Question

Consider a project with the following data: accounting break-even quantity = 5,500 units; cash break-even quantity 5,000 units; life -eight years; fixed costs $140,000; variable costs $22 per unit; required return 12 percent. Ignoring the effect of taxes, find the financial break-even quantity. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Break-even quantity

Answer 1

Part 1 : Cash break-even quantity is calculated as follows:

Cash break-even quantity = Fixed cost / ( Price - variable cost per unit)

5000 = 140000 / ( price - 22)

Price - 22 = 140000 / 5000

Price = 50 per unit

Part 2 : Accounting break-even quantity = (Fixed Costs + Depreciation) / (Unit Price - Variable Cost Per Unit)

5500 = ( 140000 + Depreciation ) / ( 50 - 22)

140000 + depreciation = 5500 * 28

Depreciation = 14000

Part 3. Assuming straight line depreciation.for a period of 8 years.

Value of the initial investment = 14000 * 8

Value of the initial investment = 112000

At financial break-even point, NPV is zer.

Therefore, PV of the operating cash flow must be equal to the initial investment

112000 = OCF*PVIFA(12%,8)

112000 = OCF * [ 1 - ( 1+ r)^-n ] / r

112000 = OCF * [ 1 - ( 1+ 0.12)^-8 ] / 0.12

112000 = OCF * 4.96764

OCF = 112000 / 4.96764

OCF = 22545.92

Therefore, Break-even level of OCF = 22545.92

We know

Break-even level of OCF = (Unit Price - Variable cost) * Break-even Level of Quantity - Fixed Costs

22545.92 = ( 50 - 22 ) * Break even level of quantity - 140000

Breakeven level of quantity = ( 22545.92 + 140000 ) / 28

Breakeven level of quantity = 5805.21

Break-even quantity 5805.21