I'll go against the grain here for a bit.
It's unethical and possibly illegal if you're billing your client by the HOUR. If you're billing your client on a lump sum / % complete basis, then they're not getting charged any more in any case, and the only thing it does is kink your internal project accounting. Which may or may not be bad depending on your corporate culture.
I worked at two big consulting firms straight out of college, and both of my managers did this all the time, because that was the game each department played to try and show billability while still coming in at or under budget for their jobs. Sometimes you worked overtime and didn't bill it, sometimes you worked less than necessary and billed overhead to a project, sometimes you worked on one project and billed another. I didn't consider it unethical because the client was paying the same fee no matter what. So why did my PM do it? Raises and bonuses.
Once these Harvard Business School nitwits got a hold of engineering consultancy and started implementing the "billable hours" model to project tracking, they borked the whole industry up. Now a poor engineer who's slow and sloppy looks 100% billable, and a good fast complete engineer looks like he's lazing about, because he's "less billable." All the project tracking tools track hours, they don't track how fast your task goes in those hours, so the Corner Office guys don't have a clue who's good and who isn't. They look at the billability, and give the slow sloppy guy the raise and the bonus. So the PM or department manager has to monkey with the timesheets to try and show the Corner Office Harvard Nitwit the sorts of indicators he's looking for on the timesheet, to ensure that what should happen does happen with regards to hiring, raises, and promotions.
Every large company I've ever worked for has worked that way. And the fundamental flaw goes back to what I call "managing by hour" instead of "managing by task."
Is it falsifying data? Sure. Does it drive Ron up the wall? Sure. But you're tracking the wrong data. You should be tracking tasks, not hours, and correctness, not billability. The first step to getting your internal systems working properly is to sever the ties between "billability" and reward. And every big company I've ever worked in goes completely the opposite direction.
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