What figures do you need before testing a discount?
Start with the normal customer price, the proposed discounted price and the cost per sold portion. Compare the same item over comparable trading periods.
Assume a café item normally sells for £12.00, costs £3.60 per sold portion and receives a basic 10% price discount. Both customer prices include an explicitly assumed 20% sales VAT. This rate is an arithmetic assumption, not a classification of the item.
The £3.60 includes the chosen direct costs on a consistent basis: exclude recoverable purchase VAT and include non-recoverable VAT. Assume any unsold-portion allowance is already included, with no further waste adjustment. Unit cost stays unchanged as sales increase.
All worked numbers were checked using Python 3. Money is displayed to pennies and percentages to two decimal places; calculations retain full precision until the final result.
How much gross profit does the normal price produce?
Net sale means the customer price before sales VAT. Gross profit is that net sale minus the entered portion cost. GP margin expresses gross profit as a percentage of the net sale.
Net sale = gross customer price ÷ (1 + VAT percentage ÷ 100). Gross profit = net sale − portion cost. GP margin = gross profit ÷ net sale × 100.
At the normal price, £12.00 ÷ 1.20 = £10.00 net sale. Gross profit is £10.00 − £3.60 = £6.40 per portion, and GP margin is 64.00%.
Selling 100 portions therefore produces £640.00 gross profit against the entered costs. That money still has to cover remaining wages, rent, energy and other expenses. It is not net or take-home profit.
What does a 10% discount do to GP?
The discounted customer price is £12.00 × 0.90 = £10.80. At the assumed VAT rate, net sale becomes £10.80 ÷ 1.20 = £9.00.
With portion cost unchanged at £3.60, gross profit becomes £9.00 − £3.60 = £5.40. GP margin is £5.40 ÷ £9.00 × 100 = 60.00%.
The discount removes £1.00 of gross profit per sale. Compared with the original £6.40, that is a 15.63% reduction in GP pounds. Margin falls by four percentage points, from 64.00% to 60.00%.
At an unchanged 100 sales, total gross profit falls from £640.00 to £540.00. A discount reduces the selling price while leaving the assumed portion cost intact, which is why the percentage loss of gross profit exceeds the percentage price reduction.
How many extra portions must you sell?
Required sales multiplier = original GP per portion ÷ discounted GP per portion.
Here, £6.40 ÷ £5.40 = 1.185185… . The required increase is (1.185185… − 1) × 100 = approximately 18.52%.
If the baseline is 100 portions, the mathematical requirement is 118.5185… discounted portions. Because you sell whole portions, round the required quantity upwards to 119.
At 118 sales, gross profit is 118 × £5.40 = £637.20, below the original £640.00. At 119 sales, it is 119 × £5.40 = £642.60, just above it.
This is the volume needed to match gross profit under the stated assumptions. It is not a forecast that the discount will attract those sales. The formula requires positive discounted GP per portion; a zero or negative figure cannot recover a positive baseline through additional identical sales.
What could make the discount comparison misleading?
Count all discounted sales, including customers who would otherwise have paid full price. Extra transactions alone do not show whether the offer recovered the lost gross profit.
Check whether producing more portions changes ingredient costs, packaging, unsold stock or staffing needs. If the cost per sold portion changes, repeat the calculation with the revised figure. Extra expenses outside the entered cost can also leave the business worse off even when total gross profit is restored.
Keep the offer simple for this comparison. HMRC states that basic discounts use the discounted price when charging VAT: https://www.gov.uk/charge-reclaim-record-vat/vat-on-discounts-and-gifts
Bundles, vouchers and offers involving different VAT rates can require different treatment. Use the rate applicable to the actual sale; HMRC’s catering guidance is at https://www.gov.uk/guidance/catering-takeaway-food-and-vat-notice-7091
Purchase VAT recovery has conditions and exceptions, explained at https://www.gov.uk/charge-reclaim-record-vat/reclaim-vat-business-expenses . This guide explains pricing arithmetic, not personalised tax advice.
How can you test your own offer in the calculator?
Open GP Calculator UK at / and choose Check my GP. Enter cost 3.60, customer menu price 12.00 and the assumed VAT rate 20. Record the £6.40 GP per portion, then change the price to 10.80 and record £5.40.
Divide the original GP pounds by the discounted GP pounds to find the required sales multiplier. Multiply your baseline portion count by that result, then round upwards for whole portions. Use your own actual cost, price and VAT inputs before making a decision.
Read /methodology/ for calculation assumptions and rounding. Set a review period for any proposed offer and compare actual quantities, costs and total gross profit. Neither this example’s margin nor its discount is a recommended target.
Sources
Try the tools
Try your own figures
Use the free GP calculator to check selling prices, compare margins and save menu items on your device. Gross profit is before remaining business expenses.
Open GP Calculator UK →