Product Price Question
Prices in Asia tend to be significantly lower, even at 5K-10K, on the sort of stuff you're talking about. Note that high-spec items such as aerospace qualified parts may be more expensive in Asia, so you really have to look it it on an item-by-item basis. 

You cannot estimate the BOM of mass-market toy using the methods you've described. The idea of finding a product that has similar or higher spec parts and comparing the sell price to your required sell price is valid for a ball-park feasibility estimate, but not highly accurate. 

Note that even if your quantity is not relatively high, you may be able to have the product built fairly cheaply, however your access to top-tier components, assembly houses etc. will be severely constrained, and your quality will suffer greatly. 

You should use an iterative process to design a prototype using parts that are available inexpensively in Asia as well as meeting all your requirements. There's no need to sweat over passives and such like, but the choice of a microcontroller, LDOs, connectors, PCB technology and such like should involve some market knowledge at some level. 

So, in summary- find a similar product to ballpark, but involve external experts or develop expertise internally before committing to a design. 



P.S. Be careful about "shopping" your design-in-progress unless you have iron-clad protection, one fellow I worked with got quotes from several potential Asian manufacturers, and by the time he got around to signing P.O.s and contacting buyers, a very similar product was already on the way to the shelves, as a direct result of his inquiries. I'm sure their "engineering" was made more efficient by having detailed drawings on-hand that they just needed to tweak a bit.