A financial consultant obtains different valuations of my company when it discounts the Free Cash Flow (FCF) as opposed to when it uses the Equity Cash Flow. Is this correct?
No. Different methods of valuation by discounting flows always give the same value (if done correctly). Fernandez presents that 10 methods of valuation by the method of flows discount always provide the similar value. This result is logical as all the methods analyze the similar reality under the same hypothesis; they differ just in the cash flows they use as a starting point in the valuation.