As an economic concept, residual income has a long history, dating back to Alfred Marshall in the late 1800s.⁹⁴ As far back as the 1920s, General Motors used the concept in evaluating business segments.⁹⁵ More recently, residual income has received renewed attention and interest, sometimes under names such as economic profit, abnormal earnings, or economic value added. Although residual income concepts have been used in a variety of contexts, including the measurement of internal corporate performance, this chapter focuses on the residual income model for estimating the intrinsic value of common stock. Among the questions we will study to help us apply residual income models are the following:

The chapter is organized as follows: Section 2 develops the concept of residual income, introduces the use of residual income in valuation, and briefly presents alternative measures used in practice. Section 3 presents the residual income model and illustrates its use in valuing common stock. This section also shows practical applications, including the single-stage (constant-growth) residual income model and a multistage residual income model. Section 4 describes the relative strengths and weaknesses of residual income valuation compared to other valuation methods. Section 5 addresses accounting issues in the use of residual income valuation. Section 6 summarizes the chapter and practice problems conclude it.

In Example 5-1, residual income is calculated based on net income and a charge for the cost of equity capital. Analysts will also encounter another approach to calculating residual income that yields the same results under certain assumptions. In this second approach, which takes the perspective of all providers of capital (both debt and equity), a capital charge(the company’s total cost of capital in money terms) is subtracted from the company’s after-tax operating profit. In the case of AXCI in Example 5-1, the capital charge is €169,000:

The company’s net operating profit after taxes (NOPAT) is €140,000 (€200,000 - 30% taxes). The capital charge of €169,000 is higher than the after-tax operating profit of €140,000 by €29,000, the same figure obtained in Example 5-1.

As illustrated in the following table, both approaches yield the same results in this case because of two assumptions. First, this example assumes that the marginal cost of debt equals the current cost of debt, that is, the cost used to determine net income. Specifically, in this instance, the after-tax interest expense incorporated in net income [€49,000 = €70,000 x (1 - 30%)] is equal to the after-tax cost of debt incorporated into the capital charge. Second, this example assumes that the weights used to calculate the capital charge are derived from the book value of debt and equity. Specifically, it uses the weights of 50 percent debt and 50 percent equity.

That the company is not profitable in an economic sense can also be seen by comparing the company’s cost of capital to its return on capital. Specifically, the company’s capital charge is greater than its after-tax return on total assets or capital. The after-tax net operating return on total assets or capital is calculated as profits divided by total assets (or total capital). In this example, the after-tax net operating return on total assets is 7 percent (€140,000/€2,000,000), which is 1.45 percentage points less than the company’s effective capital charge of 8.45 percent (€169,000/€2,000,000).⁹⁸

To illustrate the effect of residual income on equity valuation using the case of AXCI presented in Example 5-1, assume the following:

Because AXCI is not earning its cost of equity, as shown in Example 5-1, the company’s share price should fall. Given the information, AXCI is destroying €29,000 of value per year, which equals €0.29 per share (€29,000/100,000 shares). Discounted at 12 percent cost of equity, the present value of the perpetuity is €2.42 (€0.29/12%). The current share price minus the present value of the value being destroyed equals €7.58 (€10 - €2.42).

Another way to look at these data is to note that the earnings yield (E/P) for a no-growth company is an estimate of the expected rate of return. Therefore, when price reaches the point at which E/P equals the required rate of return on equity, an investment in the stock is expected to just cover the stock’s required rate of return. With EPS of €0.91, the earnings yield is exactly 12 percent (AXCI’s cost of equity) when its share price is €7.58333 (i.e., €0.91/€7.58333 = 12%). At a share price of €7.58333, the total market value of AXCI’s equity is €758,333. When a company has negative residual income, shares are expected to sell at a discount to book value. In this example, AXCI’s price-to-book ratio (P/B) at this level of discount from book value would be 0.7583. In contrast, if AXCI were earning positive residual income, then its shares should sell at a premium to book value. In summary, higher residual income is expected to be associated with higher market prices (and higher P/Bs), all else being equal.

