Lucent Manufacturing Company makes a product that it sells for $63 per unit. The

Question

Lucent Manufacturing Company makes a product that it sells for $63 per unit. The company incurs variable manufacturing costs of $20 per unit. Variable selling expenses are $17 per unit, annual fixed manufacturing costs are $190,000, and fixed selling and administrative costs are $162,820 per year.

Determine the break-even point in units and dollars using each of the following approaches:

a. equation method:

-break even point in units =

-break even point in dollars =

b. contribution margin per unit.

-contribution margin per unit =

-break even point in units =

-break even point in dollars =

c. Prepare a contribution margin income statement for the break-even sales volume.

-sales =

-variable costs =

-contribution margin =

-fixed costs =

-net income =

Explanation / Answer

a.Equation method

Selling price = $63

Variable cost = ( 17+20) = $37

Total fixed cost = $190,000 + $162,820 = $ 352,820

Let break even quantity be Q

Sales = variable cost + fixed cost

63Q= 37Q + 352,820

26Q=352,820

Q=352,820/26

=13,570

Break even point in $=break even point in unit x selling price

=13,570 x 63 =$854,910

b . Contribution method

Contribution per unit = sales – variable cost

=63-37=26

Contribution margin % =contribution per unit /sales x 100

= 26/63 x 100=41.271%

Break even point per unit = fixed cost /contribution per unit

=352,820 / 26 = 13,570

Break even point in $ =fixed cost / contribution margin %

=352,820 / 41.271% =$ 854,910

c. contribution margin income statement

Sales   = (13,570 x 63)                                 $854,910

    Variable cost =     (13,570 x 37 )               $502,090

Contribution margin = $352,820

(-) fixed cost (190,000 + 162,820)   $ 352,820

Net income 0

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