Why did Vegeta kill Nappa???

This question has always bugged me a bit since I started watching Dragonball Z (when I was 4), why did Vegeta kill Nappa? The conclusion most fans came up with, due to Vegeta's dialog with Nappa before he killed him, is because he believed Nappa was to pathetic, not truly a Sayian warrior, blah blah blah. Others think Vegeta was just evil and would kill anything, but I have came to a new conclusion; Vegeta killed Nappa because he didn't want Nappa to become stronger than him.

Nappa had a power level of 4000, him being brought to near death by Goku meant that once he recovered he'd have a power level of 8000+ roughly. Now Vegeta could stop Nappa with a power level of 4000 EASILY, even if he tried killing him in his sleep! Now Nappa with a power level of 8000+ given a strategic moment could kill Vegeta as he slept or had his back turned. Vegeta saw Nappa as a threat if he were to get stronger, AND KILLED HIM, to save his own skin later on.

Thats just my theory though...