Apex domains cannot have CNAME records.
Question and response
Question
dig cheaperhost.com. NS
Answer
cheaperhost.com. 4 NS ns3bfm.name.com.
cheaperhost.com. 4 NS ns2kry.name.com.
cheaperhost.com. 4 NS ns1kwy.name.com.
cheaperhost.com. 4 NS ns4htz.name.com.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0