# Marketing Analytics: How to calculate Customer LifeTime Value (CLTV)

As has been argued multiple times, one of the best ways to forecast the economic value of a customer is to calculate the CLTV. This works great for a SAAS business as well as any other business where you can reliably forecast the contribution margin. In this article, we will focus on how to calculate the CLTV, what are the various inputs, and what are the pitfalls of this metric that we should be aware of.

Definition: Total profit (We can also say total revenue, gross margin, profitability etc; accordingly the formula will change) that a firm can expect to earn from a customer over the entire lifecycle of the customer.

Why do we calculate CLTV? Theoretically, the value of any business should be the present value (Discounted value) of the sum of Life time value of all of its customers. Thus, the higher the CLTV or more the number of customers, the more valued the business should be. No wonder, growth companies such as Netflix put so much effort in acquiring, retaining, and increasing the CLTV of its customers.

How do we calculate CLTV? We will find many formulae online with partial explanations. I will try to tackle this mathematically so that we can see why we have so many ways to calculate and yet why they are all the same.

I will use some Jargons in this article so let us first clarify those terminologies.

Contribution Margin (M) = Revenue earned from serving a customer - VC (Variable Cost) spent in serving the customer = ARPU (Average Revenue Per User) - VC
Discount Rate (d) = \$100 in 2050 is less valuable than \$100 today, so, we will discount the profit earned to get the present value of the money.
Churn Rate(c) = Percentage of customers that leave the platform.
Retention Rate (r) = 1 - The churn rate = Percentage of customers who stay on the platform. It can also be calculated as, ((Ce-Cn)/Cs))x100.
where:
Ce = Number of customers at the end of a given period,
Cn = Number of new customers acquired during a given period,
Cs = Number of customers at the beginning of a given period.

Case I: Customer pays at the beginning of the period say Jan 1. We will assume that this payment, and hence the contribution margin, remains constant as in the Netflix model.
PV of the first payment = M
However, the next year, the chances of the customer staying on the platform is only r = retention rate. So, PV of the second payment = (M*r)/(1+d)
Similarly, PV of the third payment = (M*r²)/(1+d)²

Therefore, the customer lifetime value is the sum of the present value of each payment
CLTV = M + (M*r)/(1+d) + (M*r²)/(1+d)² + …. (Eq. 1)
This is an infinite geometrical progression. We can either use the formula of sum of an infinite Geometrical progression or calculate by multiplying both sides by r/(1+d)
CLTV * r/(1+d) = M * r/(1+d) + (M*r²)/(1+d)² + (M*r³)/(1+d)³ + …. (Eq. 2)
(Eq. 1) - (Eq. 2) => CLTV (1 - r/(1+d)) = M or CLTV(1+d-r)/(1+d) = M

Thus, CLTV = M * (1+d)/(1+d-r)

Case II: Customer pays at the end of the period say Dec 31. We will assume that this payment, and hence the contribution margin, remains constant as in the Netflix model.
PV of the first payment = M/(1+d) . [Note: We will have to discount the payment at the end of the period to get the Present value]
However, the next year, the chances of the customer staying on the platform is only r = retention rate. So, PV of the second payment = (M*r)/(1+d)²
Similarly, PV of the third payment = (M*r²)/(1+d)³

Therefore, the customer lifetime value is the sum of the present value of each payment
CLTV = (M)/(1+d) + (M*r)/(1+d)²+ (M*r²)/(1+d)³ + …. (Eq. 3)
This is an infinite geometrical progression. We can either use the formula of sum of an infinite Geometrical progression or calculate by multiplying both sides by r/(1+d)
CLTV * r/(1+d) = (M*r)/(1+d)² + (M*r²)/(1+d)³ + (M*r³)/(1+d)⁴ + …. (Eq. 4)
(Eq. 3) - (Eq. 4) => CLTV (1 - r/(1+d)) = M/(1+d) or CLTV(1+d-r)/(1+d) = M/(1+d) or CLTV = M / (1+d-r)

Thus, CLTV = M/(1+d-r)

From the above two cases, we see that CLTV can be calculated as

If we ignore the discount rate, then both formulae converge to

We know that (1-retention rate) = (1 - r) = Churn Rate = c
CLTV = M/c

Case III: In the above cases, we are assuming no churn in the first period. But what if there is a churn in the first period in Case I?
PV of the first payment = M*r (Note only r% will pay as rest will leave the platform)
However, the next year, the chances of the customer staying on the platform is only r = retention rate. So, PV of the second payment = (M*r²)/(1+d)
Similarly, PV of the third payment = (M*r³)/(1+d)²

