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 consumption of the services by each producing department. Stage two allocates the costs assigned to the producing departments (including service costs and direct costs) to the products passing through the producing departments. 2. Support-department costs are part of the cost of producing a product. Knowing the individual product costs is helpful for developing bids and cost-plus prices. 3. GAAP require that all manufacturing costs be assigned to products for inventory valuation. 4. Allocating support-department costs makes users pay attention to the level of service activity consumed and also provides an incentive for them to monitor the efficiency of the support departments. 5. Without any allocation of supportdepartment costs, users may view services as a free good and consume more of the service than is optimal. Allocating supportdepartment costs would encourage managers 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 department will exert effort to maintain a competitive 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 footage; c. Pounds of laundry; d. Orders processed; e. Maintenance hours worked; f. Number of employees; and g. Number of transactions processed.
189
9. Allocating actual costs passes on the efficiencies or inefficiencies of the support department, something which the manager of the producing department cannot control. Allocating 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 departments may use services. The sequential method allocates support-department costs sequentially. First, the costs of the center providing the greatest service to all user departments, including other support departments, are allocated. Next the costs of the second greatest provider of services are allocated to all user departments, excluding any department(s) that has already allocated costs. This continues until all supportdepartment costs have been allocated. The principal difference in the two methods is the fact that the sequential method considers some interactions among support departments and the direct method ignores interactions. 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 understand. If the results are similar, the simpler method should be used. 12. A joint cost is a cost incurred in the simultaneous 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 production. 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.
EXERCISES 7–1 a. b. c. d. e. f. g. h.
support support producing producing support support producing producing
i. j. k. l. m. n. o.
support support producing support producing support support
support support support support support producing producing support
i. j. k. l. m. n. o.
support producing producing support support support support
7–2 a. b. c. d. e. f. g. h.
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. i. j. k.
square feet square feet kilowatt-hours number of employees; direct labor cost l. square feet m. machine hours; number of repair jobs n. cubic feet
190
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:
3.
The Roost Magnolia House Oak Park Wisteria Lane Elm Street Total
Number of Units 130 70 120 50 30 400
The Roost Magnolia House Oak Park Wisteria Lane Elm Street Total
Number of Hours 35 10 45 15 25 130
×
×
Charge per Unit $20 20 20 20 20
Charge per Hour $80 80 80 80 80
=
=
Total Charges $ 2,600 1,400 2,400 1,000 600 $ 8,000 Total Charges $ 2,800 800 3,600 1,200 2,000 $ 10,400
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 legal 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.
191
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.
DM = Actual DLH × Charging Rate + New Car Sales 1,000 $30 $ 3,100 Used Car Sales 4,700 30 7,860 Service 19,400 30 86,300 Total 25,100 $97,260
Total Charges $ 33,100 148,860 668,300 $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) Actual cost Maintenance cost undercharged
$ 189,060 190,060 $ 1,000
192
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.
193
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. Direct costs Allocate: S1 (200,000) S2 Total
Support Departments S1 S2 $200,000 $ 140,000 — — $
0
120,000 (140,000) $ 0
Producing Departments Cutting Sewing $ 122,000 $ 90,500 80,000 105,000 $ 347,000
35,000 $ 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. Direct costs Allocate:S1 S2 Total
Support Departments S1 S2 $ 200,000 $ 140,000 (200,000) 40,000 — (180,000) 0 $ 0 $
194
Producing Departments Cutting Sewing $ 122,000 $ 90,500 96,000 64,000 135,000 45,000 $ 353,000 $ 199,500
7–10 1.
Allocation ratios: Proportion of Output Used by Department S2 Cutting Sewing S1 — 0.2000 0.4800 0.3200 0.0566 — 0.7075 0.2358
S1 S2 2.
S1 = S1 = S2 = S2 = S2 = S2 = 0.9887S2 = S2 =
Direct costs + Share of S2 costs $200,000 + 0.0566(S2) Direct costs + Share of S1 costs $140,000 + 0.200(S1) $140,000 + 0.200 [$200,000 + 0.0566(S2)] $140,000 + $40,000 + 0.0113(S2) $180,000 $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. Direct costs Allocated from: S1 S2 Total
Support Departments S1 S2 $200,000 $140,000
Producing Departments Cutting Sewing $122,000 $ 90,500
(210,304) 10,304 $ 0
100,946 128,805 $351,751
*Difference due to rounding.
