Discount Volume Trade-Off Calculator

How it works

Gross profit is the unit margin (price minus unit cost) times the number of units sold. A discount comes straight out of the unit margin, so each sale earns less and more sales are needed to earn the same total. A price rise adds to the unit margin, so the same gross profit is reached with fewer sales.

The calculator holds gross profit fixed and solves for the volume at the new price: current unit margin × current volume ÷ new unit margin. The volume change is that figure compared with today's volume. For a cut it is the extra sales the discount has to generate just to stand still; for a rise it is the share of sales that can be lost before the increase starts to cost money.

A percent-off promo code is entered as a percent change and a fixed dollars-off coupon as a dollar amount; the arithmetic is the same. The result does not predict how customers will respond. It is the break-even line that their response has to clear.

Formula

unit margin        = price − unit cost
new price          = price × (1 ∓ change %)   or   price ∓ change $
volume needed      = volume × unit margin ÷ new unit margin
volume change %    = −(new price − price) ÷ new unit margin × 100
                   = m ÷ (m − d) − 1   (m = margin %, d = discount % of price)

Example

A product sells for $50 and costs $35, a 30% gross margin, and 1,000 units sell a month for $15,000 of gross profit. A 10% discount drops the price to $45 and the unit margin from $15 to $10. Earning $15,000 at $10 a unit takes 1,500 units: 500 more, a 50% increase in volume. At the old volume the discount would leave $10,000.

Raising a $3.75 item with a $1.50 unit cost by $0.50 lifts gross profit at 1,500 units from $3,375 to $4,125. The old $3,375 is reached at 1,227.27 units, so sales can fall by 272.73 units, or 18.18%, before the rise costs gross profit.

Assumptions and limitations

• Unit cost is treated as fully variable and unchanged by the price change. Fixed costs are left out because they do not change with the price; overhead, payment fees and returns are not included unless you add them to the unit cost.
• The result is a break-even volume, not a forecast. How many customers a discount attracts, or a price rise drives away, depends on demand, competitors and timing, none of which the calculator models.
• A discount that only moves sales forward in time, or that goes to customers who would have paid full price, needs more extra volume than shown here to pay for itself.
• Volumes are shown to two decimals; in practice they round to whole units.
• Results are for informational and educational purposes and are not financial, tax or accounting advice.

Frequently asked questions