In general, PV of the payment in Period t = (M*r^(t+1))/(1+d)^t

Therefore, the customer lifetime value is the sum of the present value of each payment
CLTV = M*r + (M*r²)/(1+d) + (M*r³)/(1+d)² + …. (Eq. 5)
This is an infinite geometrical progression. We can either use the formula of sum of an infinite Geometrical progression or calculate by multiplying both sides by r/(1+d)
CLTV * r/(1+d) = M * r²/(1+d) + (M*r³)/(1+d)² + (M*r⁴)/(1+d)³ + …. (Eq. 6)
(Eq. 5) - (Eq. 6) => CLTV (1 - r/(1+d)) = M*r or CLTV(1+d-r)/(1+d) = M

Thus, CLTV = M * r * (1+d)/(1+d-r)

Case IV: Customer pays at the end of the period say Dec 31 and churns in the first period as well. Improving on Case II, let us add the churn rate.

PV of the first payment = M*r/(1+d) . [Note: We will have to discount the payment at the end of the period to get the Present value. Also only M*r will pay as rest all will churn out]
However, the next year, the chances of the customer staying on the platform is only r = retention rate. So, PV of the second payment = (M*r²)/(1+d)²
Similarly, PV of the third payment = (M*r³)/(1+d)³

Therefore, the customer lifetime value is the sum of the present value of each payment
CLTV = M*r/(1+d) + (M*r²)/(1+d)²+ (M*r³)/(1+d)³ + …. (Eq. 7)
This is an infinite geometrical progression. We can either use the formula of sum of an infinite Geometrical progression or calculate by multiplying both sides by r/(1+d)
CLTV * r/(1+d) = (M*r²)/(1+d)² + (M*r³)/(1+d)³ + …. (Eq. 8)
(Eq. 7) - (Eq. 8) => CLTV (1 - r/(1+d)) = M*r/(1+d) or CLTV(1+d-r)/(1+d) = M*r/(1+d) or CLTV = M*r / (1+d-r)

Thus, CLTV = M*r/(1+d-r)

In the above calculation, we ignored another important aspect, which is CAC (Customer Acquisition Cost). This is the money that companies spend in acquiring a new customer such as in Advertising, couponing, Free trial period, sign up incentives etc.

If we take that into account we can adjust our formulae to

CLTV = (M / (1 + d - r)) - CAC

This gives us four different drivers of CLTV,

M = Contribution Margin = The higher the contribution margin, the higher the CLTV. To increase this lever, we can either increase the prices and hence the ARPU or lower our variable cost.
d = Discount rate = The lower the companies discount rate, the higher the CLTV
r = Retention rate = The higher the retention rate or the lower the churn rate, the higher the CLTV. That is why businesses should think about keeping the customer on the platform. More often than not, in an attempt to achieve growth companies ignore the retention Rate. However, as is rightly pointed out growth without retention is a leaky bucket.
CAC = Customer Acquisition is a great way to bring customer to the platform, however it could be expensive and any customer acquisition campaign must identify the CLTV using the above formula to see whether the campaign makes sense.

Another important metric to evaluate the profitability of a business is to calculate CLTV/CAC. If the ratio is greater than 1 then it is a profitable business.

Pitfalls of CLTV:
1. CLTV should not be used as a means to justify marketing expenditure.
2. GIGO (Garbage-in, Garbage-Out) CLTV is only as good as the assumptions. Relaxing a few assumption may present a completely different story. Always check the assumptions behind the math.
3. Metrics in CLTV are correlated. As we increase Prices, it may increase the Churn Rate. Assuming that an increase in price will achieve a higher CLTV is a dangerous assumption. Similarly decreasing Variable cost will impact the quality unless we are achieve economies of scale. A sensitivity analysis to identify the impact of each sub-metric is a good way to find a range.
4. Infinite time horizon: CLTV calculated as above assumes infinite time horizon of a customer life. Business landscapes change and so do competitive offerings. Always have your sight on the long term strategy to create a sustainable competitive advantage.

Conclusion: Despite its limitation, CLTV is a great back of the envelope calculation to identify the value of the firm. For growing businesses keeping CLTV/CAC > 1 could be a challenge. However, over a period of time, CLTV should go up and CAC should come down. Benchmarking with competitors is a good way to identify the issue. In either case, focusing on retention through undivided attention on the current customer is always a good place to start.

Hope you found the article useful. In another article, I am diving a little deeper into how to build an attribution model to calculate CLTV/CAC — Read here.

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## More from Vinay Roy

https://www.linkedin.com/in/royvinay — Chief Product Officer @ Vista Global | MBA, UC Berkeley

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