Chapter 8: Accounting information in action II: Residual income valuation

Chapter 8: Accounting information in

action II: Residual income valuation

8.1 Introduction
In the previous chapter, we looked at a valuation technique known as
relative valuation using multiples. This method enables us to value a
company based on the value of another similar company using information
from the financial statements. Financial statement information can also be
used to establish an estimate of intrinsic value – an analyst’s estimate of
the ‘true’ value of the firm.
There are multiple techniques available for analysts to determine an
estimate of intrinsic value. However, we are primarily interested in
techniques which use accounting information as their key driver. In this
chapter, you will be introduced to the concept of ‘residual value’, what it is
and how it can be used to understand the value of a company.

8.1.1 Learning outcomes

By the end of this chapter, and having completed the Essential reading and
activities, you should be able to:
• explain the nature of a company’s ‘abnormal’ profit, how it is
calculated and the difficulties and assumptions in its use
• explain the concept and rationale behind using residual income in
valuation and the advantages and disadvantages of the technique
• calculate the value of a company using residual income.

8.1.2 Essential reading

Palepu, K., P. Healy and E. Peek Business analysis and valuation. (Cengage
Learning EMEA, 2022) 6th edition. Extracts from Chapter 7.

8.1.3 Further reading

Srinivasan, S., B. Cheng and E. Riedl ‘Coca-Cola: residual income valuation
exercise’, Harvard Business School Exercise 113–056, 2012.

8.1.4 References cited

Gordon, M.J. and E. Shapiro ‘Capital equipment analysis: the required rate of
profit’, Management Science 3(1) 1956, pp.102–10.
Ohlson, J.A. ‘Earnings, book values and dividends in security valuation’,
Contemporary Accounting Research 11(2) 1995, pp.661–687.
Annual report of Pearson plc, 2021 (https://plc.pearson.com/investors)

8.2 Core concepts of intrinsic valuation

Accounting information and valuations are inherently linked, although
it can sometimes be difficult to see this clearly. Before considering how
accounting information can be used, it is important to review key aspects
of the core valuation techniques. All these techniques ultimately rely on
the concept of ‘cash flow’.
Approaches to valuation in finance theory consider that the value of any
asset is represented by the present value of future free cashflows. This can
be stated formally as:
value of a company = present value of future cashflows
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To apply this in practice, the analyst must resolve a number of issues:

• What discount rate should we use to establish present values?
• How long into the future do we need to forecast cashflows for?
• How can we estimate what the future cashflows are going to be?
• Which cashflows should we include/exclude?
When attempting to answer these questions, it is common to start by
examining dividend flows. The only ongoing cashflows that equity
investors receive are the dividend cashflows the company is expected to
pay out. We can therefore say:
value of a company (P0) = present value of future dividends (D)
This can be considered as the sum of an ongoing stream, represented as
follows (where ‘r’ is the discount rate required):

1 2 3 4 5 n
P0 = + + + + + ⋯+
(1 + r) (1 + r) 2 (1 + r) 3 (1 + r) 4 (1 + r) 5 (1 + r) 

This is called the Dividend Discount Model (DDM).

Unfortunately, unless we are going to spend a lot of time considering what
a company’s dividend might look like in 50 years’ time, this formula does
not seem particularly useful. It should also be noted that a dividend in
50 years’ time is unlikely to have much value in current terms once it has
been discounted. As such, a few assumptions can be built in to simplify the
calculations.
One approach to dealing with this practical challenge is to assume
that dividends grow at a constant rate. For example, if we assume that
dividends grow at an annualised factor of ‘g’ (e.g. 3%), the formula above
can be reduced to:

D0(1 + g) D0(1 + g)2 D0(1 + g)3 D0(1 + g)4 D (1 + g)n

P0 = + + + + ... + 0
(1 + r) (1 + r) 2
(1 + r) 3
(1 + r) 4
(1 + r)n
Equation (1)

We can then multiply equation (1) by 1 + g to get a second version:

1+r

(1 + g) D (1 + g)2 D0(1 + g)3 D0(1 + g)4 D (1 + g)n

P0 = 0 + + + ⋯+ 0
(1 + r) (1 + r) 2
(1 + r) 3
(1 + r) 4
(1 + r)n
Equation (2)

If we then subtract equation (2) from equation (1), we are left with:

P0 = D0(1 + g)
(r – g)

This formula allows us to value a company based on a dividend that has

recently been paid out, an expected growth rate and a desired rate of
return. (This is the Gordon Shapiro model, which was developed in 1956.)

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 Chapter 8: Accounting information in action II: Residual income valuation

Activity 8.1
Heggem plc has recently paid out a dividend of 10c and the market expects this to grow
at a rate of 7% for the foreseeable future.
How valuable would a share of Heggem plc be to an investor who expects a rate of
return of 11%?

