There is also value-based billing. A lot of people talk about it, but never seen in the wild.
EG A business has a manual process that costs them £2m/year to run. Instead of calculating how long it would take you fix, you price based on what it is worth to the business to fix the issue (obviously this needs to be larger than what you would charge on a time and materials basis).
1) Are you doing something innovative? By definition there's no clear value to baseline against. Clients don't know what's even possible, much less how much $$$ it might bring them. So the value in "value-based" is correlated with some internal strategy / personal / brand politics. Good luck quantifying that as an external SW dev firm.
2) Doing something run-of-the-mill? Improving a process that's already in place? The client may have an idea about its ultimate specs & ROI. Even if they're able to articulate those to you – why would they?
In practice, value-based pricing comes down to "charge as much as they're willing to pay". Which is fine, that's the essence of sales. But more to do with social skills & play-it-by-ear, rather than some objective numbers you might hope to extract from a client.
EG A business has a manual process that costs them £2m/year to run. Instead of calculating how long it would take you fix, you price based on what it is worth to the business to fix the issue (obviously this needs to be larger than what you would charge on a time and materials basis).
Brennan Dunn was a big advocate of this, but mainly on a small consultancy scale (https://doubleyourfreelancing.com/rate/).