Question

CollegePak Company produced and sold 88,000 backpacks during the year just ended at an average price of $48 per unit. Variable manufacturing costs were $21.00 per unit, and variable marketing costs were $4.92 per unit sold. Fixed costs amounted to $558,000 for manufacturing and $230,400 for marketing. There was no year-end work-in-process inventory. (Ignore income taxes.)

Required: 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.)

Compute the number of sales units required to earn a net income of $630,000 during the year. (Do not round intermediate calculations. Round your final answer up to nearest whole number.)

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.)

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

Total variable cost per unit = Variable manufacturing cost per unit + Variable marketing cost per unit = $21 + $4.92 = $25.92

Contribution margin per unit = Selling price - Total variable cost per unit = $48 - $25.92 = $22.08

Contribution margin ratio = [ Contribution margin per unit / Selling price ] = [ $22.08 / $48 ] = 46%

Total fixed cost = Manufacturing fixed cost + Marketing fixed cost = $558,000 + $230,400 = $788,400

Break-even point in sales dollar ( for the year ) = Total fixed cost / Contribution margin ratio = $788,400 / 46% = $1,713,913

Number of sales units required ( to earn a net income of $630,000 during the year ) = [ Total fixed cost + Required net income ] / Contribution margin per unit = [ $788,400 + $630,000 ] / $22.08 = 64,239 units

It is given that in the coming year variable manufacturing cost are expected to increase by 10%.

Revised variable manufacturing cost per unit = Current variable manufacturing cost per unit * ( 100% + % Increase ) = $21 * ( 100% + 10% ) = $23.10 per unit

Revised total variable cost per unit = Revised variable manufacturing cost per unit + Variable marketing cost per unit = $23.10 + $4.92 = $28.02

Revised contribution margin ratio = [ Selling price - Revised total variable cost per unit ] / Selling price = [ $48 - $28.02 ] / $48 = 41.625%

Break-even point in sales dollars ( for the coming year ) = Total fixed cost / Revised contribution margin ratio = $788,400 / 41.625% = $1,894,054

Let the required selling price that would yield the same contribution-margin ratio in the coming year be X

Contribution margin ratio of the current year = [ Required selling price - Revised total variable cost per unit ] / Required selling price

46% = [ X - $28.02 ] / X

0.46 = [ X - $28.02 ] / X

0.46X = X - $28.02

X - 0.46X = $28.02

0.54X = $28.02

X = $28.02 / 0.54

X = $51.89

So, the required selling price is $51.89