Please make sure your PS4 is updated to 3.50 before trying this.
Streaming your Playstation 4 on your PC or Mac is now possible with the latest 3.50 PS4 firmware update.Remote Play lets you stream whatever's happening on your PS4 to your PC or Mac without the use of any wires, with very minimal lag.
To do this you'll need to be running Windows 8.1 or higher, or Mac OSX 10.10 or 10.11, you'll then need to install the Remote Play app from here.
Next, enable Remote Play on your PS4 from (Settings) > [Remote Play Connection Settings].
To use Remote Play, connect a controller to your PC or Mac via a USB cable. Launch the Remote Play app on your PC or Mac and sign in with your PSN account.
If you experience any issues during the process, just refer to this guide by Sony.