Question

Yerke Company makes jungle gyms and tree houses for children. For jungle gyms, the price is $120 and variable expenses are $90 per unit. For tree houses, the price is $200 and variable expenses are $100. Total fixed expenses are $253,750. Last year, Yerke sold 12,000 gyms and 4,000 tree houses. Now suppose that Yerke expects tree house demand to increase from 4,000 to 8,000 units. What is the number of jungle gyms sold at break-even?

1,750

668

2,625

1,002

875

Answer 1

Given:

Number of units sold of jungle gyms = 12,000 units

Number of units sold of tree houses = 4,000

Sales mix = 3:1

In the current year, number of units of tree houses sold increased from 4,000 units to 8,000 units.

New sales mix = 3:2

Sales mix in terms of percentage (Jungle gyms) = 3 / 5 = 0.6 or 60%

Sales mix in terms of percentage (Tree houses) = 2 / 5 = 0.4 or 40%

Contribution margin per unit of jungle gyms = Sales – variable cost

= 120 – 90

= $30

Contribution margin per unit of tree house = Sales – variable cost

= 200 – 100

= $100

Weighted average contribution margin per unit = (30 * 0.6) + (100 * 0.4)

= $58

Break-even point in units = Fixed cost / weighted average contribution margin per unit

= 253,750 / 58

= 4,375 units

Number of jungle gyms sold at break-even = Break-even point in units * sales mix percentage

= 4,375 * 0.6

= 2,625 units

Number of tree houses sold at break-even = 4,375 – 2,625

= 1,750 units

Therefore, 2,625 units of jungle gyms are sold at break-even.