That looks like an honest old Model 1892. I think Mike Webb's estimate on value is maybe a tad low, but that is just my opinion, which isn't worth anything more. If it is honest (i.e., no one has sanded and refinished the wood or used cold blue to fix up the blue, etc.) and if the bore is very good to excellent, I would say it would be worth at least $1,000 ....... at least that is what I would be willing to pay for a '92 like that in that caliber and in the condition mentioned above. However, I value is a hard thing to nail down. At the end of the day, it is what other people decide what they are willing to pay for it. I see lots of guns advertised at some hefty prices, but they do not sell. I tend to undervalue my guns, judging by how fast they usually sell and from the PM's of the people who weren't fast enough telling me I was crazy to let it go so cheap.
By the way, the 44-40 has taken an awful lot of deer in its heyday. I've only collected one deer, a 200 pound doe, with a 44-40, but I was impressed with the 20" of penetration it gave. I would recommend keeping shots under 100 yards, however.