8.3 Abnormal profit

In section 8.2, we suggested that dividends are the only cash flow which
an equity investor obtains from an investment. For certain companies,
however – such as those not paying dividends – there is an argument
that dividends alone do not capture all of the economic value. In these
situations, we must use other accounting information to provide a more
complete valuation.
This brings us to a concept known as ‘abnormal profit’. This is the profit
made once a charge for equity capital has been applied – that is, the profit
earned by a business above and beyond the profit required by equity
investors.

Worked example 8.1

Consider the company income statement shown below:

€’000
Revenue 65,870
Cost of sales (20,261)
Gross profit 45,609
Distribution costs (8,136)
Administrative costs (12,490)
Operating profit 24,983
Finance costs (454)
Profit before tax 25,437
Taxation (4,097)
Profit after tax 21,340
This income statement does not show the expected return that equity
investors require to be satisfied with the investment.

Assume equity investors have invested €122,910,000 and require an

expected return of 8%. This would suggest the required profit (i.e. a
cost of equity) is €16,388,000.

If this value is removed from the profit after tax, we see the following:

Profit after tax 21,340

less: Cost of equity 16,388
Abnormal profit 4,952

This abnormal profit can also be described as ‘residual profit’ or even

‘economic profit’.

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Activity 8.2
Company XYZ has capital structure which is 50% debt and 50% equity. Total assets are
£2,000,000.
Coupon on debt is 7%, cost of equity is 12% and taxes are 30%.
If EBIT is £200,000 calculate the following:
• net income
• residual income.
Comment on the results.

8.4 Residual Income Valuation Model (RIVM)

If we accept the premise that equity value is derived from the return a
company offers above and beyond the required return, then we can adjust
earlier models to reflect this.
First, consider how the book value of equity in a company’s balance sheet
may be reconciled from one year to the next.
Opening book value of equity £200
Earnings £100
Dividends (£20)
Change in retained earnings £80
Closing book value £280
Figure 8.1: Reconciliation of book value.
Assuming D is the dividend paid out, E is earnings made and B is the book
value of equity, the relationship between book value, dividends and profit
can be written as:
B₁ = B₀ + E₁ – D₁

Alternatively, if we wish to know the value of the dividend, we can write:

D₁ = E₁ – (B₁ – B₀)
or:
D₁ = E₁ + (B₀ – B₁)

Activity 8.3
Using the values in Figure 8.1, ensure you are comfortable using the two versions of the
formula for D1.

Earlier, we encountered the following model to value a company based on

dividends:
₁ 2 3 4 5 n
₀ = + + + + + ⋯+
(1 + ) (1 + )2 (1 + )3 (1 + )4 (1 + )5 (1 + )

Substituting in the second formula for D1 above, we can write:

E1 + (B0 – B1 ) E2 + (B1 – B2 ) E3 + (B2 – B3 ) E1+ (Bn–1– Bn )

P0 = + + +⋯+
(1 + r) (1 + r) 2
(1 + r) 3
(1 + r)n

This can be simplified to:

En – rBn-1
6
’
P0 = B0 +
80
n=1 (1 + r)n
 Chapter 8: Accounting information in action II: Residual income valuation

Although this may look mathematically challenging, it represents a simple

idea: the value of a company is its book value (B0) plus the stream of
discounted residual income (the part of the calculation after the + sign).

Worked example 8.2

123 Corporation generates EBIT of $500,000 per year and this is likely
to continue at the same rate for the foreseeable future. The company has
$4,000,000 of assets, financed 30% by equity and 70% by debt.

The debt coupon rate is 5%, the estimated cost of equity is 12% and tax is 40%.

Calculate the intrinsic value of 123 Corporation if the book value per share
is $12 and there are 100,000 shares outstanding.

Answer
Due to the company’s financial structure, the costs of capital can be
calculated as follows:

Capital value Cost of capital

Equity 30% $1,200,000 $ 144,000
Debt 70% $2,800,000 $ 140,000
100% $4,000,000
Based on this, the company’s income statement will be:

EBIT $ 500,000
Int $ -140,000
EBT $ 360,000
Tax $ -144,000
Earnings $ 216,000
Given the expected return required by equity investors, the residual income
can be determined as follows:

Residual income = Earnings – Capital charge

= $216,000 – $144,000
= $72,000
$72,000
The residual income per share = = $0.72 per share
100,000

Intrinsic value per share = B0+ pv of future RI

= $12 + (12%
1
× $0.72
( = $18

Activity 8.4
3 2
Braun Baum GmbH is currently funded 5
by equity and 5
by debt.
It generates a regular EBIT of €700,000 a year and this is expected to continue for the
foreseeable future.
It has €3 million of assets and 200,000 shares. The book value per share is €9.
The interest on debt is paid at 3%, corporation tax is 20% and equity investors expect a
return of 10%.
What is the value per share using the RIVM method?

