Transcript PowerPoint for Chapter 26

Chapter 26
Simultaneous Equation
Models for Security
Valuation
By
Cheng Few Lee
Joseph Finnerty
John Lee
Alice C Lee
Donald Wort
Outline
2
•
26.1
WARREN AND SHELTON MODEL
•
26.2
JOHNSON & JOHNSON AS A CASE STUDY
•
26.2.1 Data Sources and Parameter Estimations
•
26.2.2 Procedure for Calculating WS model
•
26.3
•
26.3.1 The FR Model Specification
•
26.3.2 A Brief Discussion of FR’s Empirical Results
•
26.4 FELTHAM–OHLSON MODEL FOR DETERMINING EQUITY VALUE
•
26.5
•
APPENDIX 26A: PROCEDURE OF USING MICROSOFT EXCEL TO RUN
FINPLAN PROGRAM
•
APPENDIX 26B: PROGRAM OF FINPLAN WITH AN EXAMPLE
FRANCIS AND ROWELL MODEL
SUMMARY
26.1 Warren And Shelton Model
3
•
The Warren and Shelton (1971) (hereafter, WS) devised a simultaneousequation model.
•
Table 26.1 shows that WS model has four distinct segments corresponding to
the sales, investment, financing, and return-to-investment concepts in
financial theory.
•
The entire model is a system of 20 equations of a semi-simultaneous nature.
•
The actual solution algorithm is recursive, between and within segments.
•
The 20-equation model appears in Table 26.1, and the parameters used as
inputs to the model are demonstrated in the second part of Table 26.2.
Table 26.2 List of Unknowns and List of Parameters Provided by Management
Source: Warren, J. M. and J. P.Shelton. “A Simultaneous-Equation Approach to Financial Planning.” Journal of Finance
(December 1971): Table 1. Reprinted by permission.
Unknowns
1. SALESt
2. CAt
3. FAt
4. At
5. CLt
6. NFt
7. EBITt
8. NLt
9. NSt
10. Lt
11. St
12. Rt
13. it
14.EAFCDI
15.CMDIVt
16.NUMCSt
17.NEWCSt
18.Pt
19.EPSt
20.DPSt
I.
4
Sales
Current Assets
Fixed Assets
Total Assets
Current Payables
Needed Funds
Earnings before Interest and Taxes
New Debt
New Stock
Total Debt
Common Stock
Retained Earnings
Interest Rate on Debt
Earnings Available for Common Dividends
Common Dividends
Number of Common Shares Outstanding
New Common Shares Issued
Price per Share
Earnings per Share
Dividends per Share
Table 26.2 List of Unknowns and List of Parameters Provided by Management
Source: Warren, J. M. and J. P.Shelton. “A Simultaneous-Equation Approach to Financial Planning.” Journal of Finance
(December 1971): Table 1. Reprinted by permission.
