Residual Income Valuation
What is residual income?
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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®.
Primary uses of residual income
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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.
Residual income vs traditional
accounting income
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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.
An example of residual income
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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 it’s 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 х Cost of Equity Capital in %
Cost of Equity = €1,000,000 х 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.
Other names for residual income
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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% х TC)
NOPAT is the firm’s net operating profit after taxes,
C% is the cost of capital and
TC is total capital.
Residual income model of valuation
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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

RI t
Et  rBt 1
P0  B0  

B


0
t
t
(
1

r
)
(
1

r
)
t 1
t 1

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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.
Valuing a perpetuity with the RIM
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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.
Perpetuity example
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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.
RIM valuation vs other DCF models
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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.
When to use RIM valuation
A residual income model is most appropriate when:
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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.
Derivation of the RIM of valuation
Start with the DDM:
P0 
D1
(1  r )
1

D2
(1  r )
2

D3
(1  r )
3

The relationship between earnings,
dividends and book value is given
by the clean surplus equation as
Bt  Bt 1  Et  Dt
Derivation of RIM of valuation
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This means that
Dt = Et – (Bt – Bt-1) = Et + Bt-1 – Bt
Substituting this into the DDM:
E1  B0  B1 E2  B1  B2 E3  B2  B3
P0 



1
2
3
(1  r )
(1  r )
(1  r )
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This equation can be simplified:

RI t
Et  rBt 1
P0  B0  
 B0  
t
t
(1

r
)
(1

r
)
t 1
t 1

Derivation of RIM of valuation
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This can also be expressed as:
( ROEt  r )  Bt 1
V0  B0  
t
(1

r
)
t 1

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. SIT’s book value is $8
per share and its required return on equity is 10%.
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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 stock’s value using the residual income
model.
C. Calculate return on equity and use it as an input to
the residual income model to calculate SIT’s value.
RIM of valuation example
A.
P0 = Present Value of the future dividends
B.
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P0 = 2/1.10 + 2.50/(1.1)2 + 20.50/(1.1)3
P0 = $1.818 + $2.066 + $15.402 = 19.286
B.
The book values and residual incomes for the next 3 years are:
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Year
Beginning Book Value
Retained earnings (NI–DIV)
Ending Book Value
Net income
Less equity charge (r  Begin Book Val)
Residual income
1
8.00
2.00
10.00
4.00
0.80
3.20
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
2
10.00
2.50
12.50
5.00
1.00
4.00
3
12.50
(12.50)
0.0
8.00
1.25
6.75
RIM of valuation example
C. Year
 Net income
 Begin. Bk Value
 ROE (return on equity)
 ROE – r
 Residual income
(ROE–r)  Begin Bk Val
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1
4.00
8.00
50%
40%
2
5.00
10.00
50%
40%
3.20
4.00
3
8.00
12.50
64%
54%
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.
Constant growth residual income model
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A firm’s intrinsic value under a residual income
can be expressed as:
ROE  r
V0  B0 
B0
rg
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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 firm’s
ability to generate returns in excess of its cost of
equity. The second term represents the value of
the firm’s economic profits.
If a firm earns exactly the cost of equity the price
should equal the book value per share.
Residual income, dividend, and free
cash flow valuation models
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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.
The slides from here to the finish are
for additional Information only and I will
not be covering them.
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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
Violations of the clean surplus
relationship
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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
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foreign currency translation adjustments
certain pension adjustments
fair value changes of some financial instruments
Balance sheet adjustments for fair
value
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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:
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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
Intangible assets
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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, R&D is expensed to the income statement directly. Under IAS, some
R&D costs can be capitalized and amortized over time. While R&D may lead to the
existence of an “asset in theory,” this is reflected in the firm’s ROE and hence residual
income over time. If a firm engages in unproductive R&D expenditures, these will lower
residual income through the expenditures made. If a firm engages in productive R&D
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.
Nonrecurring items
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In applying a residual income model, it is important to develop a forecast of future
residual income based upon recurring items.
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An analysts should examine the financial statement notes and other sources for
potential items that may warrant adjustment in determining recurring earnings such
as:
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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.
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.
Other aggressive accounting practices
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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.
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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 firm’s 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.
International considerations
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Some of the primary considerations
internationally are:
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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
R&D. If the adjustments recommended in the
preceding sections are made, international
comparisons should result in comparable
valuations.