The key idea is that EV/EBITDA lines up a firm’s operating profitability with the value that all providers of capital can claim. EBITDA is a pre-financing measure of operating performance—before interest, taxes, and debt service—so it reflects the cash flows available to both debt and equity holders. Enterprise value represents the total price to acquire the whole firm (debt plus equity minus cash), i.e., the value available to all capital providers. Using equity value instead would tie the multiple to the shareholders’ claim only and ignore debt and cash, making the metric heavily depend on capital structure and less comparable across firms. That’s why the broader, capital-structure-neutral EV/EBITDA is preferred.

The concept being tested is the Gordon Growth Model for a terminal value in a growing perpetuity. In this model, the value of all future cash flows beyond the terminal year is equal to the next year’s cash flow divided by the discount rate minus the growth rate: TV = CF1 / (r - g). If you start from the current year free cash flow (FCF), you must grow it to next year’s level: CF1 = FCF × (1 + g). Substituting gives TV = FCF × (1 + g) / (r - g). That is why the correct form uses FCF times (1 + g) in the numerator and the difference (r - g) in the denominator. The other forms aren’t correct here: using FCF without growing it assumes the cash flow is already next year’s, which isn’t indicated; using r + g in the denominator is incorrect for this model, and using (1 - g) in the numerator implies a shrinking perpetuity, which isn’t the standard Gordon Growth setup.

Accounts receivable turnover shows how many times a company collects its average accounts receivable during a period. In practice, it’s net credit sales divided by the average accounts receivable (often calculated as (beginning AR + ending AR) / 2). Therefore, the correct expression is Sales divided by Average Accounts Receivable. Using any other form—such as the ratio inverted, using ending AR rather than the average, or placing AR in the numerator—would not yield the turnover figure and could mislead about collection efficiency. A higher turnover means faster collections; you can also estimate the average collection period as 365 divided by turnover.

WACC represents the blended cost of financing a company uses, combining the after‑tax cost of debt with the cost of equity and weighting each by how much of the capital structure comes from debt and from equity. The debt portion is taxed-deductible, so its true cost is Rd × (1 − Tc). The weights are the proportions of debt and equity in the total capital, D/(D+E) and E/(D+E). Put together, the formula is: [Rd × D × (1 − Tc) + Re × E] / (D + E). This expands to (Rd × D × (1 − Tc))/(D+E) + (Re × E)/(D+E), which matches the correct expression. The other forms either omit the tax shield on debt, use an incorrect denominator like (D − E), or simply average the two costs without proper weighting.