If the EV/Sales multiple is 2x and the EV/EBITDA multiple is 8x, what is the EBITDA margin?

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To determine the EBITDA margin from the provided multiples, we can start by understanding what these multiples represent:

1. EV/Sales multiple measures the relationship between a company's enterprise value (EV) and its total revenue (sales). An EV/Sales multiple of 2x indicates that the company's enterprise value is twice its sales.

2. EV/EBITDA multiple captures the relationship between enterprise value and earnings before interest, taxes, depreciation, and amortization (EBITDA). An EV/EBITDA multiple of 8x means that the enterprise value is eight times the EBITDA.

To find the EBITDA margin, which is defined as EBITDA divided by Sales (expressed as a percentage), we can use the formulas derived from both multiples:

Let’s denote the Sales as ( S ) and the EBITDA as ( E ).

From the EV/Sales multiple:

[

EV = 2S

]

From the EV/EBITDA multiple:

[

EV = 8E

]

Since both expressions represent the same enterprise value (EV), we can equate them:

[

2S = 8E

]

Now, to isolate ( E ) in terms of ( S ):

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