Yes, that is exactly it. Wow! $150?!? That is expensive!
Did you check Amazon? $38
https://www.amazon.com/Microsoft-Wi...ag=hawk-future-20&ascsubtag=UUacUvbUpU6689140
Direct from Microsoft is $50.
https://forums.androidcentral.com/e...-display-adapter-2%2Fp3q-00001&token=dq5Ee92V
I take one with me whenever I travel. The TVs in almost every hotel I've stayed at, had both an HDMI and USB port. In the rare case where the TV didn't have a USB port, I just used my portable battery pack as a power source.
The only other cheaper option is what
@Galactic Zoo suggested. The downside is that you are now limited by the length of the cable and you can't charge the phone while projecting your screen.