Equity Value : Levered Vs Unlevered

More or less. I want to preface this response by reiterating that no one would ever do this. That said, if you really, really wanted to get technical about it, the way that I would conceptualize things is as follows:

- The business that you are evaluating has some overall degree of risk that would be applicable to all stakeholders, which should be the WACC that you use for the unlevered DCF

- Based on the cost of debt and percentage of debt, you would get to an appropriate cost of equity for your levered DCF

- Over time, your debt / equity ratio mix would move because A) your debt would be increasing or declining based on issuances or amortization and B) your equity value would be changing over time (primarily because you are discounting your terminal value over shorter and shorter time periods, but also because you are moving past certain years of cash flows)

- You may notice that this whole thing is circular - as your equity value moves, your % equity changes, which changes your cost of equity %, etc...

- In theory, your WACC and cost of debt could also move over time, depending on what risk free rates are doing, if you are assuming the business derisks, etc...

In practice, no one ever thinks about it this way. When people do unlevered DCFs, they get to an appropriate discount rate and then apply it throughout the entire period, regardless of any assumptions around changing risk free rates or derisked business profiles. When people do levered DCFs, they get to an appropriate cost of equity, and similarly ignore any evolutions to the capital structure over time. Also, often people get to the cost of equity based on an idealized or peer capital structure instead of the actual capital structure in place in the projections. 

The reason people don't bother with those rolling updates is because the purpose of all these exercises is not to get to a "true" value, it's to help triangulate around a defensible value. The only time I have ever had to deal with updating capital structures over time was for one fairness committee because a relatively junior person was new on the committee and wanted to show they belonged, so asked us to do it - it was a waste of time and didn't change the answer.