E6-9 (a,b)
Tiger Golf Accessories sells golf shoes, gloves, and a laser-guided range-finder that measures distance. Shown below are unit cost and sales data.
Pairs
of Shoes
Pairs
of Gloves
Range
Finder
Unit sales price $100 $30 $250
Unit variable costs
60
10
200
Unit contribution margin
$40
$20
$50
Sales mix
40%
50%
10%
Fixed costs are $620,000.
Compute the break-even point in units for the company.
Determine the number of units to be sold at the break-even point for each product line.
Shoes
Gloves
Range finders
To compute the break-even point in units for the company, we need to find the total contribution margin per unit. The contribution margin is the unit sales price minus the unit variable costs.
For shoes:
Unit contribution margin for shoes = $100 - $60 = $40
For gloves:
Unit contribution margin for gloves = $30 - $10 = $20
For range finders:
Unit contribution margin for range finders = $250 - $200 = $50
Next, we need to calculate the weighted average contribution margin percentage, which is the sum of the contribution margins for each product line multiplied by their sales mix percentages.
Weighted average contribution margin percentage = (40% * $40) + (50% * $20) + (10% * $50)
To find the break-even point in units, we divide the fixed costs by the weighted average contribution margin per unit.
Break-even point in units = Fixed costs / Weighted average contribution margin per unit
Break-even point in units = $620,000 / Weighted average contribution margin percentage
To determine the number of units to be sold at the break-even point for each product line, we can multiply the break-even point in units by the sales mix percentages for each product line.
Number of units to be sold at the break-even point for shoes = Break-even point in units * 40%
Number of units to be sold at the break-even point for gloves = Break-even point in units * 50%
Number of units to be sold at the break-even point for range finders = Break-even point in units * 10%