Depends on if the money saved on marketing and gained by white label sales (if the bottle cost more than $19.99 to make they probably wouldn't do so) minus the money from lost sales to the white label. The site below lists most 5ths (750ml) at under 3 pounds or under US$4, even for top shelf. Say that is doubled by transit costs or tripled after marketing/etc to about $12, it's still about half the white label cost so I'd argue they don't lose money making bottles for Costco.

For marketing, let's assume that cost of maintaining the relationship and dealmaking is written off and 0. If you consider Costco/Kirkland marketing at least in terms of buyer awareness it may be a net gain as for $0 they get that Kirkland trust.

For white label, they may split production/sipping costs with Costco or just provide the final bottle with split profit. Either way, each bottle may return 50-60% as profit or about $12. I can't find anything in detail on how brands split profits or if Costco takes a flat cut though so let's say 50% cut to Costco

I also didn't find anything quick on if white label sales cut into private label but as the white label is only Costco I'd guess the impact is not severe and if the private label is known might even be a boost at outside liquor stores. Even with

For their own sales, take a bottle cost of $30 - $12 to produce for a net of $18. For white label, $12/2 or $6 in profit. So perhaps their private label is 3x the profit ($18 vs $6) so as long as the white label sales don't eat more than 1/3 of the private label sales (and I'd say across the nation it won't) then they come out ahead. But either way they make money and have a huge partner with massive sales to produce for which I'd take as a win for long term revenue stability.

https://www.lovebrewing.co.uk/guides/still-spirits-liqueurs/...