Skip to content
Back to Academia

Pricing: how many sales it takes to pay for a discount

03.07Product and positioning
On this page

Early November. The owner of an IELTS prep centre in Almaty has just used the August intake to recalculate how much he can spend on advertising per student, and the price is back on the table. Back in October the marketer showed him that on the full price of the course the centre is 10,000 ₸ more expensive than the language school over three months, nowhere near 30,000 ₸. The owner isn't convinced and still wants to cut the price from 45,000 to 40,000 ₸ a month: "A discount will bring people in, we'll make it up on volume." How many people it has to bring in takes five minutes to work out. The centre's numbers are made up.

An item at 12,000 ₸ with costs of 8,000 ₸ leaves 4,000 ₸ of contribution. With a 10% discount the price is 10,800 ₸ and the contribution 2,800 ₸.
An item at 12,000 ₸ with costs of 8,000 ₸ leaves 4,000 ₸ of contribution. With a 10% discount the price is 10,800 ₸ and the contribution 2,800 ₸.

The discount comes entirely out of contribution

In the picture the discount took 10% off the price and 30% off the contribution, that is, what is left from a sale after variable costs. The whole 1,200 ₸ came out of contribution, because the costs stayed the same. The smaller the contribution relative to the price, the bigger the share of it the same discount eats.

The same thing happens at the centre. The course costs 45,000 ₸ a month, the teacher and materials come to 29,000 ₸ per student, and the centre keeps 16,000 ₸. The teacher won't accept less because of a discount, so all 5,000 ₸ of it comes out of those 16,000 ₸, leaving 11,000 ₸. For the student the price falls by 11%, for the centre the contribution falls by 31%.

October's 37 students left the centre 592,000 ₸, the same sum the owner saw when he went through the five forces. Here is how many students it takes to keep it at a different price:

Monthly priceKept per studentStudents for 592,000 ₸
48,000 ₸19,000 ₸32
45,000 ₸, current16,000 ₸37
42,000 ₸13,000 ₸46
40,000 ₸11,000 ₸54
35,000 ₸, the language school's price6,000 ₸99

The formula is simple: old contribution per unit divided by new. 16,000 / 11,000 = 1.45, so an 11% discount needs 45% more students. It works the other way too, and the two directions are not mirror images: 3,000 ₸ off the price needs nine more students, while 3,000 ₸ on top lets the centre lose five.

Two more problems. All 37 students get the discount, including the 25 who already pay 45,000 ₸ and never asked for one, so with the same number of students the centre loses 185,000 ₸ a month. And the 17 extra students still have to come from somewhere: there are two trial lessons a week with eight seats each, and growth runs into those seats.

The floor: costs

You can't sell below variable cost: under 29,000 ₸, every month of every student loses money. The real floor is higher, though, because the student also has to be acquired. If advertising costs the CAC ceiling the owner recalculated from the August intake, 20,000 ₸, and a student pays for 2.5 months on average, like the August intake, each paid month carries 8,000 ₸ of advertising. The price floor is 29,000 + 8,000 = 37,000 ₸ a month, and rent and the administrator are paid out of whatever is above it.

The school's price, 35,000 ₸, is below that floor. The centre would lose 2,000 ₸ on every month of a new student before paying any rent.

Costs are only one of the supports. The OpenStax marketing textbook names five factors in price: cost, customers, channels of distribution, competition and compatibility with the company's goals. Cost alone, the authors say, is not enough to decide a price. The centre has no intermediaries, and its goals are simple: it sells preparation for an exam date, not the cheapest course. Competitors and buyers are taken in turn below.

Competitors: the price of the basket

Against competitors you compare the full price of what the customer needs. An applicant needs three months of classes, mock exams and Speaking feedback, and in the marketer's comparison that basket costs 135,000 ₸ at the centre, 165,000 ₸ at "7.0 Guarantee" and 125,000 ₸ at the language school, which offers no Speaking feedback at all. Per month, the centre sits between its own 37,000 ₸ floor and "7.0 Guarantee" at 55,000 ₸.

The conclusion for the owner: comparing the monthly price with the school's makes no sense when their baskets differ by 10,000 ₸ over the course. If someone holds 45,000 against 35,000, nobody has shown them what the price includes. That gets fixed first, in the manager's message, and the discount can be discussed afterwards.

Buyers: the Van Westendorp survey

You can ask the applicants themselves how much they are prepared to pay. In 1976 the Dutch researcher Peter van Westendorp proposed four questions for gauging how people perceive a price. For the course they go like this:

  1. At what monthly price would the course seem so cheap that you would doubt its quality?
  2. At what price would it seem a bargain?
  3. At what price would it seem expensive, but you would still think about buying it?
  4. At what price would it be so expensive that you would not buy it?

From the answers you build four curves: the share of people who find each price too cheap, cheap, expensive and too expensive. Where they cross, you get a range of prices people consider acceptable. That is how the method is described, for example, in the documentation of the pricesensitivitymeter R package, which also says what it is good for: a rough sense of whether buyers' price perceptions sit above the seller's costs. For the centre, the question is whether the range lies above 37,000 ₸.

