Sales discounting is a technique often used by a business to try and improve its level of sales, however the method needs careful consideration as, unless the unit sales of the product increase sufficiently, the effect of sales discounting will be to reduce the gross margin (profit) of the business.

## Sales Discount Example

Suppose a business currently sells 5,600 units of a product at an average selling price of 20.00 and a cost of 14.00. From this information we can calculate the current gross margin percentage, revenue, and gross margin of the business as follows:

Units = 5,600 Selling price = 20.00 Cost = 14.00 Gross margin % = (Selling price – Cost) / Selling price Gross margin % = (20 – 14) / 20 = 30.0% Revenue = Units x Selling price Revenue = 5,600 x 20.00 = 112,000 Gross margin = Revenue x Gross margin % Gross margin = 112,000 x 30.0% = 33,600

## Effect of Sales Discounting

Suppose now that the business decides to offer a 12.5% sales discount, reducing the selling price of the product by 2.50 (20.00 x 12.5%) from 20.00 to 17.50.

Assuming no change in the level of sales, the revised gross margin percentage, revenue, and gross margin of the business can be calculated in a similar manner as follows:

Units = 5,600 Selling price = 17.50 Cost = 14.00 Gross margin % = (Selling price – Cost) / Selling price Gross margin % = (17.50 – 14.00) / 17.50 = 20.0% Revenue = Units x Selling price Revenue = 5,600 x 17.50 = 98,000 Gross margin = Revenue x Gross margin % Gross margin = 98,000 x 20% = 19,600

The effect of offering the sales discount of 12.5% is to reduce revenue and gross margin by 14,000, and the gross margin percentage from 30% to 20%, as summarized below.

Original | Discount | |
---|---|---|

Units | 5,600 | 5,600 |

Price | 20.00 | 17.50 |

Cost | 14.00 | 14.00 |

GM % | 30.0% | 20.0% |

Revenue | 112,000 | 98,000 |

Gross margin | 33,600 | 19,600 |

## Revenue Needed to Maintain the Gross Margin

The purpose of sales discounting is to try and improve unit sales and therefore the gross margin of the business.

As we have seen above, unless the number of units sold can be increased, the effect of offering the sales discount will be to reduce the revenue, gross margin percentage, and gross margin of the business.

In order for the planned sales discounting to be regarded as a success, the business must at least maintain and ideally improve the current level of gross margin.

In the example above the gross margin before discounting was 33,600. To obtain this gross margin at the original gross margin percentage of 30%, the business needs sales calculated as follows:

Gross margin % = Gross margin / Revenue Rearranged Revenue = Gross margin / Gross margin % Revenue = 33,600 / 30% = 112,000

As expected the revenue required to obtain 33,600 gross margin at a gross margin percentage of 30% is 112,000. However, following the sales discounting, the gross margin percentage as calculated above, has fallen to 20.0%, and the revenue needed to obtain the gross margin of 33,600 is now calculated as:

Revenue = Gross margin / Gross margin % Revenue = 33,600 / 20.0% = 168,000

So the revenue needed to maintain the gross margin following the sales discount of 12.5% has now increased to 168,000.

The percentage change in the revenue needed as a consequence of offering the sales discount can be calculated as follows:

Revenue after discount = 98,000 Revenue needed = 168,000 Change in revenue = 168,000 - 98,000 = 70,000 % change in revenue = 70,000 / 98,000 % change in revenue = 71%

What this means is that by offering a 12.5% sales discount, the business must increase its revenue by 71% just to maintain its current gross margin of 33,600

Notice that the same result is given in terms of the number of units required to be sold.

Units after discount = 98,000 / 17.50 = 5,600 Units needed = 168,000 / 17.50 = 9,600 Change in units = 9,600 - 5,600 = 4,000 % change in units = 4,000 / 5,600 % change in units = 71%

This is summarized in the table below.

Discount | Revised | |
---|---|---|

Units | 5,600 | 9,600 |

Price | 17.50 | 17.50 |

Cost | 14.00 | 14.00 |

GM % | 20.0% | 20.0% |

Revenue | 98,000 | 168,000 |

Gross margin | 19,600 | 33,600 |

Great care must be taken when offering a sales discount. In the above example, by offering a sales discount of 12.5%, the unit sales and revenue needed to increase by 71% simply to maintain the gross margin at its current level.

The increase in sales and revenue needed to maintain the gross margin of the business depends on the original margin before discounting (30%) and the level of sales discount given (12.5%). For reference, the table below sets out the change in unit sales and revenue needed to maintain the gross margin for a given level of gross margin percentage (GM%) and sales discount (Dis%).

GM% | 30 | 40 | 50 | 60 |
---|---|---|---|---|

Dis% | ||||

2.5 | 9% | 7% | 5% | 4% |

5.0 | 20% | 14% | 11% | 9% |

10.0 | 50% | 33% | 25% | 20% |

12.5 | 71% | 45% | 33% | 26% |

15.0 | 100% | 60% | 43% | 33% |

20.0 | 200% | 100% | 67% | 50% |

In the example above the increase in unit sales and revenue needed to maintain the gross margin was 71%, using the table, this can be found by looking the down the column headed 30% (for our original gross margin) and along the row headed 12.5% (the sales discount given), to give the answer 71%.

As a further example, if the original gross margin percentage of the business was 50%, and the sale discount given is 10%, the the unit sales and revenue would need to increase buy 25% in order to maintain the current gross margin of the business.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.