courses › Business Math

Operator II: Make the Call

level 46 course

Limits, thresholds, reserves, equity, and which move the numbers actually support.

Pen and paper is fine · no calculator needed why?

Opens at level 46.

Builds on: Operator I: Read Greenline (not open yet) · Runway & Scenarios (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

A threshold says how many customers a move needs, or can afford to lose. It is a limit, not a forecast. Round up the count that must stay, so the count that can leave comes out smaller.

Cash is a separate test: ending cash must not fall below the business's own reserve, even in a profitable month. Equity grows by profit less payouts to the owner, whether or not the cash came in. To pick a move, compare operating profits, not revenue.

Techniques

Keep enough, then subtract

A price rise, and how many customers you can lose.

Total contribution now: customers × (price − variable cost).
Divide by the new contribution per customer, and round up: that many must stay.
Subtract that from today's customers.

worked example

Example: A business has 50 customers at $300 a month and $100 variable cost each. If the price rises to $340, what is the most whole customers it can lose and still keep at least its current total contribution?

Now: 50 × ($300 − $100) = $10,000.
$10,000 ÷ ($340 − $100) ≈ 41.67, so keep 42.
50 − 42 = 8.

Answer: 8

Extra customers for a hire

A hire, and the customers needed to keep profit where it is.

Divide the hire's cost by the contribution per customer.
Round up to whole extra customers.
Add today's customers when the question asks for the total.

worked example

Example: A business has 30 customers, each contributing $250 a month, and $5,000 of fixed costs. A coordinator would add $2,200 a month. How many total customers does it need to earn at least its current profit?

$2,200 ÷ $250 = 8.8, so 9 extra.
30 + 9 = 39 customers in all.

Answer: 39

Cash against the reserve

A minimum-cash policy after slow collections.

Ending cash: opening cash plus cash collected minus cash paid.
Subtract the reserve. A minus sign means the cash is short.

worked example

Example: A business opens the month with $6,000 of cash, collects $15,000 and pays $17,000 of costs. Its policy is to keep at least $5,000 in cash. What is ending cash minus the reserve? (Use a minus sign if it's short.)

$6,000 + $15,000 − $17,000 = $4,000.
$4,000 − $5,000 = −$1,000: short by $1,000.

Answer: −$1,000

Tips by skill

TipHow many customers can you lose?: Divide total contribution now by the new contribution per customer and round up: that many must stay. The rest can leave.
TipCustomers the hire needs: Divide the hire cost by contribution per customer and round up for the extra customers. Add today's customers for the total.
TipDoes cash break the reserve?: Opening cash plus collections minus payments gives ending cash. Subtract the reserve; a minus sign means short.
TipEnding equity: Equity grows by profit, not by cash collected: opening equity plus profit minus any distributions.
TipWhich claim do the numbers support?: Work out each operating profit. Pick the claim that names the highest profit and its assumption, not the most revenue.

Watch out for

Rounding the customers you keep down, which lets one too many leave.
Giving only the extra customers when the question asks for the total.
Adding profit to opening cash as if every dollar had been collected.
Treating equity as the cash balance. Equity grows by profit, including revenue customers have not paid yet.

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.

How many customers can you lose? par 40 s not tried yet
worked example
Fernhill Pest Control (a made-up pest control service): 25 customers at $700 a month, $270 variable cost per customer. If the price rises to $800, what is the largest whole number of customers Fernhill Pest Control can lose and still keep at least its current total contribution?

Answer: 4
1. Current contribution 25 × $430 = $10,750; each customer would contribute $800 − $270 = $530.
2. $10,750 ÷ $530 ≈ 20.28, so keep 21 and lose at most 4. That's a limit, not a prediction of who leaves.
Customers the hire needs par 40 s not tried yet
worked example
Fernhill Pest Control (a made-up pest control service): 56 customers at $400 a month, $150 variable cost per customer, $10,000 fixed. A coordinator would add $2,000 a month of fixed cost. How many total customers does Fernhill Pest Control need to earn at least its current profit?

Answer: 64
1. Extra customers = $2,000 ÷ $250 = 8; 56 + 8 = 64.
2. At 64 customers profit is $4,000; at 63 it would be $3,750, below the current $4,000.
Does cash break the reserve? par 50 s not tried yet
worked example
Fernhill Pest Control (a made-up pest control service): 29 customers at $800 a month, $390 variable cost per customer, $11,000 fixed. Opening cash $7,000. Fernhill Pest Control collects only $20,200 of revenue this month and pays all $22,310 of costs. Its policy is to keep at least $6,000 in cash. What is ending cash minus the reserve? (Use a minus sign if it's short.)

Answer: -$1,110.00
1. Ending cash = $7,000 + $20,200 − $22,310 = $4,890; minus the $6,000 reserve = −$1,110.
2. Operating profit for the month is $890, but profit isn't cash.
Ending equity par 30 s not tried yet
worked example
Fernhill Pest Control (a made-up pest control service): 27 customers at $700 a month, $240 variable cost per customer, $5,000 fixed. Fernhill Pest Control opens the month with $19,000 of cash and $19,000 of equity, nothing else. It collects only $13,400 of its $18,900 revenue, pays all costs, and makes no distributions. Using accrual accounting, what is ending equity?

Answer: $26,420.00
1. Equity grows by the month's profit, and there are no distributions: $19,000 + $7,420 = $26,420.
2. Cash is only $20,920 because $5,500 is still owed by customers; cash plus that receivable equals equity.
Which claim do the numbers support? par 60 s not tried yet
worked example
Northstar IT Support (a made-up IT support business): 37 customers at $800 a month, $320 variable cost each, $8,000 fixed. Scenario 1: price $900, 32 customers stay. Scenario 2: price $750, 45 customers. Scenario 3: hire a coordinator for $5,000 a month and grow to 50 customers at $800. Costs don't change except as stated. Which claim do the numbers support?
1. Scenario 3 earns the most profit because its revenue is highest
2. Scenario 1 earns the most profit because it charges the highest price
3. Scenario 2 earns the most operating profit, if customers really grow to 45
4. All three earn the same profit
Answer: Scenario 2 earns the most operating profit, if customers really grow to 45
1. Profits: now $9,760, Scenario 1 $10,560, Scenario 2 $11,350, Scenario 3 $11,000.
2. Highest revenue isn't highest profit: Scenario 3 brings in the most ($40,000).
3. A careful operator would check that demand really grows before cutting prices.

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.

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