Residual Income Valuation:: Valuing Common Equity
Residual Income Valuation:: Valuing Common Equity
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
Total assets
EBIT
Debt-to-total capital
ratio
Cost of debt (before tax)
$5,000,000.00
$400,000 .00
0 .60
8%
Cost of equity
12%
Tax rate
40%
EBIT
$400,000
$240,000
Pretax income
$160,000
$64,000
Net income
$96,000
Equity capital
$2,000,00
0
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
Market
Value
Added
(MVA)
Market
Value of
the Firm
Book
Value of
Total
Capital
Valuation
Measuring Goodwill Impairment
Measuring Internal Corporate
Performance
Determining Executive Compensation
RIt Et re Bt 1
Residual
income
per share
Earnings
per share
(EPS)
Required
return on
equity (Re)
Beginning
book
value per
share
(BVPS)
Earnings
$2.50
$3.00
Dividends
$1.00
$1.10
Book value
Required equity
return
$20.00
10%
RIt
V0 B0
t
t 1 (1 r )
Et rBt 1
V0 B0
t
t 1 (1 r )
EXAMPLE:
VALUATION USING RESIDUAL INCOME
V0 $20
$0.50
1
1.10
V0 $20 $1.91
V0 $21.91
$0.85
1.10
$1.00
1.10
RIt ROE t r Bt 1
ROE > r
RI > 0
V>B
ROE < r
RI < 0
V<B
ROE r
V0 B0
B0
rg
V0
ROE r
1
B0
rg
EXAMPLE:
USING A SINGLE-STAGE RESIDUAL INCOME MODEL
Book value of equity per
share
$30.00
Return on equity
18%
12%
8%
EXAMPLE:
USING A SINGLE-STAGE RESIDUAL INCOME MODEL
ROE r
V0 B0
B0
rg
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%
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
High Persistence
Low Persistence
Low dividend
payout
Historically high
industry ROEs
Extreme ROE
Extreme levels
of special items
Extreme
accounting
accruals
Et rE Bt 1
Et rE BT 1
V0 B0
t
T 1
(1 rE )(1 rE )
t 1 (1 rE )
T 1
Persistence Factor ()
01
= 1 Residual income will not fade
= 0 Residual income will not persist after the initial forecast to rise
= 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 percent
Value was $21.91
Now Assume:
The firm continues operations after three years
Et rE Bt 1
ET rE BT 1
V0 B0
t
T 1
(1
r
)
(1
)(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 0)(1.10 2 )
$0.50 $0.85
$1.00
V0 $20
1
2
1.10 1.10
(1.10)(1.10 2 )
V0 $21.91
Et rE Bt 1
ET rE BT 1
V0 B0
t
T 1
(1
r
)
(1
)(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)(1.10 2 )
$0.50 $0.85
$1.00
V0 $20
1
2
2
1.10 1.10
(0.10)(1.10 )
V0 $29.42
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
1.10 1.10
(1 0.10 0.60)(1.10 2 )
$0.50 $0.85
$1.00
V0 $20
1
2
1.10 1.10
(0.50)(1.102 )
V0 $22.81
Et rE Bt 1 PT BT
V0 B0
t
T
(1 rE )
t 1 (1 rE )
T
1
2
3
1.10 1.10 1.10
1.103
V0 $23.79
$1.00
$7.00
10%
SUMMARY
SUMMARY