Extra sales needed to recover profit after a discount

Extra sales needed to recover profit after a discount

Formula & method

New contribution per original price unit = m − d
Required volume multiplier = m ÷ (m − d)
Extra units% = (multiplier − 1) × 100

Both the original contribution margin and discount must be fractions of the original selling price. The calculation assumes variable cost per unit does not fall when the price falls. Multiply the new unit contribution by the required volume to recover the original total contribution.

Recovering revenue is a different target and usually needs a smaller increase. Capacity limits, extra labour, fulfillment fees and new customers’ behaviour can invalidate the constant-cost assumption. Use this table to expose the arithmetic trade-off, not to forecast demand.

Worked example

A product sells for 100 and has variable cost 60. Discounting the price to 90 lowers unit contribution from 40 to 30. Selling 400 units instead of 300 restores contribution to 12,000: a 33.33% unit increase.

What can change the answer

When discount is at least the original margin, no finite higher volume restores positive original contribution under this model. Additional fixed costs or changing unit costs require a revised model.