195
42,061 (182,057) $ (4)*
67,297 42,929 $200,726
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 Direct labor Overhead: Baking Dept. (2 × $24) Total
$55 42 48 $145
Cost per loaf = $145/100 = $1.45 3.
Cost of Dearman wedding cake: Direct materials Direct labor Overhead: Baking Dept. (1 × $24) Decorating Dept. (8 × $7) Total cost
$ 20 50 24 56 $150
Price = 3 × $150 = $450
196
7–12 1.
Allocation ratios: Firing 0.80 0.25 0.29
Shaping 0.20 0.75 0.71
1
Kilowatt-hours Square feet2 Direct labor hours3 1
based on kilowatt hours: 20,000/(20,000+80,000); 80,000/(20,000+80,000) based on square feet: 24,000/(24,000+8,000); 8,000/(24,000+8,000) 3 based on direct labor hours: 10,000/(10,000+4,000); 4,000/(10,000+4,000) 2
Cost assignment: Power Gen. Factory HR $90,000 $$167,000 $84,000
Direct overhead costs Allocate: Power ($90,000) General Factory Human Resources Total after allocation $0 2.
(167,000) $0
Departmental overhead rates: Shaping: $274,890/10,000 = $27.49 per DLH* Firing: $368,110/4,000 = $92.03 per DLH* *Rounded
197
Shaping $72,000
Firing $230,000
18,000 - 125,250 84,000 59,640 $0 $274,890
72,000 41,750 24,360 $368,110
7–13 1.
Assume the support-department costs are allocated in order of highest to lowest cost: General Factory, Power, and Human Resources. Square feet Kilowatt-hours Labor hours
Power 0.05 — —
GF — — —
Direct costs $ 90,000 $167,000 1 General Factory : (0.05 × $167,000) 8,350 (8,350) (0.15 × $167,000) (25,050) (0.60 × $167,000) (100,200) (0.20 × $167,000) (33,400) Power2: (0.20 × $98,350) (19,670) (0.16 × $98,350) (15,736) (0.64 × $98,350) (62,944) Human Resources: (0.71 × $128,720) (0.29 × $128,720) Total $ 0 $ 0 1 based 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) 2 based 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)
HR 0.15 0.20 —
Shaping 0.60 0.16 0.71
Firing 0.20 0.64 0.29
$84,000
$ 72,000
$230,000
25,050 100,200 33,400 19,670 15,736 62,944 (91,391) 91,391 (37,329) $ 0 $279,327
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
198
37,329 $363,673
7-14 Andol Incol Ordol Exsol Total
Units 1,000 1,500 2,500 3,000 8,000
Percent × 0.1250 0.1875 0.3125 0.3750
Joint Cost $100,000 100,000 100,000 100,000
=
Allocated Joint Cost $12,500 18,750 31,250 37,500 $100,000
7-15 Andol Incol Ordol Exsol Total
Units 1,000 1,500 2,500 3,000 8,000
Price at Split-off $20.00 75.00 64.00 22.50
7-16 1. Ups Downs Total
Units 39,000 21,000
Price $2.00 2.18
Market Value at Split-off $ 20,000 112,500 160,000 67,500 $360,000
Joint Allocated Percent Cost Cost 0.0556 $100,000 $ 5,560 0.3125 100,000 31,250 0.4444 100,000 44,440 0.1875 100,000 18,750 $100,000
Eventual Separable Market Value Costs $78,000 $18,000 45,780 5,780
Joint cost × Percent of hypothetical market value Allocated joint cost
Hypothetical Market Value $60,000 40,000 $100,000
Ups $42,000 × 0.60 $25,200
2. Value of ups at split-off (39,000 × $1.80)
$70,200
Value of ups when processed further Less: Further processing cost Incremental value of further processing
$78,000 18,000 $60,000
Percent 0.60 0.40
Downs $42,000 × 0.40 $16,800
Ups should NOT be processed further as there will $10,200 more profit if sold at splitoff.
