Question

A firm’s fixed cost $50,000 and its variable cost is $3 per unit. The selling price $5 per unit. The management is considering two projects but only one would be selected. Project A will result in an increase in fixed cost, which will amount to $150,000 and a decrease in variable cost which fall to $2. Project B is less ambitious undertaking that results in fixed costs increasing to $70,000 and variable costs decreasing to $2.30 per unit. Currently 55,000 units are sold each year and sales are considered stable.

What is DOL for 55,000 for the three alternatives? Which firm is risky considering just the fixed costs?

Answer 1

Degree of operating leverage

The following is the formula for finding degree of operating leverage.

Degree of operating leverage = contribution margin / operating income

Contribution margin = sales - variable cost

Operating income = contribution margin - fixed cost

Alternative 1

Contribution margin per unit = 5 - 3 = $2

Contribution margin = 55,000 × 2 = $110,000

Operating income = 110,000 - 50,000 = $60,000

Degree of operating leverage = 110,000 / 60,000 = 1.83

Alternative 2 (project A)

Fixed cost = $150,000

Variable cost = $2

Contribution margin per unit = 5 - 2 = $3

Contribution margin = 55,000 × 3 = $165,000

Operating income = 165,000 - 150,000 = $15,000

Degree of operating leverage = 165,000 / 15,000 = 11

Alternative 2 (project B)

Fixed cost = $70,000

Contribution margin per unit = 5 - 2.30 = $2.70

Contribution margin = 55,000 × 2.7 = $148,500

Operating income = 148,500 - 70,000 = $78,500

Degree of operating leverage = 148,500 / 78,500 = 1.89

Risk

The degree of operating leverage of Project A is 11 and a fixed cost of $150,000 . The higher degree of operating leverage indicates the Project A is more riskier than compared to other two alternatives.

The above are the detailed calculations,equations and explanations.

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