36
$42.70
Memo to Hardware Division:
Hardware’s profits fell from $51.67 million last quarter to a loss of $18.66 million this quarter (or a total change of $70.33 million) because Hardware’s share of the Marketing Division’s costs went up from $133.33 million to $207.36 million (or a total change of $74.03 million). The profit report you received for this quarter is correct and continues Hallsite’s long standing cost allocation methodology of allocating the Marketing Division’s expenses back to the Hardware and Software Divisions based on the latter two divisions’ relative amount of sales.
Hallsite has adopted this non-insulating cost allocation methodology primarily to foster better cooperation between the Hardware and Software Divisions. By helping the other division to increase its sales, that division absorbs more of the Marketing Division’s costs, thereby lowering the costs absorbed by (and raising the profits of) the cooperating division. Because there are substantial synergies and interdependencies between Hardware and Software, cooperation is essential to maximize these synergies, and hence to maximize shareholder value. Moreover, this non-insulating cost allocation more efficiently shares the risks of the two divisions. This quarter Software had the unfortunate and unforeseen adverse outcome of problems with the release of version 7.0. Some of this adverse event was shifted to the Hardware Division via the cost allocation methodology. If Software had an unexpected favorable outcome that resulted in higher Software sales, Hardware would have benefited from this favorable outcome. Had Hardware suffered an adverse shock to its sales, Hardware would not bear the full brunt of the bad event. Rather, Software would in this case bear some of it. Hence, Hallsite’s current cost allocation methodology provides two major benefits: it fosters better cooperation among the divisions and it results in better risk sharing. The downside of this methodology is that it distorts the relative profitability of the divisions in the sense that each division’s profits depends not only on that division’s profits, but also on the sales in the other division. But given the large interdependencies between the Hardware and Software Divisions products, the two divisions are not separate and independent of the other division. Hallsite’s non-insulating cost allocation methodology attempts to capture to some extent the true nature of these interdependencies, and to foster cooperation incentives between Hardware and Software Divisions.
P 7–9: Solution to Rowe Waste Removal (B) (25 minutes)
[Cost allocations affect actual decisions]
a. The following table calculates profits at the various price-quantity combinations and shows that the profit maximizing price-quantity combination is $1,472 and 125 customers.
No. of
Customers
Price
Revenue
Variable
Cost
Fixed
Cost
Total
Cost
Profit
100
$1560
$156,000
$95,000
$60,000
$155,000
$1,000
105
1538
161,490
99,750
60,000
159,750
1,740
110
1516
166,760
104,500
60,000
164,500
2,260
115
1494
171,810
109,250
60,000
169,250
2,560
120
1472
176,640
114,000
60,000
174,000
2,640
125
1450
181,250
118,750
60,000
178,750
2,500
130
1428
185,640
123,500
60,000
183,500
2,140
135
1406
189,810
128,250
60,000
188,250
1,560
140
1384
193,760
133,000
60,000
193,000
760
145
1362
197,490
137,750
60,000
197,750
(260)
Alternative computations:
Profit = PQ – 950Q – $60,000
Demand curve
P = 2000 – 4.4Q
Profits = (2000 – 4.4Q) × Q – 950Q – $60,000
Profits = 2000Q – 4.4 Q2 – 950Q – $60,000
Derivative of the profit equation
2000 – 8.8 Q – 950 = 0
8.8 Q = 1050
Q* = 119
P* = 2000 – 4.4 × 119
P* = $1,475
Maximum profit
Max Profit = PQ – 950Q – $60,000
Max Profit = $1,475 × 119 – 950×119 – $60,000
Max Profit = $175,525 – $113,050 – $60,000
Max Profit = $2,475
b. The firm-profit maximizing price-quantity combinations in Rowe Waste Removal (A) in Chapter 2 part (b) was $1,450 and 125 units. Lingle chooses $1,472 and 120 units. The reason for the difference is she is charged $50 of overhead, which she treats as an additional variable cost beyond the $900 in question 1. Since each apartment unit now costs Lingle $50 more (due to the allocated cost), she raises the price from $1,450 (before the allocation) to $1,472 (after the $50 charge). Lingle treats the $50 charge as any other marginal cost increase and raises the price.
