# Financial break-even? i get how to do a normal break-even, but what do i do with the tax and discount rate?

L.J.'s Toys Inc. just purchased a \$390,000 machine to produce toy cars. The machine will be fully depreciated by the straight line method over its five-year economic life. Each toy sells for \$25. The variable cost per toy is \$11, and the firm incurs fixed costs of \$280,000 each year. The corporate tax rate for the company is 34 percent. The appropriate discount rate is 12 percent. What is the financial break-even point for the project?

I get how to do the financial break-even without the tax and discount rate, but I am just unclear what to do with those? Mostly the discount rate.

I believe it would look something like this:

(Fixed Costs+Depreciation)/(Unit Price-Unit Variable Cost)(1-tax rate)

(280000+78000)/(25-11)(1-.34)

358000/14(.66)

358000/9.24

38,744.59

But where do i throw in the discount rate? and is that the right way to use the tax rate? Thank you so much for your help!

Relevance

EAC = \$390,000 / 3.60478*

EAC = \$108,189.80

PVA = C ({1 – [1/(1 + R)] t} / R)

\$390,000 = C {[1 – (1/1.12)^5] / 12%}

C = \$108,189.80

Annual depreciation = \$390,000 / 5 = \$78,000

QF = [EAC + FC(1 – tC) – D(tC)] / [(P – VC)(1 – tC)]

QF = [\$108,189.80 + \$280,000 (1 – 34%) – \$78,000 (34%)] / [(\$25 – 11)(1 – 34%)]

QF = 28,838.72 or 28,839 units

*[1 - (1 / 1 + 12%)^5] /12% = 3.60478

• Assuming fixed cost of 280,000 includes depreciation, break even in units will be 280,000 / 14, or 20,000 units, or sales of \$500,000. At break even, there is no tax, so ignore the 34%.

The discount rate is needed for the NPV, not break even sales.