Western Electric has 24,000 shares of common stock outstanding at a price per share of $63 and a rate of return of 13.80 percent. The firm has 6,500 shares of 6.20 percent preferred stock outstanding at a price of $87.00 per share. The preferred stock has a par value of $100. The outstanding debt has a total face value of $356,000 and currently sells for 103 percent of face. The yield to maturity on the debt is 7.60 percent. What is the firm's weighted average cost of capital if the tax rate is 21 percent?

Question

BlackTom AI · Accepted Answer

We start by extracting all components and their market values to compute the weighted average cost of capital (WACC).

Step 1: Calculate market values
- Equity: 24,000 shares × $63 = $1,512,000.
- Preferred stock: 6,500 shares × $87 = $565,500. (Note: preferred has a par value of $100 and a stated dividend rate of 6.20%, but market value is given by price × shares.)
- Debt: total face value $356,000, currently selling at 103% of face, so market value = $356,000 × 1.03 = $366,680.
- Total market value (used for weighting) = $1,512,000 + $565,500 + $366,680 ≈ $2,444,180.

Step 2: Determine costs of each source of capital
- Cost of equity (Re) is given as 13.80%.
- Cost of preferred (Rp) is the dividend per share divided by the market price per share. Dividend per preferred share = 6.20% of par ($100) = $6.20. Therefore Rp = $6.20 / $87 ≈ 0.07126 (7.126%).
- Cost of debt before tax (Rd) is given by the yield to maturity on the debt, 7.60%. The after-tax cost of debt = Rd × (1 − Tc) = 0.076 × (1 − 0.21) = 0.076 × 0.79 = 0.06004 (6.004%).

Step 3: Compute weighted costs and sum
- Contribution of equity to numerator: $1,512,000 × 0.138 = $208,656.
- Contribution of preferred to numerator: $565,500 × 0.07126 ≈ $40,300 (rounded from $40,299.74).
- Contribution of debt to numerator (after tax): $366,680 × 0.06004 ≈ $22,015. (Specifically, 366,680 × 0.06004 ≈ 22,015.47.)
- Sum of weighted costs (numerator) ≈ $208,656 + $40,300 + $22,015 ≈ $270,971.
- WACC = (sum of weighted costs) / (total market value) ≈ $270,971 / $2,444,180 ≈ 0.111 or about 11.1%.

Now, evaluate each answer option with this calculation in mind.

Option 1: 11.33%
- This value is close to the computed 11.1% but slightly higher. The slight difference could arise from rounding intermediate steps or using a marginally different rounding method for Rp or Rd after tax. Consider whether small rounding choices could push the result to 11.33%; however, the core computation tends to land near 11.1%. Potential pitfall: miscomputing Rp as 7.13% vs 7.126% or using a different debt value.

Option 2: 11.09%
- This is very close to the calculated 11.10% range. If one uses precise figures ( Rp ≈ 0.071264, after-tax Rd ≈ 0.06004, exact market values, and exact total ), the weighted sum over total aligns with roughly 11.09%–11.10%. This option corresponds well to the detailed arithmetic above.

Option 3: 10.08%
- A noticeably lower figure. This would require either a much lower after-tax cost of debt, a much lower cost of equity, or a significantly different capital structure (e.g., much smaller equity weight or miscomputed market values). Given the substantial equity market value and the stated costs, 10.08% would not be consistent with the inputs.

Option 4: 10.30%
- Also lower than the computed near-11.1%. Similar reasoning to Option 3 applies: achieving 10.30% would need the weights or costs to diverge from the provided data. The debt’s after-tax cost is already around 6%, and equity is 13.8%, with equity dominating the value, so the WACC should sit above 10%. Still, 10.30% would require a combination not aligned with the given prices and yields.

Option 5: 10.49%
- Between 10.3% and 11.0%, but still below the detailed calculation region. It would imply a slightly lower weighted average than the precise arithmetic above, which is unlikely unless some inputs were rounded in a particular way. It remains less consistent with the exact numbers used in the step-by-step calculation.

Summary of reasoning across options
- By separating each capital component and applying the standard WACC formula with market-value weights and after-tax cost of debt, the numbers cluster around the 11% region. The equity portion, at 13.80%, is the dominant driver due to the large equity market value, while the after-tax cost of debt is modest (about 6.0%), and preferred adds a smaller, separate stream at roughly 7.13%. The precise arithmetic with exact figures yields a result very close to 11.09% to 11.10% depending on rounding choices.

Note on potential rounding effects
- Small differences in Rp (0.07126 vs 0.0713) or Rd after tax (0.06004 vs 0.0600), or slight variations in how the total market value is computed (e.g., carrying more precise decimal places) can shift the final WACC by a few basis points. The key is that the order of magnitude and the near-11% region remains stable.

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