II Provided by Management
21.SALESt−1
22.GSALSt
23.RCAt
24.RFAt
25.RCLt
26.PFDSKt
27.PFDIVt
28.Lt−1
29.LRt
30.St−1
31.Rt−1
32.bt
33.Tt
34.it−1
35.iet
36.REBITt
37.U1t
38.Ust
39.Kt
40.NUMCSt−1
41.mt
5
Sales in Previous Period
Growth in Sales
Current Assets as a Percent of Sales
Fixed Assets as a Percent of Sales
Current Payables as a Percent of Sales
Preferred Stock
Preferred Dividends
Debt in Previous Period
Debt Repayment
Common Stock in Previous Period
Retained Earnings in Previous Period
Retention Rate
Average Tax Rate
Average Interest Rate in Previous Period
Expected Interest Rate on New Debt
Operating Income as a Percent of Sales
Underwriting Cost of Debt
Underwriting Cost of Equity
Ratio of Debt to Equity
Number of Common Shares Outstanding in Previous Period
Price-Earnings Ratio
26.2 Johnson & Johnson as a Case Study
Variable*
Number
Data**
Variable
Description
21
61897.0
SALEt−1
Net Sales at t−1 = 2009
22
−0.2900
GCALSt
Growth in Sales
23
0.6388
RCAt−1
Current Assets as a Percentage of Sales
24
0.8909
RFAt−1
Fixed Assets as a Percentage of Sales
25
0.3109
RCLt−1
Current Payables as a Percentage of Sales
26
0.0000
PFDSKt−1
Preferred Stock
27
0.0000
PFDIVt−1
Preferred Dividends
28
8223.0
Lt−1
Long-Term Debt in Previous Period
29
219.0
LRt−1
Long-Term Debt Repayment (Reduction)
30
3120.0
St−1
Common Stock in Previous Period
31
67248.0
Rt−1
Retained Earnings in Previous Period
32
0.5657
bt−1
Retention Rate
33
0.2215
Tt−1
Average Tax Rate (Income Taxes/Pretax Income)
34
0.0671
it−1
Average Interest Rate in Previous Period
35
0.0671
ie
36
0.2710
REBITt−1
Operating Income as a Percentage of Sales
0.0671
UL
Underwriting Cost of Debt
38
0.1053
UE
Underwriting Cost of Equity
39
0.1625
Kt
Ratio of Debt to Equity
40
2754.3
NUMCSt−1
Number of Common Shares Outstanding in Previous Period
41
14.5
mt−1
Price–Earnings Ratio
37
t−1
Expected Interest Rate on New Debt
***Variables can be found in Balance Sheet, Income
Statement, and Cash Flow
** Data obtained from JNJ Balance Sheets and Income Statements.
* Variable number as defined in Table 26-2.
Table 26.3 FINPLAN Input Format
6
26.2.1 Data Sources and Parameter Estimations
7
•
The base year of the planning is 2009 and the planning period is one year, that
is, 2010.
•
Accounting and market data are required to estimate the parameters of WS
financial-planning model.
•
The COMPUSTAT data file is the major sources of accounting and market
information.
•
All dollar terms are in millions, and the number of shares outstanding is also
millions.
•
Using these parameter estimates given in Table 26.3, the 20 unknown
variables related to income statement and balance sheet can be solved for
algebraically.
26.2.2 Procedure for Calculating WS Model
8
•
For detailed procedures for calculating WS Model please look in textbook
page 1043 -1047.
•
About 18 out of 20 unknowns are listed in Table 26.4, the actual data is also
listed to allow calculation of the forecast errors.
•
In the last column of Table 26.4, the relative absolute forecasting errors (|(A −
F)/A|) are calculated to indicate the performance of the WS model in
forecasting important financial variables.
•
It was found that the quality of the sales-growth rate estimate is the key to
successfully using the WS model in financial planning and forecasting.
Table 26.4 The Comparison of Financial Forecast of JNJ: Hand Calculation and FINPLAN Forecasting
Category
INCOME STATEMENT
Sales
Operating Income
Interest Expense
Income before taxes
Taxes
Net Income
Common Dividends
Debt Repayments
BALANCE SHEET
Assets
Current Assets
Fixed Assets
Total Assets
LIABILITIES AND NET WORTH
Current Payables
Total Debt
Common Stock
Retained Earnings
Total Liabilities and Net
Worth
PER SHARE DATA
Price per Share
Earnings per Share (EPS)
Dividends per Share (DPS)
9
Manual
Calculation
Financial Plan
Model
Variance
(|(A − F)/A|) (%)
43,946.87
11,909.60
502.39
11,372.53
2,519.02
8,853.52
3,868.53
219.00
43,946.87
11,909.60
502.39
11,372.53
2,519.02
8,853.52
3,845.08
219.00
0.0
0.0
0.0
0.0
0.0
0.0
0.6
0.0
28,073.26
39,152.27
67,225.53
28,073.26
39,152.27
67,225.53
0.0
0.0
0.0
13,663.08
7,487.22
(26,211.7)
72,286.98
13,663.24
7,487.20
(26,211.89)
72,286.98
0.0
0.0
0.0
0.0
67,225.53
67,225.53
0.0
58.79
4.05
1.76
58.51
4.04
1.75
0.5
0.5
0.5
•
To do multiperiod forecasting and sensitivity analysis, the program of
FINPLAN of Microsoft Excel, as listed in Appendix 26A, can be used.
