doing math

courses › Business Math

Fixed, Variable & Step Costs

level 13 course

How each cost moves when the business gets busier.

In your head, jot if needed · no calculator why?

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Builds on: Solve for the Unknown (not open yet)

the lesson

The idea, the techniques and a tip for each skill, right here. The Learn page adds worked examples for every skill and untimed practice.

Read the lesson · about 3 minutes

The idea

Costs are sorted by how the total moves when the business gets busier over the next few months, not by how often the bill arrives.

A fixed cost stays flat: rent. A variable cost moves with every unit: flour for each loaf. A mixed cost is a flat fee plus a charge per unit: a phone plan with a monthly fee and a charge per minute. A step cost stays flat until capacity runs out, then jumps by a whole chunk: one more van, one more supervisor.

Techniques

Ask what one more unit does

Naming how a cost behaves.

  1. Picture the business doing one more unit of work.
  2. Nothing changes: fixed. A little more every time: variable.
  3. A flat fee plus a charge per unit: mixed.
  4. Nothing until a limit, then a whole chunk: step.
worked example

Example: A bakery pays $2,000 rent a month and $0.40 of flour for each loaf. How much do these two costs rise if it bakes 500 more loaves this month?

  1. Rent is fixed, so it does not move.
  2. Flour is variable: $0.40 × 500 = $200.

Answer: $200

Split a mixed bill

A bill is a monthly fee plus a charge per unit.

  1. The flat monthly fee is the fixed part.
  2. Rate × activity is the variable part.
  3. The total bill is the two added together. Answer only the part asked for.
worked example

Example: A delivery contract costs $150 per month plus $4 per stop. Last month had 300 stops. How much of last month's bill was variable?

  1. Variable: $4 × 300 = $1,200.
  2. The $150 fee is the fixed part; the whole bill was $1,350.

Answer: $1,200

Round step costs up

Each van, oven or person can handle only so much.

  1. Divide the demand by what one can handle.
  2. Any remainder needs one more: round up.
  3. Check: one fewer would leave some work uncovered.
worked example

Example: One van can handle at most 40 deliveries a day. How many vans are needed for 130 deliveries a day?

  1. 130 ÷ 40 = 3.25.
  2. 3 vans cover only 120 deliveries, so round up to 4.

Answer: 4

Tips by skill

  • TipSplit a mixed cost: The flat monthly fee is fixed, rate × activity is variable, and the bill is both. Answer only the part asked.
  • TipClassify the cost: How does the total move with activity? Flat: fixed. With each unit: variable. Fee plus per-unit: mixed. Flat, then a jump: step.
  • TipStep costs: how many do you need?: Divide the demand by what one can handle, then round up to a whole number. Part of a van or a person will not do.
  • TipTotal cost at a volume: Total cost is the fixed costs plus the variable cost per unit × the volume. Keep the fixed part in.

Watch out for

  • Calling a bill fixed because it arrives every month. Behavior is about how the total moves with activity.
  • Leaving the fixed fee out of the total bill, or putting it into the variable part.
  • Rounding a step cost down. 130 deliveries need 4 vans; 3 would leave 10 deliveries with no van.

skills · practice stats

From rounds of this course only: box, review and test-out answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

  1. 1 day
  2. 3 days
  3. 7 days
  4. 14 days
  5. 30 days
  6. 60 days
  7. mastered · every 90 days

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