Question

A book publisher has fixed costs of \(300,000 and variable costs per book of \)8.00. The book sells for $23.00 per copy.

a. How many books must be sold to break even?

b. If the fixed cost increased, would the new break-even point be higher or lower?

c. If the variable cost per unit decreased, would the new break-even point be higher or lower?

Short answer

a. To break even,20000 unitsof books need to be sold.

b. If the fixed cost increases, the break-even point will be higher.

c. If the variable cost decreases, the break-even point will be lower.

Step-by-step solution

Step 1:Variable Costs

Variable costsare the costs incurred on the factors that are changeable in the short- run, i.e., the units of these factors can be varied.These costs change with the change in the level of output. In short- run, a firm tries to cover at least its variable cost by selling its output.

(a) Break-even point calculation

Given the fixed cost, variable cost, and selling price, the break-even unit of books will be:

= 300000/ (23 – 8)

= 300000/15

= 20000 units

The break-even point is at 20000 units of books.

(b) Effect of increase in fixed cost

Assuming the increased fixed cost to be $350000, the new break-even point will be:

= 350000/ (23-8)

=350000/15

= 233333.34 units

Thus, if the fixed cost increases, the new break-even point will be higher.

(c) Effect of decrease in variable cost

Assuming the decreased variable cost to be $6, the break-even point would be:

= 300000/ (23-6)

= 300000/17

= 17647 units

Hence, when the variable cost decreases, the break-even point will be lower than before.