I do not know where to place the bathroom, and the location may change in the future.

Then there's no point. However, putting a rough-in before will be very cost effective. Otherwise, you may have to trench the concrete for new drains and the venting may be even more complicated to tie in to existing vents.

$3900 seems awful high to me, especially for new construction.

As worthy says, if you don't know where you want it, it's probably better to pass for now, so you don't end up paying twice.

No doubt that builders price is an off the top of his head price for a completed 1/2 bath, including all walls & fixtures, but as a plumber I can tell you the truth of the matter is, based upon the information at hand it is impossible to even venture a guess for the roughin cost.

First of all, what is the depth of the municipal sewer?

What is the terraine from the sewer location to the house? Is it level or does is slope up or down, and if it slopes, what is the height or drop of slope?

What is the length of the setback from the sewer tap location to the house?

The sewer line is a 3" line and it requires a 1/4" per foot pitch all the way from the house to the municipal sewer.

let us consider a typical 75' setback from the front of your property line to the structure. Now add another 5ft for the width of the utility easement from the municipal sewer line to your property line so the house sewer would then be 80' long, allowing that it is run in a straight line taking the most direct route, which is rare, but for illustration we will use it.

The house sewer is 80ft long so with a 1/4"/ft pitch that is 80 x 0.25 = 20".

You then need to know the location where the proposed watercloset will be set. The closet bend (elbow) under the watercloset requires 12" and you must have a 1/4"/ft pitch from the WC to the house sewer entry point. Hypothetically let us say that will be 20' so the pitch would be 20' x 0.25" = 5" plus 12" for the closet bend for a total of 17".

You then add the pitch for the house sewer and the DWV run to the watercloset and get a total of 37".

Now for illustration let us assume you want the basement to be 6' below grade and the terraine is flat.

The floor would then be 72" below grade and the sewer and drain line must run 37" below the finished floor, so the municipal sewer line would have to be a minimum of 109" (9ft) below grade.

Generally the sewer lines run between 3 & 10ft deep depending upon whether you are on the upstream or downstream end of the sewer run.

In most instances when building a house with a basement the sewer line will enter through the basement wall at some point above the finished floor.

If that is the case here, they could still intall a bathroom in the basement but it would require installing an effluent lift pump system. The advantage is that it could be placed wherever they want it, but it requires two vents. The pump housing is required to have a dedicated vent that cannot be attached to any other vent line in the house, and that vent must terminate through the roof. The fixtures must be vented in the conventional manner as defined by code.

We just roughed in a sink and toilet in our new basement addition, and the cost was around $800. This was pretty reasonable, because he was able to use an existing drain that was at the back of our walk-out. We were lucky. I imagine it would have cost more than twice that much if that drain wasn't already there underground.

But of course we were certain where we wanted a future bathroom. It would have been foolish in my opinion for us not to do it. In your case, I wouldn't do it, especially in light of the inflated price.

While we were shopping around for our first place, I remember always seeing a scary basement bathroom as a liability for a property. We saw lots of these - a random toilet and sink just stuck somewhere in an old house. Well, I was stupid. If the plumbing was already there, we could have worked around it. Lesson learned in the future if we ever move again.

Roughing in a bathroom in our addition was an afterthought, but clearly a good idea.

We added a half bath to the basement where none existed -- my estimate is it ran about $6,000 for the plumbing, electrical, walls, fixtures...