The math behind BOGO promotions

In a buy-one-get-one (BOGO, or 1+1) promotion, the guest pays for one item and the restaurant supplies two. BOGO can attract new guests while reducing margins; evaluate it against sales in the same period without the offer.

What decides whether BOGO pays off

• For two identical portions, a 50% gross margin on the price net of VAT is the break-even point when counting food cost alone. Packaging, card fees, and other transaction costs raise the break-even threshold to about 54.5% for the €4 coffee below. At a 45% margin, every BOGO transaction loses money.
• When guests shift their usual purchases to promotion days without buying more, sales are not incremental and the amount left per transaction after variable costs falls.
• With prolonged discounting, guests may get used to waiting for discounts.
• Coffee, alcohol, and desserts are worth checking for BOGO. Salads and entrees with expensive proteins are less likely to pass the cost calculation.
• Digital loyalty systems help track guest purchases and evaluate promotion ROI.

The core mathematics: what 1+1 costs

When both items are identical and the guest takes both, BOGO amounts to a 50% discount. First, calculate gross margin:

Gross margin (money) = Selling price − COGS

Gross margin (%) = (Selling price − COGS) / Selling price × 100%

Use the selling price net of VAT. Every threshold here is a margin on selling price, not a markup on cost. Markup = margin / (1 − margin): a 50% margin is a 100% markup, and an 80% margin is a 400% markup. Convert markup to margin before using the thresholds.

A BOGO transaction earns revenue for one item but incurs the cost of two. After all other variable costs, what remains is contribution toward fixed costs, not net profit:

BOGO transaction contribution = Price − COGS(paid item) − COGS(free item) − other variable costs

The short form, Price × 1 − COGS × 2, applies only if both items cost the same to make and there are no other variable costs. A second cup needs packaging, and a card payment incurs a fee.

Take a hypothetical coffee priced at €4 with €0.80 in COGS. At full price, gross margin is €3.20, or 80%. Under BOGO, €4 in revenue minus €1.60 in cost leaves €2.40 per transaction. That transaction serves two cups, and the calculation does not yet include packaging or fees.

€2.40 is positive, but that alone does not establish whether the offer pays off. The right comparison is the usual €3.20. Without additional transactions, the offer gives up €0.80 in gross profit per sale, or 25% of the baseline.

With €0.15 in packaging per cup and a 1.5% card fee, the coffee contributes €2.99 at full price and €2.04 under BOGO, rather than the €2.40 suggested by the short form.

In a simplified model, the transaction multiplier needed to match the result without a promotion is m / (2m − 1), where m is gross margin. This assumes a margin above 50%, identical paid and free items with the same cost, exactly one item in each baseline transaction, no other variable transaction costs, and no other changes. The required volume is ×1.33 at an 80% margin, ×1.5 at 75%, and ×3 at 60%. At exactly 50%, contribution is zero: no increase in volume recovers the usual gross profit.

Any per-transaction expense changes the ratio, even a flat charge per sale. Add €0.15 of packaging per cup and the 1.5% card fee, and the coffee needs ×1.47 transactions instead of ×1.33. The comparison is still with the same period without the promotion.

For a hypothetical €12 salad with €8.50 in ingredient costs, normal gross margin is €3.50, or about 29%. Under BOGO, €12 in revenue minus €17 in costs produces a €5 loss before packaging and fees. The restaurant has to fund that shortfall on every such sale.

The 50% break-even threshold for identical portions covers only food cost. Packaging, fees, and other variable costs raise the working threshold to about 54.5% for the coffee above. Below this working threshold, each transaction has negative contribution. Above it, extra volume still needs to offset the lower contribution per sale.

For a cheaper giveaway, the food-cost break-even margin is r/(1+r), where r is the free item’s food cost divided by the paid item’s. It is exactly 33⅓% when the free item costs half as much and 42.9% when it costs three quarters as much. These figures exclude other variable costs; packaging and fees push both thresholds higher.

When 1+1 promotions generate value

Customer acquisition

If the goal is to introduce new guests to the restaurant, treat the offer as a marketing investment. Evaluate whether subsequent purchases repay the acquisition expense, rather than judging only the first transaction.

Payback comes from contribution after variable costs, not from the entire order value. In a hypothetical example, a €25 average order at a 30% contribution margin yields €7.50 per visit, covering a €5 acquisition loss on the first return. At a 10% contribution margin, each visit yields €2.50, so two returns are needed. Use your own margin: neither average order value nor annual visit frequency answers the payback question alone.

Account for redemptions by guests who would have returned anyway. If they represented half of all redemptions, the cost per genuinely new guest would be twice the simple estimate. Assess that share against a baseline period rather than assuming it.

Sales during dead hours

A café empty between 2 p.m. and 5 p.m. earns no revenue but still pays rent, utilities, and scheduled staff. An offer confined to that window can generate contribution toward those costs.

For identical portions, BOGO contribution is Price − 2 × COGS − packaging − fees. A negative result means additional orders increase the shortfall. The €12 salad with €8.50 COGS contributes −€5.00 before packaging and fees; ten such guests add €50 to the shortfall.

A dead-hour offer needs positive contribution and genuinely additional traffic, not guests moving their purchases from 1 p.m.

High-margin product categories

Beverages, including coffee, tea, and alcohol, along with desserts and sides, can carry margins of 60% to 85%. Those margins make them candidates for BOGO, not a guarantee of profit after all costs. A cocktail with a 75% starting margin retains a 50% gross margin under BOGO, counting only product costs and excluding packaging and fees. That is still higher than the margin of many menu items at full price.

