Tiger Golf Accessories sells golf shoes, gloves and laser-guided range finder that measures distance Below are unit cost and sales data.
Shoes Gloves Range find
Unit sales $100 $30 $250
Unit VC 60 10 200
Unit CM $40 $20 $50
Sales Mix 40% 50% 10%
Fixed cost are $620,000
a.) Compute break-even point in units for the company.
b.) Determine the number of units to be sold at the break-even point for each product line.
c.) Verify that the mis of sales units determined in (b) will generate a zero new income.
test
To compute the break-even point in units for the company, we need to determine the total contribution margin (CM) and the contribution margin ratio (CM ratio).
a.) Break-even point in units can be calculated using the formula:
Break-even point (in units) = Fixed Costs / CM ratio
First, let's calculate the total CM and the CM ratio for Tiger Golf Accessories.
Total CM = (Unit CM x Unit Sales) x Sales Mix
Total CM = (($40 x 100) x 0.4) + (($20 x 30) x 0.5) + (($50 x 250) x 0.1)
Total CM = $1,600 + $300 + $1,250
Total CM = $3,150
CM ratio = Total CM / Total Sales
CM ratio = $3,150 / (100 + 30 + 250)
CM ratio = $3,150 / 380
CM ratio = $8.2895 per unit
Now, we can calculate the break-even point in units.
Break-even point (in units) = Fixed Costs / CM ratio
Break-even point (in units) = $620,000 / $8.2895
Break-even point (in units) ≈ 74,800 units
Therefore, the break-even point for Tiger Golf Accessories is approximately 74,800 units.
b.) To determine the number of units to be sold at the break-even point for each product line, we can use the sales mix.
Number of shoe units = Break-even point (in units) x Sales Mix for shoes
Number of shoe units = 74,800 x 0.4
Number of shoe units = 29,920 units
Number of glove units = Break-even point (in units) x Sales Mix for gloves
Number of glove units = 74,800 x 0.5
Number of glove units = 37,400 units
Number of range finder units = Break-even point (in units) x Sales Mix for range finder
Number of range finder units = 74,800 x 0.1
Number of range finder units = 7,480 units
At the break-even point, the company will need to sell approximately:
- 29,920 units of golf shoes
- 37,400 units of golf gloves
- 7,480 units of range finders
c.) To verify if the sales mix will generate zero net income, we need to calculate the contribution margin for each product and sum them up.
Total contribution margin = (Unit CM x Number of Units sold for each product) x Sales Mix
Total contribution margin = (($40 x 29,920) x 0.4) + (($20 x 37,400) x 0.5) + (($50 x 7,480) x 0.1)
Total contribution margin = $479,360 + $374,000 + $37,400
Total contribution margin = $890,760
Since the total contribution margin is greater than zero, it indicates that the sales mix will generate a positive net income, not zero as required by the question.