Dean's Office Official Model Question Paper

Capital Structure vs. Financial Structure

• Financial Structure: The entire right-hand side of the balance sheet, comprising all short-term current liabilities and long-term sources of funds.
• Capital Structure: The permanent long-term financing mix of the firm, comprising only long-term debt, preferred stock, and common equity (excluding short-term operating liabilities).

MM Proposition I (No Taxes)

In a perfect capital market without taxes, transaction costs, or bankruptcy risk, the total market value of a firm is independent of its capital structure: $V_L = V_U$. Financial leverage does not affect the weighted average cost of capital or firm value.

Trade-Off Theory

The Trade-Off Theory states that an optimal capital structure is achieved by balancing the tax benefits of debt financing (interest tax shield) against the escalating costs of financial distress (bankruptcy risk, legal costs) and agency costs as leverage increases.

Pecking Order Theory (Myers & Majluf)

Driven by asymmetric information, firms follow a strict financing hierarchy: first using internal retained earnings, then issuing safe debt securities, and issuing new external equity only as a last resort to avoid negative market signaling.

Rights Offering

A rights offering gives existing shareholders the pre-emptive legal privilege to purchase newly issued shares in proportion to their current holdings at a specified subscription price ($P_s$).

$$\text{Value of One Right } (R) = \frac{P_0 - P_s}{N + 1}$$

Where $P_0$ is the cum-rights share price, $P_s$ is the subscription price, and $N$ is the number of existing shares required to buy one new share.

Capital Structure Theories: MM with Taxes vs. Trade-Off Theory

1. Modigliani-Miller (MM) with Corporate Taxes (1963)

When corporate taxes are introduced, interest payments on debt become a tax-deductible expense, creating an annual Interest Tax Shield equal to $T_c \times r_d \times D$.

• Proposition I: The value of the levered firm ($V_L$) exceeds the unlevered firm ($V_U$) by the present value of the permanent tax shield:
  $$V_L = V_U + T_c D$$
• Proposition II: The cost of equity rises with leverage, but the tax shield offsets this, causing overall WACC to decline continuously as debt approaches 100%:
  $$k_{eL} = k_{eU} + (k_{eU} - k_d)(1 - T_c) \left(\frac{D}{E}\right)$$
• Theoretical Conclusion: Under pure MM with taxes, firms should finance with nearly 100% debt to maximize value.

2. The Static Trade-Off Theory

In reality, firms do not carry 100% debt because extreme leverage triggers Costs of Financial Distress (bankruptcy legal fees, lost customer confidence, supplier defections) and Agency Costs of debt.

  Firm Value (V)
        ^
        |                     Optimal Capital Structure (V*)
        |                            /\
        |                           /  \  Present Value of Financial Distress
        |     MM with Taxes       /     \  & Agency Costs
        |   --------------------/        \----------------
        |                     /           Actual Firm Value
        |  Unlevered (V_U)  /
        +----------------------------------------------------> Debt / Equity Ratio

• The Trade-Off Balance:
  $$V_L = V_U + \text{PV(Tax Shields)} - \text{PV(Financial Distress Costs)} - \text{PV(Agency Costs)}$$
• Strategic Implication: The optimal debt level occurs where the marginal tax benefit of an extra dollar of debt exactly equals the marginal increase in expected bankruptcy and agency costs.

EBIT-EPS Indifference and Financial Break-Even Analysis

1. Given Data

• Total Capital Needed = $\text{Rs. } 20,000,000$
• Corporate Tax Rate ($T$) = $25\% = 0.25$
• Plan A (All Equity): Number of shares $N_1 = 200,000$, Interest $I_1 = 0$
• Plan B (Debt + Equity): Debt = Rs. 10,000,000 @ 10% interest $\implies I_2 = \text{Rs. } 1,000,000$, Number of shares $N_2 = 100,000$

2. (a) EBIT-EPS Indifference Point Calculation

At the indifference point, $\text{EPS}_A = \text{EPS}_B$:

$$\frac{(\text{EBIT} - I_1)(1 - T)}{N_1} = \frac{(\text{EBIT} - I_2)(1 - T)}{N_2}$$

$$\frac{(\text{EBIT} - 0)(0.75)}{200,000} = \frac{(\text{EBIT} - 1,000,000)(0.75)}{100,000}$$

$$\frac{0.75\text{ EBIT}}{2} = 0.75(\text{EBIT} - 1,000,000)$$

$$\text{EBIT} = 2(\text{EBIT} - 1,000,000) \implies \text{EBIT} = 2\text{ EBIT} - 2,000,000$$

$$\mathbf{\text{EBIT}^* = Rs.\ 2,000,000}$$

3. (b) EPS at the Indifference EBIT Level

$$\text{EPS}^* = \frac{(2,000,000 - 0) \times 0.75}{200,000} = \frac{1,500,000}{200,000} = \mathbf{Rs.\ 7.50\ per share}$$

• Verification under Plan B: $\frac{(2,000,000 - 1,000,000) \times 0.75}{100,000} = \frac{750,000}{100,000} = \mathbf{\text{Rs. } 7.50}$.