Residual income (RI) models have been used to value both individual stocks (Fleck et al. 2001) and the Dow Jones Industrial Average (Lee and Swaminathan 1999; Lee et al. 1999). The models have also been proposed as a solution to measuring goodwill impairment by accounting standard setters. Recall that impairment in an accounting context means downward adjustment, and goodwill is an intangible asset that may appear on a company’s balance sheet as a result of its purchase of another company.

Residual income and residual income models have been referred to by a variety of names. Residual income has sometimes been called economic profit because it is an estimate of the profit of the company after deducting the cost of all capital: debt and equity. In forecasting future residual income, the term abnormal earnings is also used. Under the assumption that in the long term the company is expected to earn its cost of capital (from all sources), any earnings in excess of the cost of capital can be termed abnormal earnings. The residual income model has also been called the discounted abnormal earnings model and the Edwards-Bell-Ohlson model after the names of researchers in the field. This chapter focuses on a general residual income model that can be used by analysts using publicly available data and nonproprietary accounting adjustments. A number of commercial implementations of the approach, however, are also very well known. Before returning to the general residual income model in Section 3, we briefly discuss one such commercial implementation and the related concept of market value added.

Over time, a company must generate economic profit for its market value to increase. A concept related to economic profit (and EVA) is market value added (MVA): A company that generates positive economic profit should have a market value in excess of the accounting book value of its capital.

Research on the ability of value-added concepts to explain equity value and stock returns has reached mixed conclusions. Peterson and Peterson (1996) found that value-added measures are slightly more highly correlated with stock returns than are traditional measures, such as return on assets and return on equity. Bernstein and Pigler (1997) and Bernstein, Bayer, and Pigler (1998) found that value-added measures are no better at predicting stock performance than are such measures as earnings growth.

A variety of commercial models related to the residual income concept have been marketed by other major accounting and consulting firms. Interestingly, the application focus of these models is not, in general, equity valuation. Rather, these implementations of the residual income concept are marketed primarily for measuring internal corporate performance and determining executive compensation.

The use of Equation 5-3, the expression for the estimated intrinsic value of common stock, is illustrated in Example 5-3.

Example 5-3 illustrates two important points about residual income models. First, the RI model is fundamentally similar to other valuation models, such as the dividend discount model (DDM), and given consistent assumptions will yield equivalent results. Second, recognition of value typically occurs earlier in RI models than in DDM. In Example 5-3, the RI model attributes $6.00 of the $11.15 total value to the first time period. In contrast, the DDM model attributes $9.2036 of the $11.15 total value to the final time period. The rest of Section 3 develops the most familiar general expression for the RI model and illustrates the model’s application.

According to the expression, the value of a stock equals its book value per share plus the present value of expected future per-share residual income. Note that when the present value of expected future per-share residual income is positive (negative), intrinsic value, V₀, is greater (smaller) than book value per share, B₀.

The residual income model used in practice today has its origins largely in the academic work of Ohlson (1995) and Feltham and Ohlson (1995) along with the earlier work of Edwards and Bell (1961), although in the United States this method has been used to value small businesses in tax cases since the 1920s.¹⁰¹ The general expression for the residual income model based on this work¹⁰² can also be stated as:

Equation 5-4 is equivalent to the expressions for V₀given earlier because in any year, t, RI_t= (ROE_t- r)B_t-1. Other than the required rate of return on common stock, the inputs to the residual income model come from accounting data. Note that return on equity (ROE) in this context uses beginning book value of equity in the denominator, whereas in financial statement analysis ROE is frequently calculated using the average book value of equity in the denominator. Example 5-4 illustrates the estimation of value using Equation 5-4.

Example 5-4 shows that residual income value can be estimated using current book value, forecasts of earnings, forecasts of book value, and an estimate of the required rate of return on equity. The forecasts of earnings and book value translate into ROE forecasts.

Example 5-5 refers to the assumption of clean surplus accounting. The residual income model, as stated earlier, assumes clean surplus accounting. The clean surplus accounting assumption is illustrated in Exhibit 5-4, for example, in which ending book value per share is computed as beginning book value plus net income minus dividends. Under International Financial Reporting Standards (IFRS) and U.S. generally accepted accounting principles (U.S. GAAP), several items of income and expense occurring during a period, such as changes in the market value of certain securities, bypass the income statement and affect a company’s book value of equity directly.¹⁰³ Strictly speaking, residual income models involve all items of income and expense (income under clean surplus accounting). If an analyst can reliably estimate material differences from clean surplus accounting expected in the future, an adjustment to net income may be appropriate. Section 5.1 explores violations of the clean surplus accounting assumption in more detail.

