Question13 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

Question13 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 a weighted average of the after-tax cost of debt and the cost of equity. Use WACC = wE·Re + wD·Rd·(1 − Tc).

Step 1 — determine weights from the debt–equity ratio:
D/E = 0.52 ⇒ let E = 1, then D = 0.52. Total value V = D + E = 1.52.
wD = D/V = 0.52 / 1.52 = 13/38 ≈ 0.342105263
wE = E/V = 1 / 1.52 = 25/38 ≈ 0.657894737

Step 2 — plug in costs and tax rate:
Re = 12.4% = 0.124
Rd = 6.3% = 0.063
Tc = 28% = 0.28 → after-tax cost of debt = Rd·(1 − Tc) = 0.063 × 0.72 = 0.04536

Step 3 — compute each weighted component (showing intermediate steps):
wE·Re = (25/38) × 0.124 = 3.1 / 38 = 0.08157894736842105
wD·Rd·(1 − Tc) = (13/38) × 0.04536 = 0.58968 / 38 = 0.01551894736842105

Step 4 — sum to get WACC:
WACC = 0.08157894736842105 + 0.01551894736842105 = 0.0970978947368421 ≈ 0.09710 = 9.71%

Why this is correct: the formula correctly accounts for the tax shield on interest (multiplying Rd by (1 − Tc)), and the weights are derived from the D/E ratio (not from D or E alone). The arithmetic above yields 9.71%.

Why the other options are incorrect:
- 8.43%: too low — likely results from miscomputing weights or applying the tax shield incorrectly (perhaps subtracting rather than multiplying by (1 − Tc)).
- 10.28%: higher than correct because it likely omits the tax shield on debt (i.e., uses Rd not Rd·(1 − Tc)) or rounds weights incorrectly.
- 11.04%: too high — probably from using incorrect weights (for example, using D/(D+E) and E/(D+E) with a wrong interpretation of the ratio) or mixing up Rd and Re.

Confirming final answer: the calculated WACC is 9.71%, which matches the provided correct answer.

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