A walk-out basement would certainly add to your home value if you can afford it, especially if it has ample windows on the low ground level side and you put a roofed-over patio in front of it - which could be a roof, an awning, a solid deck on the next story up, an overhanging upper story on the addition, etc.
The two prior comments are good advice, but seem to assume your foundations would be going to full basement depth anyway - i.e. that your frost penetration depth is enough that it gives you a full basement.
If you are in a part of the country where shallow burial or slab on grade is the norm and that is what you have, then a half to full UNFINISHED basement depth (3-8 feet below ground surface) is likely to add in the ballpark of $20-40/SF to your cost depending on added depth, for the extra excavation, waterproofing and maybe subslab drainage, basement slab, and additional foundation wall height. To finish it (go from bare foundation walls and slab to something that is a living space) can run from $20-100/SF depending on whether you are talking just painting foundation walls and some lighting, simple economy finishing, or fully finished and conditioned space. Certainly closer to or even above the $100/SF number if the basement space is designed as a legal bedroom space with full bath.
One emphatic recommendation - when you do your addition, and most especially at the foundation, require that expansion seal be used at the interface of the walls and roof, crack control joints in all walls and slabs, and that the foundation wall and slab where it meets the old house be built with a crack control joint and waterstops, as you WILL get differential settlement and dcracking betweenthe addition and the old part of the home - the key is to control where it occurs, and provide sills and trim strips and such at those points so it does not cause random, wandering unsightly cracking. Generally, your best bet is to force the crackingto occur at the interface between the two, where it wants to occur anyway, and at the roof bridge the roof over the joint rather than making a sharp rigid transition right at the seam, that way the differential settlement might slightly slope the roof in that area but not cause loss of water shedding capacity or tearing of the sheathing and roofing waterproof membrane. Another common way to avoid the settlement sissue at the roof is to make the new addition roof a different height than the existing, so there is no actual roofing "joint" at all.