Question

Piper Ltd. has determined the following costs for making one unit of its only product:

Direct materials	$6.00
Direct labour	4.00
	$10.00

The company is, however, not sure of the behaviour of its manufacturing overhead. The controller therefore ran a simple regression based on 20 pairs of monthly observations and obtained the following results:

Y = $6,000 + 1.50X

Y represents total monthly manufacturing overhead costs while X represents total monthly manufacturing direct labour costs.

The controller also estimated that selling and administration costs, which she considers to be fixed, would amount to $21,200 for the period.

Required:

What is the company's monthly breakeven sales in units at a selling price of $20.00 per unit?

Answer 1

Break even sales in units = Fixed cost / contribution margin

The result of simple regression : Y = $6,000 + 1.5X

Y = Total monthly manufacturing overhead

X = Total monthly direct labor costs

So, " 1.5X" is the variable portion of manufacturing overhead. And $6,000 is the fixed manufacturing overhead.

For example, if monthly direct labor cost is $500 , the variable manufacturing overhead = 1.5 * 500 = $750

If monthly direct labor cost  is $1000, the variable manufacturing overhead = 1.5 * 1,000 = $1,500

So, variable manufacturing overhead per $ direct labor is $1.5.

That portion (1.5X) is varying with direct labor costs.

But $6,000 is constant. It is not affected by any factors. That's why it is considered as fixed manufacturing overhead.

Other fixed costs(selling and administration) = $21,200

Total fixed cost = $21,200 + $6,000(fixed manufacturing overhead) = $27,200

Contribution margin = Selling price - variable costs

Variable costs = Direct materials + Direct labor + variable manufacturing overhead = $6 + $4 + (1.5*$4) = $10 + $6 =$16

Selling price = $20

Contribution margin = $20 - $16 = $4

Monthly break even sales in units = Fixed costs / contribution margin

= $27,200 / $4 = 6,800 units