199
7–17 1.
1
HR Power2
HR — 0.0769
Power 0.3000 —
Mixing 0.3500 0.2308
Packaging 0.3500 0.6923
1
based 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) 2 based 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 = HR = HR = HR =
$110,000 + 0.0769P $110,000 + 0.0769($187,327) $110,000 + $14,405 $124,405
Human Resources Power Direct overhead costs $110,000 $150,000 Allocated from: HR (124,405) 37,321 Power 14,409 (187,327) Total $ 0 $ (5)* *Difference due to rounding.
2.
Mixing: $186,777/20,000 = $9.34 per DLH Packaging: $453,228/30,000 = $15.11 per DLH
200
Mixing $100,000
Packaging $280,000
43,542 43,235 $186,777
43,542 129,686 $453,228
7–18 1. Direct overhead Allocate HR1 Allocate Power Total 1
2.
Support Departments HR Power $110,000 $150,000 (110,000) - (150,000) $ 0 $ 0
Producing Departments Mixing Packaging $100,000 $280,000 55,000 55,000 37,500 112,500 $192,500 $447,500
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
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 Resources and Power do not receive any other support department costs. How important 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 complicated reciprocal method.
201
7–19 1. Direct overhead Allocate HR1 Allocate Power2 Total 1
2.
Support Departments HR Power $110,000 $150,000 (110,000) 33,000 - (183,000) $ 0 $ 0
Producing Departments Mixing Packaging $100,000 $280,000 38,500 38,500 45,750 137,250 $184,250 $455,750
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
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 recognized under the direct method.
202
7–20 A = $35,000 + 0.3B B = $40,000 + 0.2A A= A= 0.94A = A=
$35,000 + 0.3($40,000 + 0.2A) $47,000 + 0.06A $47,000 $50,000
B = $40,000 + 0.2($50,000) B = $50,000 Allocation ratios (ratios for D obtained by “plugging”): Dept. A Dept. B *(1.0 – 0.2 – 0.2) **(1.0 – 0.3 – 0.4)
Dept. A — 0.3
Dept. B 0.2 —
Allocate A: (0.2 × $50,000) (0.6 × $50,000) Allocate B: (0.4 × $50,000) (0.3 × $50,000)
Dept. C 0.2 0.4
Dept. D 0.6* 0.3**
Dept. C
Dept. D
$10,000 $30,000 20,000 15,000
203
7–21 1.
General Factory $ 230,000
HR Grinding Assembly Direct costs $ 70,000 $ 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 Grinding (1 × $33.85) Assembly (12 × $3.35) Unit product cost
$123.00 33.85 40.20 $197.05
7–22 1.
General Factory $ 230,000
HR $ 70,000
Direct costs Allocate: Gen. Factory1 76,667 (230,000) HR 2 (146,667) — $ 0 Total OH $ 0 1 HR = 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% 2 Grinding = 20,000/(20,000+80,000)=20% Assembly = 80,000/(20,000+80,000)=80%
Grinding $ 63,900
Assembly $ 39,500
38,333 29,333 $131,566
115,000 117,334 $271,834
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) Assembly (12 × $3.40) Unit product cost
32.89 40.80 $196.69
7–23 204
1.
HR 0.3333 GF-square feet1 HR-direct labor hrs2 —
GF — 0.0991
Grinding 0.1667 0.1802
Assembly 0.5000 0.7207
1
HR: 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 2 Allocation 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
Direct costs Allocate: HR GF Total OH
HR $ 70,000
General Factory $ 230,000
Grinding $ 63,900
Assembly $ 39,500
(151,666) 81,666 $ 0
15,030 (245,023) $ 7*
27,330 40,845 $132,075
109,306 122,512 $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 Grinding (1 × $33.02) Assembly (12 × $3.39) Unit product cost
$123.00 33.02 40.68 $196.70
205
7–24 1. Alpha Beta Gamma Total
Units 12,500 17,500 20,000 50,000
Percent × 0.25 0.35 0.40
Joint Cost $125,000 125,000 125,000
=
Allocated Joint Cost $31,250 43,750 50,000 $125,000
2. Alpha Beta Gamma Total
Units 12,500 17,500 20,000 50,000
Price at Split-off $20 50 18
Market Value at Split-off $ 250,000 875,000 360,000 $1,485,000
206
Joint Percent Cost 0.1684 $125,000 0.5892 125,000 0.2424 125,000
Allocated Cost $ 21,050 73,650 30,300 $125,000
PROBLEMS 7–25 1.
