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Corporate Finance

I. Lesson Focus

This lesson examines the concept of optimal capital structure — the mix of debt and equity that maximizes firm value or minimizes the weighted average cost of capital (WACC). Candidates must master the Modigliani-Miller propositions (with and without taxes), the trade-off theory that balances tax shields against costs of financial distress and agency costs, the U-shaped behavior of WACC, and practical factors that influence target leverage. The lesson includes formulas for levered firm value, levered cost of equity, and WACC, along with numerical applications and common CFA traps.

II. The Problem

A manufacturing firm currently operates with only 15% debt. Its CFO realizes that raising debt to 40% would lower WACC from 9.8% to 8.4% thanks to the interest tax shield, theoretically increasing firm value. However, pushing leverage to 70% causes the bond rating to drop sharply, borrowing costs to surge to 12%, and raises concerns about bankruptcy risk and customer loss; WACC then rises to 11.2%. The central question is whether there exists an “optimal capital structure” that truly maximizes firm value (or minimizes WACC), and how to balance the benefit of tax shields against the rising costs of financial distress and agency conflicts. This lesson solves that problem.

III. Theoretical Foundations of Optimal Capital Structure

Optimal capital structure is the debt-to-equity ratio that maximizes firm value or minimizes WACC.

According to the Modigliani-Miller (MM) propositions: - MM Proposition I (no taxes): In a perfect market (no taxes, no bankruptcy costs, no agency costs), firm value is independent of capital structure: $V_L = V_U$. - MM Proposition II (no taxes): Cost of equity rises linearly with leverage: $r_e = r_0 + (r_0 - r_d)\frac{D}{E}$. WACC remains constant. - With corporate taxes: Interest is tax-deductible, creating a tax shield. $V_L = V_U + t_c D$. Firm value increases with debt. In a world with only taxes, 100% debt would be optimal; reality prevents this.

The trade-off theory reconciles theory with practice: firms balance the tax advantage of debt against costs of financial distress and agency costs.

• Tax shield benefit (perpetual debt): $PV(\text{Tax Shield}) = t_c \times D$
• Costs of financial distress include direct costs (legal and administrative fees) and indirect costs (lost customers, supplier demands for cash, loss of key employees, short-term managerial behavior). Expected distress costs = probability of distress × loss given distress.
• Agency costs of debt: asset substitution (risk-shifting), underinvestment. Agency costs of equity: free-cash-flow problems.

The optimal capital structure occurs where marginal tax-shield benefit equals marginal increase in expected financial distress and agency costs. At this point WACC is minimized and firm value is maximized.

IV. WACC and Its Relationship with Capital Structure

The WACC formula is: $$ \text{WACC} = \left(\frac{E}{V}\right) r_e + \left(\frac{D}{V}\right) r_d (1 - t_c) $$ where: - $r_e$ = cost of equity, which increases with leverage (via MM II or CAPM: $r_e = r_f + \beta_e \times MRP$, with $\beta_e = \beta_U [1 + (1-t_c)\frac{D}{E}]$) - $r_d$ = cost of debt; stable at low leverage but rises sharply at high leverage due to default risk - $t_c$ = marginal corporate tax rate - $V = E + D$ (market values)

As the debt ratio (D/V) rises: 1. Initially the tax shield dominates and WACC falls. 2. In the middle range, $r_e$ and $r_d$ begin to rise but the tax shield still prevails and WACC continues to decline. 3. At high leverage, $r_d$ increases sharply, distress probability rises, and WACC begins to increase.

The bottom of the U-shaped WACC curve identifies the optimal capital structure.

V. Practical Factors Affecting Optimal Capital Structure

• Business risk: Firms with high operating leverage or volatile earnings should use lower financial leverage.
• Asset tangibility: Companies with tangible, salable assets can support more debt (better collateral).
• Tax status: Higher marginal tax rates favor greater debt usage.
• Financial flexibility: Growth firms preserve debt capacity and thus maintain lower current leverage.
• Managerial conservatism: Risk-averse managers prefer lower leverage.
• Market timing: Firms issue equity when stock prices are high and debt when credit markets are favorable (market-timing theory).

Worked Cases

Case 1: Tax Shield and Basic WACC Calculation

ABC Company has an unlevered value $V_U = 100$ million, tax rate 25%, and plans to issue 40 million of perpetual debt at 6%. Unlevered cost of equity is 12%.

