The scrap recovery arm costs 50 scrap and Gives you +10% scrap on acquisition other than selling items (rounded down.) Given that you have to spend scrap to earn scrap, at what sector does it make sense to invest in the SRA? I'd imagine you'd want to have a significant gain to make up for early scrap disadvantage.
This question's answer will vary based on difficulty, as that impacts scrap rewards as well as the necessity for early scrap.
In the first couple sectors, I think you easily make about 100 scrap per sector. As you move up, that amount increases to 200 or 300 per sector (assuming you are defeating all ships rather than fleeing or avoiding them). So I'd say that as long as you get it before the end of sector 4, it definitely pays for itself. After that, it gets to be risky, but could still pay for itself even if you pick it up in sector 5 or early sector 6.
There is also the opportunity cost of taking an equipment slot and not having the 50 scrap to spend on something else. I'd probably rate it as awesome in sector 1-3, good in 4, and iffy beyond that.
Comments talk about the Asteroid Field event, but I think that is rare enough that I wouldn't really take it into account. I've bought the arm numerous times, and gotten to take advantage of that event in maybe 10% of them.
Although bwarner has answered this question, there are some points where my experience (unlocking all ships, all achievements, completing the game numerous times on Hard/with AE) has made me consider the real answer a bit different.
The real answer is (IMVHO): it depends.
As already pointed out, since you buy SRA for 50 and can later resell it for 25, with the scrap reward @ 10% it only takes 250 scrap collected to make it viable. Collecting that much scrap is usually very easy, especially on Easy and Normal it can be done without much trouble in a single Sector 7 run (if it's done efficiently). I agree that AF event rewards ain't big enough to justify having SRA on board.
There are, however, other concerns.
So, to sum up: it depends. If you're aiming for a high score and feel confident with the game, have a decent enough array of weaponry, 3-4 Zoltans on board and got good luck before you got to the shop, you should get SRA - or even multiple SRAs if you're lucky enough, since they're stackable. If you're a casual player, you can take one if you have 0-1 aug already. Since I stopped playing below Hard and the risk factor increases too much with improper gear there, I skip it entirely after sector 2 - it's much more important to spend that scrap on things increasing survivability than income, since it's no longer about "how much scrap I'll be able to collect?" but rather about "how to not get reduced from 30HP to 0 in one combat" (early encounters with ships with Vulcan and Breach Missiles targeting my engines come to mind...); on the other hand, since you'll be selling some of the initial augments for scrap and free aug space, you can take 1 SRA if you get it in Sec 1/2.
