Introductory Corporate Finance: Valuation - Residual Income Model

What This Is

The Residual Income Model is a valuation technique used to estimate a company's intrinsic value. It calculates the present value of expected future residual income, which is the income earned by shareholders after deducting the cost of capital. For example, consider a company with a market value of $100 million, equity of $50 million, and a cost of capital of 10%. If the company earns $5 million in residual income, its intrinsic value would be $55 million ($50 million + $5 million).

Key Formulas & Models

• Residual Income (RI) = Earnings Before Interest and Taxes (EBIT) - (Capital × Cost of Capital): measures the income earned by shareholders after deducting the cost of capital.
  • EBIT: earnings before interest and taxes
  • Capital: total capital (debt + equity)
  • Cost of Capital: weighted average cost of capital (WACC)
• WACC = wd × rd(1-T) + wps × rps + we × re: weighted average cost of capital; used as discount rate.
  • wd: debt-to-equity ratio
  • rd: debt cost of capital
  • T: tax rate
  • wps: proportion of preferred stock
  • rps: preferred stock cost of capital
  • we: proportion of equity
  • re: equity cost of capital
• Sustainable Growth Rate (SGR) = ROE × (1 - Retention Ratio): measures the maximum rate at which a company can grow without issuing new equity.
  • ROE: return on equity
  • Retention Ratio: proportion of earnings retained by the company
• Degree of Operating Leverage (DOL) = Q(P-V) / (Q(P-V)-F): measures the sensitivity of EBIT to sales.
  • Q: sales
  • P: price per unit
  • V: variable cost per unit
  • F: fixed cost
• Residual Income Model = Present Value of Expected Future Residual Income (PVFRI): estimates a company's intrinsic value by discounting expected future residual income.
  • PVFRI: present value of expected future residual income
• Cost of Capital (r) = (wd × rd(1-T) + wps × rps + we × re) / (wd + wps + we): calculates the weighted average cost of capital.
• Market Value of Equity (MVE) = Intrinsic Value - Debt: estimates the market value of equity by subtracting debt from intrinsic value.
• Intrinsic Value = Present Value of Expected Future Cash Flows (PVFCF): estimates a company's intrinsic value by discounting expected future cash flows.
  • PVFCF: present value of expected future cash flows

Step-by-Step Calculation

1. Calculate EBIT: earnings before interest and taxes
2. Calculate Capital: total capital (debt + equity)
3. Calculate Cost of Capital: weighted average cost of capital (WACC)
4. Calculate Residual Income: EBIT - (Capital × Cost of Capital)
5. Calculate Present Value of Expected Future Residual Income (PVFRI): discount expected future residual income using the cost of capital
6. Calculate Intrinsic Value: add present value of expected future residual income to the current market value of equity

Common Mistakes

• Mistake: Using book value instead of market value for WACC.
  • Correction: Use market value for WACC to reflect the current market price of debt and equity.
• Mistake: Ignoring flotation costs when calculating WACC.
  • Correction: Include flotation costs in the calculation of WACC to reflect the true cost of capital.
• Mistake: Confusing sunk cost with opportunity cost.
  • Correction: Use opportunity cost instead of sunk cost to reflect the true cost of capital.
• Mistake: Not considering the impact of taxes on WACC.
  • Correction: Include the impact of taxes on WACC to reflect the true cost of capital.

Exam / CFA Tips

• Tip: Be able to distinguish between M&M Proposition I (no taxes) and M&M Proposition II (with taxes).
• Tip: Understand the difference between IRR and NPV ranking.
• Tip: Be able to calculate the sustainable growth rate using the ROE and retention ratio.
• Tip: Understand the concept of degree of operating leverage (DOL) and its application in corporate finance.

Quick Practice Problem

A company has EBIT of $10 million, interest of $2 million, and tax of 25%. Calculate the degree of operating leverage (DOL).

Answer: DOL = 5 (calculated using the formula Q(P-V) / (Q(P-V)-F))

Explanation: The company's DOL is 5, indicating that a 1% increase in sales will result in a 5% increase in EBIT.

Last-Minute Cram Sheet

• Residual Income (RI) = EBIT - (Capital × Cost of Capital): measures the income earned by shareholders after deducting the cost of capital.
• WACC = wd × rd(1-T) + wps × rps + we × re: weighted average cost of capital; used as discount rate.
• Sustainable Growth Rate (SGR) = ROE × (1 - Retention Ratio): measures the maximum rate at which a company can grow without issuing new equity.
• Degree of Operating Leverage (DOL) = Q(P-V) / (Q(P-V)-F): measures the sensitivity of EBIT to sales.
• Residual Income Model = Present Value of Expected Future Residual Income (PVFRI): estimates a company's intrinsic value by discounting expected future residual income.
• Cost of Capital (r) = (wd × rd(1-T) + wps × rps + we × re) / (wd + wps + we): calculates the weighted average cost of capital.
• Market Value of Equity (MVE) = Intrinsic Value - Debt: estimates the market value of equity by subtracting debt from intrinsic value.
• Intrinsic Value = Present Value of Expected Future Cash Flows (PVFCF): estimates a company's intrinsic value by discounting expected future cash flows.
• In M&M Proposition I (no taxes), firm value is independent of capital structure – but with taxes, value increases with debt due to the interest tax shield.
• The degree of operating leverage (DOL) measures the sensitivity of EBIT to sales, not the sensitivity of EPS to sales.