Residual income model

Residual Income Model

The residual income model (RIM) is an equity valuation approach that determines a company's intrinsic value by adding its current book value per share to the present value of its expected future residual income. This model is a key component of financial modeling and focuses on the economic profit a company generates above its cost of equity. Unlike traditional accounting profit, which only considers explicit costs, residual income explicitly accounts for the opportunity cost of shareholders' capital.

History and Origin

The foundational concept of residual income, sometimes referred to as economic profit or abnormal earnings, dates back to economists like Alfred Marshall in the late 1800s. Early applications were seen in corporate contexts, such as General Motors utilizing the concept for evaluating business segments in the 1920s. The formalization and widespread recognition of the residual income model in valuation theory largely stem from the work of accounting scholars. Notably, academics such as Edwards and Bell (1961), Peasnell (1982), and particularly James Ohlson (1995) significantly refined and popularized the residual income model, establishing its theoretical underpinnings for valuing common stock¹³, ¹⁴. Ohlson's 1995 paper, "Earnings, Book Values, and Dividends in Equity Valuation," provided a rigorous framework that integrated accounting numbers directly into a valuation model, demonstrating its equivalence to the dividend discount model under certain assumptions.

Key Takeaways

• The residual income model values a company based on its book value plus the present value of future earnings that exceed the required return on equity.
• It explicitly accounts for the opportunity cost of equity capital, providing a measure of economic profit.
• The model is particularly useful for companies that do not pay dividends or have unpredictable dividend patterns.
• It relies heavily on accounting data, which may necessitate adjustments for accurate application.
• Positive residual income indicates value creation for shareholders, while negative residual income suggests value destruction.

Formula and Calculation

The residual income model values a company's common equity as the sum of its current book value per share and the present value of its expected future residual income.

The formula for the intrinsic value per share ($V_0$) using the residual income model is:

Where:

• $V_0$ = Intrinsic value per share at time 0
• $B_0$ = Current book value of equity per share
• $RI_t$ = Expected residual income per share in period $t$
• $r_e$ = Required rate of return on equity (cost of equity)

The residual income ($RI_t$) for any period $t$ can be calculated as:

Where:

• $EPS_t$ = Expected earnings per share in period $t$
• $B_{t-1}$ = Book value per share at the end of the previous period ($t-1$)

Alternatively, residual income can be expressed using return on equity (ROE):

Where:

• $ROE_t$ = Expected return on equity in period $t$

The core of the model lies in discounting the abnormal earnings (residual income) to their present value using the discount rate, which is the cost of equity.

Interpreting the Residual Income Model

The residual income model provides a forward-looking perspective on a company's value, focusing on the earnings generated above what shareholders require for their investment. A positive residual income indicates that a company is generating returns exceeding its cost of capital, thereby creating economic value for shareholders. Conversely, a negative residual income suggests that the company's earnings are not covering its cost of equity, indicating a destruction of shareholder value.

Analysts interpret the calculated intrinsic value from the residual income model by comparing it to the current market price of the stock. If the intrinsic value is higher than the market price, the stock may be considered undervalued, and vice versa. This model is particularly insightful for companies that have significant intangible assets or those in early growth stages that may not yet have consistent positive free cash flows.

Hypothetical Example

Consider Tech Solutions Inc., a software company, at the end of 2024.

• Current book value per share ($B_0$) = $20
• Cost of equity ($r_e$) = 10%
• Expected earnings per share (EPS) for 2025 ($EPS_1$) = $3.00
• Expected EPS for 2026 ($EPS_2$) = $3.50
• Expected EPS for 2027 ($EPS_3$) = $3.80 (after which residual income is assumed to be zero for simplicity)

Step 1: Calculate Residual Income for each period.

• 2025 (Year 1):
  • Equity charge = $r_e \times B_0 = 0.10 \times $20 = $2.00$
  • $RI_1 = EPS_1 - \text{Equity charge} = $3.00 - $2.00 = $1.00$
  • Book value at end of 2025 ($B_1$) = $B_0 + EPS_1 - \text{Dividends}1$. Assuming dividends equal earnings after covering equity charge or using Clean Surplus: $B_1 = B_0 + RI_1$. However, typically, $B_1 = B_0 + EPS_1 - D_1$. If $RI_t = EPS_t - (r_e \times B{t-1})$ is used, then $B_t = B_{t-1} + EPS_t - D_t$. For simplicity, and aligning with the residual income definition as abnormal earnings over book value, we'll assume dividends are such that book value grows with retained earnings. Let's assume dividends are such that $B_1 = B_0 + (EPS_1 - RI_1) = 20 + 3.00 - 1.00 = 22$. Or simpler for this hypothetical, assume $B_t = B_{t-1} \times (1 + g)$ where g is growth in book value, if not explicitly calculating dividends. To keep it simple, we just use the prior period's book value for the equity charge.

Let's assume the book value for the next year is calculated as $B_t = B_{t-1} + (EPS_t - D_t)$. If the clean surplus relation holds (change in book value equals net income minus dividends), then the previous book value in the equity charge is well-defined.

Assuming a dividend payout ratio that maintains the relationship for the next period:

• Book value for 2025 ($B_0$) = $20

• Residual Income 2025 ($RI_1$) = $1.00

• 2026 (Year 2): To calculate $RI_2$, we need $B_1$. Assume no new equity issues/buybacks, so $B_1 = B_0 + (EPS_1 - D_1)$. If the clean surplus relation holds, $D_1 = EPS_1 - (B_1 - B_0)$.