•
The input parameters and the values used to produce the pro forma financial
statements are listed in Table 26.5.
Table 26.5
FINPLAN Input 2009
FINPLAN input
Value of Data (2009)
4
61897.0000
−0.2900
0.6388
0.8909
0.3109
0.0000
0.0000
8223.0000
219.0000
3120.0000
67248.0000
0.5657
0.2215
0.0671
0.0671
0.2710
0.0671
0.1053
0.1625
2,754.321
14.4700
10
Variable
Number*
1
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
Beginning
Period
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
Last
Period
0
0
4
4
4
4
4
4
0
4
0
0
4
4
0
4
4
4
4
4
0
4
Description
The number of years to be simulated
Net Sales at t−1=2009
Growth in Sales
Current Assets as a Percentage of Sales
Fixed Assets as a Percentage of Sales
Current Payables as a Percentage of Sales
Preferred Stock
Preferred Dividends
Long-Term Debt in Previous Period
Long-Term Debt Repayment (Reduction)
Common Stock in Previous Period
Retained Earnings in Previous Period
Retention Rate
Average Tax Rate (Income Taxes/Pretax Income)
Average Interest Rate in Previous Period
Expected Interest Rate on New Debt
Operating Income as a Percentage of Sales
Underwriting Cost of Debt
Underwriting Cost of Equity
Ratio of Debt to Equity
Number of Common Shares Outstanding in Previous Period
Price–Earnings Ratio
Item/ Year
Assets
Current assets
Fixed assets
Total assets
Liabilities and Net Worth
Current liabilities
Long-term debt
Preferred stock
Common stock
Retained earnings
Total liabilities and net worth
Computed DBT/EQ
Int. rate on total debt
Per Share Data
Earnings
Dividends
Price
2010
2011
2012
2013
28,073.26
39,152.27
67,225.53
19,932.01
27,798.11
47,730.12
14,151.73
19,736.66
33,888.39
10,047.73
14,013.03
24,060.76
13,663.24
7,489.12
0.00
-26,214.00
72,287.17
67,225.53
0.16
0.07
9,700.90
5,317.28
0.00
-43,199.96
75,911.90
47,730.12
0.16
0.07
6,887.64
3,775.27
0.00
-55,258.11
78,483.59
33,888.39
0.16
0.07
4,890.22
2,680.44
0.00
-63,817.52
80,307.61
24,060.76
0.16
0.07
4.04
1.75
58.42
3.43
1.49
49.59
2.95
1.28
42.68
2.54
1.10
36.74
Table 26.6
Pro forma Balance Sheet of JNJ:
2010- 2013
Item/ Year
Table 26.7
Pro forma Income Statement of JNJ:
2010- 2013
11
Sales
Operating income
Interest expense
Underwriting commission -- debt
Income before taxes
Taxes
