Module 6 · Corporate Issuers

Capital Structure

EN: WACC, MM propositions, target capital structure.
VN: WACC, lý thuyết MM, cấu trúc vốn mục tiêu.

1. Weighted Average Cost of Capital (WACC) Core

\[ WACC = \frac{E}{V}\,r_E + \frac{D}{V}\,r_D\,(1 - t) + \frac{P}{V}\,r_P \]

Components

E, D, P Market value of equity, debt, preferred.
V = E + D + P (total firm value).
r_E Cost of equity (CAPM, DDM).
r_D(1−t) After-tax cost of debt — interest tax-deductible.
r_P Cost of preferred = D_P / P_P.

Algebraic variants

No preferred$ WACC = w_E\,r_E + w_D\,r_D\,(1-t) $Form đề thường hỏi nhất (chỉ E + D)
Solve for rE$ r_E = \dfrac{WACC - w_D\,r_D\,(1-t)}{w_E} $
After-tax rD$ r_D^{\,AT} = r_D\,(1 - t) $Cost of debt sau lá chắn thuế
Cost of preferred$ r_P = \dfrac{D_P}{P_P} $
DDM cost of equity$ r_E = \dfrac{D_1}{P_0} + g $Alternative khi không có β (xem Equity M8)

Practice problem

E/V = 60%, D/V = 40%, r_E = 12%, r_D = 6%, t = 25%. Compute WACC.

Show solution

WACC = 0.60(12%) + 0.40(6%)(1 − 0.25) = 7.2% + 1.8%

= 9.0%

2. Modigliani-Miller (No Taxes) Concept

About: MM I — capital structure irrelevant to firm value. MM II — adding debt raises rE proportionally to keep WACC constant. Theoretical baseline for relaxing later.Tóm tắt: MM I: cấu trúc vốn không ảnh hưởng V. MM II: thêm debt làm rE tăng để WACC không đổi.

MM I Firm value independent of capital structure.
MM II r_E rises linearly with D/E to keep WACC constant.

3. MM with Taxes Concept

About: V_levered = V_unlevered + tD. Interest tax shield raises levered firm value. Pure tax view favors 100% debt — ignores bankruptcy costs.Tóm tắt: V_levered = V_unlevered + tD. Tax shield làm tăng V. Quan điểm thuần: 100% debt — bỏ qua bankruptcy.

\[ V_L = V_U + t \cdot D \]

Levered firm worth more than unlevered by present value of interest tax shield. Pure tax view: 100% debt optimal — but ignores bankruptcy costs.

MM with taxes — full toolkit (recapitalization)

Unlevered cost r₀$ r_0 = \dfrac{CF\,(1-t)}{V_U} $Cost of capital của firm chưa vay = after-tax perpetual CF ÷ V_U
Levered firm value$ V_L = V_U + tD $Tax shield = t·D cộng thêm vào giá trị firm
Equity value$ E = V_L - D $
Cost of equity (MM Prop II, có thuế)$ r_E = r_0 + (r_0 - r_D)(1-t)\dfrac{D}{E} $Leverage → r_E tăng tuyến tính theo D/E
WACC sau khi vay$ WACC = \dfrac{D}{V}\,r_D(1-t) + \dfrac{E}{V}\,r_E $Có thuế: WACC giảm dần khi D/E tăng (về phía r₀(1−t·D/V))

Practice problem

Unlevered firm value $1,000. Permanent debt $300, tax rate 25%. Compute levered firm value.

Show solution

VL = VU + tD = 1000 + 0.25(300)

VL = $1,075M

4. Static Trade-off Theory Concept

About: Optimal D/E balances tax-shield benefit vs expected costs of financial distress (bankruptcy + agency). Industry-specific optimal range — banks high, tech low.Tóm tắt: D/E tối ưu cân bằng tax shield và chi phí financial distress. Tùy ngành.

Optimal D/E balances the marginal tax shield benefit vs marginal expected cost of financial distress (bankruptcy + agency costs).