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The maths behind choosing a target CPA
Let’s say you’re marketing a product that makes you $10 profit each time you get a conversion. What should your target CPA be?
It seems like a pretty simple question, but it turns out there’s actually a good amount of maths behind answering it. I put together a [little article here](https://mackgrenfell.com/blog/mathematical-marketing-one-piece-of-calculus-that-can-change-the-way-you-advertise) which explains how you can calculate the target CPA which gives you the most overall profit. Would love to hear people’s thoughts.
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9 Replies
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Thank you! Don’t have time to read it at the moment but it’s in my bookmarks. Your website seems to have a lot of usefull information, thank you for this.
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Those whole write up is quite detailed and interesting. However it also might over-simplify the issue. Your model requires 1 of 2 scenarios:
1. All spend is running through a single source (only google, or only Facebook, etc)
2. Your target CPA is a blended target across all sources.
1 has obvious problems in that you are severely hampering your ability to market at scale.
2 has problems because it doesn’t answer the question of “what should my target CPA be at a source level?” Because not all sources are built equally and many are inter-relational. For example, you might market on Facebook and google. Facebook will help build awareness of your brand which people then later recall and search for on google, which would make google the conversion-driving source. Your math will tell you that Facebook is failing and google is doing great. But if you shut off Facebook, you may also be shutting off a key driver of search. So what should your ideal CPA be on Facebook and Google in these scenarios?
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Thanks! My calculus is quite bad to appreciate this fully, and it would be cool if you added a section in the end about calculating this for other numbers, maybe even some pre-made Google Sheet calculator.
But overall it was a very interesting read. -
Honestly, for me it’s a dance between scale and profitability. Disclaimer: I’m a business owner who runs my own ads, I’m not an agency.
I set a Target CPA that makes business sense – as high of margins and ROI that I can. But this is only scalable so far (at least in Google). So I’m constantly considering the effect of increasing (incrementally, of course) my Target CPA to achieve more scale. As long as the math works out and my lower margins are offset by more volume, than I’m happy. If not, I leave it and look for ways to scale horizontally. But again, as a business owner, I focus on the customer lifetime value. I’ll even take some strategies to break even because I know the shear fact that I’m getting more customers will increase my profitability in 2-6 months.
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Thanks for sharing your insights, very thoughtful. I guess there’s a bunch of assumptions that need to be true for the answer to work in your favour. For one, google simulation must be accurate and the underlaying data (campaign setup) it’s drawing on, as well as profit margin calculus.
Setting those trife concerns aside, consider a population of competing marketers running a set of basic single ad / keyword campaigns targeting one product. If they were to run same calculations and consequently set same parameters, how would it affect individual outcomes?
Thanks!
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It also depends on your model – are you CPA or are you LTV?
I have a PPC ROI calculator here [https://primaryposition.com/google-ads-ppc-roi-cpa-calculator/](https://primaryposition.com/google-ads-ppc-roi-cpa-calculator/)
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Great read. Thx
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Hey, please excuse my calculus novice question – when you calculate the derivative, why is the formula ‘189/ad-spend’ rather than ‘(478+189)/ad-spend’? Thanks! Great article and site!
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Thanks for sharing! Does this also work with Googles UAC bid guidance?
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