| | | First Proposal | First Proposal | Revised Proposal | Revised Proposal | | — Sandy Bond recent business school graduate who had recently been employed Huron

Sandy Bond, a recent business school graduate who had recently been employed by Huron Automotive Company, was asked by Huron's president to review the company's present cost accounting procedures. In outlining this project to Bond, the president had expressed three concerns about the present system: (1) its adequacy for purposes of cost control, (2) its accuracy in arriving at the true cost of products, and (3) its usefulness in providing data to judge supervisors' performance.

Questions

1. Using the data in the exhibits, determine the cost of a 100-unit batch of model CS-29, a month's spare parts, and a month's work done for other divisions under the present method, Bond's first proposal, and Bond's revised proposal.

2. Are the cost differences among the methods significant? What causes these differences?

3. Suppose that Huron purchased a new machine costing $400,000 for the custom work department. Its expected useful life is five years. This machine would reduce machining time and result in higher quality custom carburetors. As a result, the department's direct labor-hours would be reduced by 30 percent, and this extra labor would be transferred to departments outside the carburetor division. About 10 percent of the custom work department's overhead is variable with respect to direct labor-hours. Using July's data:

a. Calculate the plantwide hourly rate (present method) if the new machine were acquired. Then calculate indicated costs for the custom work department in July, using both this new plantwide rate and the former $55.96 rate.

b. Calculate the hourly rate for the custom work department only (first proposed method), assuming the machine was acquired and the first proposed costing procedure was adopted. Then calculate indicated costs for the custom work department in July, using both this new rate and the former $55.96 rate.

c. Under the present costing procedures, what is the impact on the indicated costs of custom products if the new machine is acquired? What is this impact if the first proposed costing procedure is used? What inference do you then draw concerning the usefulness of the present and proposed methods?

4. Assume that producing a batch of 100 model CS-29 injectors requires 126 hours, distributed by department as shown in Exhibit 3, and $4,200 worth of materials. Huron sells these carburetors for $113 each. Should the CS-29 price be increased? Should the CS-29 be dropped from the product line? (Answer using both the present and the first proposed costing methods.)

5. Assume that Huron also offers a model CS-30 that is identical to a CS-29 in all important aspects, including price, but is preferred for some applications because of certain design features. Because of the CS-30's relatively low sales volume, Huron buys certain major components for the CS-30 rather than making them in-house. The total cost of materials and purchased parts for 100 units of model CS-30 is $8,000; the labor required per 100 units is 12, 7, 17, and 35 hours, respectively, in the casting/stamping, grinding, machining, and assembly departments. If a customer ordered 100 units and said that either model CS-29 or CS-30 would be acceptable, which model should Huron ship? Why? (Answer using only the first proposed costing method and the assumptions regarding CS-29 from question 4.)

6. What benefits, if any. do you see to Huron if either proposed costing method is adopted? Consider this question from the standpoint of (a) product pricing, (b) cost control, (c) inventory valuation, (d) charges to outside departments, (e) judging departmental performance, and (f) diagnostic uses of cost data. What do you conclude Huron should do regarding its costing procedures?

SOLUTION

Questions 1 and 2

Costing of a 100-unit batch of CS-29 carburetors:
			First Proposal	First Proposal	Revised Proposal	Revised Proposal
Department	Hours	(%)	Rate	Total	Rate	Total	Total
Casting/Stamping	21	(17)	$52.97	$1,112.37	$53.12	$1,115.52	$1,115.52
Grinding	12	(10)	48.14	577.68	46.75	561.00	561.00
Machining	58	(46)	87.52	5,076.16	86.50	5,017.00	5,017.00
Assembly	35	(28)	40.19	1,406.65	39.14	1,369.90	1,369.90
Total, proposed method	126	= 101% due to rounding		8,172.86		8,063.42	8,063.42
Total, present method	126		55.96	7,050.96	55.96	7,050.96	7,050.96
Difference				$1,121.90	(16% more)	$1,012.46	$1,012.46	(14% more)

Indicated cost is higher under the proposed methods primarily because a CS-29 carburetor spends a higher-than-average proportion of time in the highest machining department and a less-than-average proportion in the low-cost assembly department. (Based on Exhibit 1, the “average” product spends 8%, 7%, 24%, 12%, and 49% of its time respectively in the five departments.

Costing of spare parts for inventory:
			First Proposal	First Proposal	Revised Proposal	Revised Proposal
Department	Hours	(%)	Rate	Total	Rate	Total
Casting/Stamping	304	(18)	$52.97	$16,102.88	$53.12	$16,148.48
Grinding	270	(16)	48.14	12,997.80	46.75	12,622.50
Machining	1,115	(66)	87.52	97,584.80	86.50	96,447.50
Total, proposed method	1,689			126,685.48		125,218.48
Total, present method	1,689		55.96	94,516.44	55.96	94,516.44
Difference				$32,169.04	(34% more)	$30,702.04	(32% more)

Indicated cost is higher under the proposed methods primarily because spares do not pass through the low-cost assembly department, and because they spend a higher-than-average proportion of time in the machining department.

