118899

CHAPTER 7 SUPPORT-DEPARTMENT COST ALLOCATION

QUESTIONS FOR WRITING AND DISCUSSION

1. Stage one assigns support-department costs to producing departments. Costs are assigned using factors that reflect the con-sumption of the services by each producing department. Stage two allocates the costs assigned to the producing departments (in-cluding service costs and direct costs) to the products passing through the producing de-partments.

2. Support-department costs are part of the cost of producing a product. Knowing the in-dividual product costs is helpful for develop-ing bids and cost-plus prices.

3. GAAP require that all manufacturing costs be assigned to products for inventory valua-tion.

4. Allocating support-department costs makes users pay attention to the level of service ac-tivity consumed and also provides an incen-tive for them to monitor the efficiency of the support departments.

5. Without any allocation of support-department costs, users may view services as a free good and consume more of the service than is optimal. Allocating support-department costs would encourage manag-ers to use the service until such time as the marginal cost of the service is equal to the marginal benefit.

6. Since the user departments are charged for the services provided, they will monitor the performance of the support department. If the service can be obtained more cheaply externally, then the user departments will be likely to point this out to management. Knowing this, a manager of a support de-partment will exert effort to maintain a com-petitive level of service.

7. The identification and use of causal factors ensures that support-department costs are accurately assigned to users. This increases the legitimacy of the control function and enhances product costing accuracy.

8. a. Number of employees; b. Square foo-tage; c. Pounds of laundry; d. Orders processed; e. Maintenance hours worked; f. Number of employees; and g. Number of transactions processed.

9. Allocating actual costs passes on the effi-ciencies or inefficiencies of the support de-partment, something which the manager of the producing department cannot control. Al-locating budgeted costs avoids this problem.

10. The direct method allocates the direct costs of each support department directly to the producing departments. No consideration is given to the fact that other support depart-ments may use services. The sequential method allocates support-department costs sequentially. First, the costs of the center providing the greatest service to all user de-partments, including other support depart-ments, are allocated. Next the costs of the second greatest provider of services are al-located to all user departments, excluding any department(s) that has already allocated costs. This continues until all support-department costs have been allocated. The principal difference in the two methods is the fact that the sequential method considers some interactions among support depart-ments and the direct method ignores inte-ractions.

11. Yes, the reciprocal method is more accurate because it fully considers interactions among support departments. However, the reciprocal method is much more complex and can be difficult for managers to under-stand. If the results are similar, the simpler method should be used.

12. A joint cost is a cost incurred in the simulta-neous production of two or more products. At least one of these joint products must be a main product. It is possible for the joint production process to produce a product of relatively little sales value relative to the main product(s); this product is known as a by-product.

13. Joint costs occur only in cases of joint pro-duction. A joint cost is a common cost, but a common cost is not necessarily a joint cost. Many overhead costs are common to the products manufactured in a factory but do not signify a joint production process.

119900

EXERCISES

7–1

a. support b. support c. producing d. producing e. support f. support g. producing h. producing

i. support j. support k. producing l. support m. producing n. support o. support

7–2

a. support b. support c. support d. support e. support f. producing g. producing h. support

i. support j. producing k. producing l. support m. support n. support o. support

7–3

a. direct labor hours; number of employees b. number of processing hours c. labor hours; units produced d. number of orders; materials cost e. materials cost; orders received f. orders shipped g. number of employees

h. square feet i. square feet j. kilowatt-hours k. number of employees; direct labor cost l. square feet m. machine hours; number of repair jobs n. cubic feet

119911

7–4

1. Charging rate = ($80 × 100 hours)/400 units = $20 per apartment unit 2. Amount charged = ($80 × 130 hours) = $10,400

Amount actually charged apartment building owners:

Number of Charge Total Units × per Unit = Charges The Roost 130 $20 $ 2,600 Magnolia House 70 20 1,400 Oak Park 120 20 2,400 Wisteria Lane 50 20 1,000 Elm Street 30 20 600 Total 400 $ 8,000 Number of Charge Total Hours × per Hour = Charges The Roost 35 $80 $ 2,800 Magnolia House 10 80 800 Oak Park 45 80 3,600 Wisteria Lane 15 80 1,200 Elm Street 25 80 2,000 Total 130 $ 10,400

3. The use of number of legal hours as the charging base is much better than the

number of apartment units. The number of legal hours is directly associated with the attorney’s charges. The number of units is, apparently, a poor proxy for the use of legal services. Two problems are immediately evident. First, the use of the unit charge means that Stewart will only be charging actual legal fees when the number of units times the per-unit rate happens to equal the number of hours times the per-hour rate. In this case, he will not recoup all of his spending on le-gal fees. That occurred here, where Stewart charged the owners only $8,000 for legal fees, but paid the attorney $10,400. In other years, the amount charged the apartment owners will be more than the amount charged by the attorney. Second, it is possible for apartment owners to have a smaller or larger proportion of units than of hours. Even in the example above, we can see that Elm Street has a small percentage of units, but causes a larger proportion of legal fees.

119922

7–5

1. Single charging rate = ($320,000 + $400,000)/24,000 = $30/DLH 2. Charge to the Used Car Sales Dept. = $517 + ($30 × 12 DLH) = $877 3. Actual DLH × Charging Rate + DM = Total Charges New Car Sales 1,000 $30 $ 3,100 $ 33,100 Used Car Sales 4,700 30 7,860 148,860 Service 19,400 30 86,300 668,300 Total 25,100 $97,260 $850,260

7–6

1. Billing rate for maintenance = $193,200/4,200 = $46/maintenance hour 2. $46 × 370 = $17,020 3. Total charged ($46 × 4,110) $ 189,060 Actual cost 190,060 Maintenance cost undercharged $ 1,000

119933

7–7

1. $460 = $46 × number of hours of maintenance Number of hours of maintenance = 10 hours

The controller must have looked up the usage of maintenance by the Assembly Department, found that it had used 10 hours, and multiplied those hours by the single charging rate of $46. In that case, $460 would be correct.

