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I have heard it claimed that amazon's retail business is actually not very profitable (it's claimed that most of their profit comes from their web services). A rebuttal to this claim I have heard is that it only appears their retail business is not very profitable because they reinvest so much of their revenue, and that if they wanted to "turn on the tap" and stop reinvesting so much they would have to show huge profits from retail. I know next to nothing about accounting and cash flow statements and other public financial disclosures from corporations, so I wonder who is right? And is the rebuttal at least correct that it is not possible to deduce real profitability (as opposed to, I guess, "nominal" profitability) of amazon's retail business (or I guess any business that reinvests so much) from available information?

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I don't know if Amazon breaks out downloads such as Kindle or movies from the non-AWS part of income statement. You might look at the annual filing to see if there is a breakdown. You are interested in "retail". If we take "retail" to mean non-AWS then we can use the table I posted. It looks like in 9 recent months retail made 5.7B USD in North America and AWS made 9.9B USD. This is only an operating profit so expect actual profit to be less. If they had overestimated depreciation rates and surged retail investment then it might be that reducing retail investment will increase the retail profit margin. The retail operating margin looks like 3.5% in North America and 0.5% international. At Walmart it was 4.0%. So Amazon is delivering and they make a similar amount on a margin basis in at least in North America albeit the nature of the goods is different. The international segment is the laggard at Amazon.

most recent financial statement

For comparison is this Walmart statement that follows. Note that at Amazon the recent data column is to the right of the "year ago" column and at Walmart the order of the columns is the opposite... walmart

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