In this workout, we're going to calculate the lifetime value per customer and the LTV to CAC ratio. We're given some assumptions on the total number of new customers per quarter. And as you can see here, the number of new customers increases significantly from Q1 all the way through Q4. We also have the number of customers lost each quarter, and of course the total number of customers at the end of each of these four quarters, including the most recent quarter at 98,500 customers. We also have an assumption on the percentage of total new customers that are generated from marketing campaigns, and we're assuming that is at 10% each quarter. And besides that, we have assumptions on the amount of revenue and expenses that the company's expected to incur over the next four quarters. So let's begin by computing the company's recurring revenue. For that, we simply take the total number of customers at the end of each quarter and we multiply times the SaaS price per customer, and that would give us about 2.5 million in Q1. Now let's go ahead and compute the total sales and marketing costs. And for that, we have an assumption here of 40%, and that is 40% of our recurring revenue is gonna equal our total sales and marketing costs. So I'll take that 40% and multiply times the 12.5 million here. That gives us about 5 million. Next, let's compute our churn rate, and this is gonna be the percentage of customers that are lost each quarter. So for that, we're gonna take the number of customers lost and divided by the total number of customers in the prior quarter, and that would be about 1% to be exact 1.015%.

And finally, let's, let's compute our blended CAC. And here we simply have to take our total sales and marketing costs and divide that by the total number of new customers in that quarter. And our blended CAC for the first quarter would be $2081.30 So now that we have our sales and marketing costs, revenue churn rate, and our blended cac, we can begin computing our lifetime value per customer. First, let's get our average revenue per customer. So for that, I would take the total recurring revenue and divide it by the total numbers of customers.

That gives me an average revenue per customer of $125.

The gross profit per customer, in this case, we have an assumption of a gross profit margin per customer of 70%. So we can take that 70% and multiply times our recurring revenue, and then of course divide that by the number of customers at the end of the quarter. And that gives us a gross profit per customer of $87.50. So next, what we need is to compute our average contribution per customer.

The average contribution per customer is equal to the gross profit per customer, minus any direct cost associated with that customer. Now in this example, our only direct costs are our total sales and marketing costs, but you could have other direct costs such as administrative costs or any other operating expense that is associated with serving the customer. So in this case, we simply have to subtract the sales and marketing costs per customer. So in this case, we can simply take the 40% assumption for our total sellers and marketing costs and multiply times the average revenue per customer. And that will give us an average contribution per customer of $37.50. So next, let's compute the average lifespan of a customer, and that will be actual an actual simple calculation of taking one over our already calculated term rate of about 1%. So that gives us 98.5 quarters. So if we have an average contribution per customer on a quarterly basis of 37.5, and we have an average life span per customer of 98.5 quarters, our lifetime value of a customer or LTV is just the 98.5 times the $37.50 in average contribution. And that gives us an LTV of 3693.8. Now let's take all of these numbers and copy them to the right over the four quarters to assess the behavior of our LTV. And as you can see, the LTV goes down over the next two quarters and then it goes back up in Q4. And really the main driver of this behavior in our LTV has to do with our churn rate, which initially goes up for Q2 and Q3, and it goes back down in the last quarter of this period. So finally, let's compute our LTV to CAC ratio, and that simply is a ratio of the LTV already computed 3693.8 and divided by the blended CAC of 2081.3, and that gives us an LTV to CAC ratio of 1.8. Now keep in mind that if the LTV to CAC ratio is below three, well that implies that the company might be spending too much in sales and marketing costs. However, if the LTV to CAC ratio is above three, that indicates that the company could increase its sales and marketing costs, expenses, and in this way accelerate growth.

Now in this case, of course, we're below three, but let's see what happens when we copy this formula across all four quarters. And as you can see here, the LTV to CAC ratio goes from 1.8 to 4.7 to 9.4 and 14.9. Now really what's driving this significant increase in the LTV to CAC ratio is the fact that our blended CAC drops significantly over the four quarters. Now, this is a company that is experiencing high growth in the sense that we have a rapid increase in the number of new customers. This is a company that is also experiencing relatively low churn and stable churn at about 1% over the four quarters. And it has an LTV to CAC ratio that is much higher than our benchmark of three, which means that this company could increase its spending in sales and marketing costs to help accelerate the growth even further.