Inventory management

The cost of perishables nearing expiration has already been incurred. A BOGO offer on pastries can recover some of that cost if the alternative is throwing both away. Compare revenue after additional selling costs with disposal; recovering part of a sunk cost does not necessarily mean the sale earns a profit.

When 1+1 promotions reduce value

Low-margin items

Below a 50% gross margin, counting only product costs, selling two identical portions for the price of one loses money before other expenses. Packaging and fees raise the break-even threshold. Check your own costing. A hypothetical €28 steak with €18 in costs has a margin of about 36%. It leaves €10 at full price before other costs and loses €8 per BOGO transaction.

Peak-hour promotions

When the restaurant is already at capacity, BOGO risks replacing full-price sales with discounted ones. Customers who would have paid the usual price receive the offer, and longer lines may turn away other full-price buyers.

Missing measurement

The kitchen sees more orders, and management may assume the offer is a success. But that does not necessarily mean more sales over the whole period. If Tuesday’s guests wait for Wednesday’s promotion, the restaurant serves existing demand at a lower margin. Purchase tracking is needed to distinguish shifted sales from additional ones.

Offers that run too long

A promotion running past four weeks risks being seen as a permanent price cut: guests may start waiting for the discount instead of paying full price. The restaurant risks entering a cycle in which promotions are needed just to maintain baseline traffic.

Metrics for evaluating promotions

Return on investment (ROI)

ROI = Δ profit / Investment × 100%

Δ profit is the difference between the profit of the promotional period and the profit the same period would have produced without the offer. Include all variable costs, including free portions, and campaign expenses. If fixed costs are unchanged, the change in contribution after campaign expenses equals the change in profit; contribution itself is not net profit.

Investment here means product and packaging costs for the free portions plus promotion-specific expenses, such as design, printing, advertising, or a campaign fee. Deduct each expense from the result once; in the denominator, it only sets the scale of the investment.

Break-even relative to the no-promotion baseline is ROI 0%, not 100%. An ROI of 50% means the additional result after expenses equals half the investment. A negative ROI means the result fell below the baseline.

Worked example: a €4 coffee net of VAT, €0.80 in product cost, €0.15 in packaging per cup, and a 1.5% card fee. Contribution is €2.99 at full price and €2.04 under BOGO. A baseline month with 1,000 paid coffees generates €2,990. A promotional month with 1,500 BOGO transactions generates €3,060. Deduct €200 for design and local ads, leaving €2,860.

Δ profit = €2,860 − €2,990 = −€130. Investment = 1,500 × (€0.80 + €0.15) = €1,425 for free portions, plus €200 in campaign expenses = €1,625. ROI = −€130 / €1,625 = −8%. Transactions increased by half, but the result was worse than the baseline.

Do not confuse ROI with ROAS. Standard ROAS is attributed revenue, which analytics credits to the campaign, divided by ad spend. Its numerator is revenue, not profit.

Incremental ROAS is a separate, stricter measure: it uses only additional revenue. Estimating it requires a causal test, such as a holdout, a geo test, or a switchback. The rule “break-even ROAS = 1 / contribution margin” applies only if that margin is explicit, calculated after all variable costs except advertising, and the numerator is genuinely incremental revenue. Attributed revenue can overstate or understate incremental revenue depending on the attribution model and channel mix. The direction of error is not known in advance.

Average order value (AOV)

AOV is revenue divided by the number of orders. Buying complementary items alongside BOGO can raise it. If it falls, check whether guests are replacing their usual purchases with the offer. A lower AOV alone does not prove substitution.

Incremental sales ratio

Compare sales with baseline trends. If weekly sales normally vary by 5%, growth within that range is not enough to credit the offer. For growth beyond the usual range, separate additional sales from shifted purchases.

Practical recommendations

1. Limit same-item BOGO to products with a documented gross margin above 50% of the price net of VAT, counting only product costs. Packaging and fees raise the working threshold to about 54.5% for the coffee above. For a cheaper giveaway, use the r/(1+r) calculation in the core mathematics section.
2. Set specific offer windows, preferably during documented low-traffic periods. Avoid weekends and meal rush hours unless guest acquisition is an explicit, budgeted goal.
3. Limit campaigns to 2–4 weeks. Longer offers need a separate justification and monitoring for changes in brand perception.
4. Use digital loyalty systems to track purchases at the individual guest level and compare them with the baseline period.
5. Consider cashback or loyalty points instead of a direct discount. They give guests a reason to return while preserving the full price of the current purchase.

Digital loyalty for setting up and measuring offers

The Eatery Club™ loyalty module lets restaurants specify products, offer windows, and guest segments, with automatic result tracking. Financial evaluation still requires contribution calculations and a comparison with the no-promotion baseline.

The “Piggy Bank” feature builds progress toward rewards through repeat purchases of specific items. This gives guests a reason to return while keeping the current purchase at full price. For example, a guest who buys nine coffees at full price and receives the tenth free brings in 90% of full-price revenue for the coffees served, versus 50% under BOGO. These are revenue shares, not profit margins.

Digital systems also support A/B testing of offer mechanics, targeted offers by guest segment, and real-time adjustments based on results. Before choosing between the nine-plus-one reward and BOGO, compare contribution with the no-promotion baseline.