Why do you have to add a 150+EUR GPU? There are many cheap options.
You can get Radeon R7 250 under $50, which absolutely destroys i7-6700k's integrated HD530.
You can get Radeon R7 250 under $50, which absolutely destroys i7-6700k's integrated HD530.
(Technically HDMI 1.4 also supports 4K but only at 24hz, which is fine for TVs but a miserable experience on a PC desktop)