I read this thread yesterday when it was referenced to in another post. I found it interesting. I think some people in the thread got caught up in semantics and not reality and could not get past the idea. Coins cut for change were really quite common, not just in ancient times but much later as well as most of us know. So what would one call the OP coin? Call it what you want. A 'sestertius' cut to 'As, Dupondius, Semis, etc.'. It really does not matter. Clearly in ancient times someone was making change for a specific denomination. The terminology doesnt matter as much as the historical context. Anyway, I have two cut coins in my collection (well, four, but only two were for making change):
I believe the original sestertius was rated at 2.5 asses when the early denarius was worth 10 asses. When the denarius was devalued to 16 asses to the denarius around 140 BC, the sestertius was then valued at 4 asses. I don't think the original definition of sestertius was actually two and a half asses but something like one half from three or three less one half. If that definition is correct, then a sestertius of 4 asses would not really be a correct explanation of the value.
Like I mentioned above I think its best to remember not to get caught up into details we will never know. We can easily estimate what the new denomination might have been but we will never know what the exact intent was behind the people altering the coin. For instance we cannot know when the alteration happened and that in itself means we will never know. Time, location, local economy, expectations of acceptance, these are all things (and many more) which would influence how a cut coin might have been valued in consideration to other coinage, spending ability, general acceptance, etc.
I had 27 (or so) that were mostly Roman. Then I bought a lot of 60, mostly Imperial. I have seen quite a few for sale or in pics on line.