# Equities question

Suppose an analyst estimates equity value by discounting free cash flow to equity (FCFE) at the weighted average cost of capital (WACC) in the FCFE model and estimates firm and equity value by discounting free cash flow to the firm (FCFF) at the required return on equity in the FCFF model. The analyst would most likely: A. overestimate equity value with the FCFE model and underestimate firm value and equity value with the FCFF model. Answer is A. Any idea why? WACC should be higher than the cost of equity, not lower. The answer states “WACC is less than required return on equity. Incorrectly using the WACC (which is too low) in the FCFE model will overestimate equity value. Incorrectly using required return on equity (which is too high) in the FCFF model will underestimate firm value and equity value.”

giatch Wrote: > Any idea why? WACC should be higher than the cost > of equity, not lower. The answer states “WACC is > less than required return on equity. Incorrectly > using the WACC (which is too low) in the FCFE > model will overestimate equity value. Incorrectly > using required return > on equity (which is too high) in the FCFF model > will underestimate firm value and > equity value.” The explanation is absolutely correct. WACC will always (almost) be less than Re. Why? Becasue cost of debt is less than the cost of equity, usually, and the fact that you get a tax based discount (it is 1-tax rate) brings it lower. Bottom line, WACC will always be less than cost of equity for a levered firm. If a firm is zero leveraged, WACC = Cost of Equity. Here is an example: Before tax cost of debt: 7%; cost of equity 11%; Tax rate 30%; Debt ratio 40% WACC = (0.11 * 0.6) + {0.07 * 0.4 * (1-0.3)} = 8.56% Cost of equity = 11%

Unfortunately Iginla is correct. I hate agreeing with him because he’s a dick. WACC will be lower than Re because debt has a lower rate than equity, and debt gets into the mix in WACC. with that understood, you can lay out some figures to solve, using any two simple rates where one is lower than the other. I’ve chosen .10 ® and .07 (WACC) for no particular reason. FCFF = 150 FCFE = 100 r = .10 WACC = .07 FCFF using wacc, 150/1.07 = 140.19 ; the correct figure using r, 150/1.1 = 136.36 ; PV of FCFF is too low, it has been understated FCFE using r, 100/1.1 = 90.91 ; the correct figure using wacc, 100/1.07 = 93.45 ; PV of FCFE is too high, it has been overstated

They did a flip flop on you. For discounting FCFF, WACC should be used because net borrowings is taken into account therefore the cost of capital should include what is required from the debt. WACC is also lower because you have the advantage of a tax shield For discounting FCFE, return on equity is used because that is all that remains since you took out net borrowings. Flip flopping them will overstate one and understate the other.

Debt is cheaper than equity