COST ALLOCATION: PRACTICES

P 8-1: Solution to Solution to Swedish Hospital (15 minutes)

[Effect of changing the order of the step-down allocation method and rationale for making the change]

a. The cost per meal in the FS department will increase if the FS department is moved from being the 3rd service department allocated to being the 23rd service department allocated. The cost per meal increases for two reasons. First, FS will have more other service department costs allocated to it (i.e., the numerator increases). Second, the allocation base (number of meals served) decreases (i.e., the denominator decreases) because there are fewer users being allocated FS costs. Hence the ratio increases.

b. Management should consider how changing the order of the service departments affects the hospital’s future cash flows. Future cash flows can increase if the new allocated costs improve decision making by better reflecting the opportunity costs of the various service departments (decision making), increases reimbursements because some of the hospital’s revenues are contractually based on reported costs, or changes the incentives of hospital personnel (control). Taxes are unlikely affected.

P 8-2: Solution to Outback Opals (20 minutes)

[Joint cost allocations – NRV does not necessarily minimize taxes]

a. Allocated joint cost per stone using the number of stones:

Grade I

Grade II

Grade III

Total

Number of stones per batch

105

175

350

Percent of stones

20.00%

30.00%

50.00%

100.00%

Allocated cost to each grade

A$7,000

A$10,500

A$17,500

A$35,000

Allocated joint cost per stone

A$100

Alternatively, A$35,000 / 350 stones = A$100.00 per stone.

b. Allocated joint cost per stone (before taxes) using net realizable value:

Grade I

Grade II

Grade III

Total

Selling price per stone

A$800

A$300

A$110

Additional cost to package and
sell each stone

(250)

(120)

(5)

Net realizable value per stone

A$550

A$180

A$105

X Number of stones per batch

105

175

Net realizable value per batch

A$38,500

A$18,900

A$18,375

A$75,775

Percent of net realizable value per batch

50.81%

24.94%

24.25%

100%

Allocated cost to each grade

A$17,784

A$8,729

A$8,488

A$35,000

Allocated joint cost per stone

A$254.05

A$83.13

A$48.50

c. Which of the two methods to choose depends on how the numbers will ultimately be used. If they are used for decision making, one might be tempted to argue that NRV is better because it does not distort the relative profitability of the joint products. However, this answer is short sighted because it does not consider the possible tax affects of the alternative joint cost allocations. Presumably, whichever method Outback uses for internal purposes is likely to be seen by the tax authorities if Outback’s tax returns are audited. That is, although Outback can use different joint cost allocation methods for taxes and internal purposes, separate systems undermine Outback’s tax case if they are ever audited. The following tables calculate the income tax liability arising from each method.

Income taxes based on number of stones:

Grade I

Grade II

Grade III

Total

Revenue

A$56,000

A$31,500

A$19,250

A$106,750

Allocated joint cost (based on number of stones)

(7,000)

(10,500)

(17,500)

(35,000)

Additional packaging and selling cost

(17,500)

(12,600)

(875)

(30,975)

Net income before taxes

31,500

8,400

875

40,775

Income taxes

A$ 9,450

A$ 1,260

A$394

A$ 11,104

Income taxes based on NRV:

Revenue

A$56,000

A$31,500

A$19,250

A$106,750

Allocated joint cost (based on nrv)

(17,784)

(8,729)

(8,488)

(35,000)

Additional packaging and selling cost

(17,500)

(12,600)

(875)

(30,975)

Net income before taxes

20,717

10,171

9,888

40,775

Income taxes

A$ 6,215

A$ 1,526

A$ 4,449

A$ 12,190

Notice, that the pre-tax cash flows are identical under the two joint cost allocation methods. Net income before taxes (and cash flows) is A$40,775. How the joint costs are allocated affects the amount of profit and hence taxes paid in each of the three countries, because the three tax jurisdictions have very different tax rates. The NRV method actually results in higher taxes than using the number of stones. Therefore, to minimize taxes, the number of stones should be used, assuming that it is an allowed method by all three tax jurisdictions.

