Question15 Maple Corner Market has a cost of equity of 12.4 percent, the YTM on the company’s bonds is 6.3 percent, and the tax rate is 28 percent. If the company’s debt–equity ratio is 0.52, what is the company’s weighted average cost of capital? 8.43% 9.71% 10.28% 11.04% ResetMaximum marks: 2 Flag question undefined单项选择题
A
8.43%
B
9.71%
C
10.28%
D
11.04%

Question

Question15 Maple Corner Market has a cost of equity of 12.4 percent, the YTM on the company’s bonds is 6.3 percent, and the tax rate is 28 percent. If the company’s debt–equity ratio is 0.52, what is the company’s weighted average cost of capital? 8.43% 9.71% 10.28% 11.04% ResetMaximum marks: 2 Flag question undefined单项选择题

A

8.43%

B

9.71%

C

10.28%

D

11.04%

BlackTom AI · Accepted Answer

WACC is calculated as the weighted average of the cost of equity and the after‑tax cost of debt: WACC = wE·Re + wD·Rd·(1 − Tc). Use the YTM as Rd (market cost of debt) and convert the debt–equity ratio into weights based on total value.

Knowledge points:
- Re (cost of equity) = 12.4%
- Rd (pre‑tax cost of debt, YTM) = 6.3%
- Corporate tax rate Tc = 28% → interest tax shield means use Rd·(1 − Tc)
- Debt–equity ratio D/E = 0.52 → convert to weights: if E = 1 then D = 0.52 and V = D + E = 1.52

Step‑by‑step calculation:
1. Compute weights:
   - wE = E / V = 1 / 1.52 = 0.6578947368 (≈ 65.7895%)
   - wD = D / V = 0.52 / 1.52 = 0.3421052632 (≈ 34.2105%)
2. Compute after‑tax cost of debt:
   - Rd·(1 − Tc) = 6.3% × (1 − 0.28) = 6.3% × 0.72 = 4.536%
3. Compute weighted components:
   - Equity contribution = wE × Re = 0.6578947368 × 12.4% = 8.1578947369%
   - Debt contribution = wD × Rd·(1 − Tc) = 0.3421052632 × 4.536% = 1.5517894737%
4. Sum to get WACC:
   - WACC = 8.1578947369% + 1.5517894737% = 9.7096842106% ≈ 9.71%

Why this is correct:
- The formula correctly accounts for the tax deductibility of interest and uses market weights implied by D/E. The arithmetic yields 9.7097%, which rounds to 9.71%.

Why the other options are incorrect:
- 10.28% (≈10.31%) would result from using the pre‑tax Rd (6.3%) instead of the after‑tax Rd (i.e., failing to apply the tax shield).
- 11.04% or 8.43% reflect other miscalculations (e.g., incorrect weights or omitting the tax adjustment). They do not match the correct WACC when using the given data and standard formula.