courses › Business Math

Pricing Decisions

level 18 course

What a discount must earn back, who you can lose after a price rise, and bottleneck hours.

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

Opens at level 18.

Builds on: Break-Even (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 discount comes straight out of contribution, since each sale's variable cost stays the same. At a $100 price and $60 variable cost, a 10% discount cuts contribution from $40 to $30, so sales must rise by a third to earn the same total.

After a price rise, you can lose some customers and still keep total contribution; that count is a limit, not a forecast. When hours are the bottleneck, rank jobs by contribution per scarce hour. The most revenue is not always the most profit.

Techniques

Take the discount out of contribution

A discount, and the extra sales it needs.

New price: take the discount off the price.
New contribution: new price minus variable cost.
To keep total contribution, sales must rise by old ÷ new contribution, minus 1.

worked example

Example: Price is $50 and variable cost is $30. After a 10% discount, by what percentage must sales volume rise to keep the same total contribution? Round to one decimal place.

Old contribution: $50 − $30 = $20.
At the new $45 price: $45 − $30 = $15.
$20 ÷ $15 ≈ 1.333, a rise of about 33.3%.

Answer: 33.3%

Customers you must keep

A price rise raises contribution per customer.

Total contribution now: customers × contribution each.
Divide by the new contribution per customer.
Round up: that many must stay.

worked example

Example: 30 customers each contribute $200. A price rise would lift that to $260 each. How many whole customers must stay to keep at least $6,000 of contribution?

$6,000 ÷ $260 ≈ 23.08.
Round up to 24: 23 customers bring only $5,980.

Answer: 24

Compare on profit, or per hour

Choosing between options or jobs.

For each option: units × (price − variable cost) − fixed costs.
When hours are the limit, divide each job's contribution by its scarce hours instead.
Pick the highest, not the most revenue or the biggest total.

worked example

Example: Price $40, variable cost $25, fixed costs $2,000 a month, 200 units now. Option 1: raise the price to $45 and sell 170 units. By how much does Option 1 raise operating profit?

Now: 200 × ($40 − $25) − $2,000 = $1,000.
Option 1: 170 × ($45 − $25) − $2,000 = $1,400.
Profit rises by $400, even though revenue falls.

Answer: $400

Tips by skill

TipContribution after a discount: Take the discount off the price, then subtract the variable cost.
TipExtra volume a discount needs: Work out contribution per sale before and after the discount. Sales must rise by old ÷ new, minus 1.
TipPrice rise: customers you must keep: Divide the contribution to keep by the new contribution per customer, and round up.
TipContribution per scarce hour: Divide each job's contribution by its scarce hours. The higher rate per hour wins, not the bigger total.
TipWhich price makes the most profit?: For each option work out units × (price − variable cost) − fixed costs. Pick the highest profit.

Watch out for

Taking the discount off the contribution instead of off the price.
Assuming a 10% price cut needs only 10% more sales.
Rounding the customers you must keep down, which falls short of the old total.
Choosing the job with the bigger total, or the option with more revenue.

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.

Contribution after a discount par 14 s not tried yet
worked example
Price is $280 and variable cost is $125. A 5% price discount is offered. What is the new contribution per sale?

Answer: $141.00
1. New price = $280 × 0.95 = $266; contribution = $266 − $125 = $141, down from $155.
2. The whole $14 discount comes out of contribution.
Extra volume a discount needs par 24 s not tried yet
worked example
Price is $300 and variable cost is $240. After a 5% discount, by what percentage must sales volume rise to keep the same total contribution? Round to one decimal place if needed.

Answer: 33.3%
1. Contribution per sale falls from $300 − $240 = $60 to $285 − $240 = $45.
2. Volume must rise by $60 ÷ $45 − 1 ≈ 33.3%.
Price rise: customers you must keep par 21 s not tried yet
worked example
98 customers each contribute $470. A price increase would raise contribution to $560 per customer. What is the minimum whole number of customers needed to keep at least $46,060 of contribution?

Answer: 83
1. $46,060 ÷ $560 = 82.25; round up to 83.
2. This is a threshold, not a forecast of how many will stay.
Contribution per scarce hour par 17 s not tried yet
worked example
Job A contributes $620 in 4 scarce work hours. Job B contributes $1,400 in 7 scarce work hours. Which earns more contribution per scarce hour?
1. Job B
2. They are equal
3. Job A
4. You need the selling prices to decide
Answer: Job B
1. Per hour: A = $620 ÷ 4 = $155; B = $1,400 ÷ 7 = $200.
2. When hours are the limit, rank jobs by contribution per scarce hour (assuming there's enough demand).
Which price makes the most profit? par 45 s not tried yet
worked example
Price $85, variable cost $38 per unit, fixed costs $12,000 a month, 455 units a month now, capacity 590 units. Option 1: raise the price to $92 and sell 410 units. Option 2: cut the price to $80 and sell 554 units. Which gives the highest monthly operating profit?
1. Option 1 (raise price)
2. All three are equal
3. Keep the current price
4. Option 2 (cut price)
Answer: Option 2 (cut price)
1. Profit = units × (price − variable) − fixed: now $9,385, Option 1 $10,140, Option 2 $11,268.

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