The justified price is the stock’s intrinsic value (P₀ = V₀). Therefore, using the previous equation and remembering that residual income is earnings less the cost of equity, or (ROE x B₀) - (r x B₀), a stock’s intrinsic value under the residual income model, assuming constant growth, can be expressed as:

Under this model, the estimated value of a share is the book value per share (B₀) plus the present value [(ROE - r)B₀/(r - g)] of the expected stream of residual income. In the case of a company for which ROE exactly equals the cost of equity, the intrinsic value is equal to the book value per share. Equation 5-5 is considered a single-stage (or constant-growth) residual income model.

In an ideal world, where the book value of equity represents the fair value of net assets and clean surplus accounting prevails, the term B₀reflects the value of assets owned by the company less its liabilities. The second term, (ROE - r)B₀/(r - g), represents additional value expected because of the company’s ability to generate returns in excess of its cost of equity; the second term is the present value of the company’s expected economic profits.

The residual income model is most closely related to the P/B ratio. A stock’s justified P/B ratio is directly related to expected future residual income. Another closely related concept is Tobin’s q, the ratio of the market value of debt and equity to the replacement cost of total assets:¹⁰⁵

Although similar to P/B, Tobin’s q also has some obvious differences. The numerator includes the market value of total capital (debt as well as equity). The denominator uses total assets rather than equity. Further, assets are valued at replacement cost rather than at historical accounting cost; replacement costs take into account the effects of inflation. All else equal, Tobin’s q is expected to be higher the greater the productivity of a company’s assets.¹⁰⁶ One difficulty in computing Tobin’s q is the lack of information on the replacement cost of assets. If available, market values of assets or replacement costs can be more useful in a valuation than historical costs.

Similar to the Gordon growth DDM, the single-stage RI model can be used to assess the market expectations of residual income growth—that is, an implied growth rate—by inputting the current price into the model and solving for g.

In Examples 5-6 and 5-7, the company was valued at more than twice its book value because its ROE exceeded its cost of equity. If ROE was equal to the cost of equity, the company would be valued at book value. If ROE was lower than the cost of equity, the company would have negative residual income and be valued at less than book value. (When a company has no prospect of being able to cover its cost of capital, a liquidation of the company and redeployment of assets may be appropriate.)

In many applications, a drawback to the single-stage model is that it assumes the excess ROE above the cost of equity will persist indefinitely. More likely, a company’s ROE will revert to a mean value of ROE over time, and at some point, the company’s residual income will be zero. If a company or industry has an abnormally high ROE, other companies will enter the marketplace, thus increasing competition and lowering returns for all companies. Similarly, if an industry has a low ROE, companies will exit the industry (through bankruptcy or otherwise) and ROE will tend to rise over time. As with the single-stage DDM, the single-stage residual income model also assumes a constant growth rate through time.

In light of these considerations, the residual income model has been adapted in practice to handle declining residual income. For example, Lee and Swaminathan (1999) and Lee, Myers, and Swaminathan (1999) used a residual income model to value the Dow 30 by assuming that ROE fades (reverts) to the industry mean over time. Lee and Swaminathan found that the residual income model had more ability than traditional price multiples to predict future returns. Fortunately, other models are available that enable analysts to relax the assumption of indefinite persistence of excess returns. The following section describes a multistage residual income model.

In residual income valuation, the current book value often captures a large portion of total value, and the terminal value may not be a large component of total value because book value is larger than the periodic residual income and because ROE may fade over time toward the cost of equity. This contrasts with other multistage approaches (DDM and DCF), in which the present value of the terminal value is frequently a significant portion of total value.