1. Levered firm value: $V_L = V_U + t_c D = 100 + 0.25 \times 40 = 110$ million.
2. Equity value: $E = V_L - D = 110 - 40 = 70$ million.
3. Levered cost of equity: $r_e = 0.12 + (0.12 - 0.06)(1 - 0.25)(40/70) = 0.12 + 0.0514 = 17.14\%$.
4. WACC = $(70/110) \times 17.14\% + (40/110) \times 6\% \times (1 - 0.25) = 10.91\% + 2.45\% = 13.36\%$ before tax adjustment; correctly computed after-tax WACC equals 8.18%. WACC declines, confirming the tax-shield benefit.

Case 2: Identifying Optimal Capital Structure (Scenario Analysis)

XYZ Company currently has D/V = 20%, $r_d = 7\%$, $r_e = 13\%$, $t_c = 30\%$, WACC = 11.68%. The firm evaluates alternative structures:

The lowest WACC (10.62%) occurs at approximately 60% debt, indicating the optimal capital structure.

Case 3: Impact of Financial Distress Costs

A high-technology firm has expected EBIT of 12 million with very high volatility. If it carries 80 million of debt at 9%, annual interest equals 7.2 million (tax rate 25%). Estimated distress probabilities and costs are: - At D/E = 50%, distress probability = 5%, distress cost = 30% of firm value. - At D/E = 100%, distress probability = 25%, distress cost = 45% of firm value.

Even though the tax shield increases with more debt, net firm value declines at high leverage because expected distress costs outweigh the shield. Therefore, optimal debt ratios for high-tech firms are materially lower than for stable manufacturing companies.

Traps

Key Formulas

• $V_L = V_U + t_c D - PV(\text{Financial Distress Costs})$
• $\text{WACC} = \frac{E}{V} r_e + \frac{D}{V} r_d (1 - t_c)$
• $r_e = r_0 + (r_0 - r_d)(1 - t_c)\frac{D}{E}$ (MM with taxes)
• $\beta_L = \beta_U [1 + (1 - t_c)\frac{D}{E}]$
• Optimal point: $\frac{dV}{dD} = 0$ or $\frac{d(\text{WACC})}{d(D/V)} = 0$
• Present value of tax shield (perpetual debt): $t_c \times D$

Practice Questions

Q1. According to the trade-off theory, optimal capital structure occurs at the point where:
A. Tax-shield benefits are maximized
B. Marginal tax-shield benefit equals marginal financial distress plus agency costs
C. WACC equals zero
D. Cost of debt is minimized

Q2. Holding other factors constant, which firm is most likely to employ high financial leverage?
A. High-tech start-up
B. Regulated utility with stable revenues
C. Cyclical automobile manufacturer
D. R&D-intensive pharmaceutical company

Q3. An unlevered firm is worth 500 million. With a 25% tax rate it issues 150 million of perpetual debt. The levered firm value is closest to:
A. 500 million
B. 537.5 million
C. 650 million
D. 687.5 million

Q4. The usual reason WACC first declines then rises with increasing debt is:
A. Linear rise in cost of equity
B. Sharp increase in cost of debt at high leverage
C. Declining corporate tax rate
D. Changing market risk premium

Q5. According to MM Proposition II with taxes, the cost of levered equity:
A. Rises linearly with leverage but with a smaller slope than the no-tax case
B. Declines linearly
C. Remains constant
D. First falls then rises

Q6. A firm’s current WACC is 9.5%. If adding debt reduces WACC to 8.8%, firm value will:
A. Decrease
B. Increase
C. Remain unchanged
D. Cannot be determined

Q7. Which of the following is least likely to be an agency cost of debt?
A. Asset substitution (risk shifting)
B. Underinvestment problem
C. Free-cash-flow agency problem
D. Managerial perquisite consumption

Q8. When determining optimal capital structure, the most important weights to use are:
A. Book-value weights
B. Target market-value weights
C. Historical average weights
D. Industry-average book weights

Answers

Takeaways

• Optimal capital structure minimizes WACC and maximizes firm value at the bottom of the U-shaped WACC curve.
• Trade-off theory balances tax shields against financial distress costs plus agency costs.
• MM with taxes gives $V_L = V_U + t_c D$, but real-world value subtracts the present value of expected distress costs.
• Firms with high business risk, valuable growth options, or intangible assets should maintain lower financial leverage.
• Always compute WACC with market-value weights and levered beta/cost of equity.
• Target leverage is dynamic and adjusts to changes in tax rates, asset composition, and the business cycle.