Customer Lifetime Value (LTV) is one of the most important metrics for any highgrowth business. The ratio of LTV to Cost of Customer Acquisition (CAC) tells us how quickly the company can payback the investment required to generate revenue. If customers are cheap to acquire, and have a high lifetime value, this is a strong indicator that the company can grow quickly.
Many earlystage, or highgrowth companies focus the bulk of their efforts on acquiring new customers. Having a large number of new customers feels good, and intuitively feels like the right thing to focus on. Interestingly though, when we think clearly through the dynamics of customer lifetime value, we see that the other side of the coin  customer retention  holds the key to generating a healthy LTV:CAC ratio.
An excellent Harvard Business Review article found that acquiring a new customer can cost between 5, and 25 times as much as retaining an existing one who would otherwise leave. Another fascinating study by Bain & Company showed that increasing the retention rate by just 5% can lead to an increase in profit between 25% and 95%.
These studies are great evidence that there is something interesting to explore in the relationship between acquisition and retention. I'm going to use a systems model to show you the underlying mechanism  and how you can exploit insights from these types of model to optimise your LTV:CAC ratio.
Building the LTV Systems Model
Here is a simple systems model of Customer Lifetime Value. As all systems models, it is set up as a simulation. I simulate the model from month 0  the company starting  out 3 years (36 months) into the future.
The model structure is very simple. I have four variables on the lefthand side:

Cost of Customer Acquisition,

Average monthly spend per active customer,

Monthly retention rate (the proportion of active customers who remain so),

The average number of new customers that the business acquires each month.
In future tutorials, we can look at modeling each of these separately  but here I just assume their values to keep the model simple.
At the top, you can see the flow of new customers each month. I use one of the discrete functions (the poisson distribution) to generate some randomness  but on average the value set by the fourth variable above is the number of customers that arrive each month.
Those new customers flow in to the stock of active customers. These are the customers paying us each month, so the higher this number, the better.
To the right of this stock, flowing out of it are some customers who "churn" each month. Churn rate is simply:
Churn Rate = 1  Retention Rate
I connect that outflow into another stock (Customers Lost), so we can see how this number grows over time.
In the image below, you can see below the inspector panel selected on the "Churned" flow. Note that I wrap the formula in int(), which makes sure that we get only whole numbers (integers)  as we can't have less than a whole customer!
Computing Metrics
The three rows of simulation elements below the customer modeling are simple calculations to generate financial metrics. The variables which govern costs and revenues are multiplied by the relevant stocks/flows:
Monthly Revenue = Avg. Monthly Spend * Customers Monthly Cost = CAC * New Customers
The net profit is simply the difference between revenue and cost. Note in the image below that I divide these numbers through by 1000, to show outputs in $000's. This keeps the numbers manageable and will help us when we compare alternative modeling assumptions in due course.
This gives us the full systems model structure. We can see how things are interrelated, and now we can start to use this simulation to explore how things change through time under different assumptions.
Increasing Customer Acquisition
Let's start by doing what most business strategists do  increase the number of customers we acquire each month. Let's assume that we can intervene in such a way that doubles the average number of new customers we acquire each month. To keep the model simple, we'll assume that CAC is unchanged. In a more realistic models we might want to make these two variables interrelated  but here we'll just keep things simple.
When we change the value of this variable from 50, to 100, the 36 month simulation instantly updates. Let's focus on the new customers and net profit numbers at month 36, and compare them to the previous simulation:
Original Simulation

480 Customers

$41.9k Net Profit
Doubling Average New Customers

964 Customers

$82.6k Net Profit
Increasing Customer Retention
Now let's try out the alternative stategy. This time, we'll reset the Avg. New Customers variable to 50, and just increase the retention rate from 90% to 99% (a 9 percentage point increase). We'll rerun the simulation and add these numbers to the comparison.
Original Simulation

480 Customers

$41.9k Cumulative Net Profit
Doubling Average New Customers

964 Customers

$82.6k Cumulative Net Profit
9pp Increase in Retention Rate

1500 Customers

$189.82k Cumulative Net Profit
The results of this simple experiment with the dynamics of customer acquisition and retention are pretty impressive. Assuming these two strategies were realistic alternatives for this business in the realworld, we've more than doubled cumulative net profit, and increase customer numbers by more than 50%, just by exploring two different alternatives in our systems model.
Why is this the case?
We can understand why this is so by looking at the model structure. This is very hard to do in a spreadsheet  all we get are a bunch of cell references that we need to dive into  but is visually very easy to see in a systems model.
When we inspect the model, and see how the key metrics change over time, we find that the key to building up the stock of customers is to prevent them leaking out through the "Churned" flow. Also notice the stock of customers lost. When we cranked up customer acquisition, much of that effort translated into growing that stock of lost customers. When we focused on customer retention, that stock shrank  our existing customer acquisition activity became more effective, as the customers stayed around for longer  hence their lifetime value increased.
Our systems model clearly shows that the number of churned customers (the outflow) depends on the total number of customers (the retention rate / churn rate is applied to the stock of customers). We have a socalled negative feedback loop between customer acquisition and the number of customers.
A greater stock of customers with a fixed retention rate means more leaving each period. This is analogous to trying to fill a bathtub with the plug out; the fuller the bathtub gets, the faster water flows out. This is the key feature of the system that drives our results and shows why, back in the realworld, shifting the emphasis towards retention might be a more successful strategy in the longrun.
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