Installing electric radiant heat would be primarily motivated by comfort goals.
- Since you already have a furnace, this extra heat source will exist more-or-less solely to heat your floors.
- In addition, electric resistance heat sources tend to use a lot of electricity, so unless you are getting solar PV (or another way to offset your increased consumption), you will be most likely increasing your electric bill significantly.
- Lastly, I'm assuming your basement floor is concrete, and if so, you should be aware that concrete is very good at transporting water through "capillary action". It is unlikely to be an issue given everything is installed with proper water proofing, but water + concrete + heavy electricity consumption is something I would avoid in my house.
Consider these alternatives
Now, on to the alternatives!
Carpet or rug. What I'd recommend is starting by simply buying a carpet or rug to keep the floors feeling warm. This will be cheaper than electric radiant upfront (unless you buy a really nice rug) and will have zero operating cost.
Insulation. I'd recommend making sure the basement is well insulated.
High efficiency heating system. Research upgrading your furnace and the associated ductwork to make sure you are efficiently heating the basement.
A good furnace should be 95%+ efficient, quiet during operation, and have at least two "stages".
- The high mode should get the ambient air up to a comfortable temperature and
- the low mode should be used to slowly heat all the thermal mass (walls, floor, etc.) to keep the space comfortable for longer.
Also, you should have at least R-6 insulation on the ductwork and use a "duct blaster" to ensure that the system has less than 5% air leakage overall.
Lots of information, but the simple message is that you should have a Building Performance Institute (www.bpi.org) Accredited Contractor take a look and provide more detailed recommendations based on the guidelines I provided above.
I have told you the general rules, but the details are what will make the difference for your home.
This requires someone educated and experience to take a look directly, especially considering basements can often be major combustion safety risk zones and safety comes first!
For more information:
Find an energy auditornear you in GreenHomeGuide's Find a Pro directory.
Also, read "We want to install radiant heating. How do we insulate the concrete slab floor?" a Q&A answered by Harold Remlinger.