2. Rate for routine maintenance = $48,000/2,000 = $24/routine maint. hour Rate for technical maintenance = $145,200/2,200 = $66/tech. maint. hour

New charge for Assembly Department = $24 × 10 routine hours = $240 3. When single charging rates are used by companies, they must be aware that

changes in the way work is performed may require changes in the charging rate(s). In this case, the additional complexity caused by the computer-controlled equipment means that a single charging rate does not adequately control for the differences in cost caused by different departments. Multiple charging rates do a better job of charging the using department for the resources provided by the support departments.

119944

7–8

1. Allocation ratios for S1 based on number of employees:

Cutting = 120/(120 + 80) = 0.60 Sewing = 80/(120 + 80) = 0.40

Allocation ratios for S2 based on number of maintenance hours:

Cutting = 15,000/(15,000 + 5,000) = 0.75 Sewing = 5,000/(15,000 + 5,000) = 0.25 2. Support Departments Producing Departments S1 S2 Cutting Sewing Direct costs $200,000 $ 140,000 $ 122,000 $ 90,500 Allocate: S1 (200,000) — 120,000 80,000 S2 — (140,000) 105,000 35,000 Total $ 0 $ 0 $ 347,000 $ 205,500

7–9

1. Allocation ratios for S1 based on number of employees: S2 = 50/(50 + 120 + 80) = 0.20 Cutting = 120/(50 + 120 + 80) = 0.48 Sewing = 80/(50 + 120 + 80) = 0.32

Allocation ratios for S2 based on number of maintenance hours: Cutting = 15,000/(15,000 + 5,000) = 0.75 Sewing = 5,000/(15,000 + 5,000) = 0.25 2. Support Departments Producing Departments S1 S2 Cutting Sewing Direct costs $ 200,000 $ 140,000 $ 122,000 $ 90,500 Allocate:S1 (200,000) 40,000 96,000 64,000 S2 — (180,000) 135,000 45,000 Total $ 0 $ 0 $ 353,000 $ 199,500

119955

7–10

1. Allocation ratios: Proportion of Output Used by Department S1 S2 Cutting Sewing S1 — 0.2000 0.4800 0.3200 S2 0.0566 — 0.7075 0.2358 2. S1 = Direct costs + Share of S2 costs S1 = $200,000 + 0.0566(S2) S2 = Direct costs + Share of S1 costs S2 = $140,000 + 0.200(S1) S2 = $140,000 + 0.200 [$200,000 + 0.0566(S2)] S2 = $140,000 + $40,000 + 0.0113(S2) 0.9887S2 = $180,000 S2 = $182,057

Substituting $180,057 for S2 into the S1 equation yields total S1 cost: S1 = $200,000 + 0.0566($182,057) = $200,000 + $10,304 = $210,304 3. Support Departments Producing Departments S1 S2 Cutting Sewing Direct costs $200,000 $140,000 $122,000 $ 90,500 Allocated from: S1 (210,304) 42,061 100,946 67,297 S2 10,304 (182,057) 128,805 42,929 Total $ 0 $ (4)* $351,751 $200,726

*Difference due to rounding.

119966

7–11

1. Baking Dept. overhead rate = $150,000/6,250 = $24 per MHr Decorating Dept. overhead rate = $42,000/6,000 = $7 per DLH 2. Cost per batch:

Direct materials $55 Direct labor 42 Overhead: Baking Dept. (2 × $24) 48 Total $145

Cost per loaf = $145/100 = $1.45 3. Cost of Dearman wedding cake:

Direct materials $ 20 Direct labor 50 Overhead: Baking Dept. (1 × $24) 24 Decorating Dept. (8 × $7) 56 Total cost $150

Price = 3 × $150 = $450

119977

7–12

1. Allocation ratios: Shaping Firing Kilowatt-hours1 0.20 0.80 Square feet2 0.75 0.25 Direct labor hours3 0.71 0.29 1based on kilowatt hours: 20,000/(20,000+80,000); 80,000/(20,000+80,000) 2based on square feet: 24,000/(24,000+8,000); 8,000/(24,000+8,000) 3based on direct labor hours: 10,000/(10,000+4,000); 4,000/(10,000+4,000) Cost assignment: Power Gen. Factory HR Shaping Firing Direct overhead costs $90,000 $$167,000 $84,000 $72,000 $230,000 Allocate: Power ($90,000) - - 18,000 72,000 General Factory - (167,000) - 125,250 41,750 Human Resources - - 84,000 59,640 24,360 Total after allocation $0 $0 $0 $274,890 $368,110 2. Departmental overhead rates:

Shaping: $274,890/10,000 = $27.49 per DLH* Firing: $368,110/4,000 = $92.03 per DLH*

*Rounded

119988

7–13

1. Assume the support-department costs are allocated in order of highest to lowest cost: General Factory, Power, and Human Resources.

Power GF HR Shaping Firing Square feet 0.05 — 0.15 0.60 0.20 Kilowatt-hours — — 0.20 0.16 0.64 Labor hours — — — 0.71 0.29

Direct costs $ 90,000 $167,000 $84,000 $ 72,000 $230,000 General Factory1: (0.05 × $167,000) 8,350 (8,350) (0.15 × $167,000) (25,050) 25,050 (0.60 × $167,000) (100,200) 100,200 (0.20 × $167,000) (33,400) 33,400 Power2: (0.20 × $98,350) (19,670) 19,670 (0.16 × $98,350) (15,736) 15,736 (0.64 × $98,350) (62,944) 62,944 Human Resources: (0.71 × $128,720) (91,391) 91,391 (0.29 × $128,720) (37,329) 37,329 Total $ 0 $ 0 $ 0 $279,327 $363,673 1based on square feet: Power = 2,000/(2,000+6,000+24,000+8,000) HR = 6,000/(2,000+6,000+24,000+8,000) Shaping = 24,000/(2,000+6,000+24,000+8,000) Firing = 8,000/(2,000+6,000+24,000+8,000) 2based on kilowatt hours : HR = 25,000/(25,000+20,000+80,000) Shaping = 20,000/(25,000+20,000+80,000) Firing = 80,000/(25,000+20,000+80,000) Allocation Ratios for HR department based on direct labor hours : Shaping 10,000/(10,000+4,000) Firing 4,000/(10,000+4,000) 2. Shaping: $279,327/10,000 = $27.93 per DLH* Firing: $403,576/4,000 = $90.92 per DLH*

