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Pricing Decisions

lesson · about 3 minutes

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?

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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.

  1. New price: take the discount off the price.
  2. New contribution: new price minus variable cost.
  3. 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.

  1. Old contribution: $50 − $30 = $20.
  2. At the new $45 price: $45 − $30 = $15.
  3. $20 ÷ $15 ≈ 1.333, a rise of about 33.3%.

Answer: 33.3%

Customers you must keep

A price rise raises contribution per customer.

  1. Total contribution now: customers × contribution each.
  2. Divide by the new contribution per customer.
  3. 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?

  1. $6,000 ÷ $260 ≈ 23.08.
  2. Round up to 24: 23 customers bring only $5,980.

Answer: 24

Compare on profit, or per hour

Choosing between options or jobs.

  1. For each option: units × (price − variable cost) − fixed costs.
  2. When hours are the limit, divide each job's contribution by its scarce hours instead.
  3. 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?

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

Answer: $400

watch out for

practice

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Contribution after a discount

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

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

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

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?

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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