I realise it’s a bit of a ‘how long is a piece of string’ type of question but, in other words, at what distance is it before there’s not enough energy left in the bullet to kill the beast humanely.
Blimey, there’s enough here for a complete article; if not a book!
However, the simple answer to your first question is that the maximum range at which you should shoot is that at which you can guarantee your bullet will land within a couple of inches of your point of aim.
In other words, the range at which the rifle will shoot a four inch group.
Most modern rifles will do that at 300 yards – but not when they are attached to someone who has crawled 50 yards along a ditch and forced a gap in the hedge to get a clear shot while lying awkwardly across a protruding root, a piece of barbed wire and an empty oil drum.
That may reduce the ethical range to well under 100 yards. Only you can judge.
The second part of your question refers to the maximum range at which a truly aimed bullet is capable of producing a clean kill, and that depends on two additional factors.
First, we need to ask how much energy is required and then, what type of bullet will expand and deform so as to apply that energy to the target animal at the reduced velocity of long range.
The question of energy has been hotly debated ever since we discovered how to calculate it and I’m afraid I regard the whole business as being, under hunting conditions, so much pseudoscientific clap-trap.
However, since your 100 grain .243 bullet is still carrying nearly 1000 ft/ lbs of energy at 400 yards, I don’t really think you need to worry about energy.
Then there’s bullet performance, which depends on the bullet’s construction and on its impact velocity.
It must expand vigorously at the longest range while not disintegrating at the shortest.
Such bullets do exist – but they are expensive.
If it all sounds confusing, then you could try something in .30, .33 or .35 calibre, which will remove at a stroke most of the concerns about the .243.
What is the max killing range for a 100 grain .243 bullet