Financial Valuation & Capital Structure Analysis

Valuation and Capital Structure Concepts

Q1: Perpetual Cash Flow Model (PCM)

Unlevered and Levered Valuation

Scenario: Perpetual Cash Flow Model (PCM) with 30% Debt (D) and 70% Equity (E). Cost of Debt (rD) = 5%, Free Cash Flow (FCF) = $10M, Cost of Equity (rE) = 10%. No Arbitrage.

• Unlevered Value (VU) = $10M / 10% = $100M.
• Levered Value (VL) = VU = $100M.
• Debt in Levered Firm (DL) = 0.3 * $100M = $30M.
• Equity in Levered Firm (EL) = 0.7 * $100M = $70M.

Perpetual Return Calculation

Perpetual Return VU = 1% * FCF.
VL = 1 * ($10M - 5% * $30M) + 1% * 5% * $30M.

Q2: Levered Recapitalization and Financial Distress

This section applies the Perpetual Cash Flow Model (PCM) with a corporate tax rate (Tc).

Project Valuation with Corporate Tax

Project Details:

• Project 1: $10M (50% allocation)
• Project 2: $22M (50% allocation, break-up value)

Risk-Free Rate (rF) = 10%. Corporate Tax Rate (Tc) = 20%.

• Adjusted Free Cash Flow (FCF) = $10M * (1 - 20%) = $8M.
• Project Value = ($8M / 10%) * 0.5 + ($22M / 1.1) * 0.5 = $50M.

Market Value Balance Sheet (Pre-Recap)

Market Value Balance Sheet (Assets & Liabilities/Equity):

• Assets: Project = $50M
• Liabilities & Equity: Debt (D) = $0, Equity (E) = $50M

Levered Recapitalization Details

Levered Recapitalization: The firm undertakes a levered recapitalization with perpetual coupon bonds, then repurchases equity with the proceeds.

• Par Value of Bonds = $15M
• Coupon Rate (r) = 10%

Interest Tax Shield (ITS) calculation: D * Tc * 50%.

Market Value Balance Sheet (Post-Announcement)

Market Value Balance Sheet Post-Announcement:

• Assets: Interest Tax Shield (ITS) = +$1.5M
• Equity: +$1.5M

Financial Distress Costs and Liabilities

Market Value Balance Sheet After Recapitalization with Financial Distress Costs:

• Potential Financial Distress Cost: -$7M if the project fails.
• Financial Distress Liability (FDL) = ($7M / 1.1) * 0.5 = $3.18M.
• Assets: Project = $50M, Interest Tax Shield (ITS) = $1.5M
• Liabilities & Equity: Financial Distress Liability (FDL) = $3.18M, Debt (D) = $0, Equity (E) = $48.32M.

Q3: Interest Tax Shield (ITS) Analysis

Perpetual ITS Calculation

Scenario: Free Cash Flow (FCF) = $2M, Growth Rate (g) = 3.4% (in perpetuity), Cost of Equity (rE) = 12%, Cost of Debt (rD) = 6%, Corporate Tax Rate (Tc) = 30%, Debt-to-Equity Ratio (D/E) = 0.5.

• Assuming D = 0.5 and E = 1 (for ratio calculation).
• Weighted Average Cost of Capital (RWACC) = 9.4%.
• Unlevered Cost of Equity (rU) = 10%.
• Levered Value (VL) = $2M / (9.4% - 3.4%) = $33.33M.
• Unlevered Value (VU) = (RWACC - g) = $30.30M.
• Present Value of Interest Tax Shield (PV(ITS)) = VL - VU = $33.33M - $30.30M = $3.03M.

Fixed-Term Debt ITS Impact

Alternative Scenario: What if the firm maintains a D/E ratio of 0.5 but issues $10M in fixed-term debt maturing in 20 years?

• Present Value of Interest Tax Shield (PV(ITS)) = C1 * (1/r) * [1 - 1/(1+r)^n] = $2.06M.
• Levered Value (VL) = VU + PV(ITS) = $30.30M + $2.06M = $32.37M.

Conclusion: The Interest Tax Shield is worth less when debt is non-perpetual due to fewer years of tax deductions.

Q4: Underinvestment Problem

Project Valuation and NPV

Scenario: No assets (A), owes zero-coupon bonds with a face value (FV) of $14.8M, maturing in 10 years. Initial Assets (A), Debt (D), and Equity (E) are $0.

New project offers Free Cash Flow (FCF) = $1.5M/year for 10 years, requires a $5M down payment. Asset Cost of Capital (rA) = 4%.

• Project Value = ($1.5M / 4%) * [1 - 1/(1+4%)^10] = $12.17M.
• Net Present Value (NPV) = $12.17M - $5M = $7.17M.

Equity Holders' NPV and Information Asymmetry

If the future value (FV) of the project is $18.01M and the FV of debt is $14.8M:

• Cash flow sufficient to pay debt: $14.8M / (1.04^4) = $10M in debt.
• Since $12.17M > $10M, the project can cover the debt.

NPV for Equity Holders = ($18.01M - $14.8M) / (1.04^10) - $5M = ($2.83M).

Alternatively, NPV for Equity Holders = ($12.17M - $10M) - $5M = ($2.83M).

Conclusion: Assuming no information asymmetry, management cannot convince equity holders to contribute the $5M, as debtholders would receive the positive NPV. This illustrates the underinvestment problem.

Key Financial Formulas

• EPS = EBT / #Shares
• ROE = EPS / P
• FCFE = EBIT - Interest
• rE = rU + (D/E)(rU - rD)
• BE = BU + D/E(BU - BD)
• ITS = (EBIT - i)(1 - Tc) + i
• i = d * rF
• ITS (Perpetual) = i * Tc
• Zero-Coupon Bond Price (P) = F / (1+r)^t
• Yield to Maturity (YTM) for Zero-Coupon Bond (r) = (F/P)^(1/t) - 1

Chapter 19: Capital Structure Theories

• Trade-off Theory

  Explains the benefit from leverage (Interest Tax Shield) balanced against the costs of financial distress.

• Agency Costs of Debt

  Occur when a firm faces financial distress. Equity holders may gain by undertaking risky investments, even if they have a negative Net Present Value (NPV). This can lead to asset substitution for riskier options.

• Agency Benefits of Debt

  • Reduced management enrichment
  • Concentrated ownership
  • Reduced wasteful investment with leverage
  • Reduced empire building
  • Free Cash Flow Hypothesis

• Asymmetric Information, Signaling Theory, and Adverse Selection

  The "lemon principle" where investors discount the value of a firm due to information asymmetry.