The buyer across the table is rarely a person. It is a structure, and the structure sets the price.
When a catalogue sells for eight figures, the cheque is almost never written by an individual. It comes from a fund: a pool of other people's money raised specifically to buy music IP, run by a small team who are paid by contract for managing it.
Funds buy catalogues because the income behaves like nothing else in their portfolio. A seasoned catalogue throws off year after year with slow, fairly predictable decay, and those royalties don't move with the stock market. To an investor it looks like a long, gently shrinking bond, which is exactly how they price it.
Here is the part most sellers and plenty of advisers miss: the fund's own economics decide what it can pay. Its fee structure, its promised returns, its borrowing. Two funds looking at the identical catalogue, with identical income forecasts, can be a few turns of the apart purely because their structures differ.
So before you argue about the multiple, learn to read the buyer. That means understanding how a fund is built, who gets paid what inside it, and where debt sits in the deal.