Direct method: Direct costs Allocate: Delivery1 Accounting2 Total
Delivery $240,000 (240,000) -$ 0
Accounting Laboratory $270,000 $345,000 -(270,000) $ 0
144,000 175,500 $664,500
Tissue Pathology $456,000 96,000 94,500 $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
Direct costs Allocate: Accounting1 Delivery2 Total
Delivery $ 240,000
Accounting $ 270,000
Laboratory $345,000
Tissue Pathology $456,000
13,500 (253,500) $ 0
(270,000) 0 $ 0
166,725 152,100 $663,825
89,775 101,400 $647,175
1
Delivery: 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
2
Laboratory: 70,200/(70,200+46,800) = 0.60 Tissue Pathology: 46,800/(70,200+46,800) = 0.40
207
7–26 1.
a. Direct method Maintenance $320,000
Power $400,000
Direct costs Allocate: Maintenance1 (320,000) 0 2 Power 0 (400,000) Total $ 0 $ 0 1 Drilling: 30,000/(30,000+7.500) = 0.80 Assembly: 7,500/(30,000+7,500) = 0.20 2 Drilling: 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 Drilling (2 × $15.30) Assembly (50 × $12.85) Total cost Markup (15%) Bid price
$1,817.00 30.60 642.50 $2,490.10 373.52 $2,863.62
208
Drilling $163,000
Assembly $ 90,000
256,000 40,000 $459,000
64,000 360,000 $514,000
7–26
Continued
b. Reciprocal method Maintenance — 0.100
1
Machine hours Kilowatt-hours2
Power 0.375 —
Drilling 0.500 0.090
Assembly 0.125 0.810
1
Power: 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 2 Maintenance: 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= P= M= M= 0.9625M = M= P= P= P= P=
$320,000 + 0.1P $400,000 + 0.375M $320,000 + 0.1($400,000 + 0.375M) $320,000 + $40,000 + 0.0375M $360,000 $374,026 $400,000 + 0.375M $400,000 + 0.375($374,026) $400,000 + $140,260 $540,260
Direct cost Allocate: Maintenance Power Total
Maintenance $320,000
Power $400,000
Drilling $163,000
Assembly $90,000
($374,026) 54,026 $ 0
140,260 (540,260) $ 0
187,013 48,623 $398,636
46,753 437,611 $574,364
Drilling: $398,636/30,000 = $13.29 per MHr (rounded) Assembly: $574,364/40,000 = $14.36 per DLH (rounded) Prime costs Drilling (2 × $13.29) Assembly (50 × $14.36) Total cost Markup (15%) Bid price
$1,817.00 26.58 718.00 $2,561.58 384.24 $2,945.82
2. The reciprocal method is more accurate, as it takes into account the use of support departments by other support departments.
209
7–27 1.
a. Sequential method: Allocate Maintenance first, then Power Direct costs Allocate: Maintenance1 Power2 Total
Maintenance $ 320,000
Power $ 400,000
Drilling $163,000
Assembly $ 90,000
(320,000) 0 $ 0
120,000 (520,000) $ 0
160,000 52,000 $375,000
40,000 468,000 $598,000
1
Power: 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 2 Drilling: 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 Drilling (2 × $12.50) Assembly (50 × $14.95) Total cost Markup (15%) Bid price
$1,817.00 25.00 747.50 $2,589.50 388.43 $2,977.93
210
7–27
Concluded
b. Sequential method: Allocate Power first, then Maintenance Direct costs Allocate: Power1 Maintenance2 Total
Maintenance $ 320,000 40,000 (360,000) $ 0
Power $ 400,000
Drilling $163,000
Assembly $ 90,000
(400,000) 0 $ 0
36,000 288,000 $487,000
324,000 72,000 $486,000
1
Maintenance: 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 2 Drilling: 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 Drilling (2 × $16.23) Assembly (50 × $12.15) Total cost Markup (15%) Bid price 2.
