Question

Company A produces two products—methanol (wood alcohol) and turpentine -- in a joint process. Joint costs amount to $124,200 per batch of output. Each batch totals 13,500 gallons: 25% methanol and 75% turpentine. Both products are processed further without gain or loss in volume. Separable processing costs are methanol, $11 per gallon; turpentine, $3 per gallon. Methanol sells for $22 per gallon. Turpentine sells for $16 per gallon. The company has discovered an additional process by which the methanol (wood alcohol) can be made into a pleasant-tasting alcoholic beverage. The selling price of this beverage would be $42 a gallon. Additional processing would increase separable costs by $12 per gallon (in addition to the $11 per gallon separable cost required to yield methanol). The company would have to pay excise taxes of 20% on the selling price of the beverage. Requirement: Under the following assumptions, calculate the joint cost allocated (in total $) of the turpentine product.

1. The firm chooses its product mix to maximizes operating profit.

2. The firm uses the constant gross margin method to allocate joint costs.

3.There are no beginning or ending inventories.

Answer 1

The constant gross margin method allocates joint costs in such manner that the gross margin percentage is the same for each product.

Calculation of Gross margin percentage:

	Methanol ( 3,375 gallons) (1)	Turpentine ( 10,125 gallons) (1)	Total
Sales Revenue	$ 74,250	$ 162,000	$ 236,250
Cost of goods sold:
Joint Cost			$124,200
Separable cost	$ 37,125 (2)	$ 30,375 (2)	$ 67,500
			$ 191,700
Gross Margin			$ 44,550

Gross Margin % = Gross Margin / Sales Revenue

= 44,550 / 236,250

= 18.857% (approx)

Allocation of Joint Cost in the ratio of gross margin:

	Methanol	Turpentine	Total
Sales Value	$ 74,250	$ 162,000	$ 236,250
Less: 18.857% Gross Margin	$ 14,000 (approx)	$ 30,550 (aprox)	$ 44,550
Total Cost	$ 60,250	$ 131,450	$ 191,700
Separable cost	$ 37,125	$ 30,375	$ 67,500
Joint cost (Total cost- Separable cost)	$ 23,125	$ 101,075	$124,200

Working Notes:

1) Total Output = 13,500 gallons

Methanol= 25% of 13,500 = 3,375 gallons

Turpentine= 75% of 13,500 gallons = 10,125 gallons

2) Product mix to Maximise operating profit: Determining whether Methanol should be processed further into alcoholic beverage or not:

	Alcoholic beverage	Methanol	Differential
Sales Revenue per gallon	$ 42	$ 22	$ 20
Separable cost per gallon	$ 31.4	$ 11	$ 20.4
Net Benefit/(loss)			($ 0.4)

If Methanol is further processed into alcoholic beverage, it would result in the loss of $ 0.4 per gallon. Therefore, it should not be further processed.

3) Calculation of separable costs:

Methanol = 3,375 gallons* $ 11 per gallon =$ 37,125

Turpentine = 10,125 gallons * $ 3 per gallon = $ 30,375