## Author: Carlos Hugo Barbery Alpire

*How can businesses offer discounts while maintaining margin control? The idea is to offer discounts to the public while effectively controlling those discounts based on margin calculations conducted by your team. In this article, the author presents a model for a tool to calculate the maximum sales discount feasible while still maintaining a minimum expected margin. Hugo Barbery, CPP, is the Manager of Planning and Pricing at ROHO Homecenter Retail Bolivia, a university pricing professor, and an advisor in promotions, economic regulation, pricing, and financial impact. He can be reached at hugo.barbery@gmail.com.*

*The Pricing Advisor, July 2023*

**Introduction**

How can businesses offer discounts while maintaining margin control? At first, it may seem absurd since customers are obviously unaware of product margins. However, that is not the purpose. The idea is to offer discounts to the public while effectively controlling those discounts based on margin calculations conducted by your team. This process begins with an initial assumption that you have the right product for the right audience. If this condition is not met, then this analysis becomes a secondary concern at a later stage.

The following proposal suggests providing a tool to calculate the maximum sales discount feasible while still maintaining a minimum expected margin.

**Approach 1**

To delve into the subject, let us begin by presenting the following novel and comprehensive model:

Where:

But it could also be expressed in a more direct and simplified manner, using the following concise and novel model:

Where:

**Practical demonstration 1**

In a practical example, it would be something like the following: If you have a product with a margin of 35% and the intention is to reduce it by 30%, resulting in a margin of 24.5%, what sales discount should be granted?

The answer, by substituting the data into the presented comprehensive novel model, would be as follows:

Replacing the same data from the example into the concise and novel model, it would be as follows:

However, this direct approach is typically useful for a specific analysis of a single product or service. However, when structuring discount matrices consistently based on the margin of a wide range of products or services, including complementary and substitute ones, the situation becomes more complex. Therefore, the first model is appropriate in such cases.

Consequently, the resulting discount is -13.91%, and to demonstrate this, we will provide a simple example explained in the following table:

As the data shows, at a discount of -13.91%, the margin is reduced by 30% from an initial margin of 35% to the adjusted margin of 24.5%.

Continuing with the analysis, it is essential to verify the elasticity of this adjustment. To do so, we will use the classic concept of the break-even margin in order to identify the necessary volume for it:

This amount indicates that, in order to maintain the margin in monetary terms, the sales volume must increase by 65.94%. To verify this, let’s assume that in the initial scenario 100.00 units were sold.

Therefore, it is evident that, at a minimum, the incremental units sold must increase by approximately 65.94% to maintain the margin in monetary equilibrium.

However, it is essential to perform another verification to ensure that the profitability of the inventory does not deteriorate with this 65.94% increase. For this purpose, we must ensure that at least the change in GMROI is zero or, better yet, positive. It is worth noting that one way to determine GMROI is by multiplying the turnover rate by the margin.

Therefore, let’s verify the change in GMROI based on an initial assumption of a turnover rate of 4 times and the previously obtained data. The resulting GMROI would be 1.40, as shown below:

Now, to see the change in turnover, we need to examine the change in monetary income from sales, assuming no change in average inventory. This can be calculated as follows:

So the new GMROI would be:

With this analysis, the change in GMROI is at least zero, as both values reach 1.40 based on the analysis conducted.

As a clarification, we should mention that in the example, the assumptions of 100 units initially sold and an initial turnover rate of 4 should have the same measurement period, and the variation in average inventory is zero.

Now, let’s incorporate another interesting variable into the analysis: What happens if our supplier offers a purchasing discount to be more aggressive in pricing? To address this, we simply need to incorporate this variable into the two models previously developed, as follows:

**Approach 2.**

**Practical demonstration 2**

To simplify the exercise, assuming the same initial data and the additional factor of a 2% purchasing discount granted by the supplier, by substituting the data into both models, it would be as follows:

Continuing the analysis with the same initial data, the results would be as follows:

Now, considering that a benefit has been provided by the supplier through a purchasing discount, which has been fully transferred to the end customer as an increased discount from 13.91% to 15.63%, it is necessary to validate the other indicators.

To do this, we need to examine the new break-even point of contribution in relation to the units sold. We can verify this using the following ratio:

The resulting calculation would be as follows:

This amount indicates that, in order to maintain the margin in monetary terms, the sales volume must increase by 69.34%. To verify this, let’s assume the same initial scenario of 100.00 units sold.

Now, we just need to verify that the turnover rate increases by 42.87% in order to maintain a GMROI of 1.40. To do this, using the new data from Table No. 3, it would be as follows:

This demonstrates that the analysis holds true.

**Conclusions**

This proposal can be used to structure volume discounts for end-users or different links in your distribution chain. It can also be used to create discount scales for different authorization levels, taking into account the desired hierarchical levels. Similarly, it can be applied to structure sales commissions, discounts for product bundles, and other similar concepts.

In other words, this approach allows for the structured segmentation of discount matrices while ensuring careful consideration of the monetary margin and validating the feasibility with other indicators. In this case, we used two examples: margin elasticity and inventory profitability. However, these are just illustrative examples and not limiting factors.

**Clarification note:**

This proposal is registered with the copyright office in Bolivia under file No. DA-S-200189-2023.