Residual Income Valuation 3k421b

RESIDUAL INCOME VALUATION: VALUING COMMON EQUITY

Presenter Venue Date

RESIDUAL INCOME Economic Profit

Abnormal Earnings

Economic Value Added

Residual Income

RESIDUAL INCOME

Net Income

Equity Charge

Residual Income

NOPAT

Capital Charge

Residual Income

EXAMPLE: RESIDUAL INCOME

Total assets

$5,000,000.00

Debt-to-total capital ratio

0 .60

Cost of debt (before tax)

8%

Cost of equity

12%

Tax rate

40%

EXAMPLE: RESIDUAL INCOME

EBIT

$400,000

Less interest Expense

$240,000

Pretax income

$160,000

Less income tax expense

$64,000

Net income

$96,000

EXAMPLE: RESIDUAL INCOME

Equity capital

$2,000,000

Equity charge

$240,000

Net income Less equity charge Residual income

$96,000 $240,000 -–$144,000

RELATED MEASURES Economic Value Added (EVA)

NOPAT

C% × TC

- NOPAT = Net operating profit after taxes - C% = Cost of capital - TC = Total capital

Market Value Added (MVA)

Market Value of the Firm

Book Value of Total Capital

USES OF RESIDUAL INCOME

Valuation Measuring Goodwill Impairment Measuring Internal Corporate Performance Determining Executive Compensation

FORECASTING RESIDUAL INCOME

RIt  Et  re Bt 1

Residual income per share

Earnings per share (EPS)

Required return on equity (Re)

Beginning book value per share (BVPS)

EXAMPLE: FORECASTING RESIDUAL INCOME 0

1

2

Earnings

$2.50

$3.00

Dividends

$1.00

$1.10

Book value Required equity return

$20.00 10%

EXAMPLE: FORECASTING RESIDUAL INCOME IN ONE YEAR Charge for Equity Capital = • Required return on equity × Beginning book value per share • 10% × $20.00 = $2.00 Residual Income in Year 1 = • EPS – Charge for equity capital

• $2.50 – $2.00 = $0.50

EXAMPLE: FORECASTING RESIDUAL INCOME IN TWO YEARS End-of-Year Book Value for Year 1 =

• Beginning-of-year book value + Earnings – Dividends • $20.00 + $2.50 – $1.00 = $21.50 • Beginning book value for Year 2

Charge for Equity Capital in Year 2 = • Required return on equity × Beginning book value per share • 10% × $21.50 = $2.15 Residual Income in Year 2 = • $3.00 – $2.15 = $0.85

VALUING COMMON STOCK USING RESIDUAL INCOME 

RIt V0  B0   t t 1 (1  r ) Et  rBt 1 V0  B0   t t 1 (1  r ) 

EXAMPLE: VALUATION USING RESIDUAL INCOME From the Previous Example:

• Beginning book value at time 0 = $20.00 • Residual income in Year 1 = $0.50 • Residual income in Year 2 = $0.85 • Required return on equity = 10% Additionally, Assume: • Residual income in Year 3 = $1.00 • The firm ceases operations in three years

EXAMPLE: VALUATION USING RESIDUAL INCOME

$0.50

$0.85 $1.00 V0  $20    1 2 3 1.10 1.10 1.10 V0  $20  $1.91 V0  $21.91

DETERMINANTS OF RESIDUAL INCOME

RIt   ROEt  r  Bt 1 ROE > r

RI > 0

V>B

ROE < r

RI < 0

V

RESIDUAL INCOME VALUATION AND THE P/B

ROE  r V0  B0  B0 rg V0 ROE  r  1 B0 rg

EXAMPLE: USING A SINGLE-STAGE RESIDUAL INCOME MODEL

Book value of equity per share

$30.00

Return on equity

18%

Required return on equity

12%

Residual income growth rate

8%

EXAMPLE: USING A SINGLE-STAGE RESIDUAL INCOME MODEL

ROE  r V0  B0  B0 rg 0.18  0.12 V0  $30  $30 0.12  0.08 $1.80 V0  $30   $75.00 0.12  0.08

EXAMPLE: USING A SINGLE-STAGE RESIDUAL INCOME MODEL Suppose that the current stock price is $80 in the previous example. What is the implied growth rate?

0.18  0.12 $80  $30  $30 0.12  g $1.80 $50  0.12  g g  8.4%

CONTINUING RESIDUAL INCOME = Long-Term Residual Income

• • • •

Potential Scenarios: RI is constant forever RI is zero at the terminal period RI gradually declines to zero, where ROE = r RI gradually declines to a constant level, where ROE > r

CONTINUING RESIDUAL INCOME AND PERSISTENCE FACTORS

High Persistence

Low Persistence

• Low dividend payout • Historically high industry ROEs

• Extreme ROE • Extreme levels of special items • Extreme ing accruals

VALUING CONTINUING RESIDUAL INCOME

Et  rE Bt 1 Et  rE BT 1 V0  B0    t T 1 (1  rE  ω)(1  rE ) t 1 (1  rE ) T 1

Persistence Factor (ω) • 0≤ω≤1 • ω = 1  Residual income will not fade • ω = 0  Residual income will not persist after the initial forecast to rise • ω = 0.62  It has been observed, on average, empirically

EXAMPLE: MULTISTAGE RESIDUAL INCOME MODEL From the First Valuation Example: • Beginning book value at Time 0 = $20.00 • Residual income in Year 1 = $0.50 • Residual income in Year 2 = $0.85 • Residual income in Year 3 = $1.00 • Required return on equity = 10% • Value was $21.91