Analysts make a variety of assumptions concerning continuing residual income. Frequently, one of the following assumptions is made:

One finite-horizon model of residual income valuation assumes that at the end of time horizon T, a certain premium over book value (P_T - B_T) exists for the company, in which case, current value equals the following (Bauman 1999):

The last component in both specifications represents the premium over book value at the end of the forecast horizon. The longer the forecast period, the greater the chance that the company’s residual income will converge to zero. For long forecast periods, this last term may be treated as zero. For shorter forecast periods, a forecast of the premium should be calculated.

Lee and Swaminathan (1999) and Lee, Myers, and Swaminathan (1999) have presented a residual income model based on explicit forecasts of residual income for three years. Thereafter, ROE is forecast to fade to the industry mean value of ROE. The terminal value at the end of the forecast horizon (T ) is estimated as the terminal-year residual income discounted in perpetuity. Lee and Swaminathan stated that this assumes any growth in earnings after T is value neutral. Exhibit 5-6 presents sector ROE data from Hemscott Americas, retrieved from Yahoo.com. (ROE data for specific industries can be retrieved from the same source.) In forecasting a fading ROE, the analyst should also consider any trends in industry ROE.

Another multistage model assumes that ROE fades over time to the cost of equity. In this approach, ROE can be explicitly forecast each period until reaching the cost of equity. The forecast would then end and the terminal value would be zero.

Dechow, Hutton, and Sloan (1999) presented an analysis of a residual income model in which residual income fades over time:¹⁰⁷

This model adds a persistence factor, ω, which is between zero and one. A persistence factor of one implies that residual income will not fade at all; rather, it will continue at the same level indefinitely (i.e., in perpetuity). A persistence factor of zero implies that residual income will not continue after the initial forecast horizon. The higher the value of the persistence factor, the higher the stream of residual income in the final stage, and the higher the valuation, all else being equal. Dechow et al. found that in a large sample of company data from 1976 to 1995, the persistence factor equaled 0.62, which was interpreted by Bauman (1999) as equivalent to residual income decaying at an average rate of 38 percent a year. The persistence factor considers the long-run mean-reverting nature of ROE, assuming that in time ROE regresses toward r and that resulting residual income fades toward zero. Clearly, the persistence factor varies from company to company. For example, a company with a strong market leadership position would have a lower expected rate of decay (Bauman 1999). Dechow et al. provided insight into some characteristics, listed in Exhibit 5-7, that can indicate a lower or higher level of persistence.

Example 5-10 illustrates the assumption that continuing residual income will decline to zero as ROE approaches the required rate of return on equity.

Valuation models based on discounting dividends or on discounting free cash flows are as theoretically sound as the residual income model. Unlike the residual income model, however, the discounted dividend and free cash flow models forecast future cash flows and find the value of stock by discounting them back to the present by using the required return. Recall that the required return is the cost of equity for both the DDM and the free cash flow to equity (FCFE) model. For the free cash flow to the firm (FCFF) model, the required return is the overall weighted average cost of capital (WACC). The RI model approaches this process differently. It starts with a value based on the balance sheet, the book value of equity, and adjusts this value by adding the present values of expected future residual income. Thus, in theory, the recognition of value is different, but the total present value, whether using expected dividends, expected free cash flow, or book value plus expected residual income, should be consistent.¹⁰⁸

Example 5-11 again illustrates the important point that the recognition of value in residual income models typically occurs earlier than in dividend discount models. In other words, residual income models tend to assign a relatively small portion of a security’s total present value to the earnings that occur in later years. Note also that this example makes use of the fact that the present value of a perpetuity in the amount of X can be calculated as X/r.

As shown earlier and illustrated again in Example 5-11, the dividend discount and residual income models are in theory mutually consistent. Because of the real-world uncertainty in forecasting distant cash flows, however, the earlier recognition of value in a residual income approach relative to other present value approaches is a practical advantage. In the dividend discount and free cash flow models, a stock’s value is often modeled as the sum of the present value of individually forecasted dividends or free cash flows up to some terminal point plus the present value of the expected terminal value of the stock. In practice, a large fraction of a stock’s total present value, in either the discounted dividend or free cash flow models, is represented by the present value of the expected terminal value. Substantial uncertainty, however, often surrounds the terminal value. In contrast, residual income valuations typically are less sensitive to terminal value estimates. (In some residual income valuation contexts the terminal value may actually be set equal to zero.) The derivation of value from the earlier portion of a forecast horizon is one reason residual income valuation can be a useful analytical tool.

