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Minimum Desirable Product
What's harder to measure is the less-linear effects of retention, for example, sharing. Folks invite others to join up so they can share with them. The more people that join, the easier the sharer's life gets. If those new users aren't sticking around, your service becomes less useful to your original sharer. A low retention could easily kick off a downward spiral here.
Went through your example above, and can't figure out your calculation behind the 1 month churn.
"In the short run, the numbers are close to the same:
* 80% monthly retention, after 1 month = 600
* 90% monthly retention, after 1 month = 700"
Shouldn't that be 800 and 900 instead?
80% monthly retention, after 1month= 1000*(0.8)^1=800
80% monthly retention, after 2months= 1000*(0.8)^2=640
I am sure I missing something obvious.
So the general formula to remember is ARPU * (1/churn) - COA = lifetime value of the customer.
And, as you rightly point out, churn plays a big effect here. Increasing the revenue from your customer base can be quickly wiped out by losing them quickly.
It also notes another interesting fact - it's okay to spend money to get customers - JUST MAKE SURE YOU KEEP THEM!.
Also, we (@Vindicia) have a best practices guide for those who are looking for ways to improve customer retention - http://bit.ly/cust_retention
Without doing much digging I imagine that's a reasonable simplification, but I wonder how it plays out in real life? Have there been any studies on how user attrition rates change as a function of time since they signed up?