*Rounded

119999

7-14 Units Percent × Joint Cost = Allocated Joint Cost Andol 1,000 0.1250 $100,000 $12,500 Incol 1,500 0.1875 100,000 18,750 Ordol 2,500 0.3125 100,000 31,250 Exsol 3,000 0.3750 100,000 37,500 Total 8,000 $100,000 7-15 Price at Market Value Joint Allocated Units Split-off at Split-off Percent Cost Cost Andol 1,000 $20.00 $ 20,000 0.0556 $100,000 $ 5,560 Incol 1,500 75.00 112,500 0.3125 100,000 31,250 Ordol 2,500 64.00 160,000 0.4444 100,000 44,440 Exsol 3,000 22.50 67,500 0.1875 100,000 18,750 Total 8,000 $360,000 $100,000 7-16 1. Eventual Separable Hypothetical Units Price Market Value Costs Market Value Percent Ups 39,000 $2.00 $78,000 $18,000 $60,000 0.60 Downs 21,000 2.18 45,780 5,780 40,000 0.40 Total $100,000 Ups Downs Joint cost $42,000 $42,000 × Percent of hypothetical market value × 0.60 × 0.40 Allocated joint cost $25,200 $16,800 2. Value of ups at split-off (39,000 × $1.80) $70,200 Value of ups when processed further $78,000 Less: Further processing cost 18,000 Incremental value of further processing $60,000 Ups should NOT be processed further as there will $10,200 more profit if sold at split-off.

220000

7–17

1. HR Power Mixing Packaging HR1 — 0.3000 0.3500 0.3500 Power2 0.0769 — 0.2308 0.6923 1based on payroll: 90,000/(90,000+105,000+105,000) 105,000/(90,000+105,000+105,000) 105,000/(90,000+105,000+105,000) 2based on kilowatt hours: 5,000/(5,000+15,000+45,000) 15,000/(5,000+15,000+45,000) 45,000/(5,000+15,000+45,000) P = $150,000 + 0.3HR P = $150,000 + 0.3($110,000 + 0.0769P) P = $150,000 + $33,000 + 0.0231P

0.9769P = $183,000 P = $187,327

HR = $110,000 + 0.0769P HR = $110,000 + 0.0769($187,327) HR = $110,000 + $14,405 HR = $124,405

Human Resources Power Mixing Packaging Direct overhead costs $110,000 $150,000 $100,000 $280,000 Allocated from: HR (124,405) 37,321 43,542 43,542 Power 14,409 (187,327) 43,235 129,686 Total $ 0 $ (5)* $186,777 $453,228

*Difference due to rounding. 2. Mixing: $186,777/20,000 = $9.34 per DLH Packaging: $453,228/30,000 = $15.11 per DLH

220011

7–18

1. Support Departments Producing Departments HR Power Mixing Packaging Direct overhead $110,000 $150,000 $100,000 $280,000 Allocate HR1 (110,000) - 55,000 55,000 Allocate Power - (150,000) 37,500 112,500 Total $ 0 $ 0 $192,500 $447,500 1 based on payroll: Mixing = 105,000/(105,000+105,000) = 0.50 Packaging = 105,000/(105,000+105,000) = 0.50

2 based on kilowatt hours: Mixing = 15,000/(15,000+45,000) = 0.25 Packaging = 45,000/(15,000+45,000) = 0.75 2. Mixing: $192,500/20,000 = $9.63 per DLH Packaging: $447,500/30,000 = $14.92 per DLH

The reciprocal method is more accurate because support-department costs are allocated to other support departments. Using the direct method, Human Re-sources and Power do not receive any other support department costs. How im-portant the increased accuracy is for this example is not clear. Some might argue that the departmental rates do not differ enough to justify using the more compli-cated reciprocal method.

220022

7–19

1. Support Departments Producing Departments HR Power Mixing Packaging Direct overhead $110,000 $150,000 $100,000 $280,000 Allocate HR1 (110,000) 33,000 38,500 38,500 Allocate Power2 - (183,000) 45,750 137,250 Total $ 0 $ 0 $184,250 $455,750 1 based on payroll: Power = 90,000/(90,000+105,000+105,000) = 0.30 Mixing = 105,000/(90,000 + 105,000+105,000) = 0.35 Packaging = 105,000/(90,000 + 105,000+105,000) = 0.35

2 based on kilowatt hours: Mixing = 15,000/(15,000+45,000) = 0.25 Packaging = 45,000/(15,000+45,000) = 0.75

2. Mixing: $184,250/20,000 = $9.21 per DLH Packaging: $455,750/30,000 = $15.19 per DLH

The sequential method is more accurate than the direct method and less accurate than the reciprocal method. The reason is that at least some support-department reciprocity is accounted for using the sequential method, while none is recog-nized under the direct method.

220033

7–20

A = $35,000 + 0.3B B = $40,000 + 0.2A

A = $35,000 + 0.3($40,000 + 0.2A) A = $47,000 + 0.06A 0.94A = $47,000 A = $50,000

B = $40,000 + 0.2($50,000) B = $50,000

Allocation ratios (ratios for D obtained by “plugging”):

Dept. A Dept. B Dept. C Dept. D Dept. A — 0.2 0.2 0.6* Dept. B 0.3 — 0.4 0.3** *(1.0 – 0.2 – 0.2)

**(1.0 – 0.3 – 0.4) Dept. C Dept. D Allocate A: (0.2 × $50,000) $10,000 (0.6 × $50,000) $30,000 Allocate B: (0.4 × $50,000) 20,000 (0.3 × $50,000) 15,000

220044

7–21

1. General HR Factory Grinding Assembly Direct costs $ 70,000 $ 230,000 $ 63,900 $ 39,500 Allocate: HR 1 (70,000) — 14,000 56,000 Gen. Factory2 — (230,000) 57,500 172,500 Total OH $ 0 $ 0 $135,400 $268,000 1 based on payroll: 20,000/(20,000+80,000)=20%; 80,000/(20,000+80,000)=80% 2 based on square feet: 2,000/(2,000+6,000)=25%; 6,000/(2,000+6,000)=75% 2. Grinding OH rate: $135,400/4,000 = $33.85 per MHr Assembly OH rate: $268,000/80,000 = $3.35 per DLH 3. Prime costs $123.00 Grinding (1 × $33.85) 33.85 Assembly (12 × $3.35) 40.20 Unit product cost $197.05

