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Contribution margin and break-even points

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The following cost information is available for a single product manufactured and sold by Forever You Company:

Variable costs: Direct materials $ 10 Fixed costs (in total):
(Per unit) Direct labor 12 Fixed overhead $ 540,000
Variable overhead 3 Fixed selling 360,000
Variable selling 2

Units sell for $36 each, and the firm is currently manufacturing and selling 120,000 units.

1. Determine the contribution margin per unit and the contribution margin ratio (percentage).

2. Calculate the firm's break-even point in units.

3. Calculate the firm's break-even point in sales dollars (revenues).

4. Calculate income at their current operating level of 120,000 units.

5. Suppose a change in manufacturing technology would allow the firm to reduce direct labor costs to $6 per unit, but would increase fixed overhead costs by $150,000. Compute the break-even point (in units) considering these changes to the cost structure.

6. Return to the original information (ignore changes in part 5). Suppose the firm can add a second product that would sell for $20 per unit, have unit variable costs of $13, and would increase total fixed costs by $320,000. Determine the Company's total income if they continue making and selling 120,000 units of the original product and make and sell 80,000 units of the second product.

7. Continuing with the 2 products, suppose the sales mix changes so they make and sell 100,000 units of each product (making the same total of 200,000 units). Determine the firm's total income with this mix of the two products.

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Solution Summary

The contribution margin and break-even points is provided. The income at their current operating levels of units are calculated.

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Total Variable Cost = 10+12+3+2 = $27 (add direct material & labour & variable costs)

1. Contribution Margin = Sale Price - Variable Cost
CM = 36-27 = $9

Contribution Margin Ratio = Contribution Margin/Sale Price
CMR = 9/36 = 25%

2. ...

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