Triangle Enterprises has no debt but can borrow at 9 percent. The firm's WACC is currently 14.7 percent, and there is no corporate tax. If the firm converts to 70 percent debt, what will its cost of equity be?

Question

BlackTom AI · Accepted Answer

To start, I’ll lay out the setup: the firm currently has no debt and a WACC of 14.7%, with Rd = 9% for debt and no taxes. When there is no debt, the WACC equals the cost of equity, so Re (unlevered) is 14.7% in the current structure.

Now consider the proposed capital structure: 70% debt and 30% equity. The weighted average cost of capital (WACC) with no taxes is:
WACC = (D/V) * Rd + (E/V) * Re
Plugging in the numbers: 0.70 * 9% + 0.30 * Re = 14.7%
Compute the debt portion: 0.70 * 9% = 6.3%
So: 6.3% + 0.30 * Re = 14.7%
Solve for Re: 0.30 * Re = 14.7% - 6.3% = 8.4% → Re = 8.4% / 0.30 = 28%

Now evaluate each option:
- Option A: 20.67% — This is too low given that the levered cost of equity must compensate for higher leverage to keep WACC at 14.7% without taxes. If Re were only ~20.7%, the equation 0.70*9% + 0.30*20.67% would yield a WACC well below 14.7%, which contradicts the stated WACC.
- Option B: 28.00% — Matches the algebraic solution from the levered WACC formula with no taxes. It correctly balances 6.3% from debt and the remainder from equity to hit 14.7% total.
- Option C: 24.47% — This value would produce a WACC of 0.70*9% + 0.30*24.47% = 6.3% + 7.341% ≈ 13.641%, which is not equal to the given 14.7%. Thus it cannot be correct under the stated constraints.
- Option D: 22.95% — Similarly, WACC would be 6.3% + 0.30*22.95% = 6.3% + 6.885% ≈ 13.185%, still short of 14.7%. This option fails to satisfy the WACC requirement.

In summary, only the 28.00% option satisfies the condition that the firm’s WACC remains 14.7% after shifting to 70% debt, given Rd = 9% and zero taxes. The other values do not align with the required WACC when applying the levered-cost formula.

Triangle Enterprises has no debt but can borrow at 9 percent. The firm's WACC is currently 14.7 percent, and there is no corporate tax. If the firm converts to 70 percent debt, what will its cost of equity be? 单项选择题

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