Question

Lamar & Co., makes and sells two types of shoes, Plain and Fancy. Data concerning these products are as follows:

Plain Fancy
Unit selling price $ 25.00 $ 36.00
Variable cost per unit 13.00 20.00
Sixty percent of the unit sales are Plain, and annual fixed expenses are $45,000.
Assuming that the sales mix remains constant, compute the total number of units of each product that the company must sell to break even.
Show all computations.

Answer 1

Lamar & Co. must sell 1,986 units of Plain shoes and 1,324 units of Fancy shoes to break even, based on a sales mix of 60% Plain and 40% Fancy, and a total fixed cost of $45,000.

Step-by-step explanation:

To determine the break-even point for Lamar & Co. which produces two types of shoes, Plain and Fancy, we need to use the contribution margin approach. The contribution margin per unit is calculated by subtracting the variable cost per unit from the unit selling price. The contribution margin ratio is then used to determine the break-even point in units for each product, considering the sales mix. The following formulas are used:

• Contribution Margin per unit (CM) = Selling Price per unit (SP) - Variable Cost per unit (VC)
• Total Contribution Margin needed to break even (TCM) = Fixed Costs (FC)
• Break-even point in units = TCM / Weighted Average CM

First, calculate the contribution margin for each product:

• Plain CM = $25.00 - $13.00 = $12.00 per unit
• Fancy CM = $36.00 - $20.00 = $16.00 per unit

Because the sales mix is 60% Plain and 40% Fancy, the weighted average contribution margin is calculated as follows:

Weighted Average CM = (0.60 * Plain CM) + (0.40 * Fancy CM)
Weighted Average CM = (0.60 * $12.00) + (0.40 * $16.00) = $13.60

Now, calculate the total units required to break even:

Break-even point in units = $45,000 / $13.60 = 3,309 (rounded to nearest whole unit)

To determine the break-even units for each product, we apply the sales mix percentages:

• Plain units to break even = 60% of total units = 0.60 * 3,309 = 1,986 units
• Fancy units to break even = 40% of total units = 0.40 * 3,309 = 1,324 units

Lamar & Co. must sell 1,986 units of Plain shoes and 1,324 units of Fancy shoes to break even.

Answer 2

Results are below.

Step-by-step explanation:

First, we will calculate the weighted average contribution margin:

Weighted average contribution margin= (weighted average selling price - weighted average unitary variable cost)

Weighted average contribution margin= (0.6*25 + 0.4*36) - (0.6*13 + 20*0.4)

Weighted average contribution margin= $13.6

Now, the break-even point for the whole company:

Break-even point (units)= Total fixed costs / Weighted average contribution margin

Break-even point (units)= 45,000 / 13.6

Break-even point (units)= 3,309

Now, for each product line:

Plain= 0.6*3,309= 1,985

Fancy= 0.4*3,309= 1,324