Question

North Pole Toys needs to decide on their newest product line for Christmas. They narrowed their options to two possibilities: Product A would incur a fixed cost of $3,000 and a variable cost of $6 per unit and sells for $7.50; Product B would incur a fixed cost of $1,200 and a variable cost of $9 per unit and sells for $10.

A. What is the break-even point for each of the two products?
B. What is the point of indifference between the two products?

Answer 1

A-1. Product A break-even point = 2,000 units

A.2. Product A break-even point = 1,200 units

B. Point of indifference between the two products = 600 units

Step-by-step explanation:

A. What is the break-even point for each of the two products?

Break-even point which is the point at which the total cost of production of a product is equal to the total revenue of the product can be calculated using the following formula:

Break-even point = Fixed cost / (Selling price per unit - Variable cost per unit) ........ (1)

Using equation (1), we have:

A-1. Product A break-even point = $3,000 / ($7.50 - $6) = 2,000 units

A.2. Product A break-even point = $1,200 / ($10 - $9) = 1,200 units

B. What is the point of indifference between the two products?

Point of indifference between the two products which is the point at which the total costs of the two products are the same can be calculated as follows:

Differential fixed cost = Product A fixed cost - Product B fixed cost = $3,000 - $1,200 = $1,800

Differential variable cost per unit = Product B fixed cost variable cost per unit - Product A variable cost per unit = $9 - $6 = $3

Point of indifference between the two products = Differential fixed cost / Differential variable cost per unit = $1,800 / $3 = 600 units

Note: To obtain any of the two differentials, the lower must be deducted from the higher as done above.