$1,817.00 32.46 607.50 $2,456.96 368.54 $2,825.50
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 Maintenance ($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.)
211
7–28 1. Two Oil Six Oil Distillates Total
Units 300,000 240,000 120,000 660,000
Percent 0.4545 0.3636 0.1818
×
Joint Cost $10,000,000 10,000,000 10,000,000
=
Allocated Joint Cost $4,545,000 3,636,000 1,818,000 $9,999,000
2. Units
Price at Split-off
Market Value at Split-off
300,000
$20
$6,000,000
Six Oil 240,000 Distillates 120,000 Total 660,000
30 15
7,200,000 1,800,000 $15,000,000
Two Oil
212
Percent
Joint Cost
Allocated Cost
0.4000 $10,000,000 $4,000,000 0.4800 10,000,000 0.1200 10,000,000
4,800,000 1,200,000 $10,000,000
7–29 1.
Fixed cost allocation (direct method): Cost driver Employees1 Items processed2 Square feet3 Machine hours4
Mixing 0.400 0.329 0.444 0.200
1
Allocation Ratios Cooking Packaging 0.200 0.400 0.318 0.353 0.333 0.222 0.500 0.300
Mixing = 20/(20+10+20) = 0.40 Cooking = 10/(20+10+20) = 0.20 Packaging = 20/(20+10+20) = 0.40 2 Mixing = 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 3 Mixing = 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 4 Mixing = 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
213
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 Cafeteria: (0.4 × $20,000) (0.2 × $20,000) (0.4 × $20,000) Personnel: (0.4 × $70,000) (0.2 × $70,000) (0.4 × $70,000) Custodial Services: (0.444 × $80,000) (0.333 × $80,000) (0.222 × $80,000) Maintenance: (0.2 × $100,000) (0.5 × $100,000) (0.3 × $100,000) Cost Accounting: (0.329 × $130,000) (0.318 × $130,000) (0.353 × $130,000) Direct costs Total
$
Cooking
Packaging
8,000 $
4,000 $
8,000
28,000 14,000 28,000 35,520 26,640 17,760 20,000 50,000 30,000 42,770 41,340 120,000 $254,290
214
60,000 $195,980
45,890 25,000 $154,650
7–29
Continued
Variable cost allocation (direct method): Cafeteria: Personnel: Maintenance: Cost Accounting:
$40,000/50 = $800/employee $20,000/50 = $400/employee $100,000/20,000 = $5/machine hour $16,500/8,500 = $1.94*/item processed Mixing
Cafeteria: ($800 × 20) ($800 × 10) ($800 × 20) Personnel: ($400 × 20) ($400 × 10) ($400 × 20) Maintenance: ($5 × 4,000) ($5 × 10,000) ($5 × 6,000) Cost Accounting: ($1.94 × 2,800) ($1.94 × 2,700) ($1.94 × 3,000) Direct costs Total
Cooking
Packaging
$16,000 $ 8,000 $16,000 8,000 4,000 8,000 20,000 50,000 30,000 5,432 5,238 20,000 $69,432
*Rounded
215
10,000 $77,238
5,820 40,000 $99,820
7–29 2.
Continued
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): Maint. Custod. Pers. Cafe. Mix. Cost Driver* Items 0.200 0.016 0.080 0.024 0.224 Machine hours 0.200 Square feet — — 0.069 0.049 0.392 Employees (1) — — — 0.091 0.364 Employees (2) — — — — 0.400
Cook. 0.216 0.500 0.294 0.182 0.200
Pack. 0.240 0.300 0.196 0.364 0.400
*Note: Items are used to allocate accounting costs; machine hours to allocate maintenance; square feet to allocate custodial services; and employees to allocate both personnel costs and cafeteria costs.
216
7–29
Continued
Allocation of fixed costs (expressed in thousands of dollars): Pers. Cafe. Mixing Cooking Packaging Main. Cust. 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.
