Business Math 101

I often hear people complain that Company X must be making a profit simply because of the amount that the company is charging for a particular item.

Here’s why that’s not necessarily the case.

The production of a type of item typically involves costs of two types:

  • Fixed costs — These are one-time costs that are the same no matter how many of an item are produced. For something like a collectible toy, this includes design, sculpting, tooling, etc.
  • Variable costs — These are costs that apply for each unit produced. Variable costs include such things as the price of the materials used to make the item, the cost of paint, packaging, etc.

In this blog I’ll demonstrate by example how it’s possible that an item that is sold for ten times the variable cost to produce the item can result in one of five scenarios:

  1. Losing money — Yes, it’s possible to lose money with each item sold!
  2. Breaking even — Neither losing money nor profiting. It’s good that our investors aren’t losing money, but what’s the point in investing money if you don’t earn a profit while doing so?
  3. Profiting but failing to meet expectations — This scenario also isn’t desirable, because our investors could be investing in something else that earns them more money per dollar invested.
  4. Profiting and meeting expectations — The profit earned exactly matches what was expected. This is good.
  5. Profiting and exceeding expectations — Our investors are making even more money than they expected to make. On a scale from 1 to Awesome, this is Super Great!

In this example we’ll keep things simple by assuming that every item produced is sold — in other words, that there are no unsold items. From market research Company X expects to sell 15,000 of an item with fixed costs of $550,000 and variable costs of $5 for each item sold. The item will be sold for $50. The expected net profit — that is, the profit after taxes, is only 10%.

Measure Scenario 1:
Losing Money
Scenario 2:
Breaking Even
Scenario 3:
Profiting But Failing to Meet Expectations
Scenario 4:
Profiting and Meeting Expectations
Scenario 5:
Profiting and Exceeding Expectations
Fixed Costs $550,000 $550,000 $550,000 $550,000 $550,000
Variable Costs (per item sold) $5 $5 $5 $5 $5
Sale Price (Note: The item is being sold for ten times the variable cost to produce that item!) $50 $50 $50 $50 $50
Number of Items Sold 11,250 12,223 13,500 15,000 16,500
% of Expected Items Sold 75% 81% 90% 100% 110%
Sales Revenue (Number of Items Sold, multiplied by Sale Price) $562,500 $611,150 $675,000 $750,000 $825,000
Total Cost of Items Sold (Fixed Costs + Variable Costs multiplied by Number of Items Sold) $606,250 $611,115 $617,500 $625,000 $632,000
Gross Profit (Sales Revenue minus Total Cost of Items Sold) $(43,750)
(Loss of nearly $44,000!)
$35(Essentially $0) $57,500 $125,000 $192,500
Gross Profit Margin (Gross Profit divided by Sales Revenue) -7%
(Before taxes for every dollar of revenue, there is a loss of 7 cents!)
0% 9%
(Before taxes for every dollar of revenue there is a profit of 9 cents)
20% 30%
Tax (Assumption: 40% of Gross Profit) $(17,500)
(Note: In the real world, a company doesn’t get money back from the government for losing money.)
(Essentially $0)
$23,000 $50,000 $77,000
Net Profit (Gross Profit minus Tax) $(26,250) $21
(Essentially $0)
$34,500 $75,000 $115,500
Net Profit Margin (Net Profit divided by Sales Revenue) -5% 0% 5% 10% 14%
Net Profit per Unit Sold (Net Profit divided by Number of Items Sold) $(2.33) $0 $2.56 $5.00
(Note: In this case the profit from an item sold for ten times its variable costs happens to be equal to its variable costs! That’s only $5 in net profit for every $50 item sold!)

Note that:

  • Selling just 3,277 fewer items than expected results in Company X just breaking even.
  • In the scenario in which profits meet expectations, the net profit is only 10%, meaning that after taxes, each dollar in sales results in only 10 cents of profit.
  • In the scenario in which the company loses money, it loses $2.33 for each $50 item sold.