Alternative idea:

This is my son's small condo. You're looking at the end wall of his kitchen. To the left is his sink and counter, to the immediate right where you can't see is the fridge. The light streak is the morning sun streaming through his patio door.

Yes you do. The bottom of the cabinet is not meant to hold the stuff in the cabinet AND the weight of a rack and pots.

most pot racks have either ceiling or wall mounting-do a half round rack into studs under the cabs but not attached to the cab. These half rounds are quite nice.....different materials and levels of detail.I'm not a big fan of pot racks-we removed a large one above a peninsula-but the smaller scale ones will have less chance of tiring your space and still be useful.

debdiy - do you have a tile backsplash? If not, you could do one like herbflavor describes. If you do have tile, you may be hesitant to drill holes in it, but you could.

As for drilling into the underside of the cabinet, that's iffy. You'd be drilling into the layers of plywood from the end or into the end of the mdf/furniture board. Neither of these is strong and is not likely to hold.

If you search on Amazon for "pot racks" you get 1802 results. Maybe something in there will work for you.

IF the cabinet has a 3/4'' plywood bottom and a face frame, I don't see a big problem hanging a pot rack from the bottom, assuming you won't be filling the rack w/ cast iron skillets. (Make sure the cabinet is securely anchored to the wall with either lag screws or cabinet screws.)

Given that you said this is a 'brand new building' I'm guessing that most likely your cabinet is particle board or mdf. In that case, look for alternative ways to anchor the pot rack.

I think you would do better hanging a rack on the wall right under the cabinets. Since you'll be using hooks to hold the pots, you can get up pretty close to the bottom of the cabinets.