217
7–29
Continued
Allocation ratios for variable costs: Cost Personnel Accounting Cost Driver Machine hours Employees (1) 0.137 0.178 Employees (2) 0.206 Items
Mixing 0.200 0.274 0.317 0.329
Cooking 0.500 0.137 0.159 0.318
Packaging 0.300 0.274 0.317 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.
218
7–29
Continued
Allocation of variable costs: Direct costs Maintenance: (0.200 × $100,000) (0.500 × $100,000) (0.300 × $100,000) Cafeteria: (0.137 × $40,000) (0.178 × $40,000) (0.274 × $40,000) (0.137 × $40,000) (0.274 × $40,000) Personnel: (0.206 × $25,480) (0.317 × $25,480) (0.159 × $25,480) (0.317 × $25,480) Accounting: (0.329 × $28,869) (0.318 × $28,869) (0.353 × $28,869) Total
Cafe. $40,000
Pers. Cost Acc. Mixing Cook. Pack. $20,000 $16,500 $20,000 $10,000 $40,000 20,000 50,000 30,000 5,480 7,120 10,960 5,480 10,960 5,249 8,077 4,051 8,077 9,498 9,180 10,191 $68,535 $78,711 $99,228
Note: Total of post-allocation variable costs does not equal pre-allocation total due to rounding error.
219
7–29 4.
Concluded
Overhead rates: Fixed rates: Mixing: Cooking: Packaging:
$251,812/30,000 = $8.39 per DLH* $197,871/10,000 = $19.79 per MHr* $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 Overhead* Total costs Markup (30%) Price
$ 60,000 77,220 $137,220 41,166 $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 significant, 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.
220
7–30 1.
Baton Rouge ($781,000/$4,641,000)($146,500)* Kilgore ($750,000/$4,641,000)($146,500) Longview ($912,000/$4,641,000)($146,500) Paris ($1,098,000/$4,641,000)($146,500) Shreveport ($1,100,000/$4,641,000)($146,500)
= $24,653 = $23,675 = $28,789 = $34,660 = $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 Baton Rouge Kilgore Longview Paris Shreveport
3.
Variable Cost ($18)(1,475) ($18)(1,188) ($18)(500) ($18)(525) ($18)(562)
= $26,550 = $21,384 = $9,000 = $9,450 = $10,116
+ + + + + +
Fixed Cost $10,500 $11,200 $14,000 $17,500 $16,800
= = = = = =
Total $37,050 $32,584 $23,000 $26,950 $26,916
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 efficiently. 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.
221
7–31 1. Direct overhead Maintenance: (1/8)($500,000) (7/8)($500,000) Power: (1/6)($225,000) (5/6)($225,000) Setups: (40/200)($150,000) (160/200)($150,000) General Factory: (0.272)($625,000) (0.728)($625,000) Total
Department A $200,000
Department B $ 800,000
62,500 437,500 37,500 187,500 30,000 120,000 170,000 $500,000
455,000 $ 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)
222
7–31 2.
Continued
Allocation order: General Factory, Maintenance, Power, Setups, A, and B Allocation Ratios Maint. Power Setups Dept. A Dept. B G.F. — 0.125 0.200 0.025 0.177 0.473 — — 0.150 0.050 0.100 0.700 — — — — 0.167 0.833 — — — — 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 Alloc. from: G.F. Maint. Power Setups
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 Prime cost Overhead: ($2.40 × 5,000) ($16.83 × 500) ($2.40 × 400) ($16.83 × 3,000) $140,415 Markup (50%) Total bid revenue Units Bid price
Job SS $120,000
Job TT $ 50,000
12,000 8,415 960 50,490 $101,450 70,208 $210,623 ÷ 14,400 $ 14.63
50,725 $152,175 ÷ 1,500 $ 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 producing 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.
223
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 allocations, however, are based on causal factors and reflect the consumption of resources. 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 order using the most accurate cost information available. Thus, the current allocation 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 sufficient to dissuade. According to the IMA Statement of Ethical Professional Practice, accountants should “refrain from engaging in any conduct that would prejudice 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 communicate 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 submit 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 appropriate.”
224
7–33 1.
