You've had the obvious pointed out to you. A good host has redundant connections, hardware, power, etc. to keep your site available. You're paying for your site to be up, online, available to customers, despite hardware failure (depending on how you have your agreement arranged with them).
A home system typically wouldn't have redundant power, multiple Internet connections and/or service agreements with an upstream provider and equipment providers (dead Cisco router? Working again within hours.) Rare is the home user with the networking knowledge for setting up or reconfiguring that equipment. UPS/generator. Etc.
But every time someone points out that these are what you're paying for, you counter with a "what if I just...isn't it cheaper to..."
Honestly, if you HAVE the equipment, money, connections, and knowledge, then YES it's cheaper, because these are the things YOU'RE PAYING FOR. It's "cheaper" to change your own oil in your car...and do all other maintenance...because you pay the mechanic to do the labor for you, because they have the skills and resources you don't necessarily have.
You need to measure what you have available, your skills, your experience, and your hardware budget against what you're using the server for and the affect on customers and see if that hosting cost is worth what you'd put into it. That's your answer.
You're not even mentioning what your server is for, who's accessing it, how much traffic it sees, information like that. If this is your personal website that gets ten hits a day, stick it on your home link. If it's a site that when it goes down you have a small revolt on your hands at work and coworkers with torches at the door, you should probably rethink your priorities on saving money. It's impossible to really measure the value of the site and hosting to you from the information you posted.