P 8-3: Solution to Rose Hospital (25 minutes)

[Step-down allocations]

a. & b. The first of the following two tables computes the allocation rates, and the second table applies these rates to allocate the service department costs.

Allocation Rates

Building Services

Food Service

Intensive Care

Surgery

General Medicine

Total

Direct Allocations:
Building Services

10,000
14%

20,000
29%

40,000
57%

70,000
100%

Food Service

3,000
3%

4,000
4%

98,000
93%

105,000
100%

Step-down — Building Services First:
Building Services

15,500
18%

10,000
12%

20,000
23%

40,000
47%

85,500
100%

Food Service

3,000
3%

4,000
4%

98,000
93%

105,000
100%

Step-down — Food Service First:
Building Services

10,000
14%

20,000
29%

40,000
57%

70,000
100%

Food Service

12,000
10%

3,000
3%

4,000
3%

98,000
84%

117,000
100%

Allocated Costs

Building Services

Food Service

Intensive Care

Surgery

General Medicine

Total

Direct Allocations:
Building Services

14%
$.84

29%
$1.74

57%
$3.42

$6.00

Food Service

3%
$0.09

4%
$0.12

93%
$2.79

$3.00

$0.93

$1.86

$6.21

$9.00

Step-down — Building Services First:
Building Services

18%
$1.08

12%
$0.72

23%
$1.38

47%
$2.82

$6.00
Food Service

3%
$0.12

4%
$0.16

93%
$3.79

$4.08

$0.84

$1.54

$6.61

$10.08*
Step-down — Food Service First:
Food Service

10%
$0.30

3%
$0.09

84%
$2.25

$3.00

Building Services

14%
$0.88

29%
$1.83

57%
$3.59

$6.30

$0.97

$1.92

$6.11

$9.30*

* Note: The totals allocated ($10.08 and $9.30) contain amounts allocated first to the service departments and then re-allocated to the end users. The total allocated costs to the end users in all cases sum to $9.0 million.

c. The step-down method with Food Service first allocates about $0.50 million less to General Medicine and about $0.4 million more to Surgery than using Building Services first. These differences are caused by General Medicine’s almost entire consumption of meals (ranging between 84 percent to 93 percent). By starting with Building Services, another $1.08 million of building costs are assigned to Food Service, most of which are passed through to General Medicine. Starting with Food Service reduces the total amount of Food Service costs allocated, thus lowering General Medicine’s total bill.

P 8-4: Solution to Mystic Herbals (30 minutes)

[Joint cost allocations are not useful for decision making]

a. Allocated joint cost is $60 per ounce ($30,000 ÷ 500 ounces):

QV3

VX7

HM4

LZ9

Total

% of batch by ounce

20%

16%

25%

39%

100%

Allocated joint cost

$6,000

$4,800

$7,500

$11,700

$30,000

b. Decisions to process further:

QV3

VX7

HM4

LZ9

Incremental revenue per ounce from further processing

$23

$25

$14

Number of ounces per batch

100

125

195

Incremental revenue from further processing

$2,300

$640

$3,125

$2,730

Cost of further processing

$2,400

$400

$2,500

$2,800

Decision to process further

YES

c. Batches of Xubonic root should be produced because each batch yields profits of $3,200.

QV3

VX7

HM4

LZ9

Total

Revenue from further processing or immediate sale

$6,200

$4,560

$15,875

$9,165

Cost of further processing

400

$2,500

Net realizable value

$6,200

$4,160

$13,375

$9,165

$32,900

Joint cost of processing a batch

$30,000

Profit per batch

$ 2,900

d. Profit after allocating joint cost using net realizable value:

QV3

VX7

HM4

LZ9

Total

NRV

$6,200

$4,160

$13,375

$9,165

$32,900

% of NRV

18.84%

12.64%

40.65%

27.86%

100%

Allocated joint cost

$5,653

$3,793

$12,196

$8,357

$30,000

Net income per batch

$547

$367

$1,179

$808

$2,900

e. Joint cost allocations do not enhance the decision to further process joint products. Net realizable value does not harm the decision process, but it does not add anything. The decisions in part (b) to process each joint product further or sell after the split off point were made without any joint cost allocations.

