Thanks what is the cheapest video card you recommend for HDMI 2.0 support ?
I wouldn't recommend any without more information such as how you intend to use it. Are you connecting to a TV? Are you connecting through a HDMI switch? Are you connecting to a receiver/pre-processor? Will this be for watching movies/streaming? Are you trying to do any gaming? What resolution is the display device? What resolution are you trying to play the movie/game/video content in? Are you using Netflix streaming? What operating system do you have?
Pretty much all of those questions need answering before anyone can say that a card will work because there are plenty of cards that support HDMI 2.0 output, but not all of them will work with streaming, or 4K content, or HDR, or HDR+color depth+4k+60 frames per second, or TV/monitor resolution+acceptible frame rate for gaming.
Personally if you have a choice, I would wait for a card that supports HDMI 2.1 (requires TV/monitor/receiver/pre-processor/hdmi switch that also supports HDMI 2.1) as most of the problems go away (for devices that support the full spec... not all devices will support full spec though). HDMI 2.0 is too bandwidth limited for HDR and 4k resolution to work properly without making some kind of sacrifice (either limited to 30fps or horrible compression on the color space).