How much does it cost to shoot down Russian missiles?

I was reading about Ukraine shooting down Russian hypersonic missiles, and I got to wondering what was the cost/benefit of all these missiles and anti-missiles. 

As I understand it, each Patriot interceptor missiles costs about US$4 million (the US recently donated 252 missiles at a cost of US$1,037 million), and the Patriot launcher itself costs around US$10 million. The Russian Kinzhal hypersonic missiles, on the other hand, supposedly cost US$10 million each.

Ukraine claims it shot down six Kinzhal missiles headed towards Kiev yesterday. Russia denies they were intercepted, but who would you believe, given a choice? Furthermore, Russia claims that one of their missiles destroyed a Patriot launcher (Western observers think it more likely that the launcher was just damaged, as Ukraine claims, and should be salvageable). 

So, Russia's six Kinzhals cost $60 million, and Ukraine lost 20 Patriot missiles (the best estimate of the number of missiles fired at the Kinzhals, according to local Ukrainian media) and a launcher (total $90 million), that's a pretty clear financial victory for Russia. But, of course, the value of the lives saved is incalculable.

It just goes to illustrate, though, how ridiculously expensive these modern weapons are. How can one missile cost $10 million? 

It also shows that, notwithstanding Vladimir Putin's claims, Russia's hypersonic cruise missiles, the most sophisticated weapons in its inventory and billed by the Kremlin as too fast for any missiles in the world to intercept, can in fact be stopped by Ukraine's new American-provided air-defence systems. 

It's not clear how many Kinzhal missiles Russia has at its disposal, but the Ukrainian Defence Ministry claims its stocks are critically low, and that it is not able to make more due to the restrictions of sanctions.