Net income
Preferred dividends
Available for common dividends
Common dividends
Debt repayments
Actual funds needed for investment
2010
2011
2012
2013
43,946.87
11,909.60
502.74
34.56
11,372.30
2,518.44
8,853.87
0.00
8,853.87
3,845.14
219.00
-29,848.88
31,202.28
8,455.82
356.94
131.09
7,967.78
1,764.49
6,203.29
0.00
6,203.29
2,694.03
219.00
-18,938.80
22,153.62
6,003.63
253.43
88.81
5,661.39
1,253.73
4,407.65
0.00
4,407.65
1,914.20
219.00
-13,381.16
15,729.07
4,262.58
179.93
58.79
4,023.85
891.10
3,132.75
0.00
3,132.75
1,360.52
219.00
-9,435.24
Year
GSALSt=
−0.2900
EPS =
DPS =
PPS =
GSALSt=
−0.4
EPS =
DPS =
PPS =
GSALSt=
0.09
EPS =
DPS =
PPS =
GSALSt=
−0.2900
EPS =
DPS =
PPS =
GSALSt=
−0.2900
EPS =
DPS =
PPS =
GSALSt=
−0.2900
EPS =
DPS =
PPS =
GSALSt=
−0.2900
EPS =
DPS =
PPS =
12
bt−1=
0.5657
bt−1=
0.5657
bt−1=
0.5657
bt−1=
0.3
bt−1=
0.7
bt−1=
0.5657
bt−1=
0.5657
2010
2011
2012
2013
4.04
1.75
58.42
3.43
1.49
49.59
2.95
1.28
42.68
2.54
1.10
36.74
3.69
1.60
53.47
2.88
1.25
41.71
2.29
0.99
33.10
1.82
0.79
26.27
5.09
2.21
73.61
5.65
2.46
81.81
6.23
2.70
90.11
6.86
2.98
99.26
3.97
2.78
57.46
3.31
2.32
47.92
2.80
1.96
40.52
2.37
1.66
34.27
4.07
1.22
58.90
3.49
1.05
50.44
3.03
0.91
43.80
2.63
0.79
38.03
3.97
1.72
57.42
3.46
1.50
50.02
2.99
1.30
43.23
2.58
1.12
37.37
3.94
1.71
56.97
3.39
1.47
49.01
2.86
1.24
41.40
2.42
1.05
34.98
Kt=
0.1625
Table 26.8
Results of Sensitivity Analysis
Kt=
0.1625
Kt=
0.1625
Kt=
0.1625
Kt=
0.1625
Kt=
0.1
Kt=
0.5
• Results of the sensitivity analysis
related to EPS, DPS, and PPS are
shown.
• Table 26.8 indicates that the
generated pro forma financial
statements that describe the future
financial condition of the firm for any
assumed pattern of sales.
26.3 Francis and Rowell Model
13
•
The model presented below extends the simultaneous linear-equation model
of the firm developed by WS in 1971.
•
The object of this model is to generate pro forma financial statements that
describe the future financial condition of the firm for any assumed pattern of
sales.
•
The FR model is composed of 10 sectors with a total of 36 equations.
•
The model incorporates an explicit treatment of risk by allowing for
stochastic variability in industry sales forecasts.
•
