On 1 January 20X1, a company had:• Cost of equity of 10 0%.

At 1 Jan:

Cost of equity, ke=10%k_e = 10\%ke​=10%

Cost of debt, kd=5%k_d = 5\%kd​=5%

Debt D=100D = 100D=100

Shares = 100m @ $4 → Equity E0=400E_0 = 400E0​=400

Total value V0=D+E0=500V_0 = D + E_0 = 500V0​=D+E0​=500.

WACC under Modigliani & Miller (no tax):

k0=E0V0ke+DV0kd=400500⋅10%+100500⋅5%=8%+1%=9%k_0 = \frac{E_0}{V_0}k_e + \frac{D}{V_0}k_d = \frac{400}{500} \cdot 10\% + \frac{100}{500} \cdot 5\% = 8\% + 1\% = 9\%k0​=V0​E0​​ke​+V0​D​kd​=500400​⋅10%+500100​⋅5%=8%+1%=9%

k0k_0k0​ stays constant.

After the share price falls to $3:

Equity E1=100m×3=300E_1 = 100m \times 3 = 300E1​=100m×3=300

Debt still 100 → D/E1=100/300=0.3333D/E_1 = 100/300 = 0.3333D/E1​=100/300=0.3333

MM no-tax formula:

ke=k0+(k0−kd)DE=9%+(9%−5%)⋅100300=9%+4%⋅0.3333≈9%+1.33%=10.33%k_e = k_0 + (k_0 - k_d)\frac{D}{E} = 9\% + (9\% - 5\%) \cdot \frac{100}{300} = 9\% + 4\% \cdot 0.3333 \approx 9\% + 1.33\% = 10.33\%ke​=k0​+(k0​−kd​)ED​=9%+(9%−5%)⋅300100​=9%+4%⋅0.3333≈9%+1.33%=10.33%

Rounded → 10.3%.