When a country purchases foreign assets, does it change the Net Capital Outflow?

When a country purchases foreign assets, does it change the Net Capital Outflow?
This was a discussion question in my class, and a lot ended up answering that NCO increases, but I’m not so sure.

Because when you look at the definition of Net Capital Outflow, which is

Purchase of Foreign Assets by Domestic Residents – Purchase of Domestic Assets by Foreign Residents,

The left term goes up because you bought foreign assets, but the right term also increases because the foreigners also received domestic assets (currency for instance) in exchange for giving away their assets. Therefore, the two terms should cancel each other out, and the NCO should remain constant.

In addition, since NCO = NX (Net Exports), and the activity above (purchasing foreign assets) doesn’t affect the NX at all, making NX constant, the NCO should remain constant as well considering this equality, which means that the amount you gave (like currency) in order to purchase the foreign assets counts as foreigners purchasing domestic assets by giving away their assets right? So shouldn’t the NCO remain constant?

This is what I thought, but the majority of the class somehow thinks that the NCO increases, so I’m confused. Could anyone tell me what the correct answer is, and how to correctly interpret this? Especially the right term. When a country purchases foreign assets, doesn’t this also count as foreigners having purchased domestic assets since you traded assets with assets? And if this isn’t the case and the NCO actually does increase, how do you explain why the NX remains constant while NCO increases when the two are supposed to be equal?

Thanks.