P 8–5: Solution to Berkman Financial (30 minutes)

[Step-down allocations and resulting transfer prices]

a. The cost per service unit of S1 if S1 is the first department allocated is simply the total cost of S1 ($3.5 million) divided by the total number of service units S1 provides to all the other users of S1 (149 units), or $23,490 per service unit. Since S2 uses 43 service units of S1, S2 is charged $1,010,070 (43 x $23,490). The cost per service unit of S2, as the second department in the step-down, is its total cost (including S1’s allocated cost to S2) of $7,210,070 ($6,200,000 + $1,010,070) divided by the total service units S2 provides to all users, except S1, or 140.9 (168.9 – 28). S2’s cost per service unit is $51,172 ($7,210,070 ÷ 140.9).
b. The cost per service unit of S2 if S2 is the first department allocated is simply the total cost of S2 ($6.2 million) divided by the total number of service units S2 provides to all the other users of S1 (168.9 units), or $36,708 per service unit. Since S1 uses 28 service units of S2, S1 is charged $1,027,827 (28 x $36,708). The cost per service unit of S1, as the second department in the step-down, is its total cost (including S2’s allocated cost to S1) of $4,527,827 ($3,500,000 + $1,027,827) divided by the total service units S1 provides to all users, except S2, or 106 (149 – 43). S2’s cost per service unit is $42,715 ($4,527,827 ÷ 106).
c. The following table compares the cost per service unit of S1 and S2 depending on which service department comes first.

S1 cost per unit

S2 cost

per unit

S1 is the first dept allocated

$23,490

$51,172

S2 is the first dept allocated

$42,715

$36,708

The further down in the step-down chain a service department is located increases the per unit cost of service because the numerator increases because more costs from other service departments are allocated to this department, and the denominator decreases because fewer users are being allocated this department’s costs (i.e., the number of service units used in calculating the cost per unit falls).
d. In considering how to order the service departments in the step-down allocation, the firm should chose the order that maximizes future discounted net cash flows (i.e., firm value). The order will affect the resulting costs allocated to the SBUs.
If the SBUs are located in different tax jurisdictions then taxes will be affected. This is could be an issue in Berkman if the SBUs are in different states that have different corporate income tax rates.
If revenues are contractually linked to reported costs, then the ordering can affect revenues.
These allocations are transfer prices. The higher the service cost per unit (i.e., the higher the transfer price), the fewer service units will be used by the SBUs, which could lead to a death spiral. This could be a good thing if Berkman senior management wants to eliminate a service department.
If Berkman is using these allocations for decision making on the part of the SBUs, then you want the order to capture the opportunity costs of service department utilization. In this case, order the service departments to capture the biggest flow of services among the departments. This is difficult to do in Berkman since S1 is the biggest service department user of S2 and S3. To best capture the opportunity cost, use the reciprocal allocation method, not step down.
If Berkman is using the allocated costs as part of the performance metrics of the SBUs then one needs to consider how the SBUs performance (including) gaming will change depending on the step down order.

P 8–6: Solution to Joint Products, Inc. (30 minutes)

[Joint cost allocation and further processing]

Use net realizable value to allocate joint costs. While all allocation methods are arbitrary, NRV does not distort the relative profitability of the two products.

a. Inventory values calculated using net realizable value:

Products_______

X V Total

Sales value per batch $ 8,000 $ 4,000 $12,000

less: Additional processing costs 1,800 3,400 5,200

Net realizable value $ 6,200 $ 600 $ 6,800

% of net realizable value 91.2% 8.8% 100%

Allocated joint cost $ 7,296 $ 704 $ 8,000

Processing + allocated joint cost $ 9,096 $ 4,104

Number of pounds/batch 200 400

Cost per pound $45.48 $ 10.26

Units in ending inventory 2,000 1,000

Ending Inventory value $90,960 $10,260 $101,220

These ending inventory valuations are above market value, indicating that the overall operation is unprofitable. Because of the financial accounting rule that says that inventory must be valued at the lower of cost or market, the inventory values are $40 and $10 respectively, and the ending inventory values are:

