Residual Income Valuation

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• Residual Income Valuation

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What is residual income?

• Residual income is net income less a charge
  (deduction) for common shareholders opportunity
  cost in generating net income.
• Recent years have seen a resurgence in its use as
  a valuation approach, also under such names as
  economic profit, abnormal earnings and Economic
  Value Added.

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Primary uses of residual income

• Measurement of internal corporate performance
• Estimation of the intrinsic value of common stock
• We focus on the residual income model for
  valuation of common stock.

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Residual income vs traditional accounting income

• Traditional financial statements are prepared to
  reflect earnings available to owners. Net income
  includes an expense to represent the cost of debt
  capital (interest expense). Dividends or other
  charges for equity capital are not deducted.
  Traditional accounting leaves to the owners the
  determination as to whether the resulting
  earnings are sufficient to meet the cost of
  equity capital.
• The economic concept of residual income, on the
  other hand, explicitly considers the cost of
  equity capital.

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An example of residual income

• Axis Manufacturing Company (AMC) has total assets
  of 2,000,000 financed 50 with debt and 50 with
  equity capital. The cost of debt capital is 7
  pre-tax (4.9 after tax) and the cost of equity
  capital is 12. Net income for AMC can be
  determined as follows
• EBIT 200,000
• Less Interest Expense 70,000
• Pre-Tax Income 130,000
• Income Tax Expense 39,000
• Net Income 91,000
• What is its residual income? One approach is to
  compute the cost of equity capital (in terms of
  currency), which we term an equity charge, and
  subtract this from net income, as follows
• Equity Charge Equity Capital ? Cost of Equity
  Capital in
• Cost of Equity 1,000,000 ? 12 120,000
• Net Income 91,000
• Equity Charge 120,000
• Residual Income (29,000)
• AMC did not earn enough to cover the cost of
  equity capital. As a result, it has negative
  residual income.

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Other names for residual income

• Residual income has also been called economic
  profit since it represents the economic profit of
  the firm after deducting the cost of all capital,
  debt and equity.
• The term abnormal earnings is also used. Assuming
  that over the long term the firm 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.
• One example of several competing commercial
  implementations of the residual income concept is
  Economic Value Added (EVA) trademarked by Stern
  Stewart Company. EVA is computed as
• EVA NOPAT (C ? TC)
• NOPAT is the firms net operating profit after
  taxes,
• C is the cost of capital and
• TC is total capital.

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Residual income model of valuation

• In the Residual Income Model (RIM) of valuation,
  the intrinsic value of the firm has two
  components
• The current book value of equity, plus
• The present value of future residual income
• This can be expressed algebraically as
• In the model,
• B0 is the current book value of equity,
• Bt is the book value of equity at time t,
• RIt is the residual income in future periods,
• r is the required rate of return on equity,
• Et net income during period t,
• RIt Et rBt-1.

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Valuing a perpetuity with the RIM

• A company will earn 1.00 per share forever, and
  the company also pays out all of this as
  dividends, 1.00 per share. The equity capital
  invested (book value) is 6.00 per share. Because
  the earnings and dividends will offset each
  other, the future book value of the stock will
  always stay at 6.00. The required rate of return
  on equity (or the percent cost of equity) is 10.
• 1. Calculate the value of this stock using the
  dividend discount model.
• 2. What will be the residual income each year?
  Calculate the value of the stock using a residual
  income valuation model.
• 3. Create a table summarizing the recognition of
  value in the dividend discount model and the
  residual income model.

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Perpetuity example

• Solution to 1. Since the dividend is a
  perpetuity,
• P0 D / r 1.00 / 0.10 10.00 per share.
• Solution to 2. The net income is 1.00 each year,
  the book value is always 6.00, and the required
  return is 10, so the residual income in every
  year will be
• RIt Et rBt-1 1.00 0.10 (6.00)
• 1.00 0.60 0.40.
• The value, using a residual income approach, is
  the current book value plus the present value of
  future residual income. The residual income is a
  perpetuity
• P0 Book value PV of Residual income
• 6.00 0.40 / 0.10 6.00 4.00
  10.00.

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RIM valuation vs other DCF models

• The stylized example presented above demonstrates
  that conceptually valuation is not all that
  different whether a discounted cash flow approach
  or residual income model are used. Why then does
  the analyst need a residual income model? In a
  simple cases such as the perpetuity, both DDM and
  RIM are easily applied. For other examples, there
  are two important differences
• Timing of recognition of value. Forecasting of
  future dividends and cash flows is often
  difficult. One key advantage to a residual
  income model over other models is the timing of
  the recognition of value. In DCF approaches most
  of the value is found in future dividends and in
  the terminal value computation. The longer the
  forecast period the higher the uncertainty that
  will exist regarding these future cash flows.
• Terminal value. Further, as we will see shortly,
  in many residual income valuation contexts the
  terminal value is deemed to be zero. The
  determination of book value today is much easier
  than the determination of a terminal value ten or
  twenty years hence.