7–22

1. General HR Factory Grinding Assembly Direct costs $ 70,000 $ 230,000 $ 63,900 $ 39,500 Allocate: Gen. Factory1 76,667 (230,000) 38,333 115,000 HR 2 (146,667) — 29,333 117,334 Total OH $ 0 $ 0 $131,566 $271,834 1HR = 4,000/(4,000+2,000+6,000)=33.33% Grinding = 2,000/(4,000+2,000+6,000)=16.67% Assembly = 6,000/(4,000+2,000+6,000)=50% 2Grinding = 20,000/(20,000+80,000)=20% Assembly = 80,000/(20,000+80,000)=80% 2. Grinding OH rate: $131,566/4,000 = $32.89 per MHr (rounded) Assembly OH rate: $271,834/80,000 = $3.40 per DLH (rounded)

3. Prime cost $123.00 Grinding (1 × $32.89) 32.89 Assembly (12 × $3.40) 40.80 Unit product cost $196.69

7–23

220055

1. HR GF Grinding Assembly GF-square feet1 0.3333 — 0.1667 0.5000 HR-direct labor hrs2 — 0.0991 0.1802 0.7207

1HR: 4,000/(4,000+2,000+6,000) = 0.3333 Grinding: 2,000/(4,000+2,000+6,000) = 0.1667 Assembly: 6,000/(4,000+2,000+6,000) = 0.5000 2Allocation ratios for HR based on payroll : General Factory: 11,000/(11,000+20,000+80,000) = 0.0991 Grinding: 20,000/(11,000+20,000+80,000) = 0.1802 Assembly: 80,000/(11,000+20,000+80,000) = 0.7207

HR = $70,000 + 0.3333GF GF = $230,000 + 0.0991HR

GF = $230,000 + 0.0991($70,000 + 0.3333GF) 0.967GF = $236,937 GF = $245,023

HR = $70,000 + 0.3333GF HR = $70,000 + 0.3333($245,023) HR = $151,666 General HR Factory Grinding Assembly Direct costs $ 70,000 $ 230,000 $ 63,900 $ 39,500 Allocate: HR (151,666) 15,030 27,330 109,306 GF 81,666 (245,023) 40,845 122,512 Total OH $ 0 $ 7* $132,075 $271,318

*Difference due to rounding. 2. Grinding OH rate: $132,075/4,000 = $33.02 per MHr* Assembly OH rate: $271,318/80,000 = $3.39 per DLH*

*Rounded 3. Prime costs $123.00 Grinding (1 × $33.02) 33.02 Assembly (12 × $3.39) 40.68 Unit product cost $196.70

220066

7–24

1. Units Percent × Joint Cost = Allocated Joint Cost Alpha 12,500 0.25 $125,000 $31,250 Beta 17,500 0.35 125,000 43,750 Gamma 20,000 0.40 125,000 50,000 Total 50,000 $125,000 2. Price at Market Value Joint Allocated Units Split-off at Split-off Percent Cost Cost Alpha 12,500 $20 $ 250,000 0.1684 $125,000 $ 21,050 Beta 17,500 50 875,000 0.5892 125,000 73,650 Gamma 20,000 18 360,000 0.2424 125,000 30,300 Total 50,000 $1,485,000 $125,000

220077

PROBLEMS

7–25

1. Direct method: Tissue Delivery Accounting Laboratory Pathology Direct costs $240,000 $270,000 $345,000 $456,000 Allocate: Delivery1 (240,000) -- 144,000 96,000 Accounting2 -- (270,000) 175,500 94,500 Total $ 0 $ 0 $664,500 $646,500 1 Laboratory: 70,200/(70,200+46,800) = 0.60 Tissue Pathology: 46,800/(70,200+46,800) = 0.40 2 Laboratory: 24,700/(24,700+13,300) = 0.65 Tissue Pathology: 1,3,300/(24,700+13,300) = 0.35 2. Sequential method Tissue Delivery Accounting Laboratory Pathology Direct costs $ 240,000 $ 270,000 $345,000 $456,000 Allocate: Accounting1 13,500 (270,000) 166,725 89,775 Delivery2 (253,500) 0 152,100 101,400 Total $ 0 $ 0 $663,825 $647,175

1Delivery: 2,000/(2,000+24,700+13,300) = 0.050 Laboratory: 24,700/(2,000+24,700+13,300) = 0.6175 Tissue Pathology: 13,300/(2,000+24,700+13,300) = 0.3325 2Laboratory: 70,200/(70,200+46,800) = 0.60 Tissue Pathology: 46,800/(70,200+46,800) = 0.40

220088

7–26

1. a. Direct method Maintenance Power Drilling Assembly Direct costs $320,000 $400,000 $163,000 $ 90,000 Allocate: Maintenance1 (320,000) 0 256,000 64,000

Power2 0 (400,000) 40,000 360,000 Total $ 0 $ 0 $459,000 $514,000 1Drilling: 30,000/(30,000+7.500) = 0.80

Assembly: 7,500/(30,000+7,500) = 0.20 2Drilling: 36,000/(36,000+324,000) = 0.10

Assembly: 324,000/(36,000+324,000) = 0.90 Drilling: $459,000/30,000 = $15.30 per MHr Assembly: $514,000/40,000 = $12.85 per DLH

Prime costs $1,817.00 Drilling (2 × $15.30) 30.60 Assembly (50 × $12.85) 642.50 Total cost $2,490.10 Markup (15%) 373.52 Bid price $2,863.62

220099

7–26 Continued

b. Reciprocal method Maintenance Power Drilling Assembly Machine hours1 — 0.375 0.500 0.125 Kilowatt-hours2 0.100 — 0.090 0.810

1Power: 22,500/(22,500+30,000+7.500) = 0.375 Drilling: 30,000/(22,500+30,000+7.500) = 0.500 Assembly: 7,500/(22,500+30,000+7,500) = 0.125 2Maintenance: 40,000/(40,000+36,000+324,000) = 0.100 Drilling: 36,000/(40,000+36,000+324,000) = 0.090 Assembly: 324,000/(40,000+36,000+324,000) = 0.810

