RAND Corporation study commissioned as part of the DoD's process to determine their policy on allowing transgender soldiers. (June 2016)
Found that transgender-related health care services was somewhere between $2.9 million and $8.4 million a year, out of $49.3 BILLION for all DoD health care expenditures. So the $8.4 million figure is worst-case scenario.
EDIT:
Link to said study.DOUBLE-EDIT: Study also concluded that the "disruption" portion of 45's tweet is equally bullshit. Assessment of foreign militaries where transgender soldiers were already serving found no significant impact to unit cohesion or readiness. Likewise, assessments of the US military and previous changes like integrating units on lines of race, gender, and sexual orientation found little to no impacts.
Basically, people have used these bullshit arguments every time the military takes a step to bring it in line with society (or even be out in front of society).
They said putting black soldiers in "white" units would hurt morale.
They said letting gays serve openly would hurt morale.
They said letting women serve in integrated units would hurt morale.
They said letting women serve in combat roles would hurt morale.
They were fucking idiots every time, and they're fucking idiots now.