Connect Dell laptop to Apple LED display 27

I'm about to buy a 27" Apple LED display (not the Thunderbolt one) to connect to my MacBook Pro 15". This is all fine.

For work I have a Dell laptop with a VGA and HDMI socket. Now here comes the question/problem, can I connect the Apple monitor to the Dell? The monitor has a cable with a male Mini Display-port connector. I have great difficulties finding an adapter from a Mini Display-port female to HDMI male.

I searched the web and multiple fora and didn't find a single solution that does the trick. But I did find this ('these' is actually a better word):

From Apple monitor Mini display-port male, to:

1. Mini Display-port female to Display-port male adapter. Connects to:
2. Display port female to display-port female adapter. Connects to:
3. Display-port male to HDMI female adapter. Connects to:
4. HDMI male to HDMI male adapter. Connects to laptop

This whole lot costs +/- 58,- USD. I can't believe this is the only option out there (and that it will work...).

So in short, 3 questions:

• Can I connect a Windows Dell laptop to an Apple LED display?
  
• Does this solution work?
• Is there a better solution out there?

These 4 adapters look like they just pass on the signal. So no big block halfway down the cable that looks like it is doing something to the signal.

I don't want to use the VGA connector as I want to maintain a digital signal.

Thank a lot for any feedback/help in this area!