When finance companies set target prices for stock how long is the horizon?

There is no time horizon for price targets.... You should actually read an analysts report to see how they come up with the target. They usually use some valuation model like discounted cashflow to create a reasonable price target for fair valuation given estimated future earnings. There is a lot of variability in how analysts make these numbers, price targets are only as good as the analysis do not rely on these numbers at face value

They generally tell you the timeline if you read the report.

6-24 months. Very typically 12 months and rarely 6, 18 or 24. Whoever said no horizon is wrong. Bloomberg terminals have the exact data on this sent from the banks themselves.