That's in the letter too. ATT stopped considering building out their own network for $3.8B back in Jan, right around the time they started considering acquiring T-Mobile for $38B.

They decided to spend 10 times more on a process of regulatory approval and service integration that would likely take about as long as it would to simply build out their own network.

The implication being that ATT isn't doing this for T-Mo's network, but anti-competitively to crush Sprint by preventing them from getting T-Mobile's network and customers.

The coverage improvements would take years to build out their existing infrastructure with new base stations (erect new towers or lease space on existing towers, purchase and install equipment). By buying TMO, they would get an instantaneous coverage increase and instantaneous capability increase.

There has to be a substantial cost of opportunity if it takes them (e.g.) 5 years to build the infrastructure themselves. There also is the risk that ATT could not achieve the full coverage because it has gotten increasingly difficult to get zoning permissions to build unsightly cell towers.

    > By buying TMO, they would get an instantaneous 
    > coverage increase and instantaneous capability 
    > increase.

Not really. Most of the coverage AT&T is lacking and proposed to build out to expand from 8x% to 9x% coverage is in rural areas where T-Mobile's network is even weaker than AT&T's. In other words, there are very few places where T-Mobile has coverage and AT&T doesn't already; most of the new coverage they'd get in this deal is redundant.

Beyond that, we're primarily talking about LTE coverage. That would require significant additional investment even if you added T-Mobile's (GSM/UMTS/HSPA+) infrastructure to the mix.