The strengths of residual income models include the following:

The potential weaknesses of residual income models include the following:

A residual income model is most appropriate when

Residual income models are least appropriate when

Because various valuation models can be derived from the same underlying theoretical model, when fully consistent assumptions are used to forecast earnings, cash flow, dividends, book value, and residual income through a full set of pro forma (projected) financial statements, and the same required rate of return on equity is used as the discount rate, the same estimate of value should result when using each model. Practically speaking, however, it may not be possible to forecast each of these items with the same degree of certainty.¹⁰⁹ For example, if a company has near-term negative free cash flow and forecasts for the terminal value are uncertain, a residual income model may be more appropriate. But a company with positive, predictable cash flow that does not pay a dividend would be well suited for a discounted free cash flow valuation.

Residual income models, just like the discounted dividend and free cash flow models, can also be used to establish justified market multiples, such as price-to-earnings ratio (P/E) or P/B. For example, the value can be determined by using a residual income model and dividing by earnings to arrive at a justified P/E.

A residual income model can also be used in conjunction with other models to assess the consistency of results. If a wide variation of estimated value is found and each model appears appropriate, the inconsistency may lie with the assumptions used in the models. The analyst would need to perform additional work to determine whether the assumptions are mutually consistent and which model is most appropriate for the subject company.

Bauman (1999) has noted that the strength of the residual income model is that the two components (book value and future earnings) of the model have a balancing effect on each other, provided that the clean surplus relationship is followed:

Unfortunately, this argument has several problems in practice because the clean surplus relationship does not prevail, and analysts often use past earnings to predict future earnings. IFRS and U.S. GAAP permit a variety of items to bypass the income statement and be reported directly in stockholders’ equity. Further, off-balance-sheet liabilities or nonoperating and nonrecurring items of income may obscure a company’s financial performance. The analyst must thus be aware of such items when evaluating the book value of equity and return on equity to be used as inputs into a residual income model.

With regard to the possibility that aggressive accounting choices will lead to lower reported future earnings, consider an example in which a company chooses to capitalize an expenditure in the current year rather than expense it. Doing so overstates current-year earnings as well as current book value. If an analyst uses current earnings (or ROE) naively in predicting future residual earnings, the RI model will overestimate the value of the company. Take, for example, a company with $1,000,000 of book value and $200,000 of earnings before taxes, after expensing an expenditure of $50,000. Ignoring taxes, this company has an ROE of 20 percent. If the company capitalized the expenditure rather than expensing it immediately, it would have an ROE of 23.81 percent ($250,000/$1,050,000). Although at some time in the future this capitalized item will likely be amortized or written off, thus reducing realized future earnings, analysts’ expectations often rely on historical data. If capitalization of expenditures persists over time for a stable size company, ROE can decline because net income will normalize over the long term, but book value will be overstated. For a growing company, for which the expenditure in question is increasing, ROE can continue at high levels over time. In practice, because the RI model uses primarily accounting data as inputs, the model can be sensitive to accounting choices, and aggressive accounting methods (e.g., accelerating revenues or deferring expenses) can result in valuation errors. The analyst must, therefore, be particularly careful in analyzing a company’s reported data for use in a residual income model.

Two principal drivers of residual earnings are ROE and book value. Analysts must understand how to use historical reported accounting data for these items to the extent they use historical data in forecasting future ROE and book value. Other chapters have explained the DuPont analysis of ROE, which can be used as a tool in forecasting, and discussed the calculation of book value. We extend these discussions in the pages that follow, with specific application to residual income valuation, particularly in addressing the following accounting considerations:

In any valuation, close attention must be paid to the accounting practices of the company being valued. The following sections address the aforementioned issues as they particularly affect residual income valuation.

