Chapter 7, Problem 45P

1.

To determine

Calculate the cost of the product and the gross margin for each of the three product lines using the following methods:

1. (a) physical unit method
2. (b) sales value at split-off method
3. (c) the net realizable value method
4. (d) the constant gross margin percentage method

Explanation of Solution

Cost allocation is the method of defining, collecting and allocating costs to cost items such as divisions, goods, services or a company division. It includes evaluating the cost objects in a business, recognizing the expenses involved by the cost objects and then assigning the cost objects according to different criteria.

The goals of cost allocation are as follows:

• Assess the departmental and product costs correctly.
• Motivate executives to bring a high degree of commitment into achieving top management targets.
• Provide the right opportunity for managers to make decisions in accordance with the Top management priorities.
• Assess fairly the rewards earned by the managers for their contributions and abilities and for the efficacy of their decision making.

A joint production process is one which yields multiple outputs from a common input of resources. Joint goods are products which have fairly significant market prices from the same manufacturing cycle.

1. (a) Calculate the cost of the product and the gross margin for each of the three product lines using the physical unit method

The method of physical measurement uses a physical scale, like pounds, gallon, yard, or volume units generated at the split-off point for the allocation of joint costs to joint products.

		A101		A204		B216		Total
Gallons sold		175,000		135,000		115,000		425,000
Price/gal (after additional processing)		$ 14.00		$ 10.00		$ 12.00
Total separable processing cost		$ 550,000		$ 125,000		$625,000		$1,300,000
Gallons produced		175,000		135,000		115,000		425,000
Total joint cost								$3,500,000
Sales price at split off		$10.00		$ 5.00		$ 10.00
Total sales value at split-off		$1,750,000		$675,000		1,150,000		3,575,000
Sales Value at split off		2,450,000		1,350,000		1,380,000		5,180,000

		A101		A204		B216		Total
Gallons  of production		10,000,000		12,000,000		2,000,000		24,000,000
% of Total		41.667 %		50.0000%		8.3333%		100%
Joint cost allocation		$37,500,000		$45,000,000		$7,500,000		$90,000,000
Separable processing cost		9,000,000		7,000,000		5,000,000		21,000,000
Total cost		$46,500,000		$52,000,000		$12,500,000		$111,000,000
Total cost per unit		$4.6500		$4.3333		$6.2500
Calculation of Gross Margin
Sales		$2,450,000		$1,350,000		$1,380,000		$5,180,000
Cost of goods sold:
Allocated Joint cost		1,441,176		1,111,765		947,059		$3,500,000
Separable cost		550,000		125,000		625,000		1,300,000
Total cost		1,991,176		1,236,765		1,572,059		4,800,000
Gross Margin		$ 458,824		$ 113,235		$ (192,059)		$380,000

1. (b) Calculate the cost of the product and the gross margin for each of the three product lines using the sales value at split-off method

The split-off point is the point at which individual goods can be categorized separately in a specific production cycle. The sales value in the split-off system assigns joint costs to the items at split-off based on their relative selling prices.

		A101		A204		B216		Total
Gallons sold		175,000		135,000		115,000		425,000
Price/gal (after additional processing)		$ 14.00		$ 10.00		$ 12.00
Total separable processing cost		$ 550,000		$ 125,000		$625,000		$1,300,000
Gallons produced		175,000		135,000		115,000		425,000
Total joint cost								$3,500,000
Sales price at split off		$10.00		$ 5.00		$ 10.00
Sales value after additional processing		$ 2,450,000		$ 1,350,000		$ 1,380,000		$ 5,180,000
Sales Value at split off		$ 1,750,000		$ 675,000		$ 1,150,000		$ 3,575,000

		A101		A204		B216		Total
Sales Value at split off		$ 1,750,000		$ 675,000		$ 1,150,000		$ 3,575,000
% of Total		48.95105 %		18.88112%		32.16783%		100%
Joint cost allocation		$1,713,287		$660,839		$1,125,874		$3,500,000
Separable processing cost		550,000		125,000		625,000		1,300,000
Total cost		$2,263,287		$785,839		$1,750,874		$4,800,000
Total cost per unit		$12.933		$5.821		$15.225
Calculation of Gross Margin
Sales		$2,450,000		$1,350,000		$1,380,000		$5,180,000
Cost of goods sold:
Allocated Joint cost		1,713,287		660,839		1,125,874		$3,500,000
Separable cost		550,000		125,000		625,000		1,300,000
Total cost		2,263,287		785,839		1,750,874		4,800,000
Gross Margin		$ 186,713		$ 564,161		$ (370,874)		$380,000

1. (c) Calculate the cost of the product and the gross margin for each of the three product lines using the net realizable value method.

A product's Net Realizable Value (NRV) is the actual value of the sales value calculated at the split-off point is determined by excluding the separable manufacturing and distribution costs from the expected final sales value of the product at the split-off point.

