Question

XYZ had sales of $10,000 (100 units at $100 per). Manufacturing costs consisted of direct labor $1,500, direct materials $1,000, variable factory overhead $1,100, and fixed factory overhead $500. Selling expenses totaled $1,500 ($500 variable and $1,000 fixed), and administrative expenses totaled $1,600 ($410 variable and $1,190 fixed). Operating income was $2,800. Round all final answers to nearest dollar or whole number.

1. What is the break-even point in sales dollars and in units if the fixed factory overhead increased by $1,700?
2. What is the break-even point in sales dollars and in units if costs remain as originally projected?
3. What would be the operating income if sales units increased by 10%?

Answer 1

Total fixed costs = Fixed factory overhead + Fixed administrative expense + Fixed selling expense

= 500 + 1,190 + 1,000

= $2,690

Total variable cost of producing 100 units = Direct material + Direct labor + Variable factory overhead + Variable administrative expense + Variable selling expense

= 1,000 + 1,500 + 1,100 + 410 + 500

= $4,510

Hence, variable cost per unit = 4,510/100

= $45.10

Unit Contribution margin = Unit Selling price – Unit Variable cost

= 100 - 45.10

= $54.90

Contribution margin ratio = Contribution margin per unit/Selling price per unit

= 54.90/100

= 54.90%

i)

Fixed factory overhead increase by $1,700

Total fixed costs in this case would be = 2,690 + 1,700

= $4,390

Break even point (units) = Fixed cost/Contribution margin per unit

= 4,390/54.90

= 80 units

Break even point ($) = Fixed cost/Contribution margin ratio

= 4,390/54.90%

= $8,000

ii)

Break even point (units) = Fixed cost/Contribution margin per unit

= 2,690/54.90

= 49 units

Break even point ($) = Fixed cost/Contribution margin ratio

= 2,690/54.90%

= $4,900

iii)

sales units increased by 10%

Hence, sales units = 100 x 110%

= 110

Sales = Sales units x Selling price per unit

= 110 x 100

= $11,000

Profit = Sales x Contribution margin ratio – Fixed costs

= 11,000 x 54.90% - 2,690

= $3,349

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