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I understand that 'abroad' is an adverb.
However, does the following usage sound correct to you: "A lot of abroad companies invest in Indonesian real estate."
The course material I am using insists this is a proper usage.
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abroad (FOREIGN PLACE) Show phonetics
adjective [after verb], adverb
in or to a foreign country or countries:
He's currently abroad on business.
We always go abroad in the summer.

It's not always an adverb.

It doesn't suit your sentence. Foreign is much better, unless you change the word order to 'companies abroad' but that still isn't as good.
Comments  
ganesh77I understand that 'abroad' is an adverb.

However, does the following usage sound correct to you: "A lot of abroad companies invest in Indonesian real estate."

The course material I am using insists this is a proper usage.

I'd write: A lot of foreign companies invest in Indonesian real estate.
 nona the brit's reply was promoted to an answer.