Am I right in thinking that a DCF valuation is used to come to the enterprise value of a business?
But why would you need to do a DCF if a company is public ... isn't it easier to work out enterprise value?
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You are looking at it the wrong way. How does the public determine how much the equity, and therefore the EV is worth? One way they do that is a DCF. You're correct in that with perfectly efficient markets, with perfect DCF inputs, they would give you the same answer but as you can imagine neither one of those are true.
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