The exogenous input of sales variance is transformed (through simplified
linear relations in the model) to coefficients of variation for EBIT and net
income after taxes (NIAT) (see Table 26.10 ).
Table 26.9
List of Variables for FR Model
Endogenous
𝐏
Potential industry sales (units)
GSALS𝐭
S𝐭
Full capacity unit output (company)
Sales𝐭−𝟏
Previous period potential industry sales (units)
S𝐚𝐭
Actual company unit output
S𝐅𝐂
𝐭−𝟏
S𝐏𝐭
Potential company unit output
INV𝐭−𝟏
Previous period company full capacity unit
output
Previous period company finished goods
inventory
FA𝐭−𝟏
Previous period company fixed asset base ($)
𝛄𝐭
Capacity utilization index
Sales𝐭
𝐅𝐂
𝐏
Growth rate in potential industry sales
𝛄𝟐𝐭
Measure of necessary new investment (based
on units)
Measure of slack due to underutilization of
existing resources
𝐊𝐭
Units of capital stock
𝐜𝐭
Desire market share
𝐍𝐊 𝐭
Desired new capital (capital units)
𝛉
Proportionality coefficient of to
FA𝐭
Fixed assets (current $)
P𝐤𝐭
GNP component index for capital equipment
NF𝐭
Desired new investment (current $)
P
Percentage markup of output price over ratio of
/
𝐏𝐭𝐬
Output price
𝛅𝟐
Proportionality coefficient of to $
$ 𝐒𝐭
Sales dollars (current $)
Φ
Proportionality coefficient of to
𝐂𝐎𝐆𝐭
Cost of goods (current $)
N
Proportionality coefficient of to $
𝐎𝐂𝐭
Overhead, selling, cost of goods (current $)
LR𝐭
Repayment of long-term debt
𝐎𝐂𝟐𝐭
Nonoperating income (current $)
𝐓𝐭
Corporate tax rate
𝛄𝟏𝐭
14
Exogenous
Endogenous
Exogenous
𝑫𝒕
Depreciation expense (current $)
𝒃𝒕
INV𝒕
Inventory (current $)
U𝒕
Underwriting cost of new debt
𝑳𝒕
Long-term debt
PFDIV𝒕
𝒊𝑳𝒕
Cost of new debt (%)
𝒊𝑨𝐭−𝟏
NL𝒕
New long-term debt needed ($)
𝑳𝐭−𝟏
Preferred dividend
Previous period weighted average cost of
long-term debt
Previous period long-term debt
NS𝒕
NIAT𝒕
RE𝒕
EBIT𝒕
𝒊𝑨𝒕
𝑳
New common stock (equity) needed ($)
Net income after tax (current $)
𝜶𝑳 , 𝜷𝑳
Retained earnings
𝜶𝒔 , 𝜷𝒔
Earnings before interest and taxes
Retention rate
k
Optimal capital structure assumption
Coefficients in risk-teturn tradeoff for new
debt
Coefficients in risk-return tradeoff for new
stock
Gross operating profit of previous period
GOP𝒕−𝟏
Weighted average cost of long term debt
𝜹𝟏
Ratio of to actual net sales
𝒗EBIT
𝒊𝒔𝒕
Coefficient of variation of EBIT
𝜹𝟑