4. (c) Financial Break-Even EBIT Level

• Plan A: $\text{Break-Even EBIT} = I_1 = \mathbf{\text{Rs. } 0}$
• Plan B: $\text{Break-Even EBIT} = I_2 = \mathbf{\text{Rs. } 1,000,000}$

5. Decision & Recommendation for Expected EBIT of Rs. 3,500,000

• Because the expected EBIT of Rs. 3,500,000 exceeds the indifference point of Rs. 2,000,000, financial leverage works in favor of the company.
• EPS under Plan A: $\frac{3,500,000 \times 0.75}{200,000} = \text{Rs. } 13.125$
• EPS under Plan B: $\frac{(3,500,000 - 1,000,000) \times 0.75}{100,000} = \frac{1,875,000}{100,000} = \mathbf{\text{Rs. } 18.75}$
• Recommendation: Management should choose Plan B (Debt + Equity) because it delivers a higher EPS (Rs. 18.75 vs. Rs. 13.13), maximizing shareholder earnings.

Lease vs. Purchase Decision and Net Advantage to Leasing (NAL)

Leasing is a contractual arrangement where an asset owner (lessor) grants another party (lessee) the right to use the asset for a specified period in exchange for periodic lease payments.

1. Operating Lease vs. Financial Lease

2. Net Advantage to Leasing (NAL) Framework

NAL measures the incremental net present value of leasing an asset instead of borrowing and purchasing it:

$$\text{NAL} = \text{Initial Acquisition Cost Saved} - \text{PV of After-Tax Lease Payments} - \text{PV of Lost Depreciation Tax Shields} - \text{PV of Lost Terminal Salvage Value}$$

$$\text{NAL} = I_0 - \sum_{t=1}^n \frac{L_t(1 - T)}{(1 + r_d^*)^t} - \sum_{t=1}^n \frac{T \times D_t}{(1 + r_d^*)^t} - \frac{S_n}{(1 + k)^n}$$

Where:

• $I_0 = \text{Initial purchase price avoided}$

• $L_t(1 - T) = \text{After-tax lease payments}$

• $r_d^* = r_d(1 - T) = \text{After-tax cost of debt discount rate}$

• $T \times D_t = \text{Tax shield on depreciation lost by leasing}$

• $S_n = \text{Residual salvage value lost at year } n$

• Decision Rule: If $\mathbf{\text{NAL} > 0}$, the firm should lease the asset; if $\mathbf{\text{NAL} < 0}$, the firm should borrow and purchase.

Dividend Policy Theories: Relevance vs. Irrelevance

1. Walter’s Model (Dividend Relevance)

James E. Walter argued that dividend policy is an active variable directly affecting firm share price, depending on the relationship between internal rate of return ($r$) and cost of capital ($k_e$):

$$P = \frac{D + \frac{r}{k_e}(E - D)}{k_e}$$

• Growth Firm ($r > k_e$): Optimum dividend payout is 0% (retaining earnings maximizes share price).
• Declining Firm ($r < k_e$): Optimum dividend payout is 100% (investors can earn higher returns elsewhere).
• Normal Firm ($r = k_e$): Dividend policy is neutral; payout ratio has no impact on share price.

2. Gordon’s Model (The Bird-in-the-Hand Theory)

Myron Gordon postulated that investors are inherently risk-averse and value current dividend payouts more than uncertain future capital gains (“A bird in the hand is worth two in the bush”):

$$P_0 = \frac{D_1}{k_e - g} = \frac{E_1(1 - b)}{k_e - (b \times r)}$$

Where $b$ is retention ratio, and $g = b \times r$. A higher dividend payout reduces investor uncertainty, leading to a lower cost of capital and higher share valuation.

3. Modigliani-Miller (MM) Dividend Irrelevance Theorem (1961)

• MM proved that in perfect capital markets without taxes and transaction costs, dividend policy is completely irrelevant to firm valuation.
• Share price is determined solely by the firm’s earning power and investment policy, not by how earnings are divided between dividends and retained earnings. Any cash dividend payout reduces market equity value by the exact amount paid out, leaving total shareholder wealth unchanged.

