A firm has a cost of debt of 7.5 percent and a cost of equity of 16.2 percent. The debt-equity ratio is 0.45. There are no taxes. What is the firm's weighted average cost of capital?

Question

BlackTom AI · Accepted Answer

We start by identifying the given data and the formula for WACC in a no-tax environment.
- Cost of debt rD = 7.5%
- Cost of equity rE = 16.2%
- Debt-to-equity ratio D/E = 0.45
- Taxes = 0, so ignoring tax shields: WACC = wD * rD + wE * rE, where wD and wE are the weights of debt and equity in the overall capital structure.

First, compute the weights from the D/E ratio. If D/E = 0.45, then let E = 1 unit, D = 0.45 units. Total financing = D + E = 1.45 units.
- Weight of debt wD = D / (D + E) = 0.45 / 1.45 ≈ 0.3103
- Weight of equity wE = E / (D + E) = 1 / 1.45 ≈ 0.6897

Now apply the WACC formula with these weights:
- Contribution from debt = wD * rD = 0.3103 * 7.5% ≈ 2.33%
- Contribution from equity = wE * rE = 0.6897 * 16.2% ≈ 11.17%
- Total WACC ≈ 2.33% + 11.17% ≈ 13.50%

Option-by-option analysis:
- 11.75 percent: This underestimates the equity component. If you reduce the weight of debt or the cost contributions, you drop the total below the correct weighted sum. The calculated wD and wE with D/E = 0.45 do not support such a low result, since the equity portion (which is substantial at 16.2%) is weighted heavily (about 69%). Therefore 11.75% is not consistent with the given data.
- 12.29 percent: This value is closer to a mid-range guess but still too low given the relatively high cost of equity (16.2%) and the substantial equity weight. A precise calculation using the weights above yields about 13.50%, so 12.29% reflects an error in weighting or arithmetic rather than the actual WACC.
- 13.50 percent: This matches the direct calculation with wD ≈ 0.3103 and wE ≈ 0.6897, using rD = 7.5% and rE = 16.2% in a no-tax scenario. The math aligns with the debt-to-equity structure provided.
- 14.47 percent: This would require an even larger equity weight or higher costs, or a miscalculation in weights. Given D/E = 0.45 and the specified costs, adding up to 14.47% would overstate the equity contribution relative to the calculated weights, so this is not correct here.

In summary, applying the standard WACC formula with the given D/E ratio and costs yields approximately 13.50%, and the other options fail to reproduce that result due to incorrect weighting or arithmetic.

FIN 220 01 Final Exam _ Fall 2025

A firm has a cost of debt of 7.5 percent and a cost of equity of 16.2 percent. The debt-equity ratio is 0.45. There are no taxes. What is the firm's weighted average cost of capital?

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