		A101		A204		B216		Total
Gallons sold		175,000		135,000		115,000		425,000
Price/gal (after additional processing)		$ 14		$ 10		$ 12
Total separable processing cost		$ 550,000		$ 125,000		$625,000		$1,300,000
Gallons produced		175,000		135,000		115,000		425,000
Total joint cost								$3,500,000
Sales value after additional processing		$ 2,450,000		$ 1,350,000		$ 1,380,000		$ 5,180,000

		A101		A204		B216		Total
Sales Value of production		$ 2,450,000		$ 1,350,000		$ 1,380,000		$ 5,180,000
Less: Separable cost		550,000		125,000		625,000		1,300,000
Net realizable value		$1,900,000		$1,225,000		$755,000		$3,880,000
% of total NRV		48.9691%		31.5722%		19.4588%		100%
Allocated Joint cost		1,713,918		1,105,026		681,057		3,500,000
Separable processing cost		550,000		125,000		625,000		1,300,000
Total cost		$2,263,287		$1,230,026		$1,306,057		$4,800,000
Total cost per unit		$12.937		$9.111		$11.357
Calculation of Gross Margin
Sales		$2,450,000		$1,350,000		$1,380,000		$5,180,000
Cost of goods sold:
Allocated Joint cost		1,713,918		1,105,026		681,057		$3,500,000
Separable cost		550,000		125,000		625,000		1,300,000
Total cost		2,263,918		1,230,026		1,306,057		4,800,000
Gross Margin		$ 186,082		$ 119,974		$ 73,934		$380,000
Gross margin %		7.60%		8.89%		5.36%		7.34%

1. (d) Calculate the cost of the product and the gross margin for each of the three product lines using the constant gross margin percentage method

When there are substantial separable costs and an relevant allocation goal is to obtain an allocation resulting in the same gross profit percentage for all joint goods, then a variant of the NRV approach is used. The constant gross percentage margin approach defines a joint cost allocation, such that after allocation, all joint goods have the same gross margin percentage.

		A101		A204		B216		Total
Gallons sold		175,000		135,000		115,000		425,000
Price/gal (after additional processing)		$ 14		$ 10		$ 12
Total separable processing cost		$ 550,000		$ 125,000		$625,000		$1,300,000
Gallons produced		175,000		135,000		115,000		425,000
Total joint cost								$3,500,000
Sales value after additional processing		$ 2,450,000		$ 1,350,000		$ 1,380,000		$ 5,180,000

		A101		A204		B216		Total
Final Sales Value of production		$ 2,450,000		$ 1,350,000		$ 1,380,000		$ 5,180,000
Less: Separable cost								1,300,000
Less: Joint cost								3,500,000
Gross margin								$380,000
Gross margin %								7.3359%
Cost of goods sold
Final Sales Value of production		$ 2,450,000		$ 1,350,000		$1,380,000		$ 5,180,000
Less: Gross margin		179,730		99,035		101,236		380,000
Less: Separable costs		550,000		125,000		625,000		1,300,000
Allocated joint cost		1,720,270		1,125,965		653,764		3,500,000
Total cost		$2,270,270		$1,250,965		$1,278,764		$4,800,000
Total cost per unit		$12.9730		$9.2664		$11.1197
Calculation of Gross Margin
Sales		$2,450,000		$1,350,000		$1,380,000		$5,180,000
Cost of goods sold:
Allocated Joint cost		1,720,270		1,125,965		653,764		$3,500,000
Separable cost		550,000		125,000		625,000		1,300,000
Total cost		2,270,270		1,250,965		1,278,764		4,800,000
Gross Margin		$ 179,730		990,035		$ 101,236		$380,000
Gross margin %		7.3359%		7.3359%		7.3359%		7.3359%

2.

To determine

Mention the method that will be preferred for the company, JH and explain the reason for it.

Explanation of Solution

Cost allocation is the method of defining, collecting and allocating costs to cost items such as divisions, goods, services or a company division. It includes evaluating the cost objects in a business, recognizing the expenses involved by the cost objects and then assigning the cost objects according to different criteria.

The goals of cost allocation are as follows:

• Assess the departmental and product costs correctly.
• Motivate executives to bring a high degree of commitment into achieving top management targets.
• Provide the right opportunity for managers to make decisions in accordance with the Top management priorities.
• Assess fairly the rewards earned by the managers for their contributions and abilities and for the efficacy of their decision making.

A joint production process is one which yields multiple outputs from a common input of resources. Joint goods are products which have fairly significant market prices from the same manufacturing cycle.

The net realizable value approach would be used here because the output of all Company JH is further processed, and the NRV approach accounts for the additional processing costs. Remember in particular that the gross margin for product B216 is negative under the Selling Value system at Split Off because of the high separable production costs for this product which are not included in the cost allocation. If, on the other hand, a large portion of the final sales had not been further processed, one might claim in split-off approach for the sales value.