Courses · Business Mathematics · Week 4

Break-Even Analysis

Week 4 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.

Every morning your truck opens the window already in the hole. Break-even is the number of customers it takes to climb out, and you can know it before the first burger hits the grill.

Learning objectives. After this week you can (1) build your day's fixed block and compute the break-even quantity; (2) turn it into break-even revenue; and (3) predict which way break-even moves when a price, a cost or a district changes.

Remember this: break-even = fixed costs ÷ contribution. Always round up.

1) The idea

Break-even Quantity = Fixed Costs ÷ Contribution Margin per unit

Fixed costs $600, contribution $5.00: 600 ÷ 5 = 120 units. At 120, profit is exactly $0. The 121st unit is your first dollar of profit. The fixed costs are the same on a slow day and a busy one; only the sales change.

2) Break-even in dollars

Break-even Revenue = Break-even Units × Price

120 units at $8.50 = $1,020. Units are what you count at the window; dollars are what you compare with the revenue line on your Daily Report.

3) What moves it

Bigger contribution → lower break-even. More fixed cost → higher break-even.

Keep the $600 but raise the contribution to $6.00, with a higher price or a cheaper unit cost, and break-even falls to 600 ÷ 6 = 100 units. Push fixed costs to $800 while contribution slips to $4.00, and it jumps to 800 ÷ 4 = 200 units.

4) Your real fixed block, district by district

Fixed Block = $25 overhead + $25 admin + $25 permits + district fee + (Staff × $200 × 45%)

That last piece is the committed part of wages, $90 per staffer. A Downtown day with three staff carries a fixed block of $25 + $25 + $25 + $120 + $270 = $465.

DistrictDaily feeFixed block (3 staff)Break-even at $5.30
University District$35$38072 units
City Park$45$39074 units
Farmers Market$80$42581 units
Downtown$120$46588 units
Waterfront$210$555105 units

Parking at the Waterfront instead of the University District costs you an extra 33 customers before you earn anything. Whether its crowd pays that back is something only your own reports can show you.

Try it

Wednesday's fixed costs came to $120 and you fielded 4 crew. The committed part of the wage budget is owed whether or not anything sells, so it belongs in the block you have to cover.

Fixed block = Fixed costs + (Staff × $200 × 45%)

Fill in the boxes.

Worked example 1: a go/no-go test before you open

Opening at the Waterfront with three staff means a fixed block of $555. You plan a $9.50 burger against a $3.20 cost, so contribution is $6.30 and break-even is 555 ÷ 6.30 ≈ 88.1, so 89 burgers. Now check the crowd. If your past days there sold about 60 burgers, the day cannot clear 89 as planned. Something has to change first: the price, the corner or the block. Break-even is half the test; the other half is whether the customers show up.

Try it

A $638.62 block to cover, and each burger contributes $9.30 toward it.

Break-even units = Fixed block ÷ Contribution margin

Fill in the boxes.

Quick self-check

Fixed costs $726, contribution $6.60. (a) Break-even units? (b) At a $9.90 price, break-even revenue? (c) You sold 95 units. Profit or loss? (Answers: 110; 110 × $9.90 = $1,089; a loss: 15 units short, so 15 × $6.60 = $99 in the red.)

Common mistakes

  • Dividing by the price. Divide by the contribution (price − unit cost), not the price.
  • Leaving pieces out of the block. The district fee and the committed wages both belong in it.
  • Rounding down. 87.7 burgers means you need 88. A fraction of a sale does not clear the day.

This week in the arena

Before you open one day this week, write down your fixed block, your hero item's contribution margin and your break-even. After the close, open the Daily Report and compare: did you clear it? If not, was the miss in the crowd that showed up, or in your arithmetic?

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.