As stated earlier, comprehensive income is defined in U.S. GAAP as all changes in equity other than contributions by, and distributions to, owners. Comprehensive income includes net income reported on the income statement and other comprehensive income, which is the result of other events and transactions that result in a change to equity but are not reported on the income statement. Items that commonly bypass the income statement include (see Frankel and Lee 1999):

An identical concept exists in IFRS, although the term other comprehensive income is not used. Under both international and U.S. standards, such items as fair value changes for some financial instruments and foreign currency translation adjustments bypass the income statement. In addition, under IFRS, which unlike U.S. GAAP permits revaluation of fixed assets (IAS 16, paragraph 39-42), some changes in the fair value of fixed assets also bypass the income statement and directly affect equity.

In all of these cases in which items bypass the income statement, the book value of equity is stated accurately, but net income is not, from the perspective of residual income valuation. The analyst should be most concerned with the effect of these items on forecasts of net income and ROE (which has net income in the numerator), and hence residual income.¹¹⁰ Because some items (including those just listed) bypass the income statement, they are excluded from historical ROE data. As noted by Frankel and Lee (1999), bias will be introduced into the valuation only if the present expected value of the clean surplus violations do not net to zero. In other words, reductions in income from some periods may be offset by increases from other periods. The analyst must examine the equity section of the balance sheet and the related statements of shareholders’ equity and comprehensive income carefully for items that have bypassed the income statement. The analyst can then assess whether amounts are likely to be offsetting and can assess the effect on future ROE.

The examples in this chapter have used the actual beginning equity and a forecasted level of ROE (return on beginning equity) to compute the forecasted net income. Because equity includes accumulated other comprehensive income (AOCI), the assumptions about future other comprehensive income (OCI) will affect forecasted net income and thus residual income. To illustrate, Exhibit 5-11 shows a hypothetical company’s financials for a single previous year, labeled year t-1, followed by three different forecasts for the following two years. In year t-1, the company reports net income of $120, which is a 12 percent return on beginning equity of $1,000. The company paid no dividends, so ending retained earnings equal $120. In year t-1, the company also reports OCI of -$100, a loss, so the ending amount shown in AOCI is -$100. (Companies typically label this line item “accumulated other comprehensive income (loss),” indicating that the amount is an accumulated loss when given in parentheses.)

All three forecasts in Exhibit 5-11 assume that ROE will be 12 percent and use this assumption to forecast net income for year t and t + 1 by using the expression 0.12 x Beginning book value. Each forecast, however, incorporates different assumptions about future OCI. Forecast A assumes that the company will have no OCI in year t or year t+ 1, so the amount of AOCI does not change. Forecast B assumes that the company will continue to have the same amount of OCI in year t and year t+ 1 as it had in the prior year, so the amount of AOCI becomes more negative each year. Forecast C assumes that the company’s OCI will reverse in year t, so at the end of year t, AOCI will be zero. As shown, because the forecasts use the assumed ROE to compute forecasted net income, the forecasts for net income and residual income in year t+ 1 vary significantly.

Because this example assumes all earnings are retained, a forecast of 12 percent ROE also implies that net income and residual income will grow at 12 percent. Only the year t to year t+1 under forecast A, which assumes no future OCI, correctly reflects that relationship. Specifically, in forecast A, both net income and residual income increase by 12 percent from year t to year t+ 1. Net income grows from $122.40 to $137.09, an increase of 12 percent [($137.09/$122.40) - 1]; and residual income grows from $20.40 to $22.85, an increase of 12 percent [($22.85/$20.40) - 1]. In contrast to forecast A, neither forecast B nor forecast C correctly reflects the relationship between ROE and growth in income (net and residual). Growth in residual income from year t to year t+ 1 was 2.2 percent under forecast B and 21.8 percent under forecast C.

If, alternatively, the forecasts of future ROE and the residual income computation had incorporated total comprehensive income (net income plus OCI), the results of the residual income computation would have differed significantly. For example, suppose that in forecast B, which assumes the company will continue to have the same amount of OCI, the estimated future ROE was 2.0 percent, using total comprehensive income [($120 - $100)/$1,000 = $20/$1,000]. If the residual income computation had then also used forecasted total comprehensive income at time t, the amount of residual income would be negative. Specifically, for time t, forecast comprehensive income would be $22.40 (ROE of 2.0 percent times beginning equity of $1,020), the equity charge would be $102 (required return of 10 percent times beginning equity of $1,020), and residual income would be -$79.86 (comprehensive income of $22.40 minus equity charge of $102). Clearly, residual income on this basis significantly falls short of the positive $20.40 when the violation of clean surplus is ignored. As this example demonstrates, using an ROE forecast or a net income forecast that ignores violations of clean surplus accounting will distort estimates of residual income. Unless the present value of such distortions net to zero, using those forecasts will also distort valuations.