M = $320,000 + 0.1P P = $400,000 + 0.375M M= $320,000 + 0.1($400,000 + 0.375M) M = $320,000 + $40,000 + 0.0375M 0.9625M = $360,000 M = $374,026

P = $400,000 + 0.375M P = $400,000 + 0.375($374,026) P = $400,000 + $140,260 P = $540,260

Maintenance Power Drilling Assembly Direct cost $320,000 $400,000 $163,000 $90,000 Allocate: Maintenance ($374,026) 140,260 187,013 46,753 Power 54,026 (540,260) 48,623 437,611 Total $ 0 $ 0 $398,636 $574,364

Drilling: $398,636/30,000 = $13.29 per MHr (rounded) Assembly: $574,364/40,000 = $14.36 per DLH (rounded)

Prime costs $1,817.00 Drilling (2 × $13.29) 26.58 Assembly (50 × $14.36) 718.00 Total cost $2,561.58 Markup (15%) 384.24 Bid price $2,945.82

2. The reciprocal method is more accurate, as it takes into account the use of support departments by other support departments.

221100

7–27

1. a. Sequential method: Allocate Maintenance first, then Power

Maintenance Power Drilling Assembly Direct costs $ 320,000 $ 400,000 $163,000 $ 90,000 Allocate: Maintenance1 (320,000) 120,000 160,000 40,000 Power2 0 (520,000) 52,000 468,000 Total $ 0 $ 0 $375,000 $598,000

1Power: 22,500/(22,500+30,000+7.500) = 0.375 Drilling: 30,000/(22,500+30,000+7.500) = 0.500 Assembly: 7,500/(22,500+30,000+7,500) = 0.125

2Drilling: 36,000/(36,000+324,000) = 0.100 Assembly: 324,000/(36,000+324,000) = 0.900

Drilling: $375,000/30,000 = $12.50 per MHr Assembly: $598,000/40,000 = $14.95 per DLH

Prime costs $1,817.00 Drilling (2 × $12.50) 25.00 Assembly (50 × $14.95) 747.50 Total cost $2,589.50 Markup (15%) 388.43 Bid price $2,977.93

221111

7–27 Concluded

b. Sequential method: Allocate Power first, then Maintenance

Maintenance Power Drilling Assembly Direct costs $ 320,000 $ 400,000 $163,000 $ 90,000 Allocate: Power1 40,000 (400,000) 36,000 324,000 Maintenance2 (360,000) 0 288,000 72,000 Total $ 0 $ 0 $487,000 $486,000 1Maintenance: 40,000/(40,000+36,000+324,000) = 0.10

Drilling: 36,000/(40,000+36,000+324,000) = 0.09 Assembly: 324,000/(40,000+36,000+324,000) = 0.81 2Drilling: 30,000/(30,000+7.500) = 0.80 Assembly: 7,500/(30,000+7,500) = 0.20

Drilling: $487,000/30,000 = $16.23 per MHr (rounded) Assembly: $486,000/40,000 = $12.15 per DLH

Prime costs $1,817.00 Drilling (2 × $16.23) 32.46 Assembly (50 × $12.15) 607.50 Total cost $2,456.96 Markup (15%) 368.54 Bid price $2,825.50 2. Yes, there is a difference in the bids. Ranking Maintenance first results in a higher

dollar allocation to Power ($120,000) than the allocation from Power to Mainten-ance ($40,000). Then, the greater usage of Power by Assembly results in a higher allocation to Assembly when Maintenance is ranked first. Thus, the ranking of Maintenance first gives a greater chance for support-department interaction to be reflected in the ultimate overhead rates. (These results can be compared with the results using the reciprocal method in Problem 7–26.)

221122

7–28

1. Units Percent × Joint Cost = Allocated Joint Cost Two Oil 300,000 0.4545 $10,000,000 $4,545,000 Six Oil 240,000 0.3636 10,000,000 3,636,000 Distillates 120,000 0.1818 10,000,000 1,818,000 Total 660,000 $9,999,000 2. Price at Market Value Joint Allocated Units Split-off at Split-off Percent Cost Cost

Two Oil 300,000 $20 $6,000,000 0.4000 $10,000,000 $4,000,000

Six Oil 240,000 30 7,200,000 0.4800 10,000,000 4,800,000 Distillates 120,000 15 1,800,000 0.1200 10,000,000 1,200,000 Total 660,000 $15,000,000 $10,000,000

221133

7–29

1. Fixed cost allocation (direct method): Allocation Ratios Cost driver Mixing Cooking Packaging Employees1 0.400 0.200 0.400 Items processed2 0.329 0.318 0.353 Square feet3 0.444 0.333 0.222 Machine hours4 0.200 0.500 0.300 1 Mixing = 20/(20+10+20) = 0.40 Cooking = 10/(20+10+20) = 0.20 Packaging = 20/(20+10+20) = 0.40 2Mixing = 2,800/(2,800+2,700+3,000) = 0.329 Cooking = 2,700/(2,800+2,700+3,000) = 0.318 Packaging = 3,000/(2,800+2,700+3,000) = 0.353 3Mixing = 40,000/(40,000+30,000+20,000) = 0.444 Cooking = 30,000/(40,000+30,000+20,000) = 0.333 Packaging = 20,000/(40,000+30,000+20,000) = 0.222 4Mixing = 4,000/(4,000+10,000+6,000) = 0.20 Cooking = 10,000/(4,000+10,000+6,000) = 0.50 Packaging = 6,000/(4,000+10,000+6,000) = 0.30

221144

7-29 continued Cafeteria and personnel are allocated using number of employees; custodial services

using square feet; maintenance using machine hours; and cost accounting using items processed.