  • Let's assume for this example, the book value at the end of 2025, $B_1$, is $21.50.
  • Equity charge = $0.10 \times $21.50 = $2.15$
  • $RI_2 = EPS_2 - \text{Equity charge} = $3.50 - $2.15 = $1.35$

• 2027 (Year 3): To calculate $RI_3$, we need $B_2$. Assume $B_2 = 23.00$.

  • Equity charge = $0.10 \times $23.00 = $2.30$
  • $RI_3 = EPS_3 - \text{Equity charge} = $3.80 - $2.30 = $1.50$

Step 2: Calculate the Present Value of Residual Income for each period.

• PV of $RI_1 = $1.00 / (1 + 0.10)^1 = $0.91$
• PV of $RI_2 = $1.35 / (1 + 0.10)^2 = $1.12$
• PV of $RI_3 = $1.50 / (1 + 0.10)^3 = $1.13$

Step 3: Sum the present values of residual income.

• Total PV of future residual income = $0.91 + 1.12 + 1.13 = $3.16$

Step 4: Calculate the Intrinsic Value.

• Intrinsic Value ($V_0$) = $B_0$ + Total PV of future residual income
• $V_0 = $20 + $3.16 = $23.16$

The intrinsic value per share of Tech Solutions Inc. is estimated to be $23.16.

Practical Applications

The residual income model is widely used by financial analysts and investors for several purposes, primarily in equity analysis.

• Company Valuation: It is a primary method for determining a company's intrinsic value, particularly for firms that do not pay dividends, have unstable dividend policies, or experience periods of negative free cash flow. This makes it a valuable tool for valuing growth companies that reinvest most of their earnings¹².
• Performance Measurement: Beyond valuation, the residual income concept is also employed internally by companies as a performance metric. It helps management assess whether specific business segments, projects, or the entire company are generating returns that exceed the cost of the capital employed. This can influence resource allocation and executive compensation decisions¹⁰, ¹¹.
• Goodwill Impairment Testing: The model can be applied in accounting to measure the impairment of goodwill, ensuring that the recorded value of goodwill reflects its economic reality⁹.
• Consistency Check: Analysts often use the residual income model alongside other valuation approaches, such as the discounted cash flow (DCF) model or the dividend discount model, to cross-verify valuation results and improve confidence in their estimates⁸.

Limitations and Criticisms

While the residual income model offers valuable insights, it is subject to several limitations and criticisms:

• Reliance on Accounting Data: The model is highly dependent on reported accounting data, which can be subject to manipulation, aggressive accounting practices, or may not always reflect economic reality. This reliance necessitates careful scrutiny and potential adjustments to financial statements⁷.
• Clean Surplus Violation: A critical assumption of the residual income model is the "clean surplus relation," which posits that all changes in shareholder equity, other than those from capital contributions or withdrawals, flow through the income statement. In practice, various items, such as foreign currency translation adjustments or certain pension adjustments, bypass the income statement and are directly charged to equity, violating this assumption. If the clean surplus relation does not hold, adjustments to net income are required for the model to be accurate⁵, ⁶.
• Forecasting Challenges: Like other prospective valuation models, the residual income model requires accurate forecasts of future earnings per share and book values. Forecasting these variables, especially for extended periods, can be challenging and introduce significant estimation risk⁴.
• Terminal Value Sensitivity: Although often less sensitive to terminal value than some discounted cash flow models, the terminal value still represents a substantial portion of the estimated intrinsic value, and its estimation relies on assumptions about long-term growth and profitability³.
• "Other Information" Variable: The original Ohlson (1995) model included an "other information" variable to account for non-accounting information that affects future abnormal earnings. However, this variable is often unspecified and challenging to quantify, leading some empirical studies to omit it, which can limit the model's comprehensiveness². The efficacy of the model can be impacted by how well these underlying assumptions align with real-world accounting practices and market dynamics¹.

Residual Income Model vs. Dividend Discount Model

The residual income model and the dividend discount model (DDM) are both absolute valuation methods used to estimate the intrinsic value of a company's equity, and theoretically, they should yield the same result under consistent assumptions. However, their approaches differ significantly.

While the DDM might struggle with companies that retain most of their earnings for reinvestment (and thus pay little or no dividends), the residual income model excels in such scenarios by focusing on the value created by reinvesting those earnings above the return on equity required by investors.

FAQs

Q: What is the main idea behind the residual income model?
A: The core idea is that a company creates value for shareholders only if it generates earnings that exceed the minimum return shareholders require on their invested capital. The model values a company by adding its current book value to these "excess" earnings, discounted back to the present.

Q: Why is the cost of equity important in the residual income model?
A: The cost of equity represents the minimum rate of return investors expect from their investment, compensating them for the risk taken. In the residual income model, this cost is explicitly deducted from earnings to determine the true economic profit, making it crucial for assessing value creation.

Q: Can the residual income model be used for all types of companies?
A: While versatile, the residual income model is particularly advantageous for companies that do not pay regular dividends or have unpredictable dividend patterns. It is also suitable for companies with negative free cash flow, where other valuation methods might be difficult to apply. For companies with very volatile earnings or significant accounting complexities, careful adjustments to the inputs are necessary.

Q: How does residual income differ from accounting net income?
A: Accounting net income reflects profits after all explicit expenses, including interest on debt. Residual income goes a step further by also deducting an "equity charge," which represents the implicit cost of using shareholders' equity. This makes residual income a measure of true economic profit, reflecting whether the company is earning above its cost of all capital, not just debt.