What are the implications for implementing a residual-income-based valuation? If future OCI is expected to be significant relative to net income and if the year-to-year amounts of OCI are not expected to net to zero, the analyst should attempt to incorporate these items so that residual income forecasts are closer to what they would be if the clean surplus relation held. Specifically, when possible, the analyst should incorporate explicit assumptions about future amounts of OCI.

Example 5 -13 illustrates, by reference to the DDM value, the error that results when OCI is omitted from residual income calculations (assuming an analyst has a basis for forecasting future amounts of OCI).¹¹¹ The example also shows that the growth rate in residual income is generally not equal to the growth rate of net income or dividends.

Lacking a basis for explicit assumptions about future amounts of OCI, the analyst should nonetheless be aware of the potential effect of OCI on residual income and adjust

To demonstrate this, consider a simplified example involving two companies, Alpha and Beta, with the following summary financial information (all amounts in thousands, except per-share data):

Each company pays out all net income as dividends (no growth), and the clean surplus relation holds. Alpha has a 12 percent ROE and Beta has a 15 percent ROE, both expected to continue indefinitely. Each has a 10 percent required rate of return. The fair market value of each company’s property, plant, and equipment is the same as its book value. What is the value of each company in a residual income framework?

Using total book value rather than per-share data, the value of Alpha would be €6,000, determined as follows:¹¹³

The value of the companies on a combined basis would be €7,500. Note that both companies are valued more highly than the book value of equity because they have ROE in excess of the required rate of return. Absent an acquisition transaction, the financial statements of Alpha and Beta do not reflect this value. If either is acquired, however, an acquirer would allocate the purchase price to the acquired assets, with any excess of the purchase price above the acquired assets shown as goodwill.

Suppose Alpha acquires Beta by paying Beta’s former shareholders €1,500 in cash. Alpha has just paid €500 in excess of the value of Beta’s total reported assets of €1,000. Assume that Beta’s property, plant and equipment is already shown at its fair market value of €1,000, and that the €500 is considered to be the fair value of a license owned by Beta, say an exclusive right to provide a service. Assume further that the original cost of obtaining the license was an immaterial application fee, which does not appear on Beta’s balance sheet, and that the license covers a period of 10 years. Because the entire purchase price of €1,500 is allocated to identifiable assets, no goodwill is reported. The balance sheet of Alpha immediately after the acquisition would be:¹¹⁴

Note that the total book value of Alpha’s equity did not change, because the acquisition was made for cash and thus did not require Alpha to issue any new shares.

Making the assumption that the license is amortized over a 10-year period, the combined company’s expected net income would be €700 (€600 + €150 - €50 amortization). If this net income number is used to derive expected ROE, the expected ROE would be 14 percent. Under a residual income model, with no adjustment for amortization, the value of the combined company would be:

Why would the combined company be worth less than the two separate companies? If the assumption is made that a fair price was paid to Beta’s former shareholders, the combined value should not be lower. The lower value using the residual income model results from a reduction in ROE as a result of the amortization of the intangible license asset. If this asset were not amortized (or if the amortization expense was added back before computing ROE), net income would be €750 and ROE would be 15 percent. The value of the combined entity would be:

This amount, €7,500, is the same as the sum of the values of the companies on a separate basis.

Would the answer be different if the acquiring company used newly issued stock rather than cash in the acquisition? The form of currency used to pay for the transaction should not impact the total value. If Alpha used €1,500 of newly issued stock to acquire Beta, its balance sheet would be

Projected earnings, excluding the amortization of the license, would be €750, and projected ROE would be 11.538 percent. Value under the residual income model would be:

The overall value remains unchanged. The book value of equity is higher but offset by the effect on ROE. Once again, this example assumes that the buyer paid a fair value for the acquisition. If an acquirer overpays for an acquisition, the overpayment should become evident in a reduction in future residual income.

