To answer these questions, we'll use the following formulas:
Accounting Break-Even Quantity:
Break-Even Quantity = Fixed Costs / (Price - Variable Costs)
Cash Break-Even Quantity:
Break-Even Quantity = (Fixed Costs + Initial Investment) / (Price - Variable Costs)
Financial Break-Even Quantity:
Break-Even Quantity = (Fixed Costs + Initial Investment) / (Price - Variable Costs) * (1 + Required Return)
Degree of Operating Leverage:
Degree of Operating Leverage = Contribution Margin / Net Operating Income
Let's calculate each of these values:
Given data:
Price per unit (P) = $85
Variable costs per unit (VC) = $45.05
Fixed costs (FC) = $5,700
Required return = 9%
Initial investment = $13,000
a. Accounting Break-Even Quantity:
Break-Even Quantity = 5,700 / (85 - 45.05) ≈ 197 (rounded to the nearest whole number)
b. Cash Break-Even Quantity:
Break-Even Quantity = (5,700 + 13,000) / (85 - 45.05) ≈ 143 (rounded to the nearest whole number)
c. Financial Break-Even Quantity:
Break-Even Quantity = (5,700 + 13,000) / (85 - 45.05) * (1 + 0.09) ≈ 215 (rounded to the nearest whole number)
d. Degree of Operating Leverage:
Contribution Margin = Price - Variable Costs = 85 - 45.05 = 39.95
Net Operating Income at financial break-even level = 0 (since it is the break-even point)
Degree of Operating Leverage = Contribution Margin / Net Operating Income = 39.95 / 0 = undefined (division by zero)
Therefore, the degree of operating leverage at the financial break-even level of output is undefined, as there is no net operating income at the break-even point.