Magic item crafting is (loosely) based off of a table available here.
Pertinent lines are:
Use-activated or continuous Spell level x caster level x 2,000 gp
Note: If a continuous item has an effect based on a spell with a duration measured in rounds, multiply the cost by 4. If the duration of the spell is 1 minute/level, multiply the cost by 2, and if the duration is 10 minutes/level, multiply the cost by 1.5. If the spell has a 24-hour duration or greater, divide the cost in half.
No space limitation: Multiply entire cost by 2
So we get (spell level times minimum caster level) x 2000 x duration modified x 2
Since no spell does 1d4 damage per round, we have to compare it to similar spells. Cantrips can deal 1d4 damage per round, but take up your Standard action so they are siginificantly weaker than one which is 'set and forget'. The spells I found most similar are Heat/Chill Metal and Summon Swarm, both 2nd level spells (3rd minimum CL).
Therefore, according to general guidance, your price would be:
2x3x2000x4(measured in rounds)x2 =
96,000g. Or 48,000 to craft.
Arguably, this could be accomplished by associating it with Magic Missile instead. The resultant cost for a 1st level spell would be:
2000x4x2=
16,000 or 8,000 to craft
