Imagine if I buy a $200,000 Lamborghini which, with regular servicing, will survive 100,000 miles.
That means for every mile I drive, not only am I paying for fuel, and insurance, and tyres, and servicing - I'm also paying, on average, $2/mile in depreciation.
And sure, the "true" value chart might not be linear. Maybe there'll be a sharp drop when the car ceases to be brand new, or a bump in value when it becomes a classic. But so long as it's worth $200k at 0 miles and $0 at 100k miles, the average cost of a mile must be $2.
It’s as if your car gained value with every mile driven.
I don't think that's true. All of the F9 failures[1] have been due to the 2nd stage. And that's new every time.
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1. CRS-7, AMOS-6, and Starlink 9-3
But even then, it doesn't change that the booster has a maximum lifespan and/or eventually increasing repair and therefore depreciation - we are working on an amortized basis.
That used to be true. It no longer is.
We don't know what the maximum lifespan of these boosters are. There are workhorses that have over 20 launches under their belt, and no sign of deterioration. Obviously at some point something will give, but we're not there yet.
Do we have anything proving this besides the self-serving word of a privately owned company?
I'm not saying it's false, I have no idea either. But there's a lot of highly specific speculation going on here, based on no reliable source.
Also, 15M$/launch is not widely believed to be correct. There is much creative accounting SpaceX could be doing with Starlink (is at-cost account for booster depreciation? If so how, since we don't know how much reuse a booster can be expected to give? Or is it just the cost of refurbishment?), and since the last statement where Elon claimed 1000$ per kg actual cost, SpaceX had to raise their prices, claiming it was due to inflation - is that accurate? Most estimates I've seen are that the cost is 20-30M/launch, which would instead give 1.1-1.7M/ton.
So, it's a big advantage but not an insurmountable one.