Question

A company makes two products, the variable costs are as follows;

Product A Product B

£ £

Direct materials 1 3

Direct labour (£6 per hour) 6 3

Variable overhead 1 1

8 7

The sale price of A is £14 and B is £11. During the month of July the availability of Direct Labour is limited to 5000 hours due to staff taking holidays. Sales demand is expected to be 3000 units of A and 5000 units of B.

Monthly fixed costs are £20,000 and opening stocks are zero.

Required:

1. Calculate the deficiency in labour hours for the month.
2. Determine the priority ranking for production.
3. Calculate the maximum profit that can be made next month
4. Calculate the loss of profit due to this limiting factor and consider the maximum amount the company would be willing to pay,per hour for agency staff.

Answer 1

Answer a)

Calculation of deficiency in labor hours per month

	Product A	Product B	Total
Labor hours consumed per unit	1.00	0.50
Expected sales demand per month	3,000 Units	5,000 Units
Total Labor hours required per month (A)	3,000	3,000	6,000
Total Labor hours available per month (B)			5,000
Deficiency in Labor hours (A) - (B)			1,000

Therefore 1,000 labor hours are deficient per month.

Answer b)

Calculation of priority ranking for production

	Product A	Product B
Selling Price per unit (A)	£         14.00	£           11.00
Less: Variable Costs
Direct Materials	£           1.00	£             3.00
Direct Labor	£           6.00	£             3.00
Variable Overheads	£           1.00	£             1.00
Total Variable Costs (B)	£           8.00	£             7.00
Contribution margin per unit (A) - (B)	£           6.00	£             4.00
Labor hours consumed per unit	1.00	0.50
Contribution margin per labor hour	£           6.00	£             8.00
Ranking	II	I

Working Notes:

Calculation of Labor hours required per unit of each product.

Labor hour per unit = Total labor cost per unit of the product/ Direct Labor rate per hour

Product A:

Labor hour per unit = £ 6 per unit/ £ 6 per hour

                                    = 1 labor hour per unit

Product B:

Labor hour per unit = £ 2 per unit/ £ 6 per hour

                                    = 0.50 labor hour per unit

Answer c)

Calculation of maximum profit

	Product A	Product B	Total
Number of Units produced and sold (A)	2,500	5,000
Contribution margin per unit (B)	£           6.00	£             4.00
Total Contribution margin (A) x (B)	£      15,000	£         20,000	£     35,000
Less: Monthly fixed costs			£     20,000
Net profit			£     15,000

Therefore maximum net profit with the available 5,000 labor hours is £ 15,000.

Working Note:

Calculation of optimum Product mix with available 5,000 labor hours

	Direct labor hours per unit	Number of Units Produced and Sold	Total Labor hours consumed
Product B	0.50	5,000	2,500
Product A	1.00	2,500	2,500
Total	5,000

Answer d)

Calculation of maximum profit

With the available maximum number of labor hours (i.e. 5,000 labor hours), the company is able to produce 5,000 units of product B and 2,500 units of Product A.

Maximum demand of product B is fulfilled.

Maximum demand of product A is 3,000 units. However, the company is able to produce and sell 2,500 units of Product A with the current available machine hours. Thus 500 units of product A could not be produced and sold. The loss of profit will be equal to the contribution margin that these products would have earned.

Loss Profit = Number of units of product A that could not be produced and sold X contribution margin per unit of Product A

                     = 500 units X £ 6.00 per unit

                      = £ 3,000

Therefore the loss of profit due to limiting factor is £ 3,000.

Calculation of maximum amount the company would be willing to pay for each additional labor hour

Since the maximum demand of product A could not fulfilled due to limiting factor (i.e. Labor hours), the maximum the company would be willing to pay for each additional labor hour will be equal to the contribution margin per labor hour for Product A, i.e. £ 6.00.