Variable maintenance: $246,667/3,700 = $66.67*/flying hour Allocation Ratios for Fixed Costs 206B 206L-1 500D 0.32432 0.43243 0.24324 0.33333 0.33333 0.33333 0.32432 0.43243 0.24324
Maintenance Hangar rent Administrative Alloc. of fixed costs: Maintenance—fixed: (0.32432 × $26,000) (0.43243 × $26,000) (0.24324 × $26,000) Hangar rent: (0.33333 × $18,000) (0.33333 × $18,000) (0.33333 × $18,000) Administrative: (0.32432 × $110,000) (0.43243 × $110,000) (0.24324 × $110,000) Total fixed costs
500D
206B
206L-1
$ 8,432 $11,243 $ 6,324 6,000 6,000 6,000 35,675 47,567 $50,107
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
225
$64,810
26,756 $39,080
7–33
Continued 500D $ 77.70* 25.54* 41.76 66.67 $211.67 31.75 $243.42 211.67 $ 31.75
Direct costs—fixed* Direct costs—variable** Overhead—fixed Overhead—variable Cost per unit Markup* (15%) Bid price Less cost Profit/hour
206B $ 58.88* 23.96* 40.51 66.67 $190.02 28.50 $218.52 190.02 $ 28.50
206L-1 $195.41* 110.28* 43.42 66.67 $415.78 62.37 $478.15 415.78 $ 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 Less variable costs Contribution margin Less direct fixed expenses Less indirect fixed expenses Income before taxes
$ 1,072,071 414,903 $ 657,168 (363,315) (154,000) $ 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
226
7–33 2.
Continued
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: Direct costs—fixed* Direct costs—variable** Overhead—variable*** Indirect fixed costs* Total
500D $46,623 7,636 19,934
206B $47,100 3,834 10,667
206L-1 $87,935 22,497 13,601
*Half of total annual costs **Per-unit variable costs × Actual flying hours ***Per-unit variable cost ($66.67) × Actual flying hours Income statement: Revenue Variable costs Contribution margin Fixed costs Loss
$ 205,289 78,169 $ 127,120 258,658 $(131,538)
Profit that should have been earned (for the first six months): Profit per hour 50% of projected hours
500D $ 31.75 × 600 $ 19,050
206B $ 28.50 × 800 $ 22,800
Total profit: $69,917 ($19,050 + $22,800 + $28,067)
227
206L-1 $ 62.37 × 450 $ 28,067
Total $181,658 33,967 44,202 77,000 $336,827
7–33 3.
Continued
Revenue: 450 × $243.42 = 600 × $218.52 = 800 × $478.15 =
$109,539 131,112 382,520 $623,171
Costs: 500D $ 93,245 11,493 50,107 30,002 $184,847
Direct costs—fixed Direct costs—variable Overhead—fixed Overhead—variable Total
206B $ 94,200 14,376 64,810 40,002 $213,388
206L-1 $175,870 88,224 39,080 53,336 $356,510
Total $363,315 114,093 153,997 123,340 $754,745
Income statement: Revenue Variable costs Contribution margin Fixed costs Loss 4.
$ 623,171 237,433 $ 385,738 517,312 $(131,574)
Variable maintenance: $246,667/3,700 = $66.67 per flying hour Allocation ratios for fixed costs (based on revised hours): Maintenance Hangar rent Administrative
500D 0.24324 0.33333 0.24324
206B 0.32432 0.33333 0.32432
206L-1 0.43243 0.33333 0.43243
500D $ 6,324 6,000 26,756 $39,080
206B $ 8,432 6,000 35,675 $50,107
206L-1 $11,243 6,000 47,567 $64,810
Allocation of fixed costs: Maintenance—fixed Hangar rent Administrative Total fixed costs
228
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 Direct costs—fixed* Direct costs—variable** Overhead—fixed Overhead—variable Cost per unit
500D $207.21 25.54 86.84 66.67 $386.26
206B $157.00 23.96 83.51 66.67 $331.14
206L-1 $219.84 110.28 81.01 66.67 $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
229
RESEARCH ASSIGNMENTS 7–34 Answers will vary.
7–35 Answers will vary.
230
