Morris Industries' total variable costs are $215 per unit sold. They need to sell 1200 units to break even, generating $30,000 in revenue.
Morris Industries manufactures and sells three products (AA, BB, and CC). The sales price and unit variable cost for the three products are as follows:
| Product | Sales price per unit | Unit variable cost |
| AA | $50 | $30 |
| BB | $40 | $15 |
| CC | $30 | $10 |
Their sales mix is reflected as a ratio of 5:3:2. Annual fixed costs shared by the three products are $258,000 per year.
A. What are total variable costs for Morris with their current product mix?
Total variable costs are the sum of the variable costs for each product, multiplied by the number of units of each product sold. Given the sales mix ratio of 5:3:2, the total variable costs can be calculated as follows:
Total variable cost = (Variable cost per unit of AA) * (Units sold of AA) + (Variable cost per unit of BB) * (Units sold of BB) + (Variable cost per unit of CC) * (Units sold of CC)
Total variable cost = ($30/unit) * (5/10) * (Total units) + ($15/unit) * (3/10) * (Total units) + ($10/unit) * (2/10) * (Total units)
Total variable cost = ($150/10) * (Total units) + ($45/10) * (Total units) + ($20/10) * (Total units)
Total variable cost = $215 * (Total units)
B. Calculate the number of units of each product that will need to be sold in order for Morris to break even.
The break-even point is the point at which total revenue equals total costs. In other words, it is the number of units of each product that must be sold to cover all fixed and variable costs.
To calculate the break-even point, we can set the total revenue equal to the total costs and solve for the total number of units.
Total revenue = Total costs
(Sales price per unit of AA) * (Units sold of AA) + (Sales price per unit of BB) * (Units sold of BB) + (Sales price per unit of CC) * (Units sold of CC) = Fixed costs + Total variable cost
($50/unit) * (5/10) * (Total units) + ($40/unit) * (3/10) * (Total units) + ($30/unit) * (2/10) * (Total units) = $258,000 + ($215 * Total units)
($250/10) * (Total units) + ($120/10) * (Total units) + ($60/10) * (Total units) = $258,000 + ($215 * Total units)
($430/10) * (Total units) = $258,000 + ($215 * Total units)
$43 * (Total units) = $25,800 + ($21.5 * Total units)
$21.5 * (Total units) = $25,800
Total units = 1200
Given the sales mix ratio, the number of units of each product that need to be sold to break even is:
| Product | Units sold to break even |
| AA | 600 |
| BB | 360 |
| CC | 240 |
C. What is their break-even point in sales dollars?
The break-even point in sales dollars is the total revenue at the break-even point.
Break-even point in sales dollars = (Sales price per unit of AA) * (Units sold of AA) + (Sales price per unit of BB) * (Units sold of BB) + (Sales price per unit of CC) * (Units sold of CC)
Break-even point in sales dollars = ($50/unit) * (600 units) + ($40/unit) * (360 units) + ($30/unit) * (240 units)
Break-even point in sales dollars = $3