Do you know exactly how much more you need to sell to make up for a discount?

Source: AI generated image (Dall-e)

All of us who have worked in marketing or in sales have at some point had the brilliant idea of offering a discount to reach the sales goal, and the best thing we have convinced ourselves and others of the idea that this is financially viable because the decrease in price is compensated by an increase in volume. This, basically, knowing how the price elasticity of demand works, has it happened to you?

Logically, the above may be true, the issue is that many don’t know exactly how much to sell in addition to what was estimated at the beginning so as not to affect profit, and this is why so many financial managers and analysts lose faith in the sales or marketing guy. However, I must warn that offering discounts requires much more analysis, but that’s something I discuss in this post.

Calculation of the adjustment in sales

What I’m going to explain next is what is known in the academic literature as the calculation of the sales adjustment, the percentage of critical point of sales, or break-even sales change. And this is nothing more than being able to determine by what percentage sales must be increased to compensate for a change in price or costs, or both.

For this recipe we need at least 4 ingredients:

  1. Current Price
  2. New Price
  3. Current Sales Goal
  4. Current Unit Cost

The goal will then be to estimate the new sales target based on the previous data.

If you don’t want the “long” explanation, download this template in Excel (File >> Save As), enter the above data and voila, you get the adjustment in sales.

The procedure assumes that, with the current sales target, the business obtains at least the minimum profit required by shareholders, so we do not expect that because of the change in price, there will be an impact on fixed expenses. If this is fulfilled, we can move on. This allows us to assume that if we keep the contribution margin constant, and the fixed expenses as well (after all, they are “fixed”) then the profit will be maintained.

According to this, what we are going to do is calculate three things: (1) current unit margin and (2) the new unit margin, then we calculate (3) the difference between the two and divide the result by the new unit margin. The result is the percentage by which we must increase unit sales to maintain the same profit. Just in case, “unit margin” is the subtraction between unit price and unit cost.

Let’s look at it with an example.

Practical example – Offsetting a 20% discount.

Let’s say our product, a new ergonomic mouse, came to market with a price tag of $50 (before VAT) and its sales aren’t going as expected. Management estimated it could sell 5,000 units, and for whatever reason, that goal is looking increasingly difficult to meet. The sales guy then proposes to offer a 20% discount, i.e. sell it for $40 (before VAT). Now let’s assume that the cost of each mouse is $27.50 (before VAT, put in the warehouse). In the end, the logical question would be: how much more do you have to sell to compensate for the discount offered?

Based on this data, we calculate the current and new margin:

  • Current Margin = Current Price – Current Cost = $50.00 – $27.50 = $22.50
  • New Margin = New Price – Current Cost = $40.00 – $27.50 = $12.50

Now we calculate the difference between the two margins:

  • Margin Difference = $22.50 – $12.50 = $10.00

Finally, to find out how much we need to adjust the sale, we divide this difference by the new margin:

  • Increase in Sales Volume = $10.00 / $12.50 = 0.80 –> 80%

And with this we calculate the new sales goal:

  • New Goal = Current Goal * (1 + Incr. in Volume) = 5,000 * (1 + 0.80) = 9,000 pcs.

From these results, one could interpret that, for this specific case, a 20% discount requires increasing the sales goal by 80% to maintain the same margin and not affect profit.

This can be easily verified by calculating the total contribution margin in both scenarios.

In the current scenario, the contribution margin would be:

  • Current Contribution Margin = Current Margin * Current Goal = $22.50 * 5,000 pcs.
  • Current Contribution Margin = $112,500

And the same goes for the new scenario:

  • New Contribution Margin = New Margin * New Goal = $12.50 * 9,000 pc.
  • New Contribution Margin = $112,500

Constant Margin Curve

Finally, an interesting exercise to quickly see price-quantity sensitivity is to build a constant margin curve in which you can see how much additional units you need to sell with various price levels, including what happens if you increase the price instead of lowering it, how much then the target could go down then. This can be seen in the constant margin curve for the example above that I show below:

Source: Own elaboration.

Conclusion

In conclusion, understanding the impact of discounts on sales and profitability is essential to any effective business strategy. As we have seen, correctly calculating the increase in sales needed to compensate for a discount can be the key to maintaining the financial health of the company. I hope this analysis and the tool provided will be helpful to you in making informed decisions in your own pricing strategies.

Have you ever had the need to estimate how much more to sell to compensate for a discount? What were the results? I invite you to share your experiences and tips in the comments. Also, if you have questions about how to apply these calculations or improve your pricing strategies, don’t hesitate to ask. I’m here to help and learn together!

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