Let's make it more obvious then.
A Type-55 cruiser costs $850M
An Arleigh Burke destroyer costs $1700M
So you can buy 2 Type-55 Cruisers for the price of a single Burke Destroyer.
And note that a Type-55 Cruiser is significantly bigger and better armed than a Burke.
This still implies that the PPP exchange rate underestimates how Chinese industry can produce warships at low cost.
Going to put in my two cents here.
That kind of price difference is more than just PPP. There are other deep underlying structural factors in play here, factors that don't favor the US either.
The first is that the US shipbuilding industry has shrunk massively from its World War 2 years. You can write an entire book on this, cite pages of links but for the sake of brevity I'm not going to do that. Let's just say that when it comes to the shipbuilding industry, the US has been reduced to a dwarf. The remaining US large shipbuilders rely two things, Jones Act ships and ships for the US Navy. Shipbuilders like Austal USA, Fincantieri Marinette Marine, Bath Iron Works and Huntington Ingalls require US Navy contracts to survive. This means the cost of the shipyard's survival is tacked to the cost of each ship. This isn't the case with China when mega SOE shipyards have a huge civilian production. These shipyards do not need to tact the entire cost of survival to each warship they make, they make plenty enough ships to distribute their direct operating costs. Note that two of these shipyards are already foreign owned --- Austal USA is a subsidiary of Austal from Australia, and Marinette Marine is owned by Italian shipbuilder Fincantieri. These are the two shipyards that make the two LCS classes.
The second is that when you have a shrinking shipbuilding industry, so are the technical schools that are needed to train the welders and technicians needed. The US shipbuilding industry faces this ever shrinking pool of shipbuilding workers, and wages are going to get higher. The reason why US unemployment is low is actually due to a shrinking labor base. HII recently is looking for at least 3,400 workers to hire. If this keeps on, there will be manpower shortages with the US shipbuilding industry.
Lets add in contrast to the shrinking US shipbuilding industry, the Chinese shipbuilding industry is the world's number one in volume, is oversized and for years, is facing a glut. Your skilled labor base is much larger, your transportation infrastructure means you can bullet train lower wage workers in from surrounding areas outside of the city, increasing the size of the labor poll available for the shipyard. Not only wages are low, you can have construction being done 24/7. You also don't have unions.
The third is that as US companies have their usual high corporate margins and stockholders to satisfy. In China, the military industrial complex are SOEs. In China, the state owns the MIC, and not the other way around as Eisenhower once warned. That's another incentive for the SOE to keep their prices low and with lower profit margins. I heard before that Chinese shipyards prefer doing foreign contracts because they can tact a larger profit margin on those ships.
With the Chinese MIC being SOEs, every point of purchase of components from engines to weapons systems are also from SOEs.
The fourth is politics. In the US even these ship contracts have to be passed by Congress. Every politician wants the best for their states and constituents over the other. One result is that contracts are handed out in a year to year basis. This puts long term uncertainty for the shipyards which results to #1, where they have to tack their survival costs for every contract. If you are ordering one or two ships in a two or three year contract, the cost per ship will be much higher than say ordering a batch of 10 ships for 10 years production run. The Zumwalts costs like that because only three ships are made. If they decided to make 20, the costs will drop to the floor for each ship. The LCS classes are also into these single to two year contracts, with approvals done on a ship to ship basis, though the main point of doing this is keeping the shipyards contracted till hopefully, you get multi year, multi block contracts for the FFG(X). In China, you can see ships running in large production blocks, corvettes at over 60, a single frigate class up to 30 ships. If you consider the 052C/D a single class with two variants, the total class may well exceed 30 ships.
I'm pretty sure at some point, early in the production, a 052C would have cost like hell for the Chinese when they only built two. AESA radars are particularly costly, but once more of 052C are made, and transitions to the 052D which even more is made, the AESA radar costs would drop thanks to mass production of its component elements. The price of a 055 would hit the ceiling if only one, two or three are made, but for its prices to be low, it would have to be guaranteed a large batch in multiyear contracts. Regardless whether there are two shipyards making it, the component sources are the same for both. The AESA radars might potentially be the largest cost component of these ships, but having them produced in an unprecedented scale should take their prices from the ceiling to the floor.
Compare that to the Zumwalts where its largest AESA had to be expunged from the ship, because of cost. The SPY-4 AESA is the role equivalent to the Type 346A, intended to be the main S-band search radar of the ship. This leaves the Ford class to be the only users of this radar, which raises its cost higher. The only way I can see out of this, is when they mass produce the SPY-6 for the AB Flight III and its small sibling EASR for the FFG(X), the Ford class needs to be revised to use SPY-6 in future ships, and the unmade third Zumwalt also has to change to radar. The Zumwalt currently only has the SPY-3 as its sole and main radar, but its an X-band, its main role was to be an FCR but now has to do search radar functions as well, and its not optimized for that. Ford class also uses SPY-3, X-band radars on a carrier is not only for defensive purposes but for tracking and landing planes. But the SPY-3 is not being adopted on the AB Flight III nor the FFG(X), and with such low numbers, this radar set is going to be sky high (both ships decided to use SPQ-9B, a dual backed PESA by the way that's already in service and proven). The higher the price for an item, the more Congress gets sticker shock, the more contracts are cut, the more production is lessened, and the prices go even higher. Its an upward spiral.
Consider let's say, the new X-band radar on top of the 055. That's going to be expensive on top of the 346B radars. But if you have 055s being built like 20, the prices would drop. If these radars are also used on other ships, from the carrier 003 and onwards, to the 054B or the 052E, the prices would drop even further. You don't need the equivalent of full sized radars on the smaller ships. AESAs can scale down to smaller sizes, even down to rotary single or double faced ones. But its their building blocks, namely the elements and T/R modules that are being mass produced, and the more is made, the more the prices go lower, making them cheaper to apply on lower ships, which further lowers the prices of these components in a downward price spiral. There also other indirect factors along the production chain, and things like China having cornered the world's production of Gallium and rare earths also helps.
