- It costs money to acquire a user. Let's call this the cost per click (CPC)
- It not all clicks lead to registered users. Let's call this the conversion rate for ads (CONV-ADS)
- Each registered user is worth money. We can break this out in terms of click through rates etc. but for now lets just stick to average revenue per user (ARPU)
- Each user refers one or more users (REF)
- Each referred user has its own conversion rate (CONV-REF)
- Finally, refers take time. We can break out average time per referral and use a yearly discount rate, but to simplify let's assume you did that and now just have a discount rate per referral iteration (DIS)
The equation starts out like this:
NPV = -CPC + CONV-AD * ARPU
Which is simply chance of getting a registered user times value of that user minus cost of acquisition.
Now to add referrals, we change the value of that user:
NPV = -CPC + CONV-AD * (ARPU + REF * CONV-REF * ARPU)
This prices in the value of the referrals to the value of the original user. The discount rate leads to:
NPV = -CPC + CONV-AD * (ARPU + REF * CONV-REF * (1 / (1 + DIS)) * ARPU)
But of course each referal can refer someone else:
NPV = -CPC + CONV-AD * (ARPU + REF * CONV-REF * (1 / (1 + DIS)) * (ARPU + REF * CONV-REF * (1 / (1 + DIS)) * (ARPU + REF * CONV-REF * (1 / (1 + DIS)) * ...
You get a geometric series which converts back down to:
NPV = -CPC + CONV-AD * ARPU / ( 1 - X)
Where X = REF * CONV-REF / ( 1 + DIS)
This converges if X < 1, otherwise you get infinite value per user. Of course this assumes conversion rates, referral rate and ARPU are constant as your user base grows and therefore can't really 'price' infinite iterations of referrals, but I'm finding it useful to do sensitivity analysis on various changes to web sites when I set N in the geometric series to something like 3 rather than infinity as above.
Renaming some of the terms will probably make this equation less web centric, but the web vocabulary is what I'm most familiar with these days.
1 comment:
This makes sense. Rather than try to consolidate the equation, though, I can see reasons not to apply it:
1. Estimation error swamps the result.
2. Referral rates vary wildly through time.
Example. HotOrNot's early referral rate was astronomical. Their promotion was simply to email a link to a few dozen friends -- this produced tens of thousands of hits in the first week. Today, by contrast, that site is in decline, and gets much less referral traffic.
Thus, at various points on the the development curve of HotOrNot, the equation's results would have been either high or low by an order of magnitude or more, because it projects a referral rate that isn't fixed.
Thus it cannot be used in real-world conditions to choose a spend level.
I'll think about it to see if there's a way around this. It's quite similar to the growth rate estimation problem in other NPV calculations, but more extreme.
---
Post a Comment