Residual income valuation model

What Is the Residual Income Valuation Model?

The Residual Income Valuation (RIV) model is an equity valuation method that determines the intrinsic value of a company's stock based on its current book value of equity and the present value of its expected future residual income. This approach belongs to the broader category of Equity valuation within financial modeling. Residual income, also known as abnormal earnings or economic profit, represents the earnings a company generates beyond the minimum return required by its shareholders on their invested capital²³. Unlike traditional accounting net income, which accounts for the cost of debt but not explicitly the cost of equity, residual income explicitly deducts a charge for the use of equity capital, providing a more comprehensive view of economic profitability²¹, ²². The residual income valuation model posits that value is created only when a company's earnings exceed this cost of equity.

History and Origin

The concept of residual income has a long history, with roots tracing back to economists like Alfred Marshall in the late 1800s, and its application in business performance evaluation as early as the 1920s by companies such as General Motors²⁰. However, the formalization of the residual income concept into a comprehensive equity valuation model gained significant academic and practical traction with the seminal work of James Ohlson in his 1995 paper, "Earnings, Book Values, and Dividends in Security Valuation"¹⁸, ¹⁹.

Ohlson's model provided a theoretical framework that linked market value directly to accounting fundamentals—specifically, book value and future residual income—under certain assumptions about the persistence of earnings and the role of "other information." This framework demonstrated the theoretical equivalence of the residual income model to other prominent valuation methods like the Dividend discount model and the Discounted cash flow model, given specific accounting relations are met. Th¹⁷e work of academics like Aswath Damodaran has further popularized and refined the application and understanding of the residual income valuation model in contemporary finance.

#¹⁶# Key Takeaways

• The Residual Income Valuation (RIV) model calculates a company's intrinsic value by adding the present value of its future residual income to its current Book value.
• Residual income represents the earnings a company generates above and beyond the cost of its equity capital.
• The model explicitly accounts for the Cost of equity, which is often overlooked in traditional financial statements.
• RIV is particularly useful for valuing companies that do not pay dividends or have inconsistent free cash flows, as it relies on accounting earnings and book values.
• ¹⁵ It provides a perspective on economic profitability, revealing whether a company is truly adding value for shareholders after considering all capital costs.

Formula and Calculation

The residual income valuation model calculates the intrinsic value of a company's equity by summing the current book value per share and the present value of all expected future residual incomes.

The formula for the intrinsic value per share using the residual income valuation model is:

Where:

• (V_0) = Intrinsic value per share today
• (BV_0) = Current Book value per share
• (RI_t) = Expected residual income per share in period (t)
• (r_e) = Required rate of return on equity (cost of equity)
• (T) = The number of periods over which residual income is forecast

The residual income ((RI_t)) for any given period is calculated as:

Where:

• (EPS_t) = Expected Earnings per share in period (t)
• (r_e \times BV_{t-1}) = The equity charge (the cost of equity multiplied by the beginning book value per share)

Alternatively, residual income can be expressed as:

Where:

• (ROE_t) = Expected Return on Equity in period (t)

This formulation highlights that residual income is generated only when the company's Return on Equity exceeds the required rate of return on equity.

Interpreting the Residual Income Valuation Model

Interpreting the output of the residual income valuation model involves understanding what the resulting intrinsic value signifies. The model's core principle is that a company creates value for its shareholders only when its return on equity exceeds the Required rate of return that investors demand for their capital.

A¹⁴ positive residual income for a given period indicates that the company is generating profits in excess of its cost of equity, thereby increasing shareholder value. Conversely, a negative residual income implies that the company is not earning enough to cover its cost of equity, effectively destroying shareholder value, even if it reports a positive net income under traditional Accounting principles.

When the residual income valuation model produces an Intrinsic value higher than the current Market value of the stock, it suggests that the stock may be undervalued. If the intrinsic value is lower, it might indicate overvaluation. The residual income model, by beginning with the current book value, explicitly incorporates the balance sheet into the valuation process, providing a different perspective compared to cash flow-based models that might give more weight to future projections. This makes it particularly useful for assessing firms with stable book values but fluctuating earnings or those in industries where assets are critical drivers of value.

Hypothetical Example

Consider XYZ Corp., a company whose shares currently trade at $40. An analyst wants to value XYZ Corp. using the residual income valuation model.

