Resistors, capacitors and potentiometer would cost ~7 USD.
Diode, transistor, logic chips and LM386 would cost around 4 USD.
Two Yamaha chips can be bought on aliexpress for 6.86 USD shipped.
That is about 18 USD for all of the components.
PCB can be etched in home with help of the laser printer and some cheap chemistry. You can then cut it out with a knife (scratch the surface multiple times and break it) and sand the edges. Or buy old school FR2 phenolic-cotton-paper laminate for PCB, instead of modern glass fiber FR4 and you can cut that using scissors 😜 It will be cheaper and it has the smell of old electronics. It is possible to make a PCB for 5 USD (it would look like this http://www.atari8ethernet.com/hires/D500_Etched_hr.jpg )
So, in theory, it would be possible to make that card for 23 USD (that's the price when you buy components just for a single card). If you know where to find parts that are not overpriced.
I calculated this price checking electronic stores in the country I live (Poland), so we possibly have lower profit margin in the stores than in the US. Retail price for single resistor or ceramic capacitor here is around 0.03 USD.
And of course you need to have some experience in DIY-stuff and experimenting to make it in home for such low cost, because not everyone likes or knows how to make PCBs with use of clothes iron and laser printer :p