Ending Inventory $80,000 $10,000 $90,000

Inventory values calculated using pounds:

Products_______

X V Total

Pounds per batch 200 400 600

% of batch 33.33% 66.66% 100%

Allocated joint cost $ 2,667 $ 5,333 $8,000

Processing cost 1,800 3,400

Total cost $ 4,467 $ 8,733

Number of pounds/batch 200 400

Cost per pound $ 22.33 $ 21.83

Units in ending inventory 2,000 1,000

Ending Inventory value $44,670 $21,830 $66,500

b. Currently, the firm is losing money processing the joint products. Each batch has joint costs of $8,000 plus additional processing costs of $5,200 or total costs of $13,200. Each batch generates revenues of $12,000, thus producing a loss of $1,200.

The table below indicates X should be sold before additional processing whereas V should be processed further.

Products

Further Processing

Revenues
$8,000
$4,000

Additional costs
1,800
3,400

Net realizable value
$6,200
$ 600

Sale of intermediate product
$7,000
$ 400

Optimal decision

Sell

Process Further

If X is sold and V is processed, the net receipts are $7,000(X) + $600(V) – $8,000 = $-400. The best the firm can do is lose $400 on each batch processed.

The question is whether the firm can make money by purchasing the intermediate products, X and V, in the market and processing them further.

Net realizable value from additional X V

processing/lb. $31 $1.50

Price of intermediate products $35 $1.00

If these prices are expected to persist, the firm should stop buying the common input and separating it into X and V. Rather, it should buy the intermediate product V for $1 and process it into a final product. V can be purchased for $1, processed into a final product for $8.50, and sold for a $.50 profit. If they decide to continue to process the joint products, then to minimize their losses, X should be sold at $35 without further processing, but V should be processed further.

P 8–7: Solution to Upstate Growers (35 minutes)

[Allocating fixed costs can distort optimum decision making]

The following table computes the net profits of each apple product after allocating the joint costs. The total joint costs of $322,000 ($274,000 + $48,000) are allocated based on total apple weight (4.6 million) or $0.07 per pound. Since each crate of apples contains 100 pounds, each crate is allocated $7.00 of joint costs.

Processing

Selling price per

NRV per

Allocated

Net Profits after

costs

100 lbs of apples

joint cost

joint costs

Unbruised Apples

$12

$31

$19

$7.00

$12.00

Applesauce

$60

$80

$20

$7.00

$13.00

Apple Juice

$28

$34

$7.00

-$1.00

While small apples if processed into juice show a net loss of $1.00 per crate, you do not want to base the decision of avoiding producing juice based on allocated joint costs. Apple juice is yielding a positive NRV, and hence is covering some of the fixed joint costs. The following table reports the various net cash flows (per 100 pound crate) that are available for each type of apple:

Livestock

Whole

Apple

Best

Apple type

Feed

Apples

Sauce

Juice

Alternative

Large unbruised

$11

$19

$20

Apple sauce

Large bruised

$11

$20

Apple sauce

Small

$11

Livestock feed

Here we see that while large un-bruised apples can be sold as whole apples that yield $19 per crate, it is better to turn them into applesauce, which yields $20 per crate. Large bruised apples likewise should be converted into sauce. No juice should be made from small apples, as it is more profitable to sell them directly as livestock feed. Note that all these production decisions do not involve allocated joint costs. The reason is that once the apples are harvested, washed, and sorted, the joint costs have been incurred and are sunk costs. Hence, they do not enter the decision regarding future uses of the apples.