The method has three limits, and the centre runs into all three:

  • It measures opinions about price rather than purchases. To estimate how many people will buy, two questions are added: would the person buy the course at the "cheap" and at the "expensive" price they named themselves (the Newton, Miller and Smith extension, which the same package supports).
  • People who saw 45,000 ₸ in ads and on the website will name prices around that figure.
  • The answer depends on whom you ask. Current students are already happy with the price, so you ask everyone who came to a trial lesson, those who bought and those who didn't.

How to present the price

The first number a person sees shifts how they judge the next ones. Tversky and Kahneman described this anchoring in 1974, and the effect has held up in replications. At the centre, the first number in the chat is "45,000 ₸ a month", and the person sets it next to the school's 35,000 ₸. If the manager leads with the basket, "three months, two mock exams and Speaking feedback, 135,000 ₸, paid monthly at 45,000 ₸", the comparison becomes course against course. The centre is already testing a similar line: in the hypothesis from the competitor comparison, the manager adds to the reply what the price includes and notes who goes quiet after it. The anchor has to be true, though: show a crossed-out price only if the course really sold at it.

Be more careful with decoys. In 1982 Huber, Payne and Puto showed that if you place a third option next to one, similar to it but clearly worse, people start choosing the first one more often. For the centre this could be a course without mock exams for the same 45,000 ₸, next to the full one. But in 2014 Frederick, Lee and Baskin found that the effect holds up mainly in tables of numbers and typically vanishes when people try the product themselves or see its qualities as something other than figures, and they questioned its practical use. There is no reason to build the centre's price list around a decoy.

Payment terms are part of the price too. The school takes 105,000 ₸ for all three months up front; the centre is paid monthly. Suppose the centre wants to offer three months paid at once, say for 129,000 ₸. A student who stays all three months leaves 129,000 − 3 × 29,000 = 42,000 ₸, while a monthly student brings in 40,000 ₸ on average (16,000 × 2.5). The centre wins on the students who would otherwise have left early, and only if the centre does not have to refund unused months: the law may give a right to that refund, so check the terms with a lawyer. If, on the other hand, prepayment is chosen only by those who were going to finish anyway, the centre loses 6,000 ₸ on each of them: paying monthly, they would have left it the full 48,000 ₸. Monthly payment stays either way: in the interviews with applicants, what put people off was committing to three months.

The price in ads, and taxes

The Law "On Advertising" calls advertising unreliable if it contains untrue information about the price and additional payment terms at the time it runs (Article 7(2)(3)). As we read it, that means a price changes everywhere on the same day: in the ads, on the website, in the 2GIS listing and in the Instagram bio. A promotion "until 30 November" comes down from every platform on 1 December, and "pay monthly" in an ad has to match the contract.

Comparing yourself with competitors in ads runs into the same law: it calls advertising unfair if it compares the advertised goods or services with those of other persons (Article 7(1)(1)). So the basket table stays an internal working document, and the ads and the website talk only about what the centre's own price includes. This is our reading of the law as amended up to 17 May 2026, and it is not legal advice.

Taxes are a separate question. Whether VAT is included in the price depends on the seller's status, and if it is, contribution is calculated on the amount without the tax. The centre's example leaves taxes out. For your own client, ask an accountant; official guidance comes from the State Revenue Committee at kgd.gov.kz.

How to check a pricing decision

Change one thing at a time and watch the new intakes. After a price change, track the share of trial-lesson attendees who pay for the course (currently one in three), how many students pay for the second month, the intake's contribution and the reasons for refusal in the CRM. The centre's numbers are small: 12-20 new students a month, so a difference of one or two people means nothing and you judge by two or three intakes. The survey is the same: in thirty questionnaires one person moves a curve by 3.3 percentage points. Change the price, the advertising and the programme in the same month, and you will never find out which one did it.

Exercise: a first-month discount

Take a client who is asking for a discount or wants to change a price. If you have no client, use the centre from this lesson.

A last problem. The owner has dropped the idea of cutting the price for everyone and proposes 20% off the first month for new students: 36,000 ₸ instead of 45,000 ₸. "We leave current students alone, and more new ones will come." How many new students does the centre need so it doesn't lose out?

In the first month the centre keeps 36,000 − 29,000 = 7,000 ₸ instead of 16,000 ₸. If students drop out like the August intake (80% pay for the second month, 70% for the third), a student brings in 7,000 + 16,000 × 0.8 + 16,000 × 0.7 = 31,000 ₸ over the course instead of 40,000 ₸. October's 12 new students would have left 480,000 ₸, and to keep that sum with the discount you need 480,000 / 31,000 = 15.5, so 16 students, a third more. The CAC ceiling, half of a student's contribution, falls from 20,000 to 15,500 ₸.

And that assumes retention stays the same. A first-month discount may attract people who come for exactly one cheap month, in which case fewer than 80% pay for the second month and the 31,000 ₸ shrinks. You will not know until the first discounted intake reaches its second month. If the discount is advertised, the end date and the price in the ad must be true on every day it runs. Two sentences to the owner are enough: "The discount pays off only if we get 16 new students instead of 12 and they stay as well as the August intake did. Let's first see what the new message about the basket price does."

Video: price and pricing strategy

Marketing Mix: Price and Pricing Strategy - Mike Clayton

As you watch, try the approaches to price from the video on the centre: what they say about its costs, competitors and buyers.

Need help applying this to your analytics? Discuss your project with Goodlabs →