(AMZN 2.08%) is adding tons of Prime members -- in December the company confirmed that it had "tens of millions of members," including adding more than 1 million new members in the third week of December. This raises the question: What are these new Prime members worth to the company? To answer that question, I sharpened my pencil and calculated the lifetime value of a Prime member.

Hand inside of an open Amazon box

Image Source: Getty Images.

The customer lifetime value approach
Although it's not a traditional stock valuation technique, customer lifetime value is an interesting way to gauge the economics of subscription businesses. It can be calculated several different ways, but it comes down to how much extra profit a customer will contribute over time. To calculate it for Amazon Prime members, you need to know three things: How much will Prime members spend, at what contribution margin, and over how many years? Below, using a few assumptions, I've roughly answered those questions, and I've calculated an estimated lifetime value.

1. How much will each Prime member spend per year?
According to a 2013 study by the Consumer Intelligence Research Partners, Amazon Prime members spend $1,340 annually -- more than twice as much as non-Prime shoppers, who spend $650 annually. Those estimates were for 2013, and I expect spending per customer to increase each year. Thus for 2014, I'm assuming that Prime members will spend $1,500 and non-Prime customers will spend $700.

2. What is the contribution margin Amazon Prime members?
Contribution margin is a managerial account concept, so it may not be familiar to many investors. Essentially, it's a customer revenue less the variable costs necessary to earn that revenue. Amazon generated $75 billion in net revenue in 2013. Subtracting the variable costs associated with earning that revenue, i.e., cost of goods, shipping, fulfillment, estimated content costs and estimated Prime fees (to avoid double counting later), leaves $10 billion of contribution margin, which is 14% of revenue. That is the average across all Amazon customers. Since Prime members generate higher shipping costs, I assumed that the contribution margin for Prime members and non-Prime shoppers are 12% and 16%, respectively.

3. How long will Prime members stay with Amazon?
The average expected tenure of members can be estimated based on churn rates. For Amazon Prime members, Piper Jaffray estimates annual churn will be 5%; CIRP estimates it will be 6%. Those estimates both look low for me, so I assumed slightly higher churn of 7%.

Bringing it all together
Using the estimates described above, I calculated the lifetime value of Prime ($2,283) and non-Prime members ($916) using a 10% discount rate. Admittedly, these numbers are imprecise. Since Amazon doesn't disclose all the data necessary, I had to use numerous assumptions and estimates to fill gaps and simplify the model. Often, though, back-of-the-envelope calculations are the most useful for forming big-picture conclusions.

From this model, I concluded three things. First, new Prime members do contribute significant additional value to Amazon's business, and the more Prime members that Amazon adds, the better. Second, Prime members are significantly more valuable than non-Prime shoppers. Third, as Amazon's business mix shifts to include more Prime members, there is potential for operating leverage and margin expansion.