Finding Unit Sales

Dear Professor Cram:

When annual sales, variable cost, contribution margin, fixed costs, and operating income are all known, how can the number of units be determined?

Elias, Baker College

The categories you mention are actually more information than is required, but that is not unusual in word problem assignments. I am going to show how to do it using my own example, since you didn't give me a specific problem to solve. (This way I can use nice round numbers that I know won't get hung up on long division.) Here is my example – let's say:

• annual sales are \$1,000,000
• variable cost is \$100 per unit
• contribution margin is 50%
• fixed costs are \$100,000
• operating income is \$400,000

With sales of \$1,000,000 and operating income of \$400,000, operating expenses had to be \$600,000. Since we know \$100,000 of those expenses were fixed costs, the balance of \$500,000 in operating expenses had to be variable costs. These came at a rate of \$100 per unit, so we sold 5,000 units. Just that simple!

Are we really there yet? Do the rest of the numbers work? We haven't used the contribution margin, have we? Let's check that. I think we need the selling price. We had \$1,000,000 in sales and we said that was from 5,000 units, so there must have been a selling price of \$200 each. Variable cost was \$100, leaving a contribution margin of 50%. Well OK, then…

I hope this helps. Let us know if you need anything else.

Good Studying,

Professor Cram