Free cash flow (new debt and new equity)

Wonder why only the debt issuance is relevant to the free cash flow calculation and not the equity issuance?

Why not ?

Equity issuance is a contra account and is immediately diluted at cost without affecting the cash account.

Issuance at premium, if retained in the company will enhance the cash balance else the excess cash will go to the promoter who diluted their stake. If so, the company gets nothing and equity is still diluted at cost net net leaving the cash balance unaffected.