So the title is basically my question.
We use the WACC to discount the FCF and I do not completely understand why we are using something levered to discount something unlevered!

Well, free cash flow should correspond with your discount rate.

If you use a levered free cash flow value (with interest expense subtracted) you are effectively calculating an equity value with a DCF model, and so discount rate is just cost of equity (all other forms of capital don't matter).

If you use an unlevered free cash flow value (with interest expense included) you are effectively calculating an enterprise value with a DCF model, and so discount rate is what you call "WACC", or cost of debt, equity, and other forms of capital.

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Hold on, levered free cash flow's interest expense is subtracted? I'm pretty sure that's unlevered free cash flow since the effect of interest is taken out of consideration and thus no leverage. I could be wrong but if that's the case then neither of my boss and my professors spotted out in my DCF models

Sorry for the confusion, and you are correct. It has more to do with my wording than the theory - if our unlevered FCF is 100 and interest expense is 10 our levered FCF is 90. That's what I meant.

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I think you're mixing up the concept of a levered beta and a levered cash flow (I'd suggest reading into the differences between the two).

For the purpose of a "traditional" DCF that uses FCFF(unlevered) and WACC, the output is enterprise value as it captures the value of both debt and equity stakeholders within the company. The levered beta is used to calculate the cost of equity, however by adding the proportion of debt to the WACC calculation, its representative of both.

I would think of it another way entirely:

DCF is used to calculate the value of invested capital
That invested capital can take many forms (sr debt, unsec debt, converts, equity) with varying risk profiles and weightings
We use public company securities to approximate the sector average expected return (WACC) on that invested capital
Because of the different funding weightings across companies your comps universe you must assess the expected return before interest has been deducted from cash flow (i.e. unlevered cash flow)

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Best Response

unlevered fcf = cash flow to equity and debt holders so you discount at weighted avg of cost of equity and cost of debt

levered fcf = cash flow to equity holders only so you discount at cost of equity

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