Costing of work done for other divisions:
			First Proposal	First Proposal	Revised Proposal	Revised Proposal
Department	Hours	(%)	Rate	Total	Rate	Total
Casting/Stamping	674	(20)	$52.97	$ 35,701.78	$53.12	$ 35,802.88
Grinding	540	(16)	48.14	25,995.60	46.75	25,245.00
Machining	2,158	(64)	87.52	188,868.16	86.50	186,667.00
Total, proposed method	3,372			250,565.54		247,714.88
Total, present method	3,372		55.96	188,697.12	55.96	188,697.12
Difference				$ 61,868.42	(33% more)	$ 59,017.76	(31% more)

The difference in indicated cost arises for the same reasons as given above for spare parts.

The differences between the costs that result from the two proposed methods are not so great as the differences between the present method and either proposal. This is because the actual average overhead cost per hour in each department in July (Exhibit 2) did not differ greatly from the predetermined rates in Exhibit 4. The greatest difference in departmental actual versus predetermined rates is in assembly (5% higher actual than predetermined), which doesn’t enter into the calculations for spares or work for other divisions.

The machining department costs dominate all three calculations, and there is only 1.7% ($62.52 versus $61.50) difference in the overhead rates. Of course, whether the same would be true for months other than July depends on the variations in monthly volumes from the normal volume in those other months.

All three of these examples cited show that the present method gives lower costs than those under the proposed methods. However, it should be noted that some products are being overvalued by the present system. It is reasonable to assume that there are some products that require a relatively large amount of assembling time. Such products would, under the present system, be costed at more than their costs under the proposed systems.

Question 3

a. Plant as a single cost center:

Labor cost in custom work reduced by 30 percent	$ 81,664	* 30% = $24,499
Reduced labor cost for the plant:	$ 658,448	- 24,499 = $633,949
Overhead is:
Increased by new depreciation: $400,000/60 months =	$ 6,667
Decreased by variable costs with reduced labor:
10% $40.48 3,712 hours *30% =	4,508
Net increase in overhead	$2,159
Total overhead becomes $1,099,323 + $2,159 =	$1,101,482
Total labor cost	633,949
Total cost becomes	$1,735,431
Total hours become 31,412 - (3,712*30%) = 30,298 hours
Plant-wide rate per hour is $1,735,431/30,298 hours = $57.28
Custom work costs if entire plant is treated as a single cost center:
Prior to new machine: 3,712 hrs. @ $55.96 =	$207,724
After new machine: 2,598 hrs. @ $57.28 =	148,813
Net decrease of 28%, or in total dollars =	$ 58,911
b.	Treating each department as a cost center:

Present overhead is $40.48 *3,712 hours =	$150,262
Add: Additional overhead (net)	2,159
New total custom work overhead	$152,421
New total hours: 3,712 *70% = 2,598 hrs.
New hourly overhead rate: $152,421/2,598 =	$ 58.67
Labor hourly rate	22.00
New custom work hourly rate	$ 80.67
Custom work costs using five cost center approach:
Prior to new machine: 3,712 hrs. @ $62.48 =	$231,926
After new machine: 2,598 hrs. @ $80.67 =	209,581
Net decrease of 9.6%, or in total dollars =	$ 22,345
c.	The calculations are shown above. If there is only one cost center, the purchase of a new machine results in a substantial decrease in the cost of custom carburetors and fuel injectors; whereas if there are five cost centers, the purchase of the machine results in significantly less change in the cost of items going through the custom work department. This is an interesting phenomenon. The proposed system reflects more accurately what has actually happened to costs. Furthermore, under the single cost center, an event in one department (such as the purchase of the machine in custom work) can have repercussions on the costs of other departments, and indeed can even affect the cost of products that do not pass through custom world

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Question 4

On a full-cost basis, we have the following indicated margins for a batch of 100 model CS-29 carburetors:

	Present Method	Proposed Method
Revenues (100 units @ $113)	$11,300	$11,300
Less: Materials	4,200	4,200
Labor and overhead	7,051*	8,173*
Gross margin	$ 49	$ (1,073)
*From Question 1 calculations.

This suggests that with the more accurate costing under the proposed method, carburetor CS-29 is a “loss leader”. Students will suggest increasing the price and/or cutting costs. I then ask them to assume neither is feasible: then many will want to drop the product. However, consider the differential income, assuming all overhead is fixed (and nondifferential with respect to CS-29):

Revenues	Revenues	$11,300	$11,300	$11,300
Less: Materials	Less: Materials	4,200	4,200	4,200
Labor	Labor	2,641*	2,785+
Differential income	Differential income	$ 4,459	$ 4,315	$ 4,315
*1.26 hrs. @ $20.96 +21 hrs. @ $21.60 + 12 hrs. @ $18.00 + 58 hrs. @ $25.00 + 35 hours @ $19.00 = $2,785

Both methods reveal that, if Huron has excess capacity, in the short run (at least), CS-29 should not be dropped, unless so doing would save about $5,400 in overhead costs that were assumed to be nondifferential in the above calculation (proposed method). The “moral” of this question is: neither the present nor the refined full cost data were helpful in making this decision, although the refined data did signal that CS-29 is, in a long-run sense, a “sick” product.