Mixing Cooking Packaging Cafeteria: (0.4 × $20,000) $ 8,000 (0.2 × $20,000) $ 4,000 (0.4 × $20,000) $ 8,000 Personnel: (0.4 × $70,000) 28,000 (0.2 × $70,000) 14,000 (0.4 × $70,000) 28,000 Custodial Services: (0.444 × $80,000) 35,520 (0.333 × $80,000) 26,640 (0.222 × $80,000) 17,760 Maintenance: (0.2 × $100,000) 20,000 (0.5 × $100,000) 50,000 (0.3 × $100,000) 30,000 Cost Accounting: (0.329 × $130,000) 42,770 (0.318 × $130,000) 41,340 (0.353 × $130,000) 45,890 Direct costs 120,000 60,000 25,000 Total $254,290 $195,980 $154,650

221155

7–29 Continued

Variable cost allocation (direct method):

Cafeteria: $40,000/50 = $800/employee Personnel: $20,000/50 = $400/employee Maintenance: $100,000/20,000 = $5/machine hour Cost Accounting: $16,500/8,500 = $1.94*/item processed

Mixing Cooking Packaging Cafeteria: ($800 × 20) $16,000 ($800 × 10) $ 8,000 ($800 × 20) $16,000 Personnel: ($400 × 20) 8,000 ($400 × 10) 4,000 ($400 × 20) 8,000 Maintenance: ($5 × 4,000) 20,000 ($5 × 10,000) 50,000 ($5 × 6,000) 30,000 Cost Accounting: ($1.94 × 2,800) 5,432 ($1.94 × 2,700) 5,238 ($1.94 × 3,000) 5,820 Direct costs 20,000 10,000 40,000 Total $69,432 $77,238 $99,820

*Rounded

221166

7–29 Continued

2. Fixed overhead rates:

Mixing: $254,290/30,000 = $8.48 per DLH* Cooking: $195,980/10,000 = $19.60 per MHr* Packaging: $154,650/50,000 = $3.09 per DLH*

Variable overhead rates:

Mixing: $69,432/30,000 = $2.31 per DLH* Cooking: $77,238/10,000 = $7.72 per MHr* Packaging: $99,820/50,000 = $2.00 per DLH*

*Rounded 3. Sequential method: Fixed cost allocation ratios (descending order of magnitude): Cost Driver* Maint. Custod. Pers. Cafe. Mix. Cook. Pack. Items 0.200 0.016 0.080 0.024 0.224 0.216 0.240 Machine hours 0.200 0.500 0.300 Square feet — — 0.069 0.049 0.392 0.294 0.196 Employees (1) — — — 0.091 0.364 0.182 0.364 Employees (2) — — — — 0.400 0.200 0.400

*Note: Items are used to allocate accounting costs; machine hours to allocate maintenance; square feet to allocate custodial services; and employees to allo-cate both personnel costs and cafeteria costs.

221177

7–29 Continued

Allocation of fixed costs (expressed in thousands of dollars): Main. Cust. Pers. Cafe. Mixing Cooking Packaging Direct costs $100 $80.000 $70.000 $20.000 $120.000 $60.000 $25.000 Accounting: (0.200 × $130) 26 (0.016 × $130) 2.080 (0.080 × $130) 10.400 (0.024 × $130) 3.120 (0.224 × $130) 29.120 (0.216 × $130) 28.080 (0.240 × $130) 31.200 Maintenance: (0.2 × $126) 25.200 (0.5 × $126) 63.000 (0.3 × $126) 37.800 Custodial: (0.069 × $82.08) 5.664 (0.049 × $82.08) 4.022 (0.392 × $82.08) 32.175 (0.294 × $82.08) 24.132 (0.196 × $82.08) 16.088 Personnel: (0.091 × $86.064) 7.832 (0.364 × $86.064) 31.327 (0.182 × $86.064) 15.664 (0.364 × $86.064) 31.327 Cafeteria: (0.4 × $34.974) 13.990 (0.2 × $34.974) 6.995 (0.4 × $34.974) 13.990 Total $251.812 $197.871 $155.405

Note: Total of post-allocation fixed costs does not equal pre-allocation total due to rounding error.

221188

7–29 Continued

Allocation ratios for variable costs: Cost Cost Driver Personnel Accounting Mixing Cooking Packaging Machine hours 0.200 0.500 0.300 Employees (1) 0.137 0.178 0.274 0.137 0.274 Employees (2) 0.206 0.317 0.159 0.317 Items 0.329 0.318 0.353

Note 1: Custodial services was not included as it had no direct variable costs.

Note 2: The order of allocation was based on the magnitude of direct variable costs as follows: maintenance, cafeteria, personnel, and cost accounting.

Note 3: Employees is the base for allocating cafeteria and personnel. Employees (1) pertains to cafeteria and employees (2) to personnel.

221199

7–29 Continued

Allocation of variable costs:

Cafe. Pers. Cost Acc. Mixing Cook. Pack. Direct costs $40,000 $20,000 $16,500 $20,000 $10,000 $40,000

Maintenance: (0.200 × $100,000) 20,000 (0.500 × $100,000) 50,000 (0.300 × $100,000) 30,000 Cafeteria: (0.137 × $40,000) 5,480 (0.178 × $40,000) 7,120 (0.274 × $40,000) 10,960 (0.137 × $40,000) 5,480 (0.274 × $40,000) 10,960 Personnel: (0.206 × $25,480) 5,249 (0.317 × $25,480) 8,077 (0.159 × $25,480) 4,051 (0.317 × $25,480) 8,077 Accounting: (0.329 × $28,869) 9,498 (0.318 × $28,869) 9,180 (0.353 × $28,869) 10,191 Total $68,535 $78,711 $99,228

Note: Total of post-allocation variable costs does not equal pre-allocation total due to rounding error.

222200

7–29 Concluded

4. Overhead rates:

Fixed rates: Mixing: $251,812/30,000 = $8.39 per DLH* Cooking: $197,871/10,000 = $19.79 per MHr* Packaging: $155,405/50,000 = $3.11 per DLH*

Variable rates: Mixing: $68,535/30,000 = $2.28 per DLH* Cooking: $78,711/10,000 = $7.87 per MHr* Packaging: $99,228/50,000 = $1.98 per DLH*

*Rounded 5. Selling price computation:

a. With direct method: Prime costs $ 60,000 Overhead* 77,220 Total costs $137,220 Markup (30%) 41,166 Price $178,386

*($8.48 + $2.31)1,000 + ($19.60 + $7.72)1,500 + ($3.09 + $2.00)5,000 b. With sequential method: Prime costs $ 60,000 Overhead* 77,610 Total costs $137,610 Markup (30%) 41,283 Price $178,893

*($8.39 + $2.28)1,000 + ($19.79 + $7.87)1,500 + ($3.11 + $1.98)5,000

The methods assign costs differently and produce different prices for the batch of chocolate bars. The difference in price is over $500. This amount could be sig-nificant, depending on the competitive conditions facing the firm. Assuming that the sequential method provides more accurate cost assignments, this method should be used if the increased accuracy is important for the firm’s well-being. Otherwise, the firm should use the much simpler direct method.