c. Charging Lingle the $50 causes her to alter her pricing decision. If Rowe has excess capacity in its billing and accounting systems and other central services provided to Lingle, and the existence of the apartment collection services imposes no costs on other parts of Rowe, then this $50 charge does not represent additional marginal costs generated by Lingle’s operations. In this case, Lingle should not be charged $50 per apartment customer. However, if each additional apartment customer imposes some delay costs on residential customers in terms of Rowes’ billing or accounting processes, or consumes scarce central resources that could be used on residential services, then the $50 charge approximates the externalities an apartment customer imposes on Rowe. In this case, Lingle should be charged $50 per apartment customer because this $50 charge acts like a tax on this externality.
P 7–10: Solution to Winterton Group (25 minutes)
[Fairness of cost allocations]
a.
Winterton Group
Revised Profits by Office
Current Year (Millions)
Rochester
Syracuse
Buffalo
Total
Revenue
$16.00
$14.00
$20.00
$50.00
Operating Expenses
(12.67)
(11.20)
(16.30)
(40.17)
Central Services*
(2.10)
(2.10)
(1.80)
(6.00)
Profits
$ 1.23
$ 1.70
$ 1.90
$ 3.83
*Allocated cost per investment advisor: 1/20 × $6 million = $300,000
b. It is not fairer because the criteria of fairness is not operational. What is fair to one manager (which means less allocated cost) is unfair to another (who bears more allocated cost).
c. Fairness is being used as a code word to avoid arguing self-interest. If adopted, the Buffalo manager’s bonus rises by $48,000 [8%($1.9m – $1.3m)]. Thus, it is in the Buffalo manager’s interest to get the cost allocation basis changed.
P 7–11: Solution to National Training Institute (30 minutes)
[Allocation of space costs]
Allocations:
Rent Costs
Department
Revenue
% Revenue
% of
Space
% of
Revenue
Administration
$ 3,600,000
12%
$180,000
$240,000
Support Services
11,000,000
37%
620,000
740,000
Computer Services
8,800,000
29%
160,000
580,000
Technical Training
1,900,000
6%
80,000
120,000
Transportation
4,700,000
16%
960,000
320,000
Total Allocated
$30,000,000
100%
$2,000,000
$2,000,000
Off-Time Usage
The square footage allocation plan places a cost burden on Technical Training that it can avoid paying. Since Technical Training has the ability to move off-time training to other sites at no additional cost, rent should not be charged to them for off-time space usage. The opportunity costs of the off-time use of the facility are currently zero. Unless other uses are developed, these opportunity costs would remain at zero.
Rent Allocation
Mr. Daniels’ plan distributes rent based on space allocated. His plan provides incentive for departments to use and request space efficiently. Departments would know rent costs during budget preparation time (assuming space allocations do not change). Since allocated space is the cost driver here, this plan distributes rental costs appropriately.
Ms. Richards’ allocation plan places more of the burden of rent on those departments that generate the most revenue. Since these same departments have little or no competition, and are cost centers, the costs would be passed along as part of their service fee. The Transportation department would be the only department that would not have an increase under Mrs. Richards’ plan. From the information provided, it is unknown whether or not the customers of the other departments would tolerate the service fee changes necessary to make up for such increases. This rent allocation plan penalizes the departments that generate greater revenue and yet may not require additional space.
Under this plan departments can request and use space inefficiently. Departments can hold onto space they are not using yet not pay the costs. This agency problem does not exist under the space allocation plan.
Recommendations:
1. Rent allocation should be based on space expected to be used during the coming year.
2. Do not charge Technical Training additional costs for off-time use.
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