Question

Barclay Enterprises manufactures and sells three distinct styles of bicycles: the Youth model sells for $300 and has a unit contribution margin of $105; the Adult model sells for $850 and has a unit contribution margin of $450; and the Recreational model sells for $1,000 and has a unit contribution margin of $500. The company's sales mix includes: 5 Youth models; 9 Adult models; and 6 Recreational models. If the firm's annual fixed costs total $6,500,000, calculate the firm's break-even point in total sales dollars.

Answer 1

Firm's break even point in sales = $12,998,700

Step-by-step explanation:

Provided contribution per unit from each bicycle

Youth = $105

Adult = $450

Recreational = $500

As per sales mix,

5 Youth models; 9 Adult models; and 6 Recreational models are to be sold

Total contribution of each mix

$105
`*` 5 + $450
`*` 9 + $500
`*` 6

= $525 + $4,050 + $3,000 = $7,575

Whenever there is standard sales mix we calculate break even point according to that,

Break even point = Fixed Cost/Contribution

Fixed cost = $6,500,000

Contribution per mix = $7,575

Break even point in units = $6,500,000/7575 = 858 units

These will be in the ratio of 5:9:6

Youth = 858
`*` 5 = 4,290 units

Adult = 858
`*` 9 = 7,722 units

Recreational = 858
`*` 6 = 5,148 units

Total break even point in dollars

4,290
`*` $300 = $1,287,000

7,722
`*` $850 = $6,563,700

5,148
`*` $1,000 = $5,148,000

Total = $12,998,700

Firm's break even point in sales = $12,998,700