222211

7–30

1. Baton Rouge ($781,000/$4,641,000)($146,500)* = $24,653 Kilgore ($750,000/$4,641,000)($146,500) = $23,675 Longview ($912,000/$4,641,000)($146,500) = $28,789 Paris ($1,098,000/$4,641,000)($146,500) = $34,660 Shreveport ($1,100,000/$4,641,000)($146,500) = $34,723

*($18)(4,250) + $70,000 = $146,500 2. Share of Purchasing Department fixed costs based on 2005 revenues:

Baton Rouge ($675,000/$4,500,000)($70,000) = $10,500 Kilgore ($720,000/$4,500,000)($70,000) = $11,200 Longview ($900,000/$4,500,000)($70,000) = $14,000 Paris ($1,125,000/$4,500,000)($70,000) = $17,500 Shreveport ($1,080,000/$4,500,000)($70,000) = $16,800

Variable Cost + Fixed Cost = Total Baton Rouge ($18)(1,475) = $26,550 + $10,500 = $37,050 Kilgore ($18)(1,188) = $21,384 + $11,200 = $32,584 Longview ($18)(500) = $9,000 + $14,000 = $23,000 Paris ($18)(525) = $9,450 + $17,500 = $26,950 Shreveport ($18)(562) = $10,116 + $16,800 = $26,916 3. Method 2 allocates cost on the basis of the cost driver which causes it and would

be more likely to encourage managers to use Purchasing Department time effi-ciently. Method 1 assigns purchasing costs according to a base that may not be causally related. Therefore, an apartment complex with stable rentals from one year to the next may still experience wild fluctuations in allocated cost due to changing rental patterns of other apartment complexes.

222222

7–31

1. Department A Department B Direct overhead $200,000 $ 800,000 Maintenance: (1/8)($500,000) 62,500 (7/8)($500,000) 437,500 Power: (1/6)($225,000) 37,500 (5/6)($225,000) 187,500 Setups: (40/200)($150,000) 30,000 (160/200)($150,000) 120,000 General Factory: (0.272)($625,000) 170,000 (0.728)($625,000) 455,000 Total $500,000 $ 2,000,000

Dept. A overhead rate: $500,000/200,000 = $2.50 per DLH Dept. B overhead rate: $2,000,000/120,000 = $16.67 per MHr (rounded)

222233

7–31 Continued

2. Allocation order: General Factory, Maintenance, Power, Setups, A, and B

Allocation Ratios Alloc. from: G.F. Maint. Power Setups Dept. A Dept. B G.F. — 0.125 0.200 0.025 0.177 0.473 Maint. — — 0.150 0.050 0.100 0.700 Power — — — — 0.167 0.833 Setups — — — — 0.200 0.800 G.F. Maint. Power Setups Dept. A Dept. B Direct $ 625,000 $ 500,000 $ 225,000 $ 150,000 $200,000 $ 800,000 G.F. (625,000) 78,125 125,000 15,625 110,625 295,625 Maint. — (578,125) 86,719 28,906 57,813 404,687 Power — — (436,719) — 72,932 363,787 Setups — — — (194,531) 38,906 155,625 Total $ 0 $ 0 $ 0 $ 0 $480,276 $2,019,724

Dept. A overhead rate: ($480,276/200,000) = $2.40 per DLH* Dept. B overhead rate: ($2,019,724/120,000) = $16.83 per MHr*

*Rounded Job SS Job TT Prime cost $120,000 $ 50,000 Overhead: ($2.40 × 5,000) 12,000 ($16.83 × 500) 8,415 ($2.40 × 400) 960 ($16.83 × 3,000) 50,490 $140,415 $101,450 Markup (50%) 70,208 50,725 Total bid revenue $210,623 $152,175 Units ÷ 14,400 ÷ 1,500 Bid price $ 14.63 $ 101.45

Although the difference is small, it appears to make the bids more attractive. 3. The use of the sequential method to allocate support-department costs to produc-

ing departments gives more accurate overhead rates. 4. If the best competing bid was $4.10 lower than the original bid, then it would be

$14.65. In this case, the sequential method of allocating overhead costs would provide a bid ($14.63) that is just below the competing bid. Since the sequential method is more accurate, the $14.63 bid is a good one.

222244

MANAGERIAL DECISION CASES

7–32

1. Emma’s argument about the arbitrary nature of allocations has little merit. Even if the allocation is arbitrary, changing it to exploit a customer is wrong. Many allo-cations, however, are based on causal factors and reflect the consumption of re-sources. If we accept cause and effect as a reasonable criterion for allocation, then switching to a factor that is less related to overhead consumption certainly will increase the inaccuracy of the product cost. Emma should price the new or-der using the most accurate cost information available. Thus, the current alloca-tion scheme should be maintained.

2. The controller (Lenny) should refuse to change the allocation method and make

every attempt to tactfully convince Emma of the impropriety of the recommended action. Often, a simple comment questioning the propriety of an action is suffi-cient to dissuade. According to the IMA Statement of Ethical Professional Prac-tice, accountants should “refrain from engaging in any conduct that would preju-dice carrying out duties ethically.” (III-2) The accountant should also abstain from engaging in or supporting any activity that might discredit the profession. (III-3) By changing allocation procedures, the controller would obtain personal gain (a bonus) from unethical means. Furthermore, Lenny has an obligation to communi-cate information fairly and objectively (IV-1). Choosing an allocation method that is known to be less accurate is not consistent with this requirement.

3. Lenny should pursue all levels of internal review until a satisfactory resolution is

achieved. Then, after exhausting all levels of internal review, Lenny should sub-mit his resignation.

