Chapter 4, Problem 1AE

To determine

Traditional costing In this costing system, a predetermined overhead rate is calculated by using direct labor hours or machine hours and overhead costs (indirect costs) are allocated to all the products by using this rate.

Activity-based costing In this costing system, certain activities are identified (which give rise to indirect costs), costs are first allocated to these activities and then to products.

Unit product cost under traditional costing method and activity-based costing method after making certain changes, to determine change in predetermined overhead rate and to state, which model allocates overhead cost more accurately.

Answer to Problem 1AE

After making certain changes, unit product cost for both the products under traditional costing system is:

Deluxe	$74
Tourists	$115

After making certain changes, unit product cost for both the products under activity-based costing system is:

Deluxe	$143.87
Tourists	$101.02

Predetermined overhead rates are:

For 5 hours	$11 per hour
For 2 hours	$12.5 per hour

Activity-based costing system allocates overhead costs more accurately as compared to traditional costing system.

Explanation of Solution

Calculation of per unit cost under traditional costing:

After changing per unit direct labor hours from 5 hours to 2 hours, per unit cost for the deluxe model will be calculated as follows:

Particulars	Deluxe (in $)
Direct material (per unit)	25
Direct labor (per unit)	24 (2×$12)
Overhead cost per unit	25 (2×$12.5)
Unit product cost	74

And here, predetermined overhead rate is calculated as follows:

  $\begin{array}{l}\text{Predetermined overhead rate = }\frac{\text{Total overhead cost }}{\text{Total Dircet labor hours }}\\ \text{ = }\frac{\$550,000}{(2,000\times 2)+(10,000\times 4)}\\ \text{ = }\frac{\$550,000}{44,000}\\ \text{ = \$12}\text{.5 per hour }\end{array}$

Yes, Unit product cost for deluxe model is $74 after making the said changes.

Calculation of per unit cost under activity-based costing:

Per unit cost will be calculated after adding per unit direct material cost, direct labor cost and per unit overhead cost. To calculate per unit overhead cost, first we will calculate the ratio in which different products use or consume different activities then, we will calculate the total overhead cost and per unit overhead cost.

Calculation of ratio:

Activity cost pool	Deluxe	Tourists	RatioDeluxe: Tourists
Labor related (direct labor hours)	4,000	40,000	4:40 or 1:10
Machine setups (setups)	3,000	2,000	3:2
Production orders (orders)	100	300	1:3
General factory (machine hours)	12,000	28,000	12:28 or 3:7

Calculation of total overhead costs and per unit overhead cost:

Cost pool	Expected overhead costs(in $)	Ratio	Deluxe (in $)	Tourists (in $)	Total(in $)
Labor related	80,000	1:10	7,272.73	72,727.27	80,000
Machine setups	150,000	3:2	90,000	60,000	150,000
Production orders	70,000	1:3	17,500	52,500	70,000
General factory	250,000	3:7	75,000	175,000	250,000
Total overhead cost			189,772.73	360,227.27	550,000
Number of units			2,000	10,000	-
Overhead cost (per unit)			94.87	36.02	-

Per unit cost for deluxe model will be calculated as follows:

Particulars	Deluxe (in $)
Direct material (per unit)	25
Direct labor (per unit)	24 (2×$12)
Overhead cost per unit	94.87
Unit product cost	143.87

Yes, after making the said changes per unit cost for deluxe model is $143.87 approximately.

Part a

When direct labor hours for one unit for deluxe model were 5, predetermined overhead rate was:

  $\begin{array}{l}\text{Predetermined overhead rate = }\frac{\text{Total overhead cost }}{\text{Total Dircet labor hours }}\\ \text{ = }\frac{\$550,000}{(2,000\times 5)+(10,000\times 4)}\\ \text{ = }\frac{\$550,000}{50,000}\\ \text{ = \$11 per hour }\end{array}$

And when direct labor hours are 2, predetermined overhead rate will be:

  $\begin{array}{l}\text{Predetermined overhead rate = }\frac{\text{Total overhead cost }}{\text{Total Dircet labor hours }}\\ \text{ = }\frac{\$550,000}{(2,000\times 2)+(10,000\times 4)}\\ \text{ = }\frac{\$550,000}{44,000}\\ \text{ = \$12}\text{.5 per hour }\end{array}$

Part b

After changing the per unit direct labor hours for deluxe model, per unit cost of tourist model under traditional costing will be:

Particulars	Tourist model (in $)
Direct material (per unit)	17
Direct labor (per unit)	48 (4×$12)
Overhead cost per unit	50 (4×$12.5)
Unit product cost	115

Per unit cost of tourist model under activity-based costing will be:

Particulars	Deluxe (in $)
Direct material (per unit)	17
Direct labor (per unit)	48 (4×$12)
Overhead cost per unit (calculated above)	36.02
Unit product cost	101.02

So, after making the said changes per unit cost for tourist model under traditional method is $115 and under ABC method is $101.02.

Traditional costing system and activity-based costing system, Both the methods are used in cost accounting to allocate the overheads or indirect cost to all the products. Traditional costing system uses only one base for such allocation and activity-based costing system uses more than one bases based on different activities.

ABC system identifies all the causes that give rise to indirect costs, known as activities and then assign cost of all the activities to products in the ratio in which products consume or use these activities. Traditional system calculates only one rate and uses that one rate for the whole allocation process.

Therefore, activity-based costing uses a more accurate and efficient method for the allocation process. However, this system is more complex and more expensive. Traditional system is less accurate, but this system is simple and comparatively, less expensive.