Now Assume: • The firm continues operations after three years

EXAMPLE: MULTISTAGE MODEL CASE 1:  = 0

Et  rE Bt 1 ET  rE BT 1 V0  B0    t T 1 (1  r ) (1  r   )(1  r ) t 1 E E E T 1

$0.50 $0.85 $1.00 V0  $20    1 2 2 1.10 1.10 (1  0.10  0)(1.10 ) $0.50 $0.85 $1.00 V0  $20    1 2 2 1.10 1.10 (1.10)(1.10 ) V0  $21.91

EXAMPLE: MULTISTAGE MODEL CASE 2:  = 1.0

Et  rE Bt 1 ET  rE BT 1 V0  B0    t T 1 (1  r ) (1  r   )(1  r ) t 1 E E E T 1

$0.50 $0.85 $1.00 V0  $20    1 2 1.10 1.10 (1  0.10  1.0)(1.102 ) $0.50 $0.85 $1.00 V0  $20    1 2 1.10 1.10 (0.10)(1.102 ) V0  $29.42

EXAMPLE: MULTISTAGE MODEL CASE 3:  = 0.60

Et  rE Bt 1 ET  rE BT 1 V0  B0    t T 1 (1  rE  )(1  rE ) t 1 (1  rE ) T 1

$0.50 $0.85 $1.00 V0  $20    1 2 2 1.10 1.10 (1  0.10  0.60)(1.10 ) $0.50 $0.85 $1.00 V0  $20    1 2 1.10 1.10 (0.50)(1.102 ) V0  $22.81

EXAMPLE: MULTISTAGE MODEL USING THE P/B Calculate the PV of continuing residual income using P/B • Use this to determine terminal value Assume for the previous example

• Book value in Year 3 = $25.00 • P/B is projected in Year 3 as 1.10 The projected stock price in Year 3: • $25 × 1.10 = $27.50

EXAMPLE: MULTISTAGE MODEL USING THE P/B

Et  rE Bt 1 PT  BT V0  B0    t T (1  rE ) t 1 (1  rE ) T

$0.50 $0.85 $1.00 $27.50  $25.00 V0  $20     1 2 3 3 1.10 1.10 1.10 1.10 V0  $23.79

RESIDUAL INCOME AND DIVIDEND AND FCFE MODEL VALUATIONS

Residual Income Model Valuation • Required return on equity • Book value + PV (residual income)

Dividend and FCFE Model Valuations • Required return on equity • PV (equity cash flows)

EXAMPLE: RESIDUAL INCOME AND DIVIDEND MODELS Example Assumptions

All earnings are paid out as dividends so book value is constant Earnings and dividends are constant forever Earnings per share

$1.00

Book value of equity

$7.00

Required return on equity

10%

EXAMPLE: RESIDUAL INCOME AND DIVIDEND MODELS Valuation Using a Constant Dividend Model Assume a 100% dividend payout ratio

V0  D / r  $1.00 / 0.10  $10.00 Valuation Using a Residual Income Model

V0  $7.00  $0.30 / 0.10 V0  $7.00  $3.00 V0  $10.00

RESIDUAL INCOME VS. DIVIDEND AND FCFE MODELS Residual Income Model Valuation

Dividend and FCFE Model Valuations

Value = Book value + PV (residual income)

Value = PV (Early cash flows + Terminal value)

Large weight on current book value

Large weight on later cash flows

RESIDUAL INCOME MODEL STRENGTHS AND WEAKNESSES Strengths • Puts less weight on the terminal value • Uses available ing data • Is useful for non-dividend-paying firms • Is useful for firms without free cash flows • Is useful when cash flows are unpredictable • Is based on economic value

Weaknesses • Relies on ing data • May require adjustments to ing data • Relies on clean surplus relation • Assumes that Cost of debt = Interest expense

RESIDUAL INCOME MODEL APPROPRIATENESS Most Appropriate • At non-dividend-paying firms • At firms without free cash flows • When terminal values are highly uncertain

Least Appropriate • When the clean surplus relationship does not hold • When the determinants of residual income are not predictable

CLEAN SURPLUS ING

Beginning book value of equity

Net income

Dividends

Ending book value of equity

ING ADJUSTMENTS FOR THE RESIDUAL INCOME MODEL Example

Adjustment to Financial Statement

Over several years, Firm A has consistently recorded losses in its available-for-sale securities

Adjust net income downward

Firm B consistently capitalizes expenditures that should have been expensed

Adjust net income and book value downward

Firm C has recorded foreign currency translation losses on its balance sheet over several years; the losses are expected to continue

Adjust net income downward

Firm D accelerates revenues to the current period and defers expenses to later periods

Adjust net income and book value downward

SUMMARY Residual Income = Income Leftover after All Capital Charges

• = Net income – (Equity required return × Book value) • = (ROE – Equity required return) × Book value • Related to EVA and MVA Equity Value = Book Value + PV (Residual Income)

• Can be used with single-stage and multistage models • Can be specified with a persistence factor • Firms with stronger market positions will have greater persistence factors

SUMMARY Relative to Other Valuation Models

• Useful when a firm does not have dividends or free cash flow • Puts less emphasis on later cash flows

Use of ing Data

• Assumes clean surplus relation holds • May require adjustments to ing data