Courses · Business Mathematics · Week 3

Gross & Contribution Margin

Week 3 of Business Mathematics, a fifteen-week course taught through Food Truck Wars, a live business simulation. Free to read; the practice boxes check your arithmetic as you go.

Last week your $8.50 burger had a 166% markup. This week the very same burger has a 62% margin. Neither number is lying: they just divide by different things.

Learning objectives. After this week you can (1) compute gross margin as a percent of price; (2) compute contribution margin in dollars and count the sales it takes to cover your fixed costs; and (3) turn a target margin into the most an item can cost.

Remember this: markup divides by cost, margin divides by price, and contribution stays in dollars.

1) Gross margin: a percent of price

Gross Margin % = (Price − Unit Cost) ÷ Price × 100

The $8.50 burger costing $3.20: 5.30 ÷ 8.50 ≈ 62%. Same $5.30 gap as last week's 166% markup, but margin divides by the price, the bigger number, so margin is always the smaller percent. If the price rises and the cost does not, the margin rises.

Try it

Your burger costs $3.20 and you charge $12.50.

Gross margin % = (Price − Cost) ÷ Price × 100

Fill in the boxes.

2) Contribution margin: dollars per unit

Contribution Margin = Price − Variable Cost per unit

$8.50 − $3.20 = $5.30 per burger. Each sale contributes that much toward your fixed costs first: overhead, admin, permits, the district fee and the committed part of wages. Once they are covered, every further $5.30 is profit. Opening Downtown with three staff carries a fixed block of $465. At $5.30 a burger that is 465 ÷ 5.30 ≈ 87.7, so 88 burgers before you earn a cent. Always round a hurdle up.

3) Margin vs. markup, side by side

MeasureDivide $5.30 by…ResultAnswers
MarkupCost ($3.20)166%how much I added on top of cost
Gross marginPrice ($8.50)62%what share of the sale I kept
Contribution marginnothing, it stays in dollars$5.30what one sale puts toward fixed costs

One gap, three readings. A "60% markup" and a "60% margin" are very different prices.

4) Target margin: turning a goal into a cost ceiling

Max Unit Cost = Price × (1 − Target Margin)

Want a 65% margin on a $10.00 item? The margin takes 65% of the price, so the cost gets the other 35%: $10.00 × 0.35 = $3.50. Any more than that and the margin slips below your goal.

Try it

You want to hold a 55% margin at a $12.50 price. How dear can the ingredients get?

Highest cost = Price × (1 − Margin)

Fill in the boxes.

Quick self-check

Price $12.00, cost $4.20. (a) Gross margin? (b) Contribution margin? (c) How many sales cover a $500 fixed block? (Answers: 7.80 ÷ 12.00 = 65%; $7.80; 500 ÷ 7.80 ≈ 64.1, so 65 sales.)

Common mistakes

  • Dividing by cost and calling it margin. That is markup. Margin divides by price.
  • Subtracting fixed costs to get contribution. Contribution uses variable cost only.
  • Ranking items by margin percent. The dollars each sale brings in are what pay for the day.

This week in the arena

Work out your hero item's gross margin and contribution margin from the decision form. Then divide your fixed block for one day by that contribution: that is how many hero sales the day needed. Check your last few Daily Reports. Which days cleared the number, and by how much?

In the course, the reading is where the week starts

Students who take Business Mathematics on Extrapoli run a business in Food Truck Wars all term. Each week pairs this reading with a quiz and a two-part assignment worked from the numbers their own team produced in the simulation, and the numbers are graded automatically against the simulation that team actually ran.