Why does FCFE increase when a firm borrows money?

Starting with the basic accounting equation, A = E + L.  Let's imagine that the firm issues traded bonds as debt and all its assets are at market values, tangible etc, this would mean that E = Market Cap. The FCFE is defined as CFO - Investing Cash flow + Net Borrowing. When a firm borrows, it's liabilities and assets increase, no doubt there, but why would equity increase? This just doesn't make any sense to me, a company can't increase it's market cap by the amount of borrowing by borrowing more, this is utter nonsense. 

 
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There's no cash outflow here. OP didn't say anything about them using the issuance proceeds to buy fixed capital.

OP is confused that FCFE would increase equity for some reason. This isn't the case.

It just increases FCFE for the very simple reason that FCFE is the operating cash a business has left over after paying its debt/investment obligations. In other words, a proxy for what it can distribute to equity holders. If a business issues debt and gets cash for it, they could technically turn around and use that cash to pay a dividend or buy back shares (and this isn't unheard of), thus debt issuance increases FCFE.

 

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