Can google earn enough to justify their capex spend

Here is my thinking, there are 3 ways a company can earn from AI. 1. Field of dreams, build it and they will come. 2. Boost their core product 3. Sell compute Clearly, Google are doing 3 with their Google Cloud growing 80%, but it's becoming harder to ignore the fact that they are doing 2. Search rev growth was falling, barring the pandemic it was below 10% from 2020 through 2024. It has been near or above 15% for the last 4 quarters. I played around with some very rough numbers, guesstimates at best. I figure they have spent at most $120 billion since 2024, extra on CapEx, that is the amount their CapEx is above what it usually is. For that they have gotten 5% extra revenue in search and at least 30% extra in cloud. With each of there margins figured in, that is $13 billion in extra income from the $120 spend. But that is Capex, on Q2 they mentioned 60% of capex was servers (4 year depreciation cycle) and the rest was data centres and networking. I am guesstimating at least 6 years depriation cycle over all. so that 13 can be looked at as 78. So really, looking at the highest they likely spent and the lowest they likely earned, we get $78 returned for $120 spent. A loss of 35% at worst. But then they still have the, build it and they will come, hope. I don't necessarily think google are wise to spend the eye watering capex amounts they are slated to spend in the coming years, but I think some commentary I see seems to ignore that they have already got alot from the capex they have already spent. Lately, I have been trying to write articles to help focus my thinking on a company, makes me double check my assumptions. Anyway I wrote one on this. It is mostly a longer version of what is above, with the addition of my thoughts on their future and a DCF model where I find they are only about fair value. I am not crazy enough to link the article, I'll already get downvoted enough for mentioning it, but if you want to read 2 or 3 poorly written articles a year from a wannabe analyst, check out my substack, you can find the link in my profile.