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I found this related question: What is the CR/XP-Character Level relationship for opponents? but it was asked before the DMG was released and it does not appear to have been updated to include information from the DMG. I could be mistaken but from my reading through the DMG I don't know that this information is contained therein (though the related question and information from the MM seem to indicate there should be something). The section on creating monsters does have a way of calculating CR.

Is it intended for the DM to use the custom monster CR calculations to calculate CR for NPCs? Is the information needed to calculate CR for NPCs with class levels in the DMG or is this left as an exercise for the DM?

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The CR calculation for an NPC with class levels is the same as the CR calculation for a custom monster.

DMG, p92:

Challenge Rating An NPC built for combat needs a challenge rating. Use the rules in chapter 9 to determine the NPC's challenge rating, just as you would for a monster you designed.

It is referring you to the section in Chapter 9 entitled, "Creating a Monster", p273.

Answering your questions specifically:

Is it intended for the DM to use the custom monster CR calculations to calculate CR for NPCs?

Yes.

Is the information needed to calculate CR for NPCs with class levels in the DMG or is this left as an exercise for the DM?

Well, both. The guide for determining CR based on abilities is there, but applying it to a classed character is up to the DM.

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Depending on the monster and the number of class levels you add to it, its challenge rating might change very little or increase dramatically.

DMG Pg 283

CR Table page 274

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    \$\begingroup\$ Question “necromancy” is fine here—successful necromancy even earns a badge—so I’ve removed that part of the post. Part of why it’s fine is that these aren’t “threads” and the site isn’t a discussion forum: the site is so unlike threaded discussion fora that necromancy is good, not bad. For more info, take the tour or browse the help center. Cheers! \$\endgroup\$ – SevenSidedDie Aug 15 '18 at 18:10

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