Break-even and target profit

The break-even point is the volume at which total contribution exactly covers fixed costs, so profit is zero.

> Break-even units = fixed costs ÷ contribution per unit > Break-even revenue = fixed costs ÷ contribution margin ratio

Because you can't sell part of a unit, always round break-even units up: at 3,333 units a business is still a few pounds short; at 3,334 it has crossed the line.

Target profit. To earn a target profit, contribution must cover fixed costs and the target:

> Units for target profit = (fixed costs + target profit) ÷ contribution per unit

If the target is stated after tax, gross it up first: pre-tax target = after-tax target ÷ (1 − tax rate). A 36,000 after-tax target at a 20% tax rate needs 45,000 before tax.

Margin of safety is how far sales can fall before the business makes a loss: - in units: budgeted (or actual) sales − break-even sales; - as a percentage: margin of safety ÷ budgeted sales.

A thin margin of safety means a small shortfall wipes out profit.

Comparing cost structures. Automating usually swaps variable cost for fixed cost. The indifference point is the volume where both structures give the same profit: set the two profit equations equal, or divide the extra fixed cost by the saving in variable cost per unit. Below it the low-fixed-cost structure is better; above it, the automated one wins.

More than one product. With several products, use a weighted-average contribution based on the expected sales mix (or a weighted CM ratio for revenue). Suppose Fennick also sold floor lamps with a contribution of 50, three desk lamps for every floor lamp, and total fixed costs of 140,000: the weighted contribution is (3 × 30 + 1 × 50) ÷ 4 = 35 a lamp, so break-even is 140,000 ÷ 35 = 4,000 lamps — 3,000 desk and 1,000 floor. The result holds only while the mix holds: if the mix shifted to four desk lamps per floor lamp, the weighted contribution would fall to 34 and break-even would rise to 4,118 lamps, even with no change in any price or cost.