Question

Assume that an investor has a manufacturing plant that produces automotive spare parts. The sale price of the part is 18 $/unit. The annual fixed cost of the plant is $1,500,000. Unit variable labor cost is 4 $/unit, unit variable material cost 3 $/unit, unit variable overhead cost 1 $/unit. a )How many units should be produced to start making profit (X)? b) How many units should be produced to make $1000,000 profit (Y)?

a. X= 200000, Y= 325000

b. X= 166667, Y= 250000

c. X= 150000, Y= 250000

d. X= 200000, Y= 200000

e. X= 250000, Y= 250000

f. X= 154545, Y= 245454

Answer 1

Requirement a):

To start making profit a company must reach its break-even point. Break-even point is where the total sales revenue is equal to the total costs (total costs includes both fixed and variable costs). The number of units required to reach the break-even point is called the break-even quantity. In other words break-even point in terms of units is called break-even quantity.

Formula,

Break-even quantity = Total Fixed cost / Contribution margin per unit

For calculating the break-even quantity first, we need to calculate the contribution margin.

Contribution margin is calculated by subtracting variable cost per unit from the sales price per unit.

Calculation of Contribution Margin
Sales price per unit		$ 18
Less: Variable Costs:
Material cost per unit	$ 3
Labor cost per unit	$ 4
Overhead cost per unit	$ 1	$ 8
Contribution margin per unit	$ 10

So,

The number of units company should produce to start making profit or the break-even quantity (X)

= Fixed cost of the plant / Contribution margin per unit

= $1,500,000 / $10

= 150,000 units

Requirement b):

Number of units should be produced to make $1,000,000 profit (Y)

= (Fixed cost of the plant + Target profit) / Contribution margin per unit

= ($1,500,000 + $1,000,000) / $10

= 250,000 units

(Here targeted profit is $1,000,000.)

So, from the above calculation we can see that, option C i.e. X = 150,000 and Y = 250,000 is the correct one.