Assuming this was done in 1938, this would cost the equivalent of $5.6 million today. And it was made obsolete by the frequency change just 7 years later.
Insert "(nearly a third of a billion in today's dollars)" there.
I don't know the actual figure.
When I was growing up, he was the market engineering director for one of the two or three local FM conglomerates, and through the past 30 years or so, they kept getting gobbled up by larger corporations until probably 90% of the AM/FM radio audience was owned by either Clear Channel or CBS-then-Entercom-now-Audacy.
These groups also cut back substantially not only on local radio talent (there used to be shows through the day run by local DJs, now you're lucky to get a morning show and maybe an afternoon drive show), but also on the radio engineers deployed to the stations.
A lot is due to automation and ease of IP audio (and popularity of alternative formats like YouTube and Podcasts), but it's a bit of a sad, slow death of something I remember more fondly as a kid.
I recently had my Dad take me on a tour of a 'megawatt' (ERP) FM tower site in St. Louis (we posted a YouTube video of it) and it's incredible the engineering that goes into getting a signal (in the case of this site, 10 signals) into an FM antenna system 300m above the earth!
That said, David Sarnoff was a nasty opportunistic litigious man and frankly the way he treated Armstrong, Philo Farnsworth and others was despicable.
Another inventor Sarnoff stole from was Philo Farnsworth (https://en.wikipedia.org/wiki/Philo_Farnsworth). He didn’t kill himself like Armstrong but was broke and forgotten when he died in 1971.
Also I like Damn Interesting Week podcast that discusses fun news articles, they have so much fun with them.
An article at the UPC website  seems to trivialize the conflict of interests raised by the community: https://www.juve-patent.com/news-and-stories/people-and-busi...
While Sarnoff did try to kill FM as a threat (more NIH than The move to 88-108 had some other good technical reasons - the higher frequency is less prone to skip, multipath, and tropospheric ducting. When the band opens on 6m (where the original band was) stations hundreds of miles away can swamp local traffic. Because Television isnt subject to the capture effect, there are less issues with it with analog TV. The interference of remote stations at the frequency it happens on low band VHF, would have sunk FM in the long term.
AM Radio Bandwidth. The original allocated channel bandwidth for AM allowed closer to 11-12kc of audio bandpass, with 8-10 being pretty common - the quality was more a function of how the lines feeding the network traffic to the station and the station to transmitter link were conditioned, and often well into the 70's the STL link was a leased conditioned line from the telco.
I do not disagree that RCA used its market position as holder of most of the radio related patents to shut out Armstrong, and it was/is despicable - but not all of the bad thind that happened were just malicious to be malicious.
According to him, Sarnoff and Armstrong were friends at some point and RCA financed the development of FM radio initially although they just wanted a more efficient AM network.
Perhaps after he traveled back in time our future government(s) outlawed that sort of thing.