Here are the assumptions:

• Current Book Value per share ((BV_0)) = $30
• Required Rate of Return on Equity ((r_e)) = 10%
• Expected Earnings per share ((EPS)) for the next three years:
  • Year 1: $3.50
  • Year 2: $4.00
  • Year 3: $4.50
• Expected Book Value per share ((BV)) for the next three years (calculated using clean surplus assumption: (BV_t = BV_{t-1} + EPS_t - Dividends_t). For simplicity, assume all residual income is retained, or a stable dividend policy ensures this relationship holds for book value progression).
  • Year 1: $30 + $3.50 - $0.50 (assumed dividend) = $33
  • Year 2: $33 + $4.00 - $0.70 (assumed dividend) = $36.30
  • Year 3: $36.30 + $4.50 - $0.90 (assumed dividend) = $39.90

Let's calculate the expected residual income for each year:

Year 1:

• Equity Charge = (r_e \times BV_0 = 0.10 \times $30 = $3.00)
• Residual Income ((RI_1)) = (EPS_1 - \text{Equity Charge} = $3.50 - $3.00 = $0.50)
• Present Value of (RI_1) = (\frac{$0.50}{(1 + 0.10)^1} = \frac{$0.50}{1.10} \approx $0.45)

Year 2:

• Equity Charge = (r_e \times BV_1 = 0.10 \times $33 = $3.30)
• Residual Income ((RI_2)) = (EPS_2 - \text{Equity Charge} = $4.00 - $3.30 = $0.70)
• Present Value of (RI_2) = (\frac{$0.70}{(1 + 0.10)^2} = \frac{$0.70}{1.21} \approx $0.58)

Year 3:

• Equity Charge = (r_e \times BV_2 = 0.10 \times $36.30 = $3.63)
• Residual Income ((RI_3)) = (EPS_3 - \text{Equity Charge} = $4.50 - $3.63 = $0.87)
• Present Value of (RI_3) = (\frac{$0.87}{(1 + 0.10)^3} = \frac{$0.87}{1.331} \approx $0.65)

Assuming the company enters a stable growth phase after Year 3 where residual income grows at a constant rate, a terminal value for residual income would be calculated and discounted. For this simplified example, let's assume the forecast explicitly covers the period where residual income is significant, or the terminal value beyond Year 3 is negligible.

Total Present Value of Future Residual Income = (PV(RI_1) + PV(RI_2) + PV(RI_3))
Total Present Value of Future Residual Income = ($0.45 + $0.58 + $0.65 = $1.68)

Intrinsic Value ((V_0)) = Current Book Value + Total Present Value of Future Residual Income
Intrinsic Value ((V_0)) = ($30 + $1.68 = $31.68)

Based on this hypothetical scenario, the calculated intrinsic value per share for XYZ Corp. is $31.68. If the market price is $40, this model suggests the stock might be overvalued. This exercise highlights how the residual income model integrates elements from the Balance sheet (book value) and Income statement (earnings) to arrive at a valuation.

Practical Applications

The residual income valuation model finds several practical applications across finance and investment analysis. It is a fundamental tool used in Valuation models for determining the worth of public and private companies, particularly those where dividends are low or non-existent, or where free cash flows are volatile. Th¹³is makes it especially relevant for valuing growth companies that reinvest most of their earnings back into the business rather than distributing them as dividends.

Financial analysts often employ the residual income model to complement other valuation techniques, as it offers a perspective on a company's true economic profitability, considering the cost of equity. For example, it can be used to assess whether a company is generating returns above its cost of capital, indicating genuine value creation for shareholders.

F¹²urthermore, the residual income concept extends beyond mere valuation. It is utilized in corporate performance measurement, strategic decision-making, and even in determining executive compensation, incentivizing management to maximize returns above the cost of capital. It¹¹ provides a framework for analyzing how a company's Future earnings relate to its capital base and the efficiency with which that capital is employed. Academic materials often outline the application of residual income in practical valuation scenarios. Fo¹⁰r instance, it can be particularly useful in cases where companies have significant intangible assets or where Market value may not fully reflect the underlying economic value. The University of Texas at Dallas provides course materials that explain the practical application of the Residual Income Model.

