Just a quick disclaimer, this cost analysis is based upon the euro-gamer rumor, that the NX will be a hybrid device powered by nvidia tegra technology, essentially a tablet with detachable controllers and a docking station (Dumb.)
My career is based around business performance analysis so I thought I would do a bit of research to give an estimation of the true cost of the rumored device. I do not work within the gaming sector nor the mobile sector so my estimations are based on data available on the internet, I will provide sources. Now to begin!
So with a device such as the NX the logical place to start would be to evaluate the cost of a tablet style device first. So what do the rumors suggest?
Tegra based, presumed it will be current tegra technology. (Eurogamer) 720p Screen. (Emily Rogers) 32GB internal storage. (Emily Rogers)
So we need to first find a device that comes close to that already. Cue the 2012 (First Generation) Google Nexus 7 Tablet.
1280 * 800 Resolution. Tegra 3 SOC with accelerometer and Gyro. (The Tegra 3 was released on November 9, 2011 so this chip was cutting edge at the time.) 16GB Internal Storage.
So what was the cost to manufacture this device in 2012?
I found an article that breaks down the manufacturing cost of the entire tablet attached below.
https://technology.ihs.com/408150/low-end-google-nexus-7-carries-152-bom-teardown-reveals
I quote the article now "The high-end model with 16GBytes of NAND flash memory has a $159.25 BOM, for a total cost of $166.75"
However we are now in 2016, not 2012. Manufacturing costs have dropped for memory however we have to factor in inflation. The average inflation per year for the years between 2012 and 2016 is 2.1% per year. So when factoring this in we get $181.20. Now the NX will most likely have 32gb of storage at least, more RAM and of course V Ram for the GPU.
The only thing I can find around memory costs is the below website, http://www.jcmit.com/flashprice.htm, which outlines both Flash and SSD storage mediums (Not RAM). It appears the price per GB for storage has dropped to 1/4 of what it was in 2012 so I am going to assume that this cost estimate will allow for a device with 64GB of storage and 4GB of Memory (4 * the 2012 Nexus 7.)
So what of the other costs? The costing above includes box contents which includes a charger for the unit, so all we have left is the dock and detachable controls.
Lets start with the Dock, the plastic shell of it will cost $1-$2 at most, you can get a hard plastic case for a tablet for $2 from China but what of the tech itself? Now lets presume at best the Device will have WiFi direct streaming, think reverse Wii U, now you can buy a MIRACast dongle on Ebay from China for $11 Including shipping! This is consumer cost, the cost to manufacture has to be significantly cheaper.
http://www.ebay.com/itm/MiraScreen-HD-WiFi-Display-Receiver-DLNA-Airplay-Miracast-TV-Dongle-HDMI-1080P-/272035477934?hash=item3f5693f9ae:g:IvkAAOSwnNBXZ835
So the I would assume this to be the maximum cost of any kind of dumb dock.
Now we have controllers to account for. Current estimated manufacturing cost of an XBOX One controller is $15.
http://allthingsd.com/20131126/microsofts-xbox-one-cost-90-more-to-build-than-sonys-ps4-teardown-shows/
"The controller costs about $15, and contains Wi-Fi and Bluetooth components from Marvell Technology."
So we have
$200 For the tablet and charger (I added $19 to allow nvidia a profit margin on the tegra chips of $10 per unit sold plus a little extra due to it being new tech on a new manufacturing process, this nets nvidia $100,000,000 in profit with the estimated production volumes per year!) $11 for the dock $20 for the controller. (I added $5 to account for their detachable nature.)
So I estimate roughly $231 in total as a cost to manufacture the unit.
I cannot put a price on R and D however, Nintendo did state they would not sell project NX at a loss. Source : http://www.geek.com/games/nintendo-nx-will-not-be-sold-at-a-loss-from-launch-1653853/
The average profit margin for a phone or tablet is around 1.5 so lets assume to break even or profit that markup will absorb Nintendo's R and D costs.
$346.50 is the new price.
I cannot find any stats on how much retailers earn on console sales, but I am going to assume a 10% markup based on what smartphone markups are like. http://www.wisebread.com/cheat-sheet-retail-markup-on-common-items
Total cost now to the consumer $381.50.
So Nintendo could essentially offer a cutting edge tablet device, with dock and detachable controllers for under $400. This is all estimations. I honestly think that due to the volume Nintendo are manufacturing costs per unit may be lower when compared to a tablet like the Nexus 7. So my final estimate is between $300 - $350.
Strangely this almost matches up exactly to the recent Tesco leak! ;) http://www.trustedreviews.com/news/did-tesco-just-accidentally-leak-the-nintendo-nx-s-price.
TLDR : I estimate that the console itself will cost $300-$350 based on manufacturing costs of tablets, controllers and the markups you would expect within retail.