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When to use RIM valuation

• A residual income model is most appropriate when
• A firm is not paying dividends of if it exhibits
  an unpredictable dividend pattern.
• A firm has negative free cash flow many years
  out, but is expected to generate positive cash
  flow at some point in the future (for example, a
  young or rapidly growing firm where capital
  expenditures are being made to fuel future
  growth.
• There is a great deal of uncertainty in
  forecasting terminal values.

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Derivation of the RIM of valuation

• Start with the DDM
• The relationship between earnings, dividends and
  book value is given by the clean surplus equation
  as

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Derivation of RIM of valuation

• This means that
• Dt Et (Bt Bt-1) Et Bt-1 Bt
• Substituting this into the DDM
• This equation can be simplified

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Derivation of RIM of valuation

• This can also be expressed as
• This equation is logically equivalent to the one
  above since
• RIt (ROEt r)Bt-1.
• Other than the required rate of return, the
  inputs to the residual income model are based
  upon accounting data.

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RIM of valuation example

• Simon Investment Trust (SIT) is expected to earn
  4.00, 5.00, and 8.00 for the next three years.
  SIT will pay annual dividends of 2.00, 2.50,
  and 20.50 in each of these years. The last
  dividend includes the liquidating payment to
  shareholders at the end of year 3 when the trust
  will terminate. SITs book value is 8 per share
  and its required return on equity is 10.
• A. What is the current value per share of SIT
  according to the dividend discount model?
• B. Calculate the book value and residual income
  for SIT for each of the next 3 years and use
  those results to find the stocks value using the
  residual income model.
• C. Calculate return on equity and use it as an
  input to the residual income model to calculate
  SITs value.

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RIM of valuation example

• P0 Present Value of the future dividends
• P0 2/1.10 2.50/(1.1)2 20.50/(1.1)3
• P0 1.818 2.066 15.402 19.286
• The book values and residual incomes for the next
  3 years are
• Year 1 2 3
• Beginning Book Value 8.00 10.00 12.50
• Retained earnings (NIDIV) 2.00 2.50 (12.50)
• Ending Book Value 10.00 12.50 0.0
• Net income 4.00 5.00 8.00
• Less equity charge (r ? Begin Book Val) 0.80
  1.00 1.25
• Residual income 3.20 4.00 6.75
• P0 8.00 3.20/1.1 4.00/(1.1)2 6.75/(1.1)3
• P0 8.00 2.909 3.306 5.071 19.286

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RIM of valuation example

• C. Year 1 2 3
• Net income 4.00 5.00 8.00
• Begin. Bk Value 8.00 10.00 12.50
• ROE (return on equity) 50 50 64
• ROE r 40 40 54
• Residual income
• (ROEr) ? Begin Bk Val 3.20 4.00 6.75
• P0 8.00 3.20/1.1 4.00/(1.1)2 6.75/(1.1)3
• P0 8.00 2.909 3.306 5.071 19.286
• Note since the residual incomes for each year
  are necessarily the same in questions B C, the
  results for stock valuation are identical.

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Constant growth residual income model

• A firms intrinsic value under a residual income
  can be expressed as
• The first term, B0, reflects the value of assets
  owned by the firm less its liabilities.
• The second term, B0(ROE-r)/(r-g), represents
  additional value that is expected due to the
  firms ability to generate returns in excess of
  its cost of equity. The second term represents
  the value of the firms economic profits.
• If a firm earns exactly the cost of equity the
  price should equal the book value per share.

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Residual income, dividend, and free cash flow
valuation models

• Residual income models, dividend discount models,
  and free cash flow models are all theoretically
  sound.
• The difference is that DDM and FCFE models
  forecast future cash flows and find the value of
  stock by discounting them back to the present
  using the required return on equity.
• The RI model approaches this process differently.
  It starts with a beginning value, the book value
  or investment in equity, and then makes
  adjustments to this value by adding the present
  values of future residual income (which can be
  positive or negative).
• The recognition of value is different, but the
  total present value of these values (whether
  future dividends, future free cash flow, or book
  value plus future residual income) should be
  logically consistent.

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The slides from here to the finish are for
additional Information only and I will not be
covering them.

