That is a first class basic explanation of the issues involved! If you are not playing music, maker this clear. But always remember that music is somebody's property!
I normally think your comments are well thought through and spot on, but you've said this a few times through the thread and it's got annoying, so here's my unfiltered rant:
You seem to be forgetting that before any of this music is played, unless you're talking about the one very specific use case of playing the radio, the business has BOUGHT and PAID FOR the music already. We are not getting it for free. We're paying to buy it, making it ours, then we're expected to pay again to actually play it - and pay each and every time we play it.
The arts industries, particularly the entertainment industries have managed to pull off the biggest scam of all time, by convincing us that we should pay every single time we use the product we purchased from them (and music is a product, not a service).
Can you imagine what would happen if, say, Samsung started trying to charge you a fee every time you opened your fridge? How about if you buy a painting - should you not pay the artist every time someone looks at it?
Or, to bring in the workplace part of the problem, if I buy a kettle from Robert Dyas and take it into the office, should I not pay a license fee to Robert Dyas every time I boil said kettle to make a cup of tea for a client. What's the difference? Cup of tea - no license - have some quiet music in the background, license required. Both products, both being used by a client (or the public), yet both treated completely differently.
The law is completely confused, unenforceable (thankfully) and immoral. I do not accept this 'oh, the poor lowly artists need their pennies so they can eat' argument. They get paid by every single person who purchases their music. End of.
And to retort to paulears - I'll wager a lot more work goes into writing the average book than writing the average song (just based purely on the time it takes to produce). I don't hear you saying that authors should be paid every time someone picks up a copy of their book, even if that copy has already been bought and paid for (you mentioned someone finding a CD with your music on it - someone must have originally bought that CD, unless you gave it away). Libraries would overnight become the most expensive places to go to if books were treated the same way that music is.
I actually can't think of another product we routinely purchase that comes with such restrictions on usage. Pretty much any other product can be used as you see fit, safety concerns aside.
The fact that I paid for the CD, and the fact that I can receive money for selling the CD on, should mean that it's mine and I can do what I like with it. Yes, I might choose to use said CD to help make my business more inviting to customers - but that's what the nice decor does too. I don't pay Dulux every time someone looks at my lovely walls.
This system is insanity and self evidently does more for the people at PRS/PPL than it does for the artists they claim to help. Having had a long chat with a writer/session drummer I am friendly with, he appreciates the money, but it really isn't going to pay the bills, but annoyed that they base payments on how many times your music has been played, which of course they have absolutely no way of determining in a lot of cases. It's a joke.