## Introduction and definition

The Return-on-Investment (ROI) is often considered as one of the most important metrics in marketing. We, at Peak, disagree with this broadly spread convention and wish to show why you should never look at your ROI only. Indeed, **maximising the ROI does not maximise your profit ^{[1]}**!

Firstly, let us define formally what the ROI is: the ROI is a ratio which measures the sales growth **directly attributable** to a marketing action. As a formula, we could write it as follows:

## Maximising the ROI does not maximise your profit

It is a common belief that setting ROI objectives is a good way to manage your marketing costs. As strategic advisors, we must convince our clients that setting a fixed (average) ROI for your campaigns is far from being the best strategy to maximise the profit. **Setting an ROI objective which is too high will make you miss business opportunities.** Below is the explanation why.

#### Definition of the profit and CPA

The profit is defined as the sum of the differences between the LTV and the Cost per Acquisition (CPA) over all the customers. We consider the LTV to be fixed across customers and the **CPA to increase with the number of customers**. The company profitability is defined as follows (*I* being the number of customers):

We always start by targeting the most profitable customers. In the formula (2), we first target the audience with the lowest CPA. As we expand marketing activities, we target audiences of lesser quality and less profitable (with a higher CPA). Consequently, every new customer decreases the average profit per customer but adds their own profit to the total profit. The optimum is found when attracting a new customer does not change the total profit. At this specific point, the new customer’s LTV is equal to their CPA and the marginal profit is equal to zero. **In terms of ROI, this implies it is high when targeting a smaller number of customers and gets lower the more you acquire customers.**

#### Visual demonstration

Figures 1 to 4 demonstrate visually why the profit is maximised when the CPA is equal to the LTV. Following the assumptions stated above, namely a fixed LTV and an increasing CPA, let us imagine we decide to acquire 10 customers. We will also set two new assumptions: the LTV is equal to half the revenues and the marginal CPA increase is constant^{[2]}.

In this case, the cost to acquire these customers, represented by the blue dashed area, is equal to: 5*10+(5*5)/2 = 62.5. On the other hand, the sum of the LTV generated by these customers is equal to 10 * 30 = 300. Consequently, the total profit is equal to 300 – 62.5 = 237.5 CHF. This is represented by the yellow dashed area.

When acquiring 20 customers (Figure 2), the marketing costs are equal to: 5*20+(15*15)/2 = 212.5. The sum of the LTV amounts to 600. Thus, the profit is 600 – 212.5 = 387.5, which is higher than when acquiring 10 customers.

I think you got the idea. As long as the CPA is smaller than the LTV, the marginal profit is higher than the marginal cost. The optimum is reached at *I* = 30, where the profit amounts to 437.5 CHF and the CPA is equal to the LTV (Figure 3). At this point, it is not possible anymore to improve the total profit.

Now, let us have a look at the ROI between these three situations.

Not surprisingly, **the ROI decreases when acquiring more customers**. When maximising the profit, the ROI is slightly smaller than 4. You can now directly see it would not be optimal in terms of profit to maximise ROI between those three situations. If doing so, you would actually end up in the worst of the three situations in terms of profit. Figure 4 illustrates how the total profit varies with the number of customers. The inverted U-shape profit curve, typical of profit maximisation problems, allows you to grasp the problematic from a different perspective. The total profit goes up until it reaches its maximum at *I* = 30. From this point on, acquiring a customer becomes too costly (LTV < CPA_{i}) and the profit starts diminishing.

When plotting the ROI against the total profit (Figure 5), we note this negative relationship between the ROI and the number of clients. **This is virtually always the case in reality as you first target the most profitable clients. **To determine the optimal ROI which maximises your profit, you will need to calculate the LTV of your customers and estimate your CPA function. Only at this stage, you will be able to set the optimal ROI for your business. The only thing you can for sure affirm for any business and marketing campaign is that your ROI must always be bigger than 1.

## Conclusion

ROI is a key metric in marketing and reporting it gives a concise overview of your marketing actions efficiency. It has also the advantage to be simple to understand and can be useful to compare different acquisition channels. Nevertheless, the ROI does not tell you how much to invest in a specific marketing action and must not be used as a criterion to manage your company^{[3]}.

We have shown that setting ROI objectives prior to thoroughly analysing your CPA and the LTV of your customers is not a good idea if you wish to maximise your profit. You will under- or overspend in marketing costs and it will be damaging for your profit.

[1] In case you have a budget constraint, maximising the ROI maximises the profit.

[2] For sake of simplicity, we assume in this article that the marginal CPA increase is constant (from 5 customers on). It results from it that the CPA function you see in the following graphs (Figure 1 to 3) is linear. Reality is usually not that simple, but it does not add any value to complexify this element for what we wish to demonstrate.

[3] Companies usually have a fixed marketing budget. For political reasons, departments of some (big) corporations sometimes want to spend the entirety of the budget they were allocated. Considering this as a constraint, optimising the ROI in this case leads to the best possible outcome in terms of total profit.