Ratio of OC2 to net sales
𝒗NIAT
Coefficient of variation of NIAT
Cost of new stock issue
𝜶𝟏 , 𝜶𝟐 , 𝜶𝟑
Production function coefficients
Ratio of to net sales
𝟏
TEV𝒕
Total equity value
Ratio of to net sales
𝟐
𝒈𝒂𝒕
15
Growth rate in $
EAFCD𝒕
Earnings available for common dividend
CMDIV𝒕
Common dividend
𝜟RE𝒕
Contributions to RE made in the period
GPO𝒕
Gross operating profit (current $)
𝝈2
Sale𝜹
𝝆
𝑷
Standard deviation of potential industry
sales
Table 26.9
List of Variables for FR Model
(Cont.)
Table 26.10
List of Equations for FR Model
1. Industry Sales
5. Production Cost Sector
𝑝
𝑝
(1) = Sales𝑡 = Sales𝑡−1 (1 + GSALS𝑡
2. Company Production Sector
𝐹𝐶
S𝐹𝐶
𝑡 = 𝛼1 𝑆𝑡−1 + 𝛼2 INV𝑡−1 +
(2)
𝛼3 FA𝑡−1
𝑆𝑎
𝑡
(3) 𝑆 𝐹𝐶
= 𝛾𝑡 → 𝑆𝑡𝑎 = 𝛾𝑡 𝑆𝑡𝐹𝐶
𝑡
𝑝
𝑝
3. Capital Stock Requirements Sector
𝑝
𝑆𝑡
−
(14) OC𝑡 = 𝛿2 $𝑆𝑡𝑎
𝑝
𝑆𝑡 − 𝑆𝑡𝑎 = 𝑆𝑡𝐹𝐶 − 𝑆𝑡𝑎 +
𝑆𝑡𝐹𝐶
(15) COG𝑡 = 𝛿1 $𝑆𝑡𝑎
2 = 𝜃2 · 𝜃2 · 𝜃2 · 𝜎2
(28) 𝜎niat
𝑝
6
2
5
Sales𝑡
(16) GOP𝑡 = $𝑆𝑡𝑎 − COG𝑡
(17) OC2𝑡 = 𝛿3 $𝑆𝑡𝑎
9. Costs of Financing Sector
6. Income Sector
(29) 𝑖𝑡𝐿 = 𝛼𝐿 + 𝛽𝐿 𝑣EBIT
(18) INV𝑡 = 𝑁($𝑆𝑡𝑎
(20) NIAT𝑡 = (EBIT2 − 𝑖𝑡𝐴 𝐿𝑡 (1 − 𝑇
(20′) CL𝑡 =
( $𝑆𝑡𝑎
2
7. New Financing Required Sector
(6) 𝑆𝑡𝐹𝐶 − 𝑆𝑡𝑎 = 𝛾2𝑡
𝑝
(7) 𝑆𝑡 − 𝑆𝑡𝐹𝐶 = 𝛾1𝑡
(21) NF𝑡 + 𝑏𝑡 1 − 𝑇 [𝑖𝑡𝐿 NL𝑡 + 𝑈𝑡𝐿 NL𝑡
(0 ≤ 𝛾1𝑡
= NLS𝑡 + 𝛥RE𝑡 + CL𝑡 − CL𝑡−1
(8) 𝐾1 = 𝜃𝑆𝑡𝐹𝐶
(22) NLS𝑡 = NS𝑡 + NL𝑡
(9) 𝑁𝐾𝑡 = 𝜃𝛾1𝑡
(23)
4. Pricing Sector
(10) 𝑃𝐾𝑡 · 𝐾𝑡 = 𝐹𝐴𝑡 or 𝐹 𝐴𝑡 𝐾𝑡 = 𝑃𝐾𝑡
(11) 𝑃𝐾𝑡 · 𝑁𝐾𝑡 = 𝑁𝐹𝑡
(12) 𝑃𝑠𝑡 ·
2 = 𝜃2 · 𝜃2 · 𝜎2
(27) 𝜎ebit
𝑝
1
2
Sales𝑡
(19) EBIT𝑡 = $𝑆𝑡𝑎 − OCt + OC2𝑡 − 𝐷𝑡
(4) 𝑆𝑡 = 𝑐𝑡 Sales𝑡
(5)
8. Risk Sector
𝑆𝑡𝑎
=
(33) TEV𝑡 =
(34)
CMDIV𝑡
𝑖𝑡𝑠 −𝑔𝑡𝑠
EAFCD𝑡 = (1 − 𝑇𝑡 × [EBIT𝑡 −
1 − 𝑇 [EBIT𝑡 − 𝑖𝑡𝐴 𝐿𝑡 − 𝑈𝑡𝐿 NL𝑡 ] − 𝑖 𝐴 𝐿 − 𝑈 𝐿 NL ] − PFDIV
t
𝑡
𝑡 𝑡
𝑡
(24)
(25)
𝑖𝑡𝐴
=
𝐿𝑡−1 −LR𝑡
𝐴
𝑖𝑡−1
𝐿
𝑡
+
𝑖𝑡𝐿
NL𝑡
=𝑘
NS𝑡 +𝛥RE𝑡
(26) 𝐿𝑡 = 𝐿𝑡−1 − LR𝑡 + NL𝑡
16
𝜎
(32) 𝑣NIAT = 𝑅NIAT
NIAT
10. Valuation of Equity Sector
PFDIV𝑡
$𝑆𝑡𝑎
(13) 𝑃𝑡𝑠 = 𝑝 GOP𝑡−1 INV𝑡−1
𝛥RE𝑡 = 𝑏𝑡
𝜎
(30) 𝑣EBIT = EBIT
𝑅
EBIT
𝑎
(31) 𝑖𝑡 = 𝛼𝑠 + 𝛽𝑠 𝑣NIAT
(35) CMDIV𝑡 = (1 − 𝑏𝑡 EAFCD𝑡
NL𝑡
𝐿𝑡
(36) 𝑔𝑡𝑎 =
$𝑆𝑡 −$𝑆𝑡−1
$𝑆𝑡−1
26.3.1 FR Model Specification
•
17
The FR model is composed of 10 sectors:
(1)
industry sales
(2)
production sector
(3)
fixed capital-stock requirements
(4)
Pricing
(5)
production costs
(6)
Income
(7)
new financing required
(8)
Risk
(9)
costs of financing
(10)
common stock valuation.
