Question

The joint cost to produce Products 1A, 2A, 3A and 4A is $4,000.  Each of these products can either be sold at the end of the joint production process, or can be processed further into 1B, 2B, 3B and 4B.

Production and selling information is as follows:

Product Name	Product 1A	Product 2A	Product 3A	Product 4A
Batch size (kg)	30	20	6	4
Sales Value ($ per kg)	100	50	2	0.5
If further processed:
processed from:	Product 1A	Product 2A	Product 3A	Product 4A
processed into:	Product 1B	Product 2B	Product 3B	Product 4B
additional costs (in $)	50	130	120	10
Final batch size (kg)	29	15	6	3
Final Sales value ($/kg)	120	200	100	6

For example, at the end of the joint production process, there are 30 kg of Product 1A produced, and each kg of Product 1A sells for $100/kg.  The 30kg batch of Product 1A can either be sold at this point for $3,000 (30kg x $100/kg) or the batch can be further processed into a batch of Product 1B at an additional cost of $50.  This will produce a 29kg batch of Production 1B that sells for $120/kg for a total sales value of $3,480 (29kg x $120/kg).

Required:

Part A    Assuming that none of the products are byproducts, calculate how much of the $4,000 joint cost should be allocated to each product using the four methods discussed in class (Physical measure method, Sales value at split-off method, net realizable value method, Constant gross margin NRV method).

Part B    Allocate the $4,000 joint cost assuming using the Net Realizable Value method and assuming that product 3 and product 4 are both by-products.  (hint: first determine if 3A should be processed further in 3B, and if 4A should be processed further into 4B)

Answer 1

Part (A)

1- Physical measure method

Joint cost here apportioned based on the number of units in a batch

Allocation joint cost based on physical measure method
Product	Product 1 A	Product 2 A	Product 3 A	Product 4 A	Total
Batch size in kg	30	20	6	4	60

Joint cost of $ 4000 should be allocated as follows
Product 1 A	(4000/60) x 30	2000
Product 2 A	(4000/60) x 20	1333.3
Product 3 A	(4000/60) x 6	400.0
Product 4 A	(4000/60) x 4	266.7

Product	Product 1 A	Product 2 A	Product 3 A	Product 4 A	Total
Batch size in kg	30	20	6	4	60
Joint cost allocation	2000	1333.3	400.0	266.7	4000.0

2 - Sales value at split off point method

Under this method sales value at the split off point is taken as the base for apportioning joint cost

Allocation joint cost based on sales value at the split -off method
Product	Product 1 A	Product 2 A	Product 3 A	Product 4 A	Total
Batch size in kg	30	20	6	4
Sales value per Kg	100	50	2	0.5
Total Sales value at split off point	3000	1000	12	2	4014

Joint cost of $ 4000 should be allocated as follows
Product 1 A	(4000/4014)*3000	2989.5
Product 2 A	(4000/4014)*1000	996.5
Product 3 A	(4000/4014)*12	12.0
Product 4 A	(4000/4014)*2	2.0

Product	Product 1 B	Product 2 B	Product 3 B	Product 4 B	Total
Batch size in kg	29	15	6	3
Joint cost allocation	2989.5	996.5	12.0	2.0	4000.0

3 - Net realizable value method

Under this method net realizable value after further processing is taken as the base for apportioning joint cost

Allocation joint cost based on Net realizable value method method
Product	Product 1 B	Product 2 B	Product 3 B	Product 4 B	Total
Final batch size	29	15	6	3
Final sales value per kg	120	200	100	6
Sales revenue	3480	3000	600	18	7098
Less:Seperable cost (further processing)	50	130	120	10	310
Net realizable value after further processing	3430	2870	480	8	6788

Joint cost of $ 4000 should be allocated as follows
Product 1 B	(4000/6788)*3430	2021.2
Product 2 B	(4000/6788)*2870	1691.2
Product 3 B	(4000/6788)*480	282.9
Product 4 B	(4000/6788)*8	4.7

Product	Product 1 B	Product 2 B	Product 3 B	Product 4 B	Total
Batch size in kg	30	20	6	4	60
Joint cost allocation	2021.2	1691.2	282.9	4.7	4000.0

4 - Costant gross margin NRV method

First we have to calculte the gross margin after further processing incorporating the joint cost to arrive at the correct rate of gross profit.This percentage is taken as gross margin rate for all product and cost should be identified accordingly

Allocation joint cost based on constant gross margin NRV method method
Product	Product 1 B	Product 2 B	Product 3 B	Product 4 B	Total
Final batch size	29	15	6	3
Final sales value per kg	120	200	100	6
Sales revenue	3480	3000	600	18	7098
Less:Seperable cost (further processing)	50	130	120	10	310
Net realizable value after further processing	3430	2870	480	8	6788

Total sales revenue	6788
Less:Joint cost	4000
Gross margin	2788
Percentage of gross margin (2788/7098)	39.28%

This percentage is taken as gross margin rate for all product and cost should be identified accordingly,calculations are as follows
Product	Product 1 B	Product 2 B	Product 3 B	Product 4 B	Total
Final batch size	29	15	6	3
Final sales value per kg	120	200	100	6
Sales revenue	3480	3000	600	18	7098
Less:Gross margin (39.28%) (B)	1367	1178	236	7	2788
Cost (A-B)	2113	1822	364	11	4310
Less :seperable cost	50	130	120	10	310
Joint cost allocation	2063	1692	244	1	4000

Part (B)

step -1 Calculation of Sales revenue without further processing
Product	Product 3 A	Product 4 A
Batch size in kg	6	4
Sales value per Kg	2	0.5
Total Sales Revenue	12	2

step -1 Calculation of Sales revenue with further processing
Product	Product 3 B	Product 4 B
Batch size in kg	6	3
Sales value per Kg	100	6
Sales revenue	600	18
Less:Further processing cost	120	10
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