Find the Real Discount of a Buy-X-Get-One Punch Card

Excel Formulas › Coffee Shop & Cafe

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A punch card feels generous, but what discount is it really giving? Once you express 'buy 9, get one free' as a percentage, you can compare it to a straight price cut.


Quick formula: The free drink is one out of every (buys + 1) drinks:
=1/(B2+1)

Buy 9 and get the 10th free means 1 free in every 10 — a 10% effective discount.

Functions used (tap for the full reference guide):

The example

A card stamps nine paid drinks, then the tenth is free.

AB
1LabelValue
2Paid drinks before free9
3Drink price$5.00
4Effective discount10%

The formula

One free drink spread across the full cycle:

=1/(B2+1) // 1 free out of 10 total = 0.10

How it works

The reasoning:

  1. A full cycle is the paid drinks plus the one free drink: B2+1 = 10 drinks.
  2. Exactly one of those ten is free, so the customer pays for 9 and gets 10.
  3. 1/(B2+1) = 1/10 = 0.10, i.e. a 10% effective discount.
  4. Format the cell as a percentage to display 10%.

Compare that to your margin: a 10% discount on a $5 drink is $0.50 of revenue per cycle.

Try it: interactive demo

Interactive

Set how many paid drinks earn a free one — see the real discount.

Variations

Revenue given up per cycle

Multiply the free drink's price by how many cards complete.

=B3*B5

Discount on the COGS basis

If the free drink only costs you its ingredients, use the cost instead of the price.

=B6/((B2+1)*B3)

Pitfalls & errors

The free drink costs you its ingredients, not the full menu price — your real margin hit is smaller than the headline discount.

Breakage (cards never completed) lowers the true discount. Track completion rate and multiply it in.

Practice workbook

📊
Download the free Find the Real Discount of a Buy-X-Get-One Punch Card practice workbook
Change the yellow inputs; the effective discount and revenue impact recalculate.

Frequently asked questions

Is buy-9-get-1 really only 10% off?
Yes, on price. The customer gets 10 drinks for the price of 9, which is a 10% effective discount.
How is this cheaper than a 10% discount for me?
The free drink costs you ingredients, not full price, and some cards are never completed — so your true cost is below 10%.
What about a buy-5-get-1 card?
That's 1 free in 6, or about 16.7% — more generous. Use =1/(5+1) to see it.

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Function references: ROUNDSUM