Question

4. Lake Corporation manufactures two products, AA and BB, from a joint process. A production run costs $20,000 and results in 500 units of AA and 2,000 units of BB. Both products must be processed past the split-off point, incurring separable costs of $5 per unit for AA and $10 per unit for BB. The market price is $25 for AA and $20 for BB.

I have the answers I just need the work shown in detail with step-by-step instructions.

Required:

a.	Allocate joint production costs to each product using the physical units method. (Ans:AA=$4,000; BB=$16,000)
b.	Allocate joint production costs to each product using the net realizable value method. (Ans: AA=$6,667; BB=$13,333)
c.	Allocate joint production costs to each product using the constant gross margin percentage method. (Ans: AA=$7,619.05; BB=$12,380.96)

Answer 1

Solution

Lake Corporation

1. Allocation of joint product costs to each product using physical units method:

Joint costs = $20,000

Product	Physical units	Proportion	Allocated joint costs
AA	500	20%	$4,000
BB	2,000	80%	$16,000

Computations –

Total physical units of both products = 500 + 2,000 = 2,500 units

Proportion of AA = 500/2,500 = 20%

Proportion of BB = 2,000/2,500 = 80%

Joint cost allocation is as follows,

AA = $20,000 x 20% = $4,000

BB = $20,000 x 80% = $16,000

1. Allocation of joint product costs to each product using net realizable value method:

Net realizable value = sales – separation costs

For Product AA –

Sales price of AA = $25

Sales = $25 x 500 = $12,500

Separation costs at $5 = 500 x $5 = $2,500

Net realizable value = $12,500 - $2,500 = $10,000

For Product BB –

Sales price of BB = $20

Sales = $20 x 2,000 = $40,000

Separation costs at $10 = 2,000 x $10 = $20,000

Net realizable value = $40,000 - $20,000 = $20,000

Product	Net Realizable Value	Proportion	Allocated Joint Costs
AA	$10,000	33.33%	$6,667
BB	20,000	66.67%	$13,333
Total	$30,000		$20,000

Allocated joint costs –

For Product AA:

Proportion = 10,000/30,000 = 33.33%

Joint cost allocation = $20,000 x 33.33% = $6,667

For Product BB:

Proportion = 20,000/30,000 = 66.67%

Joint cost allocation = $20,000 x 66.67% = $13,333

1. Allocation of joint costs to product using the constant gross margin percentage method:

Gross margin percentage = gross margin/sales

Gross margin = sales – cost of goods sold

Sales = sales of AA + Sales of BB

            = (500 x $25) + (2,000 x $20) = $52,500

Cost of goods sold = cost of goods sold of AA + cost of goods sold BB

COGS = $20,000 + (500 x $5) + (2,000 x $10) = $42,500

Gross margin = $52,500 - $42,500 = $10,000

Grand gross margin percentage = (total revenue – total costs)/total revenue

= ($52,500 -$42,500)/$52,500 = 19.05%

Joint product gross margin = market price x grand gross margin

Joint cost allocated to product = market value – gross margin – separable costs

Gross margin for each product = sales revenue x gross margin percentage

Product AA –

= $12,500 – (12,500 x 19.05%) - $2,500 = $7,619

Product BB –

= $40,000 – (40,000 x 19.05%) - $20,000 = $12,381