How Equity Value Changes the WACC in FCFF and FCFE Valuation
Summary
The example compares equity valuations based on free cash flow to the firm (FCFF) and free cash flow to equity (FCFE). With the original assumptions, both approaches produce the same equity value. When the example raises return on invested capital while holding the original WACC fixed, the FCFF valuation and FCFE valuation diverge. The answer explains that the discrepancy comes from using a WACC based on the old capital structure after the modeled equity value has changed.
Recalculating WACC with the equity value implied by FCFE makes the two valuation methods consistent in the example. The response derives the revised WACC from the updated equity and debt weights, then applies it to FCFF. This illustrates that WACC depends on capital structure, so valuation inputs cannot always be held fixed when projected values change. The discussion is a compact algebraic example, not a general treatment of valuation: it assumes the stated cash flows and financing costs, and does not address growth, changing risk, or other real-world complications.
Key ideas
- FCFF valuation subtracts debt from enterprise value to derive equity value.
- FCFE valuation discounts cash flow available to equity holders at the cost of equity.
- Changing projected equity value changes the equity weight used in WACC.
- Consistent capital structure assumptions can reconcile the FCFF and FCFE approaches.
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# Using Market vs. "Projected" Equity Value in WACC Calculation # Using Market vs. "Projected" Equity Value in WACC Calculation Suppose a business: - Has a market value of equity of \$50 and a market value of debt of \$50, - Has a cost of equity of 15% and a cost of debt of 5%, and - Earns a return on invested capital (ROIC) of 10%. Therefore, the business would: - Generate $10 in free cash flow to the firm (FCFF; 10% * (\$50 + \$50)) per year, - Have a 10% WACC (50% * 15% + 50% * 5%), and - Have an equity value of \$50, since its enterprise value is \$100 (\$10 / 10%) and it has \$50 of debt. We can confirm this by dividing the free cash flow to equity (FCFE; \$10 - (5% * \$50)) of \$7.5 by the cost of equity of 15%, which also yields \$50 of equity value. Now, suppose the firm earns a 20% ROIC: - FCFF is \$20, implying equity value of \$150 (\$20 / 10% - \$50) and - FCFE is \$17.5, implying equity value of \$116.7 ((\$20 - 5% * \$50) / 15%). Why is there now a discrepancy in equity value between methods? If we instead take the equity value calculated using FCFE of \$116.7 (instead of $50) and the original, debt, cost of equity, and cost of debt assumptions, we can calculate a new WACC of 12%. Using this WACC, the "projected" equity value is \$116.7 (\$20 / 12% - \$50). This suggests that using the "projected" equity value in our WACC calculation makes both methods consistent. Why is this? ## Answer by João (score 2) https://quant.stackexchange.com/a/83927 > Why is there now a discrepancy in equity value between methods? There isn't, you changed the ROIC (thus increasing FCFF obviously) while maintaining the WACC unchanged. I assume you calculated the 12% WACC via back out. But: Implied WACC = 0.15 - 0.10 * ( 50/166.67) = 12% And: FCFF = 20/0.12-50=116.667 FCFE = (20-0.05*50)/15 =116.7 > This suggests that using the "projected" equity value in our WACC calculation makes both methods consistent. Why is this? Using the projected equity value => recompute WACC with the new E
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