Comprehensive Problem Solution: Capital Restructuring & MM Propositions

(a) MM with Corporate Taxes: Firm Value and Share Repurchase (7 Marks)

1. Value of Unlevered Firm ($V_U$):

$$V_U = \text{Number of Shares} \times \text{Current Share Price} = 1,000,000 \times \text{Rs. } 250 = \mathbf{Rs.\ 250,000,000}$$

2. Value of Levered Firm ($V_L$):

• Debt Issued ($D$) = $\text{Rs. } 100,000,000$
• Corporate Tax Rate ($T_c$) = $25\% = 0.25$
• Present Value of Tax Shield = $T_c \times D = 0.25 \times 100,000,000 = \text{Rs. } 25,000,000$$V_L = V_U + T_c D = 250,000,000 + 25,000,000 = \mathbf{Rs.\ 275,000,000}$$

3. Market Value of Levered Equity ($E_L$):

$$E_L = V_L - D = 275,000,000 - 100,000,000 = \mathbf{Rs.\ 175,000,000}$$

4. New Share Price and Repurchase:

• Because the announcement of the debt tax shield creates Rs. 25M in value shared across the initial 1,000,000 shares:
  $$\text{New Share Price } (P_1) = \frac{V_L}{N_0} = \frac{275,000,000}{1,000,000} = \mathbf{Rs.\ 275\ per share}$$
• Number of shares repurchased with Rs. 100M debt proceeds:
  $$\text{Shares Repurchased} = \frac{\text{Debt Proceeds}}{P_1} = \frac{100,000,000}{275} = \mathbf{363,636\ shares}$$
• Remaining shares outstanding: $1,000,000 - 363,636 = \mathbf{636,364\ shares}$
• Check: $636,364 \times 275 \approx \text{Rs. } 175,000,000$ (Matches $E_L$).

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(b) Levered Cost of Equity ($k_{eL}$) and WACC (7 Marks)

1. MM Proposition II with Taxes:

$$k_{eL} = k_{eU} + (k_{eU} - k_d)(1 - T_c) \left(\frac{D}{E}\right)$$

Where:

• $k_{eU} = 15\% = 0.15$
• $k_d = 9\% = 0.09$
• $T_c = 0.25$
• $\frac{D}{E} = \frac{100,000,000}{175,000,000} = 0.5714$$k_{eL} = 0.15 + (0.15 - 0.09)(1 - 0.25)(0.5714) = 0.15 + (0.06)(0.75)(0.5714) = 0.15 + 0.0257 = \mathbf{17.57\%}$$

2. Weighted Average Cost of Capital (WACC):

• Weight of Debt: $w_d = \frac{100}{275} = 0.3636$
• Weight of Equity: $w_e = \frac{175}{275} = 0.6364$
• After-Tax Cost of Debt: $k_d(1 - T_c) = 9\% \times (1 - 0.25) = 6.75\%$$\text{WACC} = [w_e \times k_{eL}] + [w_d \times k_d(1 - T_c)] = (0.6364 \times 17.57\%) + (0.3636 \times 6.75\%) = 11.18\% + 2.45\% = \mathbf{13.63\%}$$
• Proof: Unlevered WACC was $15.00\%$. The introduction of debt lowered WACC from 15.00% to 13.63%, creating Rs. 25 Million in corporate value.

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(c) Trade-Off Theory & Net Valuation (6 Marks)

1. Factoring in Expected Bankruptcy Costs:

$$\text{Actual Firm Value } (V^*) = V_L - \text{PV of Financial Distress Costs} = 275,000,000 - 18,000,000 = \mathbf{Rs.\ 257,000,000}$$

• The net economic benefit of debt is reduced from Rs. 25 Million to: $\text{Rs. } 257\text{M} - 250\text{M} = \mathbf{\text{Rs. } 7\text{ Million}}$.

2. Strategic Advice to Board of Directors:

• Issuing Rs. 100 Million of debt is still net value-accretive (+Rs. 7 Million net gain), but the firm is nearing its debt capacity limit.
• Increasing debt beyond Rs. 100 Million will cause marginal bankruptcy distress costs to exceed marginal tax shields, eroding firm value.
• Recommendation: Proceed with the Rs. 100 Million debt issue, but implement restrictive debt covenants and maintain minimum cash liquidity reserves to manage seasonal agricultural cash-flow volatility.