•
Table 26.11 summarized sectors one through ten in the interdependence table.
•
An "X" is placed in the table to represent the direction of an arrow (from
explaining to explained) on the flow chart.
•
The simultaneity of the FR model is primarily within each sector's equations.
•
For example, this is illustrated for sector
Table 26.11
Sector Interdependence
seven in the variable interdependence
table shown below.
1
Explained
Sector
Table 26.12
Variable Interdependence within Sector Seven
Explained
Variables
18
RE𝑡
L𝑡
NL𝑡
NS𝑡
𝑖𝑡𝐴
NLS𝑡
RE𝑡
X
1
2
3
4
5
6
7
8
9
10
Explaining Variables
L𝑡
NL𝑡
X
X
X
X
X
X
X
X
2
Earning Sector
3
4
5
6
7
8
9
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
NS𝑡
X
𝑖𝑡𝐴
X
X
NLS𝑡
X
10
Sector One: Industry Sales
19
•
The industry sales forecast sector influences directly the risk sector and
production sector and, indirectly, every sector of the model.
•
The industry-sales equation shows that an industry-sales forecast must be
made by some means over a predefined forecast period and given as an
exogenous input to the FR model.
•
It’s the industry sales that drive the model, since it can be more accurately
forecasted than company sales.
•
The mean and standard deviation are parameters emloyed from the industry
sales forecast
•
The mean enters the model in the conventional way, whereas the standard
deviation is mathematically transformed to obtain the standard deviation of its
derivative quantities, the company's NIAT and EBIT.
Sector Two: Company Sales and Production
20
•
Potential company sales is obtained from forecasted industry sales through
the market-share assumption.
•
The FR model distinguishes between potential and actual sales levels; this
allows a realistic treatment of slack or idle capacity in the firm.
•
The production function allows explicit definition of the company's fullcapacity production levels (see Equation (2) in Table 26-10 for the exact
specification).
•
It serves the useful purpose of relaxing the unrealistic assumption (used in
many models) that whatever is produced is sold.
•
Actual company production is derived from full-capacity production by a
capacity-utilization index in Equation (3) of Table 26-10.
Sector Three: Fixed Capital-Stock Requirements
21
•
Necessary new investments is not linked directly to company sales in the FR
model, but instead results from comparison between potential and actual
company sales.
•
A capacity–utilization index for the simulated company and industry
translates full-capacity output (from the production function) into actual
company sales, just as a market-share assumption is used to translate potential
industry sales into potential company sales.
•
Any positive difference between potential company sales and actual company
sales is decomposed into the contribution due to idle capacity and the
contribution due to company expansion possibility, as shown mathematically
in Equation (5) of Table 26-10.
Sector Four: Pricing
22
•
The pricing sector of the model plays a key role by relating real or units sector
to the nominal or dollar sectors.
•
The real sectors and the nominal sectors are connected by the pricing sector.
•
This sector separation allows explicit treatment of the product-pricing
decision apart from the sales and production decisions.
•
Also, it maintains the important distinction between real and nominal
quantities and thus permits an analysis of inflation's impact on the firm.
•
FR Equation (13) is a simple formula that generates product price by relating
it, through a markup, to the ratio of previous-period gross operating profit to
inventory. Real units of company sales are priced out in FR Equation (12).
Sector Five: Production Costs
•
The production cost sector is similar to previous models; production cost and
inventory are related directly to actual company sales dollars.
•
Also, depreciation is linked directly to existing fixed investment.
Sector Six: Income
23
•
As in the production cost sector, the income-sector ties inventory, earnings
before interest and taxes, and net income after taxes directly to actual
company sales dollars.
