doing math

courses › Business Math

Operator I: Read Greenline

level 40 course

Work out Greenline's profit, three possible moves, and a cash squeeze, one case card at a time.

Pen and paper is fine · no calculator needed why?

Learn first (about 3 minutes)

Opens at level 40.

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Builds on: Break-Even (not open yet) · Pricing Decisions (not open yet) · Profit Is Not Cash (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

Greenline is a made-up office-plant care business. In its base month, 40 customers each pay $500 and each costs $200 to serve; fixed expenses are $6,000. Each customer contributes $300, so contribution is $12,000 and operating profit is $6,000.

Every scenario runs through the same line: customers × (price − variable cost) − fixed costs. Change only what the scenario changes, and compare the result with the base month.

Profit is not cash. Revenue a customer has not paid yet counts in profit, but it sits in receivables until it is collected.

Techniques

Same line, new inputs

A price change, a discount, a hire or a change in customers.

  1. Contribution per customer: the scenario's price minus variable cost.
  2. Multiply by the customers the scenario gives, not today's count.
  3. Subtract the fixed costs, plus any hire, once.
  4. Compare with the base profit, not with revenue.
worked example

Example: A cleaning business has 30 customers at $400 a month, $150 variable cost each, $5,000 fixed. Scenario: price rises to $450 and 28 customers stay; costs don't change. What is operating profit?

  1. 28 × ($450 − $150) = 28 × $300 = $8,400.
  2. $8,400 − $5,000 = $3,400.
  3. Today's profit: 30 × $250 − $5,000 = $2,500.

Answer: $3,400

Follow the cash

Not every dollar of revenue was collected.

  1. Start from the opening cash.
  2. Add only the cash actually collected.
  3. Subtract the costs actually paid.
worked example

Example: A cleaning business opens the month with $4,000 of cash. It earns $12,000 of revenue but collects only $9,000, and pays all $9,500 of its costs. What is ending cash?

  1. $4,000 + $9,000 − $9,500 = $3,500.
  2. Profit is $2,500, but $3,000 is still owed by customers.

Answer: $3,500

Tips by skill

  • TipBase month operating profit: Customers × (price − variable cost) is contribution. Subtract the fixed expenses; use a minus sign for a loss.
  • TipScenario: raise the price: Use the new price and only the customers who stay. The cost per customer and the fixed costs stay the same.
  • TipScenario: discount to grow: Every customer pays the lower price, old and new. Then subtract variable and fixed costs as usual.
  • TipScenario: hire and grow: Contribution per customer stays the same. Add the coordinator to the fixed costs once, then subtract.
  • TipCash stress test: Opening cash plus what was actually collected minus what was paid. Uncollected revenue is not cash yet.

Watch out for

  • Stopping at contribution. Greenline's $12,000 comes before the $6,000 of fixed expenses.
  • Assuming every customer stays at the new price, or that extra revenue is extra profit.
  • Forgetting the hire, or counting it twice. Add it to fixed costs once.
  • Adding the whole profit to opening cash when some revenue was not collected.

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

your rounds

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