(Weighted average cost of capital) Great Minds Inc. has a target capital structure of 45% debt, 35% preferred stock, and 20% common stock. The before-tax costs of debt, preferred stock, and common stock are 7%, 9%, and 15%, respectively. What is Great Mind’s after-tax WACC? Assume a 35% tax rate.

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BlackTom AI · Accepted Answer

We start by identifying the components of Great Minds Inc.'s target capital structure and the given costs: debt 45%, preferred stock 35%, and common stock 20%; before-tax costs are 7% for debt, 9% for preferred, and 15% for equity. The tax rate is 35%.

Option A: 5.58% — To get this lower value, one might inappropriately apply taxes to the equity or miscalculate the tax shield. If you applied tax to debt correctly, you would reduce debt cost to 7% × (1 − 0.35) = 4.55%, and then weigh it by 0.45, giving 2.0475%. Adding the other components (preferred 0.35 × 9% = 3.15%; equity 0.20 × 15% = 3.0%) would still yield a total above 6%, not 5.58%, so this option inaccurately aggregates the components.

Option B: 8.20% — This value arises when you compute the after-tax cost of debt, then weight all three sources correctly: after-tax debt cost = 7% × (1 − 0.35) = 4.55%; contribution from debt = 0.45 × 4.55% = 2.0475%; contribution from preferred = 0.35 × 9% = 3.15%; contribution from equity = 0.20 × 15% = 3.0%. Sum = 2.0475% + 3.15% + 3.0% = 8.1975%, which rounds to 8.20%. This aligns with standard WACC calculations where taxes affect debt but not equity or preferred dividends.

Option C: 5.71% — This would require a misapplication such as assuming a tax shield that’s too large or misweighting the components. If you incorrectly applied taxes to preferred or equity, or used a smaller after-tax debt cost, you could land in this vicinity, but the correct tax treatment under typical WACC formulas keeps debt tax-advantaged and does not tax-prefer equity or preferred at the same rate, leading away from 5.71%.

Option D: 6.20% — A possible misstep is to underweight the debt tax shield or to miscalculate one of the component contributions. For instance, using an inaccurate after-tax debt cost or miscomputing the weighted sums would produce a result lower than the correct WACC, such as 6.20%. However, when properly applying the 35% tax shield to debt and summing exactly as 0.45×(7%×0.65) + 0.35×9% + 0.20×15%, the total resolves to a value near 8.20% rather than 6.20%.

Putting it together, the correct approach is to apply the tax shield to debt only, weight each component by its target proportion, and sum the results. The after-tax debt cost is 4.55%, and the weighted contributions from debt, preferred, and equity sum to approximately 8.20%.

MSB-250-300-002 Topic 9 Quiz

(Weighted average cost of capital) Great Minds Inc. has a target capital structure of 45% debt, 35% preferred stock, and 20% common stock. The before-tax costs of debt, preferred stock, and common stock are 7%, 9%, and 15%, respectively. What is Great Mind’s after-tax WACC? Assume a 35% tax rate.

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