DCF valuation question.?

I was asked this on an interview (investment banking).

You have two companies which are identical aside from the fact that one is all fixed costs and the other is all variable costs. Which would be worth more in a valuation?

My logic was that an all fixed cost company would have a higher beta, and therefore a higher discount rate by CAPM, and thus a lower valuation by DCF, making the variable cost one worth more.

Sound right?

To me it would depend on the type of costs and the amount of variability in them.

I dont have the answer for this. Did you by any chance find out the answer to this question. I have an ibd internship interview coming and i'm trying to cover my grounds.

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