EV / EBITDA

Going_for_CFA_a

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Hello, could someone please confirm if my understanding is correct regarding the below:
1) Is it correct to say that Firm Value which is FCFF(1+g) / (WACC - g) is the same exact thing as Enterprise Value which is the Market Value of all invested capital (equity, preferred stock, debt) less cash, cash equivalents and short term investments. I get the idea that they are the same thing, but the textbook makes no specific mention to their equivalence.
2) To justify an EV / EBITDA multiple, the text mentions that the fundamentals drivers of this ratio are WACC, expected sustainable growth in FCFF, and ROIC. It doesnt show the derivation but I asumme it is based on the Firm Value formula: FCFF (1+g) / (WACC - g). Assuming firm value and enterprise value are the same concept, we can divide bother sides by EBITDA to get an expression for EV / EBITDA.
EV / EBITDA = (FCFF / EBITDA)(1+g) / (WACC - g). I am not sure of the role played by ROIC in this foumula, I assume it has something to do with the ratio of FCFF / EBITDA, which is the portion of pre-interest earnings that is availble for distribution to all providers of capital. If ROIC increases, then the portion of ROIC that is FCFF increases which increases EV / EBITDA.
Could someone please comment. Thanks in advance.
 
1.) They are the same thing to the extent that the working capital requirement reflected in your Free cash flows exclude cash. If cash is included in working capital, you get MVIC (not EV), bc this implies that cash is being captured in the cash flows; if cash is included, it can’t be EV. There are two indications of firm value: MVIC and EV (MVIC less cash). They both indicate firm value. One is with and the other is without cash. The reason the distinction is made is becuase an acquirer will often not pay for the cash, you’re essentially just swapping cash. If a company’s operating value is worth $95mm and it has $5mm in excess cash on the balance sheet, the total company value is $100mm. A buyer could pay $100mm, and keep the excess cash to with what he pleases. Or, he could pay $95mm and let the buyer take the excess cash. EV is the latter case bc why would you pay cash to buy cash. At the end of the day though, it’s six one way, half dozen the other. Doesn’t matter, you’re paying and receiving the same thing at the end of the day.
2.) Bro, you’re way overcooking with the second question. No need to go through that mental exercise. By all means, if it works for you (thinking through it like that), then go with it. But if the text didn’t bother to show, let alone describe, in depth the derivation (as it did for the others), then I wouldn’t waste my time.
Nevertheless, just know that they all boil down to growth and risk for the most part. Profitability/return is also key to understanding multiples. ROIC, the way you’re thinking about it, would be reflected in the FCFF. Your FCFF would reflect the return your operations are generating. But again, while I applaud your appetite for thought, I say you’ve got it, keep going.
 
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