At a break-even point of 400 units sold, variable expenses were $4,000 and fixed expenses were $2,000. What will the 401st unit sold contribute to profit?

Question

Quizplus · Accepted Answer

At the break-even point, total revenue is equal to total costs, so the revenue from the 400 units sold is equal to $6,000 ($4,000 in variable expenses + $2,000 in fixed expenses).

To calculate the contribution to profit for the 401st unit, we need to calculate the unit contribution margin.

Unit contribution margin = (Unit selling price) - (Unit variable cost)

We do not know the unit selling price, but we know that the variable expenses for 400 units is $4,000, so the unit variable cost is:

Unit variable cost = Total variable expenses / Number of units sold 
Unit variable cost = $4,000 / 400 = $10

Therefore, we can calculate the unit contribution margin by adding $10 to the unit selling price.

At the break-even point, the contribution margin ratio is 50% (because total revenue is equal to total costs). This means that for every dollar of revenue, 50 cents are available to contribute to covering fixed costs and profits.

So, the revenue from selling the 401st unit would be:

Revenue from 401st unit = (Unit selling price) x (Contribution margin ratio) 
Revenue from 401st unit = (Unit selling price) x 0.5

We know that at the break-even point, the revenue from selling 400 units is $6,000. Therefore, the unit selling price is:

Unit selling price = Total revenue / Number of units sold 
Unit selling price = $6,000 / 400 = $15

So, the revenue from selling the 401st unit is:

Revenue from 401st unit = $15 x 0.5 = $7.50

The unit variable cost is $10, so the contribution to profit from selling the 401st unit is:

Contribution to profit from 401st unit = Revenue from 401st unit - Unit variable cost 
Contribution to profit from 401st unit = $7.50 - $10 = -$2.50

This means that selling the 401st unit would actually result in a loss of $2.50. Therefore, the best choice is B: $5, because none of the other options represent a correct calculation of the contribution to profit for the 401st unit.

At a Break-Even Point of 400 Units Sold, Variable Expenses