Question 5

Again, a differential analysis is called for. The relevant numbers for both a full-cost analysis and a differential analysis are as follows:

Full-cost analysis:	Full-cost analysis:	CS-29	CS-30	CS-30
Revenues	Revenues	$11,300	$11,300	$11,300
Less Materials	Less Materials	4,200	8,000	8,000
Labor and overhead	Labor and overhead	8,173*	3,867+
Gross margin	Gross margin	$ (1,073)	$ (567)
*From Question 1 calculations +12 hrs. @ $52.97 + 7 hrs. @ 48.14 + 17 hrs. @ $87.52 + 35 hrs. @ $40.19 = $3,867
Differential cost analysis (assuming all overhead costs are fixed):	Differential cost analysis (assuming all overhead costs are fixed):	CS-29	CS-30
Revenues	Revenues	$11,300	$11,300
Less: Materials	Less: Materials	4,200	8,000
Labor	Labor	2,785*	1,475*
Differential income	Differential income	$ 4,315	$ 1,825
*21 hrs. @ $21.60 + 12 hrs. @ $18.00 + 58 hrs. @ $25.00 + 35 hrs. @ $19.00 = $2,785 (see Question 4.)
**12 @ $21.60 + 7 @ $18.00 + 17 @ $25.00 + 35 @ $19.00 = $1,475

This analysis shows that, if all factory overhead is nondifferential with respect to whether CS-29 or CS-30 carburetors are produced, CS-29 is the more attractive product.

The full-cost analysis would be valid if all overhead costs assigned to the CS-29 and CS-30 carburetors were in fact differential; i.e., Huron would prefer to fill the order with the CS-30 if differential CS-29 overhead costs were $5,388 ($8,173 - $2,785) and differential CS-30 overhead costs were $2,392 ($3,867 - $1,475). But if we assume all overhead is unaffected by this decision, CS-29 is preferred. Thus, there must be some percentage rate of overhead-variability that would make Huron indifferent as to which carburetor is shipped. Let X equal this percentage. (For the following calculation to be feasible, we must assume X is the same for both carburetors, which is an admittedly questionable assumption; but I feel the worth of illustrating a sensitivity analysis at this point in the course warrants it.)

For CS-29 income ≥ CS-30 income

4,315-X (5,388) ≥ 1,825 - X (2,392)

2,996X ≤ 2,490

C ≤ .83

Thus, if less than 83 percent of the overhead assigned to each product is variable, then shipping CS-29 is more attractive than shipping CS-30. Again note that neither the present nor the proposed costing method was particularly helpful in making this kind of decision. In fact, the indiscriminate use of cost data can lead to the wrong decision in both of the question 4 and 5 decisions.

Question 6

In my opinion, the following comments concerning benefits from the proposed five-cost-center approach are valid. They are based on an overall conclusion that this approach will provide more accurate costs, product by product, than the present method.

a. Pricing. Since Huron appears be a price follower, I see no benefits here from the proposed method. A possible exception might be the pricing of spares.

b. Cost control. Again, I see no benefits from the proposal in this regard. If Huron wants better cost control, it should develop flexible budgets for labor and overhead on a department-by-department (responsibility center) basis.

c. Inventory valuation. I see no benefits here from the proposal’s more accurate costing. If adopted for tax purposes, it appears that the proposed approach would cause a one-shot tax increase (because since more production costs are capitalized in inventoriable spares, less will be charged to cost of the goods sold which are not inventoried).

d. Charges to other divisions. In the long run, it is probably beneficial that these transfer prices be made more accurate. For example, there is no reason for the machining department to maintain capacity for an outside division and then “sell” this capacity at below the “true” full costs. More accurate costs here might suggest in the long run that some other division’s machining capacity should be expanded.

e. Judging departmental performance. (Same comments as for cost control.)

f. Diagnostic uses. It is here that I think the proposal has most merit; for example, if carburetor CS-29 is revealed to be a “loss leader” by more accurate costing, I think this is something of which management should be aware.

Overall, I conclude that the proposal should be adopted in this case, but only because the costs of implementing it appear to be minimal. If the proposal were costly, the chief benefit, diagnostic information, could be gained by an annual ad hoc five-cost-center product costing, without changing the routine costing system. Whatever your assumptions about implementation costs, I feel they all should recognize that the proposal should not be adopted solely on the justification of improved accuracy; the improved accuracy is worthless if it doesn’t lead to better decision making (as reflected in higher income).

Incidentally, whether the one- or five-cost center approach is used, at least the overhead portion of the hourly costing rate should be a predetermined rate based on estimates of annual volume and overhead costs; otherwise, month-to-month volume variations will result in erratic product costs, because of spreading the monthly fixed overhead over varying volumes. Thus, the revised proposal is superior to the first proposal.