4. Reacting with anger and contacting the customer was not an appropriate action

(as defined by the code for management accountants). According to the code, “Except where legally prescribed, communication of such problems to authorities or individuals not employed or engaged by the organization is not considered ap-propriate.”

222255

7–33

1. Variable maintenance: $246,667/3,700 = $66.67*/flying hour

Allocation Ratios for Fixed Costs 500D 206B 206L-1 Maintenance 0.32432 0.43243 0.24324 Hangar rent 0.33333 0.33333 0.33333 Administrative 0.32432 0.43243 0.24324

Alloc. of fixed costs: 500D 206B 206L-1 Maintenance—fixed: (0.32432 × $26,000) $ 8,432 (0.43243 × $26,000) $11,243 (0.24324 × $26,000) $ 6,324 Hangar rent: (0.33333 × $18,000) 6,000 (0.33333 × $18,000) 6,000 (0.33333 × $18,000) 6,000 Administrative: (0.32432 × $110,000) 35,675 (0.43243 × $110,000) 47,567 (0.24324 × $110,000) 26,756 Total fixed costs $50,107 $64,810 $39,080

Indirect fixed costs per unit: 500D: $50,107/1,200 = $41.76* per hour 206B: $64,810/1,600 = $40.51* per hour 206L-1: $39,080/900 = $43.42* per hour

*Rounded

222266

7–33 Continued

500D 206B 206L-1 Direct costs—fixed* $ 77.70* $ 58.88* $195.41* Direct costs—variable** 25.54* 23.96* 110.28* Overhead—fixed 41.76 40.51 43.42 Overhead—variable 66.67 66.67 66.67 Cost per unit $211.67 $190.02 $415.78 Markup* (15%) 31.75 28.50 62.37 Bid price $243.42 $218.52 $478.15 Less cost 211.67 190.02 415.78 Profit/hour $ 31.75 $ 28.50 $ 62.37

*Total direct fixed costs/Flying hours **Total direct variable costs/Flying hours

Original expected profit (uses the original hours and the above bid prices and unit variable costs):

Revenues: 1,200 × $243.42 = $292,104 ,600 × $218.52 = 349,632 900 × $478.15 = 430,335 $ 1,072,071 Less variable costs 414,903 Contribution margin $ 657,168 Less direct fixed expenses (363,315) Less indirect fixed expenses (154,000) Income before taxes $ 139,853

Note: The answer can also be obtained by multiplying the profit per hour for each helicopter by the original hours and summing. (Any slight difference is due to rounding error.)

*Rounded

222277

7–33 Continued

2. The actual revenues earned (for the first six months) were as follows: 299 × $243.42 = $ 72,783 160 × $218.52 = 34,963 204 × $478.15 = 97,543 $205,289

Actual costs incurred: 500D 206B 206L-1 Total Direct costs—fixed* $46,623 $47,100 $87,935 $181,658 Direct costs—variable** 7,636 3,834 22,497 33,967 Overhead—variable*** 19,934 10,667 13,601 44,202 Indirect fixed costs* 77,000 Total $336,827

*Half of total annual costs **Per-unit variable costs × Actual flying hours

***Per-unit variable cost ($66.67) × Actual flying hours

Income statement:

Revenue $ 205,289 Variable costs 78,169 Contribution margin $ 127,120 Fixed costs 258,658 Loss $(131,538)

Profit that should have been earned (for the first six months):

500D 206B 206L-1 Profit per hour $ 31.75 $ 28.50 $ 62.37 50% of projected hours × 600 × 800 × 450 $ 19,050 $ 22,800 $ 28,067

Total profit: $69,917 ($19,050 + $22,800 + $28,067)

222288

7–33 Continued

3. Revenue: 450 × $243.42 = $109,539 600 × $218.52 = 131,112 800 × $478.15 = 382,520 $623,171

Costs: 500D 206B 206L-1 Total Direct costs—fixed $ 93,245 $ 94,200 $175,870 $363,315 Direct costs—variable 11,493 14,376 88,224 114,093 Overhead—fixed 50,107 64,810 39,080 153,997 Overhead—variable 30,002 40,002 53,336 123,340 Total $184,847 $213,388 $356,510 $754,745

Income statement:

Revenue $ 623,171 Variable costs 237,433 Contribution margin $ 385,738 Fixed costs 517,312 Loss $(131,574) 4. Variable maintenance: $246,667/3,700 = $66.67 per flying hour

Allocation ratios for fixed costs (based on revised hours):

500D 206B 206L-1 Maintenance 0.24324 0.32432 0.43243 Hangar rent 0.33333 0.33333 0.33333 Administrative 0.24324 0.32432 0.43243

Allocation of fixed costs:

500D 206B 206L-1 Maintenance—fixed $ 6,324 $ 8,432 $11,243 Hangar rent 6,000 6,000 6,000 Administrative 26,756 35,675 47,567 Total fixed costs $39,080 $50,107 $64,810

222299

7–33 Concluded

500D: $39,080/450 = $86.84* per hour 206B: $50,107/600 = $83.51* per hour 206L-1: $64,810/800 = $81.01* per hour

*Rounded

500D 206B 206L-1 Direct costs—fixed* $207.21 $157.00 $219.84 Direct costs—variable** 25.54 23.96 110.28 Overhead—fixed 86.84 83.51 81.01 Overhead—variable 66.67 66.67 66.67 Cost per unit $386.26 $331.14 $477.80

*Direct fixed costs/Revised flying hours **Direct variable costs/Original flying hours

Revenues needed = Total costs for revised hours + Original profit = [($386.26 × 450) + ($331.14 × 600) + ($477.80 × 800)] + $139,853 = $754,741 + $139,853 = $894,594

Let m = Markup

Revenues needed = (1 + m)(Total costs for revised hours) = (1 + m)($754,741) $894,594 = (1 + m)($754,741) 1 + m = $894,594/$754,741 1 + m = 1.185 m = 0.185

Thus, the revised prices are as follows: 500D: (1.185)($386.26) = $457.72* per hour 206B: (1.185)($331.14) = $392.40* per hour 206L-1: (1.185)($477.80) = $566.19* per hour

*Rounded

223300

RESEARCH ASSIGNMENTS

7–34

Answers will vary.

7–35

Answers will vary.