Consider the information for the following four firms: [table]
Firm | Cash | Debt | Equity | rD | rE | τc Eenie | 0 | 150 | 150 | 5% | 10% | 40% Meenie | 0 | 250 | 750 | 6% | 12% | 35% Minie | 25 | 175 | 325 | 6% | 11% | 35% Moe | 50 | 350 | 150 | 7.50% | 15% | 30%
[/table] The weighted average cost of capital for "Minie" is closest to:

Question

BlackTom AI · Accepted Answer

WACC for the firm’s operating assets uses market values of equity and net debt (debt minus cash). Use the formula: WACC = (E/VE)·rE + (Dnet/VE)·rD·(1 − τc), where VE = E + Dnet and Dnet = Debt − Cash.

1) Relevant concepts:
- Use net debt (debt less non-operating cash) when computing the WACC that applies to operating assets.
- After-tax cost of debt = rD · (1 − τc).
- Weights are market-value weights of equity and net debt.

2) Step-by-step calculations:
- Given for Minie: Cash = 25, Debt = 175, Equity = 325, rD = 6%, rE = 11%, τc = 35%.
- Compute net debt: Dnet = Debt − Cash = 175 − 25 = 150.
- Compute the enterprise capital base: VE = Equity + Dnet = 325 + 150 = 475.
- Compute weights:
  - Weight of equity = E / VE = 325 / 475 = 0.6842105 (≈ 0.68421).
  - Weight of net debt = Dnet / VE = 150 / 475 = 0.3157895 (≈ 0.31579).
- After-tax cost of debt = rD·(1 − τc) = 6% · (1 − 0.35) = 6% · 0.65 = 3.9%.
- Compute WACC:
  - Equity component = 0.6842105 · 11% = 0.0752632 (7.52632%).
  - Debt component = 0.3157895 · 3.9% = 0.012316 (1.2316%).
  - WACC = 7.52632% + 1.2316% = 8.7579% ≈ 8.75%.

3) Why this is correct:
Subtracting cash gives the appropriate capital structure for operating assets; using those weights with the after-tax debt cost yields 8.7579%, which rounds to 8.75%.

4) Why other choices are incorrect:
- b. 6.75% is far too low (would require much lower equity or debt costs).
- c. 8.25% is slightly below the correct 8.758% and results from different weighting (e.g., ignoring cash or miscomputing weights).
- d. 9.50% is too high (would require a higher rE or larger equity weight).

Conclusion: The weighted average cost of capital for Minie is approximately 8.75%, matching answer (a).

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