(Continued) What is the cost of capital (WACC) after moving to a 30% debt ratio?

Question

BlackTom AI · Accepted Answer

The question asks for the cost of capital (WACC) after moving to a 30% debt ratio. 
Option evaluation context:
Option 1: 8.4%.
Since the WACC combines the cost of equity and after-tax cost of debt in the proportions of financing, the general formula is WACC = (E/V) * Re + (D/V) * Rd * (1 - T), where E/V is the equity weight, D/V is the debt weight, Re is the cost of equity, Rd is the cost of debt, and T is the tax rate. Moving to a 30% debt ratio means D/V = 0.30 and E/V = 0.70. 
What this implies for the reasoning: if the company increases leverage from all-equity toward a debt ratio of 30%, the after-tax cost of debt (Rd*(1-T)) typically adds a cheaper component to financing and can reduce the WACC relative to an all-equity structure, assuming Rd is not excessively high and tax advantages apply. Therefore, 8.4% could plausibly be the resulting WACC in a scenario where the equity cost and debt cost combine to yield that level.
Now, why other potential interpretations (not shown here) would matter:
- If Rd were very high or the tax rate T were very low, the debt component might not bring down WACC as much, potentially yielding a higher WACC than 8.4%. 
- If Re is extremely sensitive to leverage and rises steeply, the equity portion could pull the WACC upward rather than downward, depending on the exact numbers.
- If the debt ratio target is not accompanied by appropriate cost inputs (Re, Rd, T), any numeric WACC like 8.4% would be speculative without the underlying rates.
Given the provided single option, and typical intuition that introducing moderate debt lowers WACC due to the tax shield and cheaper debt financing (assuming reasonable Rd and T), option 8.4% aligns with a plausible WACC outcome after moving to 30% debt. 
In short, the argument for why this result can be correct rests on the standard WACC decomposition and the expectation that the debt component reduces the overall cost when the tax shield applies and debt is not prohibitively expensive. 
If you had the exact Re, Rd, and T values used in the scenario, you could plug them into WACC = (0.70)*Re + (0.30)*Rd*(1-T) to verify whether 8.4% is achieved.

FA25-BL-BUS-F305-1130 Problem Set 5 (Please read the instruction)

(Continued) What is the cost of capital (WACC) after moving to a 30% debt ratio?

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