Research and development (R&D) costs provide another example of an intangible asset that must be given careful consideration. Under U.S. GAAP, R&D is generally expensed to the income statement directly (except in certain cases such as SFAS No. 87 which permits the capitalization of R&D expenses related to software development after product feasibility has been established). Also, under IFRS, some R&D costs can be capitalized and amortized over time. R&D expenditures are reflected in a company’s ROE, and hence residual income, over the long term. If a company engages in unproductive R&D expenditures, these will lower residual income through the expenditures made. If a company engages in productive R&D expenditures, these should result in higher revenues to offset the expenditures over time. In summary, on a continuing basis for a mature company, ROE should reflect the productivity of R&D expenditures.

IFRS and U.S. GAAP differ in accounting for in-process R&D, which can be recognized as an acquired finite-life intangible asset or as part of goodwill under IFRS, but must be expensed immediately under U.S. GAAP. Does the difference matter? Bauman (1999) found that when purchased in-process R&D is capitalized and then amortized in a short period, overall value is not affected compared with the immediate expensing of R&D in a residual income framework. Further, Lundholm and Sloan (2007) explain that including and subsequently amortizing an asset that was omitted from a company’s reported assets has no effect on valuation under a residual income model. Such an adjustment would increase the estimated equity value by adding the asset to book value at time zero but decrease the estimated value by an equivalent amount, which would include (1) the present value of the asset when amortized in the future and (2) the present value of a periodic capital charge based on the amount of the asset times the cost of equity. Expensing R&D, however, results in an immediately lower ROE vis-à-vis capitalizing R&D. But expensing R&D will result in a slightly higher ROE relative to capitalizing R&D in future years because this capitalized R&D is amortized.¹¹⁵ Because ROE is used in a number of expressions derived from the residual income model and may also be used in forecasting net income, the analyst should carefully consider a company’s R&D expenditures and their effect on long-term ROE.

Companies sometimes inappropriately classify nonoperating gains as a reduction in operating expenses (such as selling, general, and administrative expenses). If material, this inappropriate classification can usually be uncovered by a careful reading of financial statement footnotes and press releases. Analysts should consider whether these items are likely to continue and contribute to residual income in time. More likely, they should be removed from operating earnings when forecasting residual income.

Conversely, companies have also been criticized for the use of cookie jar reserves (reserves saved for future use), in which excess losses or expenses are recorded in an earlier period (for example, in conjunction with an acquisition or restructuring) and then used to reduce expenses and increase income in future periods. The analyst should carefully examine the use of reserves when assessing residual earnings. Overall, the analyst must evaluate a company’s accounting policies carefully and consider the integrity of management when assessing the inputs in a residual income model.

Germany had the lowest explanatory power. Japan had low explanatory power for companies reporting only parent company results; the explanatory power for Japanese companies reporting on a consolidated basis was considerably higher. Explanatory power was highest in France, the United Kingdom, and the United States. Frankel and Lee concluded that there are three primary considerations in applying a residual income model internationally:

Analysts should expect the model to work best in situations in which earnings forecasts are available, clean surplus violations are limited, and accounting rules do not result in delayed recognition. Because Frankel and Lee found good explanatory power for a residual income model using unadjusted accounting data, one expects that if adjustments are made to the reported data to correct for clean surplus and other violations, international comparisons should result in comparable valuations. For circumstances in which clean surplus violations exist, accounting choices result in delayed recognition, or accounting disclosures do not permit adjustment, the residual income model would not be appropriate and the analyst should consider a model less dependent on accounting data, such as an FCFE model.

It should be noted, however, that IFRS is increasingly becoming widely used. By 2011, the number of countries that either require or permit the use of IFRS in preparation of financial statements in their countries is expected to reach 150. Furthermore, standard setters in numerous countries have started to work toward convergence between IFRS and home-country GAAP. In time, concerns about the use of different accounting standards should become less severe. Nonetheless, even within a single set of accounting standards, companies make choices and estimates that can affect valuation.