Question

Royale Aluminum desires an after-tax income of $500,000. It has fixed costs of $2,500,000, a unit sales price of $300, and unit variable costs of $150, and is in the 40% tax bracket.

Required:

1.) What is the break-even point in units?

2.) What is the break-even point in dollars?

3.) How many units needed to earn $500,000 net operating income when no income tax existed?

4.) What amount of pre-tax income is needed to earn an after-tax income of $500,000?

Answer 1

Contribution margin per unit = Selling price per unit - Variable costs per unit

= $300 - $150

= $150

Contribution margin ratio = Contribution margin per unit / Selling price per unit

= $150 / $300

= 0.5

1. Break-even point in units = Fixed costs / Contribution margin per unit

= $2,500,000 / $150

= 16,667

2. Break-even point in dollars = Fixed costs / Contribution margin ratio

= $2,500,000 / 0.5

= $5,000,000

3. Units to be sold = (Fixed costs + Desired operating income) / Contribution margin per unit

= ($2,500,000 + $500,000) / $150

= 20,000

4. Pretax income = $500,000 / (1-0.4)

= $833,333