If you already have unused disk capacity, the cost is near zero. Even if you decide to purchase an extra hard drive or two, drives are cheaper than tape units and can be converted to other uses should your needs change. And, of course, there are no tapes to purchase. There are fewer points of failure. If critical data is backed up in five different locations, it is unlikely that all five locations will fail simultaneously.
Hard drives are much less temperamental and require less human intervention than tape drives.
This system can provide added protection if some of the machines on your LAN are in physical locations removed from the central server. The data backed up on them will be safe in case of a fire or other catastrophic event. Of course, if you are currently using tape as a backup medium, it would probably be wise to continue. Networked backups can still be used to provide that extra bit of insurance against a tape system failure that will occur sooner or later. As a bonus, retrieving data from a recent backup on a hard drive is easier than recovering the same information from a tape even if your tape backups are running smoothly.