P 8-8: Solution to Murray Hill’s Untimely Demise (30 minutes)

[Step-down allocations]

(a) The first step is to re-compute the allocation percentages for the remaining service and operating departments. For example, when allocating B’s costs to C, D1, D2, and D3, you cannot use the percentage of A’s use of B (8 percent) because this would allocate 8 percent of B back to A and then not all of B’s costs are allocated DOWN to the remaining departments. So C’s use of B is 15 percent/92 percent, or about 16.30 percent. Panel B re-computes the revised utilizations and Panel C completes poor Murray’s spreadsheet using these recomputed utilization percentages.

Panel A: Utilization Data
Service

Service Departments

Operating Departments
Dept. Cost

Total

$600,000

5%
10%
20%

30%

15%

20%

100%

300,000

8%
0%
15%

22%

20%

35%

100%

200,000

15%
5%
7%

20%

30%

23%

100%

1,100,000

Panel B: Revised Utilizations

0.105263

0.210526

0.315789

0.157895

0.210526

1.0000

0.163043

0.23913

0.217391

0.380435

1.0000

0.273973

0.410959

0.315068

1.0000

Panel C: Completed Step-Down Allocations

$600,000

$63,158

$126,316

$189,474

$94,737

$126,316

$600,001

$363,158

$59,211

$86,842

$78,947

$138,158

$363,158

$385,527

$105,624

$158,436

$121,467

$385,527

$381,940

$332,120

$385,941

$1,100,001

b. The following table lists the dollar utilization of each service department (percentage utilized times the department costs)

Service

Service Departments

Dept. Cost

600000

$30,000

$60,000

$120,000

300000

$24,000

$45,000

200000

$30,000

$10,000

$14,000

Here we see that the three largest dollar utilizations are $120,000, $60,000, and $45,000. So the preferred step-down order should capture these large dollar flows. A should be allocated first in order that the $60,000 of B’s use of A and C’s $120,000 use of A are captured. B should be second in order to allocate the $45,000 of C’s use of B. Finally, C is allocated last. Thus, the preferred step-down order that captures the largest dollar utilizations is A, then B, and finally C.

P 8–9: Solution to Enzymes (30 minutes)

[Pricing joint products and allocating joint costs]

a. The analysis of the pricing decisions is completely wrong because it takes the joint cost of the batch (which is a fixed cost), allocates it to the products, and then treats it as though the allocated costs are marginal costs.

There are separate demand curves for the final, fully processed enzymes:

PQ = 1,300 – 2Q

PY = 950 – 4Y

The $200,000 joint cost is a fixed cost of each batch. The marginal cost of Q = $100, and the marginal cost of Y = $150. These should be the only costs that enter the pricing decision.

In the problem, it appears as if Q is generating profits of $80,000 and Y is generating profits of $10,000, or in total $90,000. But this $90,000 profit ignores the fixed costs that are included in the 250 ounces that are not sold. Only half the output is sold. The other 250 ounces have been allocated $100,000 of joint costs (250 ounces × [$200,000 ÷ 500]) that have been incurred, but not included in the profits of $90,000. So, in reality, the firm is losing $10,000 ($90,000 – $100,000) per batch. Another way to see this is: each ounce of Q has a contribution margin of $800, and each ounce of Y has a contribution margin of $600. Selling 200 ounces of Q and 50 ounces of Y yields total contribution margin of $190,000 ($800 × 200 + $600 × 50). Deducting the $200,000 of joint costs again yields a loss of $10,000 per batch.

b. The joint cost of producing a batch is a fixed cost, once a batch is produced. As long as the maximum profits from the optimum pricing decisions for Q and Y exceed the joint cost of $225,000, they should continue to produce batches. The table below shows that the maximum profit is $220,000. When the cost per batch was $200,000, maximum profit after batch costs was $20,000. However, once batch costs rise to $225,000, the firm should stop producing.

