It's $4,100 and...
Tesla’s extended service program covers the repair or replacement of Model S parts due to defects in materials or workmanship provided by Tesla. Coverage lasts for four years or 80,000 kilometers (whichever comes first) and begins on the date your warranty expires, as long as you purchase this service within 30 days of your warranty’s expiration.
$4,100 buys a pretty significant repair. If the repair costs more than that, the issue becomes whether you have resources to pay for it without causing significant financial concern. An extended warranty is, in essence, an insurance plan. So if a major repair is not something you can comfortably afford, but you can afford $4,100, then you might want to consider this insurance. Then again, you might want to consider buying TSLA (Tesla shares) or PCRFY (Panasonic shares since it seems to be the silent partner in the battery factory) with the $4,100 instead of the extended warranty. That way, years down the road if you have a problem you can sell the shares to pay to fix it but if you don't have any problems you will still have the shares (hopefully, unless the companies go bankrupt, which seems unlikely -- or the share values fall significantly) whereas the extended warranty will be worth nothing if you don't have any problems. Please note though buying any shares is gambling so don't rely on my advice... it's worth what you paid for it!