Customer Lifetime Value

When margins and retention rates are constant, the following formula can be used to calculate the lifetime value of a customer relationship:

${\displaystyle {\text{Customer Lifetime Value}}={\text{Margin}}\cdot {\frac {\text{Retention Rate}}{1+{\text{Discount Rate}}-{\text{Retention Rate}}}}}$

The model for customer cash flows treats the firm's customer relationships as something of a leaky bucket. Each period, a fraction (1 less the retention rate) of the firm's customers leave and are lost for good.

The CLV model has only three parameters: (1) constant margin (contribution after deducting variable costs including retention spending) per period, (2) constant retention probability per period, and (3) discount rate. Furthermore, the model assumes that in the event that the customer is not retained, they are lost for good. Finally, the model assumes that the first margin will be received (with probability equal to the retention rate) at the end of the first period.

The one other assumption of the model is that the firm uses an infinite horizon when it calculates the present value of future cash flows. Although no firm actually has an infinite horizon, the consequences of assuming one are discussed in the following.

Under the assumptions of the model, CLV is a multiple of the margin. The multiplicative factor represents the present value of the expected length (number of periods) of the customer relationship. When retention equals 0, the customer will never be retained, and the multiplicative factor is zero. When retention equals 1, the customer is always retained, and the firm receives the margin in perpetuity. The present value of the margin in perpetuity turns out to be the Margin divided by the Discount Rate. For retention values in between, the CLV formula tells us the appropriate multiplier.