Limitations and Criticisms

Despite its theoretical appeal and practical utility, the residual income valuation model is subject to several limitations and criticisms. A primary concern is its heavy reliance on accounting data, specifically reported Earnings per share and Book value. Th⁹ese figures can be influenced by management's accounting choices, estimates, and variations in Accounting principles (e.g., GAAP vs. IFRS), potentially leading to distortions in the residual income calculation. This sensitivity to accounting accruals can make comparisons across different firms or industries challenging and can also be manipulated through "earnings management" practices.

A⁷, ⁸nother significant limitation is the need for accurate forecasts of future earnings and book values over an extended period. Sm⁶all errors in these projections can lead to substantial inaccuracies in the estimated intrinsic value. Estimating the Required rate of return (cost of equity) is also subjective and challenging, as it involves assumptions about risk-free rates, equity risk premiums, and company-specific risk adjustments. Aswath Damodaran provides insights into the complexities of estimating equity risk premiums, a critical component of the cost of equity.

T⁴, ⁵he residual income model also assumes a "clean surplus" relationship, meaning that all changes in book value not attributable to shareholder transactions (like dividends or share repurchases) flow through the income statement. In³ reality, certain comprehensive income items (e.g., foreign currency translation adjustments or unrealized gains/losses on available-for-sale securities) bypass the income statement, affecting book value without being reflected in net income, thus violating the clean surplus assumption and potentially distorting the model's accuracy.

Furthermore, the model may not be suitable for all types of companies, particularly those with highly volatile or unpredictable earnings, or firms in early growth stages that consistently report negative residual income. Wh²ile theoretically equivalent to other Valuation models like the dividend discount model and discounted cash flow model under ideal conditions, in practice, accounting complexities and the need for numerous assumptions can make its application less straightforward and its results more prone to error.

Residual Income Valuation Model vs. Discounted Cash Flow

The Residual Income Valuation (RIV) model and the Discounted cash flow (DCF) model are both widely used approaches in Valuation models to determine a company's intrinsic value, but they differ fundamentally in their starting points and the nature of the "income" they discount.

The Residual Income Valuation model values a company's equity by starting with its current Book value of equity and adding the Present value of all expected future residual income. Residual income, or "abnormal earnings," represents the income earned by a company that exceeds the Required rate of return on its equity capital. It is an accounting-based approach that explicitly incorporates the cost of equity into the earnings calculation. This model is particularly useful for companies that do not pay dividends, have volatile free cash flows, or where assets and accounting profitability are key drivers of value.

T¹he Discounted Cash Flow (DCF) model, on the other hand, values a company based on the present value of its projected future free cash flows, discounted back to the present using an appropriate discount rate, typically the Weighted Average Cost of Capital (WACC) for a firm-level DCF or the Cost of equity for an equity-level DCF. The DCF model focuses on the actual cash generated by the business that is available to all capital providers (firm DCF) or just equity holders (equity DCF). It is generally considered robust because cash flows are less susceptible to accounting conventions and accrual manipulations than reported earnings.

The key differences can be summarized as follows:

While theoretically equivalent under certain assumptions, in practice, the choice between RIV and DCF often depends on the specific characteristics of the company being valued and the availability and reliability of data.

FAQs

What is residual income?

Residual income is the profit a company generates after deducting the cost of capital, particularly the cost associated with its equity. It's often referred to as "economic profit" or "abnormal earnings" because it measures how much a company's earnings exceed the minimum return required by its shareholders.

Why is the residual income valuation model used?

The residual income valuation model is used to estimate a company's Intrinsic value by explicitly incorporating the cost of equity. It is particularly useful for valuing companies that do not pay dividends or have unpredictable cash flows, as it relies on readily available Financial statements data such as earnings and book value.

How does the residual income model differ from the Dividend Discount Model?

Unlike the Dividend discount model, which values a stock based on the present value of its future dividends, the residual income model uses the present value of expected future residual income. This means the residual income model can be applied to companies that retain most of their earnings for reinvestment rather than paying them out as dividends.

What are the main challenges in using the residual income valuation model?

The primary challenges include its heavy reliance on accurate forecasts of future Earnings per share and Book value, which can be sensitive to accounting policies and management estimates. Accurately estimating the cost of equity is also a complex task that can significantly impact the valuation outcome.