Price of

Revenue of

Incremental cost of

Total profit

Revenue of

Incremental cost of

Total profit

QTY

of Q

of Y

$1200

$750

$60000

$5000

$55000

$37500

$7500

$30000

100

1100

550

110000

10000

100000

55000

15000

40000

150

1000

350

150000

15000

135000

52500

22500

30000

200

900

150

180000

20000

160000

30000

250

800

200000

25000

175000

300

700

210000

30000

180000

P 8–10: Solution to Sunder Toys (30 minutes)

[Ignoring fixed costs when excess capacity exists leads to overinvestment]

The following table shows that Sunder should produce 1,000 chewies daily:

Price

Quantity

Variable
Cost/unit

Contribution Margin/unit

Contribution Margin

Lease
Cost

Profit

$16.11
900
$3
$13.11

$11,800

$10,000

$1,800
15.00
1,000
3
12.00

12,000

10,000

2,000
14.18
1,100
3
11.18

12,300

10,800

1,500
12.83
1,200
3
9.83

11,800

10,800

1,000
12.23
1,300
3
9.23

12,000

11,200

800
11.50
1,400
3
8.50

11,900

11,200

700

b. The table below shows that with private information the manager produces 1,100 chewies daily and will buy a machine with 1,200 units of capacity so as not to be charged any fixed cost. There is no reason to lease the machine with 1,400 units of capacity since the 1,200 unit machine gives excess capacity (and hence no fixed costs are charged). In fact, leasing the 1,400 unit machine may cause senior managers to review this lease if they begin to see 300 units of unused capacity, whereas they are more likely to ignore 100 units of excess capacity on the 1,200 unit machine.

Price

Leased
Capacity

Quantity

Variable
Cost/unit

Contribution Margin

Profit

16.11

1,000
900

13.11

11,799

15.00

1,200
1,000

12.00

12,000

14.18

1,200
1,100

11.18

12,298

12.83

1,400
1,200

9.83

11,796

12.23

1,400
1,300

9.23

11,999

11.50

1,400
1,400

8.50

700

c. The policy of not charging managers fixed cost when excess capacity exists causes the firm to overinvest in capacity.

P 8-11: Solution to WWWeb Marketing (35 minutes)

[Tradeoff between over investment and underutilization]

a. WWWeb Marketing’s current policy of not charging the profit centers the IT costs as long as IT has excess capacity creates the incentive for the three divisions to always lobby for more capacity to ensure that the divisions are not charged IT costs. This leads to an over investment problem in IT capacity. This over investment in IT capacity is contributing to WWWeb’s current low profitability. The advantage of the current policy is that it causes the divisions to efficiently utilize the existing excess capacity – WWWeb is avoiding the under utilization problem. That is, whenever IT has unused capacity (and the opportunity cost of this capacity is zero because the users are not interfering with each other), by charging the divisions zero for their use of this excess capacity encourages the divisions to more fully utilize these resources. However, since the divisions view IT resources as free, they are probably not considering IT costs when pricing the services the divisions charge WWWeb clients. Each division is maximizing their division profits, which excludes IT costs.

By not charging IT costs to the three profit centers, the profit center managers have no incentive to monitor IT’s spending. That is, there is no mutual monitoring of IT by the profit centers.

With respect to the decision as to whether WWWeb should double its IT capacity at an additional cost of 20 percent, this decision should be deferred until after they evaluate the current treatment of IT charges to the divisions.

b. To reduce WWWeb’s over investment problem, the divisions should be charged for IT services. The cost recovery system or cost allocation should be based on the long-run cost IT incurs for hardware, software, and access line fees. For example, if the IT system tracks megabytes uploaded or downloaded, then IT can develop a cost per megabyte transferred by dividing the budgeted cost of the IT department ($548,000) by the budgeted number of megabytes transferred. In this way, each division is charged the average cost of the IT resources consumed by the division. Such a non-insulating allocation or recharge system encourages cooperation among the profit centers. If one expands, the overhead rate falls and the other divisions’ IT costs call.

After they implement this cost allocation scheme, WWWeb can then determine whether to double its existing capacity. The “cost” of this change in the policy of charging the divisions for IT resources consumed is that there will be a tendency for the divisions to under utilize any excess capacity of the IT group.