
Dave Justus |

Initiative isn't really spelled out as a bonus. The closest example I know of is the cracked dusty rose prism ioun stone that gives a +1 competence bonus to initiative for 500 gp. Since the ioun stone is slotless, a slotted version would cost 250 gp, giving us a likely formula of 250 gp X bonus squared.
Another way of looking at it is the fairly accepted view that an average feat without prerequisites is worth about 5000 gp, so improved initiative would, a +4 untyped bonus, would be worth 5000 gp as a slotted item. This is fairly close to the 4000 gp the above formula provides.
Typically an alternate bonus type such as profane or luck is more expensive than the standard bonus type. Initiative seems to usually be competence or insight when it is typed. Profane or luck would probably double the cost then.
Using this formula, you would get 5 squared (25) * 250 * 2 for 12500.
As always, any determination of price and of a custom magic item is up the the GM.

kane.malakos |

There is an Ioun Stone in the book Seekers of Secrets which gives a +1 bonus for 500 gp. By the magic item creation rules that means a +1 bonus is 250 gp (the price gets doubled because Ioun Stones are slotless), so the formula for price should be bonus squared * 250 gp. So the ring you're thinking of would cost 6250 gp.