XYZ Inc. has a project with an accounting break-even quantity of 28,700 units, a life of 4 years. The fixed production costs are $178,000 and variable costs are $18.40 per unit. The project needs an investment of $500,000 in equipment which will be depreciated straight-line to zero over the life of the project. The equipment will be worthless in 4 years. No working capital investment will be required for the project. If the required return is 14 percent, and there are no taxes, what is the financial break-even quantity?

 

Answer:

Financial break-even quantity = 33115 Units

Step-by-step explanation

Annual Depreciation = Equipment Cost/Useful life

Annual Depreciation = 500000/4

Annual Depreciation = 125000

Contribution Margin per unit = (Fixed Cost+ Annual Depreciation)/Accounting break-even quantity

Contribution Margin per unit = (178000+125000)/28700

Contribution Margin per unit = 10.5575

Financial Break Even Annual Cash Flow = Initial Investment/((1-1/(1+r)^n)/r)

Financial Break Even Annual Cash Flow = 500000/((1-1/(1+14%)^4)/14%)

Financial Break Even Annual Cash Flow = 171602.39

In case there is no taxes

Financial break-even quantity = (Financial Break Even Annual Cash Flow + fixed production costs)/Contribution Margin per unit

Financial break-even quantity = (171602.39+178000)/10.5575

Financial break-even quantity = 33114.15

Financial break-even quantity = 33115 (rounded up)