I think the reason most people underestimate tape requirements is, they
assume that if you have 20 GB of data to back up, you need 20GB of tape to
store it.

With TSM (unlike the backup systems that just do "full" dumps to tape), your
tapes become fragmented over time as incremental versions expire.  Unless
you do an unreasonable amount of reclaiming, you will be doing very well to
keep your storage pool tapes averaging 65% full.

The formula I use is:

Need to back up xxx TB
Divid by the number of GB that will fit on a tape.
Adjust as you have suggested for extra versions
Divide by .65 on the assumption that the not-yet-reclaimed tapes will be, on
average, 65% full
Multiply by 2 for the offsite copies

If all you are backing up is large data bases, you might get a higher number
than 65% in your system.  If you don't reclaim frequently, it might be
lower.

Run this query  to see the average utilization of your tapes that have
already been marked FULL, and adjust your tape estimates accordingly:

 select stgpool_name, status,cast( mean(pct_utilized)as
  decimal(5,2)) as avg_pctu from volumes -
 where devclass_name <> 'DISK'  group by stgpool_name, status