There's a Scientific American article, Cost of Medical Care for Transgender Service Members Would Be Minimal, Studies Show, which cites two studies:
The summary of the RAND report includes the estimated number of transgender service members (1,320–6,630), the estimated number per year of those who would seek transition-related healthcare treatment (129 or 2%): from which one can determine their estimated cost per treatment (I reckon about $60K), and average cost per transgender service member (I reckon about $1200).
The corresponding estimates from the New England Journal of Medicine article are:
- Number of transgender service members (who are eligible for health care): 12800
- Number who would seek transition-related treatment: 188
- Cost per treatment: $30K over 6.5 years
Having analyzed the cost that the military will incur by providing transition-related care, I am convinced that it is too low to warrant consideration in the current policy debate. Specifically, I estimate that the provision of transition-related care will cost the military $5.6 million annually, or 22 cents per member per month. Of course, the cost will depend on how many transgender personnel serve and utilize care, and estimates are sensitive to certain assumptions, such as the expectation that the military will not become a “magnet” employer for transgender people seeking health care benefits. Though my utilization and cost estimates are quite close to actual data provided by an allied military force, it seems clear that under any plausible estimation method, the cost amounts to little more than a rounding error in the military's $47.8 billion annual health care budget.
... the "actual data" being data from Australia:
As an accuracy check, consider the Australian military, which covers the cost of transition-related care: over a 30-month period, 13 Australian troops out of a full-time force of 58,000 underwent gender transition — an average of 1 service member out of 11,154 per year.3 If the Australian rate were applicable to the U.S. military, the Pentagon could expect 192 service members to undergo gender transition annually.
Incidentally it also says (and includes as a factor in its estimate) that,
However, transgender persons are overrepresented in the military by a factor of two
In other word, transgender persons are already more likely than average to volunteer for service.
Another article Inside Trump’s snap decision to ban transgender troops claims that the real cost was that the issue was (for political reasons) threatening funding for the border wall with Mexico:
House Republicans were planning to pass a spending bill stacked with his campaign promises, including money to build his border wall with Mexico.
But an internal House Republican fight over transgender troops was threatening to blow up the bill.
It quotes a Republican congressman as saying,
“It’s not so much the transgender surgery issue as much as we continue to let the defense bill be the mule for all of these social experiments that the left wants to try to hoist on government,”
Rep. Trent Franks (R-Ariz.), a conservative supporter of the Hartzler proposal, said last week.
... so perhaps their motive too wasn't that the economic cost is significant.