In order to start a financial projection, a business needs to decide at what level to set the unit selling price of its product. Depending on the elasticity of demand for the product, subsequent changes in the selling price will have an impact on sales volume (the number of units sold), and consequently the gross profit of the business.

The gross profit shown in any financial projection depends on the unit selling price, the cost price, and the sales volume.

Gross profit = Sales volume x (Price - Cost)

**Variables used in the formula**

Price = Unit selling price of the product

Cost = Unit cost of the product

Sales volume = Number of units sold

Having established a target level of gross profit, it is useful to be able to flex the financial projections to understand how a change in price can be compensated for by a change in unit sales volume in order to maintain the same gross profit.

## Pricing for Profit Formula

The pricing for profit formula shows the relationship between a change in the product selling price and the necessary change in sales volume to maintain a target level gross profit, and is derived from the formula above by equating the profit before and after the price changes.

The pricing for profit formula can be state as follows:

% Change in sales volume = (GM% / (GM% + % Change in price)) - 1

**Variables used in the formula**

GM% = Gross margin percentage

% Change in price = Percentage change in selling price

% Change in sales volume = Required percentage change in unit sales required to maintain the same gross profit

It can be seen from the above formula that the change in sales volume required depends only on the change in the selling price and the current gross margin percentage.

## Raising the Selling Price Example

Suppose a business is currently selling a product with a gross margin percentage of 35%, and plans to increase selling prices by 5%.

It is likely that as the business increases its prices the unit sales will fall. Using the pricing for profit formula, the percentage the volume of units can fall in order to maintain the same total gross profit is calculated as follows:

GM% = 35% % Change in price = 5% % Change in sales volume = (GM% / (GM% + % Change in price)) - 1 % Change in sales volume = (35% / (35% + 5%)) - 1 % Change in sales volume = -12.50%

What the calculation tells us is that if the business increases its prices by 5%, then the unit sales volume can fall by 12.5% before the gross profit falls below its current level.

To see this in action, suppose the business currently has a selling price of 100.00 and a sales volume of 1,000 units. With the 5% increase, the selling price will change from 100.00 to 105.00, and using the result from the calculations above, the sales volume can fall by 12.5% from 1,000 to 875.

The effect on gross profit is summarized in the table below.

Before | Change | After | |
---|---|---|---|

GM% | 35.0% | 38.1% | |

Price | 100 | 5.0% | 105 |

Cost | 65 | 65 | |

Margin | 35 | 40 | |

Sales volume | 1,000 | -12.5% | 875 |

Profit | 35,000 | 35,000 |

Notice that as the cost of the product remains the same at 65, the increase in selling price of 5% results in the gross margin percentage increasing from 35% to 38.1%. The result of this is that unit sales volume can fall by 12.5% while still maintaining the same total profit of 35,000.

## Lowering the Selling Price Example

Suppose the same business is instead planning to lower selling prices by 10%.

It is likely in this case that as the business lowers its prices the unit sales volume will hopefully increase. Using the pricing for profit formula, the percentage the sales volume has to increase in order to maintain the same total profit is calculated as follows:

GM% = 35% % Change in price = -10% (a reduction) % Change in sales volume = (GM% / (GM% + % Price change)) - 1 % Change in sales volume = (35% / (35% - 10%)) - 1 % Change in sales volume = 40%

In this case the calculation tells us that if the business lowers its prices by 10%, then the unit sales volume will have to increase by 40% in order to maintain profits at their current levels. This is summarized in the table below.

Before | Change | After | |
---|---|---|---|

GM% | 35.0% | 27.8% | |

Price | 100 | -10.0% | 90 |

Cost | 65 | 65 | |

Margin | 35 | 25 | |

Sales volume | 1,000 | 40.0% | 1,400 |

Profit | 35,000 | 35,000 |

Notice again that as the cost of the product remains the same at 65, the lowering of the selling price by 10% results in the gross margin percentage decreasing from 35% to 27.8%. The result of this is that unit sales volume has to increase by a massive 40% to maintain the same total profit of 35,000.

Depending on the gross margin of the business, the formula shows that lowering the prices can often require a substantial increase in sales volume to compensate. This calculation is only one factor in determining the selling price of a product, however, by using the pricing for profit formula when preparing financial projections, a business can quickly evaluate the changes it needs in sales volume to maintain the same gross profit before and after a selling price change.

Our pricing for profit calculator is available to help carry out the unit sales volume calculations discussed in this post.

## 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.