Selling 10% more after a 10% discount may not restore profit
A 10% price cut followed by a 10% increase in units sold may leave you with less profit than before. The discount reduces the selling price, while purchasing and packaging costs need not fall by the same percentage.
The calculation starts with the selling price minus the cost incurred for each unit sold. Costs that change with sales volume are variable costs; the difference is contribution margin per unit. Subtract fixed costs, such as rent, from total contribution to calculate profit under this cost model. (損益分岐点を使った目標売上高)
The example below compares the units needed to restore revenue with those needed to restore profit for one product over the same one-month period. All amounts exclude tax, and variable and fixed costs account for all expenses in the model. Amounts remain in Japanese yen to preserve the original example.
A ¥100 discount cuts contribution per unit from ¥300 to ¥200
Suppose a product sells for ¥1,000, has variable costs of ¥700 per unit, and sells 100 units per month. The ¥700 includes purchasing, packaging, transaction fees, and other costs incurred with each sale. Fixed costs are ¥20,000 per month. The figures form a hypothetical worked example.
Before the discount, each sale contributes ¥1,000 − ¥700 = ¥300. Selling 100 units generates ¥30,000 in total contribution. After ¥20,000 in fixed costs, profit is ¥10,000.
A 10% discount brings the price to ¥900. If variable costs remain ¥700 per unit, contribution falls to ¥200. The ¥100 discount consumes roughly 33.3% of the ¥300 previously retained from each sale.
Use the selling price minus variable cost per unit for this calculation. Iowa State University’s guide likewise explains that this difference contributes toward covering fixed costs. (Breakeven Sales Volume)
Revenue recovers at 112 units while the same profit requires 150
Keeping the original ¥10,000 profit requires ¥30,000 in contribution, including ¥20,000 to cover fixed costs. Divide that by the discounted contribution of ¥200 per unit: ¥30,000 ÷ ¥200 = 150 units.
| Price and units sold | Revenue | Total variable costs | Total contribution | Profit after fixed costs |
|---|
| ¥1,000 for 100 units | ¥100,000 | ¥70,000 | ¥30,000 | ¥10,000 |
| ¥900 for 110 units | ¥99,000 | ¥77,000 | ¥22,000 | ¥2,000 |
| ¥900 for 112 units | ¥100,800 | ¥78,400 | ¥22,400 | ¥2,400 |
| ¥900 for 150 units | ¥135,000 | ¥105,000 | ¥30,000 | ¥10,000 |
A 10% increase to 110 units does not even restore the original ¥100,000 revenue. Restoring revenue requires ¥100,000 ÷ ¥900, or approximately 111.1 units. For a product sold in whole units, that means 112 units. Profit is still only ¥2,400, which is ¥7,600 below the original ¥10,000.
The 150 units needed to retain ¥10,000 profit represent a 50% increase over the original 100 units. The revenue target requires 112 units, while the profit target requires 150.
At ¥900, selling 100 units generates ¥20,000 in contribution, exactly covering fixed costs. That is the zero-profit break-even point. The 100 units needed to avoid a loss and the 150 needed to preserve the original profit are also different thresholds.
Additional advertising or staffing can make 150 units insufficient
The 150-unit answer assumes that variable costs remain ¥700 per unit and fixed costs remain ¥20,000. If promoting the discount adds a flat ¥10,000 in advertising costs for the month, retaining ¥10,000 profit requires ¥40,000 in total contribution. At ¥200 per unit, that requires 200 units.
Include that flat monthly advertising charge as an additional expense without also counting it as a cost incurred on each sale. By contrast, recalculate transaction fees charged on each sale using the discounted price and include them in variable cost per unit. Changes in purchasing prices at higher quantities, additional shifts, and extra warehouse space also require a calculation using the costs actually incurred.
The units needed to retain the same profit follow this relationship.
Required units = (original profit + revised fixed costs) ÷ revised contribution per unit
Original profit is calculated using the previous sales volume, price, and costs. If the result is fractional and the product sells in whole units, round up.
If revised contribution is zero or negative, the formula cannot produce a sales quantity that achieves a positive profit target. With variable costs still ¥700, a ¥700 selling price contributes nothing toward fixed costs regardless of volume. Below ¥700, every additional sale increases the loss.
Compare required volume with expected demand before discounting
The decision turns on whether sales can plausibly rise from 100 to 150 units. Compare the required 150 with expected demand based on past sales, reservations, or orders, and compare it with the number of units you can pack and ship that month.
Suppose you expect to sell 100 units without a discount or 130 with it during the same month. If those forecasts are realized, discounted profit is ¥200 × 130 − ¥20,000 = ¥6,000, which is ¥4,000 less than the ¥10,000 without discounting. A projected 30% increase in unit sales would still mean a 40% reduction in profit. If the purpose of the discount is to maintain profit, an expected 130 units falls short of the required volume.
After implementation, reassess the estimate of sales without discounting alongside actual volume and costs per unit. A comparison with the same month last year also includes changes in seasonality and customer traffic. If only some customers receive the discount, calculate total monthly profit including purchases at the regular price.
Base the decision on contribution per sale as well as the discount rate
The discount percentage alone cannot tell you how many units preserve profit. In this example, a 10% price cut reduces contribution per unit from ¥300 to ¥200, requiring a 50% increase in units sold. Additional expenses raise the required volume further.
Before approving the promotion, calculate required units using discounted contribution per unit and compare that quantity with both expected demand and shipping capacity. When publishing the offer on your website, state the eligible products, purchase period, shipping charges, and service scope so the published offer matches the sales arrangement used in the calculation.
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