1 (of 22)

FIN 468: Intermediate Corporate Finance

Topic 6–Residual Income Valuation

Larry Schrenk, Instructor

Topics

What is Residual Income (RI)?

The Residual Income Method

Problems with Residual Income

Residual Income Valuation

What is residual income?

Residual income net income less common equity opportunity cost in generating net

income.

Other names economic profit abnormal earnings Economic Value Added

Primary uses of residual income

Internal corporate performance

Intrinsic value of common stock

Our focus

Residual income vs accounting income

Traditional financial statements

Reflect earnings available to owners

Net income includes interest expense

Dividends or other charges for equity capital not deducted

Does not show if earnings are meet the cost of equity capital.

The economic concept of residual income

Explicitly considers the cost of equity capital.

Residual Income Example

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 $ 200,000Less: Interest Expense 70,000Pre-Tax Income $ 130,000Income Tax Expense 39,000Net 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 $ 91,000Equity Charge 120,000Residual 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

Economic profit Profit of the firm after deducting the cost of all capital, debt and equity.

Abnormal earnings Earnings in excess of the cost of capital are ‘abnormal’

Economic Value Added (EVA) Trademarked by Stern Stewart & Company

EVA® = NOPAT – (C% х TC)

NOPAT = net operating profit after taxes C% = cost of capital TC = total capital

Residual income model of valuation (RIM)

Intrinsic value of the firm has two components:

The current book value of equity, plus The present value of future residual income

Algebraically:

B0 =current book value of equity, Bt =book value of equity at time t, RIt =residual income in future periods, r =required rate of return on equity, Et = net income during period t, RIt = Et – rBt-1.

1

10

100 )1()1( t

ttt

tt

t

r

rBEB

r

RIBP

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.

Perpetuity exampleSolution 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.

RI valuation vs DDM

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. 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 RI 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.

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

3

3

2

2

1

10

)1()1()1( r

D

r

D

r

DP

1t t t tB B E D

Derivation of RI Valuation

This means that

Dt = Et – (Bt – Bt-1) = Et + Bt-1 – Bt Substituting this into the DDM:

This equation can be simplified:

1 0 1 3 2 32 1 20 1 2 3(1 ) (1 ) (1 )

E B B E B BE B BP

r r r

10 0 0

1 1(1 ) (1 )t t tt t

t t

RI E rBP B B

r r

Derivation of RI 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.

10 0

1

( )

(1 )

t tt

t

ROE r BV B

r

RI 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%.

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.

RI Valuation Example

A. 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

B. The book values and residual incomes for the next 3 years are:

Year 1 2 3Beginning Book Value 8.00 10.00 12.50Retained earnings (NI–DIV) 2.00 2.50 (12.50)Ending Book Value 10.00 12.50 0.0Net income 4.00 5.00 8.00Less equity charge (r Begin Book Val) 0.80 1.00 1.25Residual 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

RI Valuation Example

C. Year 1 2 3Net income 4.00 5.00 8.00Begin. Bk Value 8.00 10.00 12.50ROE (return on equity) 50% 50% 64%ROE – r 40% 40% 54%Residual income

(ROE–r) 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.

Constant growth residual income model

A firm’s 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 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.

0 0 0

ROE rV B B

r g

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.

Practical Problems

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

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

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

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, 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

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.

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 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

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 R&D. If the adjustments recommended in the preceding sections are made, international comparisons should result in comparable valuations.