Can I Get Clarification

I just need some quick clarification.

Lets Assume a 300 f/4L IS is on a 50D. Due to the 1.6x crop factor, this effectively means the 300mm is actually 480mm.
If i put my 1.4x TC on, does this boost the focal length to 672mm? I also understand i will lose a stop and it will become a f/5.6 and i can still retain AF.

I've searched for an answer, and even asked a camera store, but failed to tell me if this is true.

Sorry if it sounds noob!

No the focal length, which is an optical value, would be 300 times 1.4 or 420mm. But with a 1.6 crop factor, the photos would appear with the same magnification as if they were taken on a 35mm film or full frame digital sensor with a 672mm focal length lens.

The 300/4 is a 300mm lens no matter what. Add a 1.4 TC and it is a 420mm f/5.6 lens. That is pretty much all you need to know.

The crop factor is only of interest if you also own or are used to FF (135 format) cameras. In this case, yes, the 300mm prime used on your 50D will give the same angle of view as a 480mm lens would give when used on a 135 format camera. And yes, the TC does the same thing.....420mm on the 50D gives the same angle of view as 672mm would on 135 format.

Many thanks for your replies!