
doi: 10.2139/ssrn.6677578
<div> <span>Setting a market-derived EBITDA multiple equal to the discounted cash flow expression for the same enterprise value and canceling EBITDA from both sides yields a simple bridge equation: M = f ÷ (WACC − g), where M is the EBITDA multiple, f is the ratio of free cash flow to EBITDA, g is the long-run growth rate, and WACC is the required rate of return. The equation converts in either direction: a known market multiple implies a specific hurdle rate, and a known hurdle rate implies the multiple that income and market approaches must agree on. </span> </div> <div> <span><br></span> </div> <div> <span>The bridge equation reframes the market approach as a hurdle rate discovery exercise rather than a comparability exercise. Every arm's-length EBITDA transaction embeds a required return; the bridge equation extracts it. When that embedded rate is applied in the income approach, the two methods reconcile by construction. When the income approach uses a rate inconsistent with any documented buyer class, the bridge equation identifies the source of the disconnect — not the math, but the input. </span> </div> <div> <span><br></span> </div> <div> <span>The article derives the equation, illustrates its application in both directions, develops a practitioner framework for its use, and examines what it reveals about standard CAPM build-up methodology when applied to closely held business valuation.</span> </div>
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