• The residual income valuation model has two
  components (book value and future earnings) that
  have a balancing effect on each other, provided
  that the clean surplus relationship is followed.
  Unfortunately, there are several possible
  problems in practice
• Violations of the Clean Surplus Relationship
• Balance Sheet Adjustments for Fair Value
• Intangible Assets
• Non-Recurring Items
• Aggressive Accounting Practices
• International considerations

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Violations of the clean surplus relationship

• Violations of clean surplus accounting occur when
  accounting standards permit charges directly to
  stockholders equity, bypassing the income
  statement.
• An example is the case of changes in the market
  value of long-term investments. International
  Accounting Standards provide that the change in
  market value can be reported either in current
  profits or in stockholders equity.
• Under U.S. GAAP investments that are considered
  to be available for sale are included on the
  balance sheet at market value however, any
  change in their market value is reflected in
  stockholders equity as other comprehensive
  income rather than as income on the income
  statement. (Comprehensive income is all changes
  in equity other than contributions by and
  distributions to owners.) Comprehensive income
  includes net income reported on the income
  statement. Other comprehensive income is the
  result of other events and transactions which
  result in a change to equity but are not reported
  on the income statement. Other items that
  commonly bypass the income statement are
• foreign currency translation adjustments
• certain pension adjustments
• fair value changes of some financial instruments

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Balance sheet adjustments for fair value

• In order to have a reliable measure of book value
  of equity, the balance sheet should be
  scrutinized for significant off-balance sheet
  assets and liabilities. Additionally, reported
  assets and liabilities should be adjusted to fair
  value where possible. Some common items to review
  for balance include
• Inventory
• Deferred tax assets and liabilities
• Pension plan assets and liabilities
• Operating leases
• Special purpose entities
• Reserves and allowances (for example, bad debts)
• Intangible assets

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Intangible assets

• For specifically identifiable intangibles that
  can be separated from the entity (e.g., sold), it
  is appropriate to include these in the
  determination of book value of equity. If these
  assets are wasting (declining in value over
  time), they will be amortized over time as an
  expense.
• Goodwill, on the other hand, requires special
  consideration, particularly due to recent changes
  in accounting for goodwill. Goodwill is
  generally not recognized as an asset unless it
  results from an acquisition (under most
  international accounting standards, internally
  generated goodwill is not recognized on the
  balance sheet). Goodwill represents the excess of
  the purchase price of an acquisition over the
  value of the net assets acquired.
• Research and development costs provide also must
  be given careful consideration. Under U.S. GAAP,
  RD is expensed to the income statement directly.
  Under IAS, some RD costs can be capitalized and
  amortized over time. While RD may lead to the
  existence of an asset in theory, this is
  reflected in the firms ROE and hence residual
  income over time. If a firm engages in
  unproductive RD expenditures, these will lower
  residual income through the expenditures made. If
  a firm engages in productive RD expenditures
  they should result in higher revenues to offset
  the expenditures over time. On an ongoing basis
  this should be reflected in ROE forecasts for a
  mature firm.

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Nonrecurring items

• In applying a residual income model, it is
  important to develop a forecast of future
  residual income based upon recurring items.
• Often companies report non-recurring charges as
  part of earnings or classify non-operating income
  (e.g., sale of assets) as part of operating
  income. These misclassifications can lead
  over-estimates and under-estimates of future
  residual earnings if no adjustments are made.
  Note that adjustments to book value are not
  necessary for these items since non-recurring
  gains and losses do impact the value of assets in
  place. Non-recurring items sometimes result from
  accounting rules and at other times result from
  strategic management decisions.
• An analysts should examine the financial
  statement notes and other sources for potential
  items that may warrant adjustment in determining
  recurring earnings such as
• Unusual items
• Extraordinary items
• Restructuring charges
• Discontinued operations
• Accounting changes
• In some cases, management may be recording
  restructuring or unusual charges in every period.
  In these cases, the item may be considered an
  ordinary operating expense and may not require
  adjustment.

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Other aggressive accounting practices

• Firms may engage in accounting practices that
  result in the overstatement of assets (book
  value) and/or overstatement of earnings. Many of
  these were included in the preceding sections.
• Other activities that a firm may engage in
  include accelerating revenues to the current
  period or deferring expenses to a later period.
  Both activities simultaneously increase earnings
  and book value.
• For example, a firm might ship unordered goods to
  customers at yearend, recording revenues and a
  receivable.
• Conversely, a firm could capitalize rather than
  expense a cash payment resulting in lower
  expenses and an asset.
• The analyst must carefully evaluate a firms
  accounting policies and consider the integrity of
  management in assessing the inputs in a residual
  income model.
• Firms have also been criticized recently for the
  use of cookie jar reserves where excess losses
  or expenses are recorded in an earlier period
  (for example in conjunction with an acquisition
  or restructuring) and then used to reduce expense
  and increase income in future periods. The
  analysts should carefully examine the use of
  reserves in an assessment of residual earnings.

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International considerations

• Some of the primary considerations
  internationally are
• The availability of reliable earnings forecasts
• Systematic violations of the clean surplus
  assumption
• Poor Quality accounting rules that result in
  delayed recognition of value changes.
• We noted earlier that there are differences in
  standards worldwide particularly for goodwill and
  RD. If the adjustments recommended in the
  preceding sections are made, international
  comparisons should result in comparable
  valuations.