Firm value vs equity value

Dear Mr. Moffat,

solving the MOCK I realized that I still mix total value of the firm and equity value.

Would it be correct, if I summarize the following (?):

Firm value:

1. If I use free cash flow to firm (where I ignore % and use WACC, can also include growth model of free cash flow) – would give me firm total value and I must substract market value of debt to arrive to the equity value

2. In all other cases:
– bootstrapping P/E to earnings
– using growth model based on PAT
– free cash flow to EQUITY (including % expense and discounting at cost of equity)

would give me directly cost of equity and no substracting of debt is needed.

Would it be the correct summary?

Thank you!