Hi guys , just want to make sure a few facts straight here,

1, FCFF(Free Cash Flow to Firm) also called Unlevered FCF, FCFE(free cash flow to Equity) also called Levered FCF?
2, FCFF discounted by WACC ( cost of equity is calculated using unlevered Beta)=Enterprise Value
FCFE discounted by Cost of Equity (calculated using levered beta)=equity value
So, Enterprise Value- Mrkt value of Debt=Equity Value. this relationship should hold theoretically , Correct?
In what circumstances they do not hold?what am i missing if any?

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You mean net debt right? if you mean market value of debt, then its not right. because cash on hand can be used to service some of the debt.

Therefore,
Enterprise Value = Net Debt + Equity Market Value + Preferred Stock (acts like debt) + Minority Interest.

Hopefully this helps.

1) Yes
2) The beta is levered (The beta does not change whether or not you use unlevered or levered FCF)

Enterprise Value = MVE (Equity Value) + Net Debt + Preferred Stock + Minority Interest - Cash

Someone correct me if I'm wrong on statement #2.

-- "Those who say don't know, and those who know don't say."

Net debt - cash? Net debt is just debt - cash. So, I am not sure about it.
For statement 2 - you are right. it should be levered beta to calculate cost of equity.

Enterprise value =
common equity at market value
+ debt at market value
+ minority interest at market value, if any
– associate company at market value, if any
+ preferred equity at market value
– cash and cash-equivalents.

This is what Wikipedia claims. Anyone care to comment?

EV = market value of equity (common & preferred) + (market value of debt - cash) [also known as net debt]

FCFF discounted at WACC does NOT use unlevered beta, the cash flows are unlevered (i.e. calculated starting at EBIT(1-T) rather than NI), but the beta used in the discount rate is not. The appropriate WACC will use the company's target leverage going forward.

However,

If you were to use an APV method, the discount rate would use the unlevered beta. The unlevered cash flows would then be discounted at this rate, while the tax savings associated with leverage each year would be discounted at Rd.

This will yield a slightly different (but theoretically more accurate) valuation than WACC.