Question

A project has the following estimated data: price = $85 per unit; variable costs = $45.05 per unit; fixed costs = $5,700; required return = 9 percent; initial investment = $13,000; life = six years. Ignore the effect of taxes.

a. What is the accounting break-even quantity?
197
143
236
217
187
b. What is the cash break-even quantity?
143
197
136
114
129
c. What is the financial break-even quantity?
215
258
237
194
172
d. What is the degree of operating leverage at the financial break-even level of output?
2.9669
1.9606
1.7347
1.2822

Answer 1

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.