mark-up for south facing

THis is just too abstract a question. We don't know what the light is like in front or in back, how close other buildings are, type of building and apartment, etc . All of this bears on value in a particular situation. For example, if you are talking about views of a park from the front and a brick wall in the back, then there's a big difference. If it is a narrow, unattractive street view and a wide open courtyard with plenty of sky visible, there may also be a difference but the value is reversed. I don't think there is a formula for this. I would look closely at comps within the building for guidance.

Assume almost EVERYTHING is the same. For example, south is facing another building, which it clears, with a street and north is facing another building, which it also clears, with the same exact distance in between as the street to the south. And both views are the same amount of attractiveness.

The front of a building is usually noisier.

it is a personal preference - south facing may be too hot in the summer, plus maybe better view to face the courtyard (i.e north in your case)

bottom line not sure you should pay more for south at all - it might be the other way around

I think most people prefer sunlight and open views. Courtyard-facing apartments, especially those with a northern exposure, tend to be dark. Sure you'll get more heat in the summer with a southern exposure but it's a small (electric) price to pay for cheery, mood-enhancing all-day light.

In OP's case, where the units are practically identical except for the exposures, I'd say there'd be a slight premium on the apartment that faces south (unless, of course, you're renting to painters, in which case the north side would be preferable), as it will simply feel brighter than its northern counterpart. Remember, northern light has a much cooler tone since there's no direct sun, so it can feel austere and 'cold'.

North has better, more consistent light.

I dont see any reason to demand more for the same unit just because it faces south.

In our building, the people facing south (front/street) think the people in the rear have it so much better because of the noise. People facing north (rear/other buildings) think the people in the front have it better because of the sunlight.

The grass is always greener!

In the situation you describe there is no discernable difference. No price difference. Remember "north" in Manhattan is really NNE. That is why in the summer the sun actually shines into "north"-facing windows in Manhattan when it is rising. If there are no buildings blocking the light, then here all things are equal.

small premium for south 5%.