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8.5 Alternative model

The version of the RIVM used above requires the calculation of earnings
after a capital charge for equity has been applied. It can however be
written in a slightly different way (as devised by Ohlson, 1995).
The current RIVM version is:

Σ
∞ En –rBn–1
P0 = B 0 +
n=1 (1 + r)n

With a quick adjustment, we can write:

Σ
∞ (En/Bn–1 –r)Bn–1
P0 = B 0 +
n=1 (1 + r)n

We can then see that En /Bn–1 is the effective return a company is able
to generate on equity each year – that is, the Return on Equity (ROE). As
such, one final rearrangement gives:

Σ
∞ (ROE – r)Bn–1
P0 = B 0 +
n=1 (1 + r)n

This provides a slightly different view: the (ROEïr) part of the formula
is deemed to be ‘investment spread’ and shows the excess return that a
company can offer over and above the required return, while allowing for
analysis using percentages rather than currency figures.

8.6 Clean surplus assumption

The above model was built on two assumptions:
• An investor is expected to receive a dividend which reflects the
required return.
• The book value of equity is reconciled from one year to the next by
adding earnings and subtracting dividends.
Although these assumptions ensure a cleanly derived formula, they are
only valid when we have what is referred to as ‘clean surplus’. Clean
surplus means that the change in a company’s book value comes from
earnings and transactions with owners (e.g. dividends) alone. In other
words, ignoring share issuance and repurchases:
Closing BV = Opening BV + Earnings – Dividends
However, we know that this is not the case for many companies. For
example, other gains and losses which impact book value are shown in a
‘Statement of Other Comprehensive Income’. You can view an example of a
‘Consolidated statement of comprehensive income’ on p.135 of the annual
report of Pearson plc (2022), available at https://plc.pearson.com/sites/
pearson-corp/files/pearson/annual-report-2022/Pearson_2022_annual_
report.pdf.
This is therefore a limitation of the model. Fortunately, analysts rarely
forecast the types of items that are recognised in the ‘Statement of Other
Comprehensive Income’ and so this limitation should not materially distort
forecasts.

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8.7 Activities to try

Activity 8.5
GHJ Inc is expected to earn $1 earnings per year for the foreseeable future. The dividend
pay-out ratio is 100% and the company has a book value per share of $6.
Investors expect an average return of 10% on their investment.
Calculate the value of stock using:
• the dividend discount model
• the Residual Income Valuation Model.
Comment on the results.

Activity 8.6
DFG Ltd is expected to have an EPS over the next three years equal to $2, $2.50 and
$4 per share.
The pay-out ratio is likely to be 50% in years 1 and 2; however, the business is expected
to close in year 3 and pay out all retained earnings as a dividend.
The current book value per share is $6 and the company’s cost of capital is 10%.
What is the current value per share using the residual income valuation model?

8.8 Advantages and disadvantages of using accounting

data for both multiple and RIVM valuation models
Key advantages of multiple and RIVM valuation models are that:
• they are useful to double check other valuation methods
• they can be used if cash flows are negative
• valuation is consistent with accounting principles.
Key disadvantages of multiple and RIVM valuation models are that:
• accounting information could have been distorted by accounting
choices (see Chapters 9 and 10)
• there is a need to understand the expected shareholder return.

Activity 8.7
Read the following sections from Chapter 7 of Palepu et al. (2022):
• Defining value for shareholders
• The discounted abnormal profit model
• Accounting methods and discounted abnormal profit.

8.9 Overview of chapter

This chapter has introduced the concept of residual income and showed
how this can be calculated from a company’s income statement. The chapter
has then suggested that this residual income is the extra value that a
company is able to generate, above and beyond its book value. As such, if
we combine the value of the company’s balance sheet with the present value
of this future residual income, we can determine the value of equity.
The chapter provided numerous examples and activities to demonstrate
these ideas, concluding with a discussion of why this methodology is
useful for analysts.

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8.10 Reminder of learning outcomes

Having completed this chapter, and the Essential reading and activities,
you should be able to:
• explain the nature of a company’s ‘abnormal’ profit, how it is
calculated and the difficulties and assumptions in its use
• explain the concept and rationale behind using residual income in
valuation and the advantages and disadvantages of the technique
• calculate the value of a company using residual income.

8.11 Test your knowledge and understanding

1. Explain why residual income valuation methodologies typically result
in a smaller proportion of the overall valuation being attributed to the
terminal value.
2. The Ohlson model (1995) equates value to:

Σ
∞ (ROE – r)Bn–1
n=1 (1 + r)n

Explain the role of the investment spread in this formulation of value.

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