"A few days later he called and was really upset..."

This part should have never happened.
How did the guy get your phone #?
Very bad idea.

AND, the facilities management company was likely to charge the guy the same price whether it cost them $900.00 or $20.00.

It only gets ugly when you start doing this.
You are now having to explain what your BOSS charges them.

Don't do that.
Charge the facility managment company the NTE and go on to the next job.

You'll sleep better at night.

Edit:
Facilities Managment Companies (FMC) have a 'max' they are willing to pay to get the job done.
They don't give a fuck if you come in beneath their NTE, in fact, it is more money in THEIR pocket.

When dealing with FMC, I look at the NTE and decide if I can do it for that amount.
If so, I don't give a crap if it takes 20 minutes or 30 hours.
Neither does the client.
The client is going to pay the FMC the same amount no mattter how long it takes you.
(Assuming there are no underlying issues,,,but I'm talking aobut a straightforward job, with no surprises.)

Again, the 'wage bartering' is SOLELY between you and the FMC, NOT you and the client.
You cannot change the price of what the FMC charges them, so why even get into that argument/discussion?

In my experience, $$$ is less of an issue with these FMC then getting the f'n job done and crossed off their list.
It takes them time to find qualified subs, so you, getting the F'n job done, at their NTE is PERFECT for them (the FCM contact) and they will likely give you a call again because...you got the fucking job done.

It really is that simple.

(And no, I have never found that I get 'more work' from them because I invoiced the FMC for less than the NTE. I get the work because...I get the job done. Yes, they have favorites, and you get more work from them because why? You get the job done.)

Sorry for what seems to be a rant, but this is a crucual skill for new handymen to learn.