Question

CollegePak Company produced and sold 73,000 backpacks during the year just ended at an average price of $33 per unit. Variable manufacturing costs were $13.50 per unit, and variable marketing costs were $4.32 per unit sold. Fixed costs amounted to $543,000 for manufacturing and $218,400 for marketing. There was no year-end work-in-process inventory. (Ignore income taxes.)

Required:
1. Compute CollegePak’s break-even point in sales dollars for the year. (Do not round intermediate calculations. Round your final answer up to the nearest whole dollar.)
2. Compute the number of sales units required to earn a net income of $555,000 during the year. (Do not round intermediate calculations. Round your final answer up to the nearest whole dollar.)
3. CollegePak's variable manufacturing costs are expected to increase by 10 percent in the coming year. Compute the firm’s break-even point in sales dollars for the coming year. (Do not round intermediate calculations. Round your final answer up to the nearest whole dollar.)
4. If CollegePak’s variable manufacturing costs do increase by 10 percent, compute the selling price that would yield the same contribution-margin ratio in the coming year. (Do not round intermediate calculations. Round your final answer to 2 decimal places.)

Answer 1

1.

Break even point in sales dollars = Total fixed costs / Contribution margin ratio

Total fixed costs = Fixed manufacturing costs + Fixed marketing costs

= $543,000 + $218,400

= $761,400

Contribution margin ratio = Contribution margin / Selling price

Contribution margin = Sales price - Variable cost

= $33 - ($13.50 + $4.32)

= $33.00 - $17.82

= $15.18

Contribution margin ratio = $15.18 / $33.00

= 46%

Break even point in sales dollars = $761,400 / 46%

= $1,655,217

2.

Target units = (Fixed costs + Target profit) / Contribution margin ratio

= ($761,400 + $555,000) / 46%

= $2,861,739

3.

Revised variable manufacturing cost = $13.50 * 1.10

= $14.85

Contribution margin per unit decreases by $1.35 ($13.50 * 10%)

Revised contribution margin per unit = $15.18 - $1.35

= $13.83

Revised contribution margin ratio = $13.83 / $33.00

= 41.9091%

Break even point in sales dollars = $761,400 / 41.9091%

= $1,816,789

4.

Contribution margin ratio = (selling price - variable cost per unit) / Selling price

Variable cost per unit = $14.85 + $4.32

= $19.17

let selling price = x

46% = (x - $19.17) / x

0.46 x = x - $19.17

0.54x = $19.17

x = $35.50

let selling price = $35.50