•
This simplicity is preserved here to create a linear-determined income
statement that produces EBIT as a function of actual company sales (given a
few simplifying assumptions).
•
The NIAT is derived from EBIT after deduction of interest expense (also
linearly related to actual sales levels and taxes).
Sector Seven: New Financing Required
24
•
The new-financing-required sector is composed primarily of accounting
relationships that determine the dollar amount of external financing required
from the new capital requirements (Sector Three) and internal financing
capability (Sector Six).
•
The breakdown of new external financing into new equity and new debt
occurs in FR Equation (25), where the notion of optimal capital structure is
exploited.
•
The weighted-average cost of debt, FR Equation (24), consists of a weighted
sum of new debt costs and the cost of existing debt.
•
The cost of the new debt is not exogenous in this model; it is estimated in a
simplified risk–return tradeoff from Sector Nine.
Sector Eight: Risk
25
•
The linear derivation of both EBIT and NIAT in the income sector is used
(with simplifying assumptions) in the risk sector to obtain the standard
deviation of each income measure.
•
The derivation (presented in Table 26.13) demonstrates how management's
judgment as to the variability (i.e., standard deviation) of forecasting industry
sales affects the risk character (of both the business and financial risk) of the
company.
•
This risk character influences the costs of financing new stock and debt in
risk–return tradeoff equations of Sector Nine.
•
The debt-to-equity ratio (a financial leverage ratio) also positively influences
the NIAT standard deviation.
•
Thus, the leverage structure of the firm endogenously influences the costs of
financing in a realistic way.
Table 26.13
Transformation of Industry Sales Moments to Company
NIAT and EBIT Moments
EBIT
𝑝
𝑝
If 𝑆𝑡 = 𝑆𝑡𝐹𝐶 then 𝑆𝑡𝐹𝐶 = 𝑐𝑡 Sales𝑡
EBIT𝑡 = $𝑆𝑡𝑎 − OC𝑡 − 𝐷𝑡
𝑝
𝑝
∴ 𝑆𝑡 = 𝑐𝑡 Sales𝑡
= $𝑆𝑡𝑎 − 𝛿2 $𝑆𝑡𝑎 − 𝛷FA𝑡
𝑎
1
$𝑆
𝑡
= $𝑆𝑡𝑎 − 𝛿2 $𝑆𝑡𝑎 − 𝛷𝑃𝑘𝑡 𝜃 · ∴
𝛾𝑡 𝑃𝑠𝑡
Since: 𝑆𝑡𝑎 = 𝛾𝑡 𝑆𝑡𝐹𝐶 = 𝛾𝑡 𝑐𝑡 Sales𝑎𝑡
𝑝
So: 𝑃𝑡𝑠 𝑆𝑡𝑎 = $𝑆𝑡 = 𝑃𝑡𝑠 𝛾𝑡 𝑐𝑡 Sales𝑡
𝑝
= 1 − 𝛿2 − 𝛷
𝑃𝑘𝑡
1
·𝜃
𝑃𝑡𝑠
𝛾𝑡
= 𝜃1 $𝑆𝑡
$𝑆𝑡𝑎
And: $𝑆𝑡𝑎 = 𝜃2 Sales𝑡
Hence: EBIT𝑡 = 𝜃12 · 𝜃22 𝜎 2
𝑝
Sales𝑡
2
Then:𝜎EBIT
= 𝜃12 · 𝜃22 𝜎 2
𝑝
Sales𝑡
26
Table 26.13
Transformation of Industry Sales Moments to Company
NIAT and EBIT Moments (Cont.)
NIAT
𝐴
𝐿
NIAT𝑡 = 1 − 𝑇 EBIT𝑡 − 𝑖 𝐿𝑡 − 𝑈 NL𝑡
If 𝑈 𝐼 = 0 also:
𝐿𝑡 =
𝑃𝑘 𝜃𝑡
1+𝛾 𝑃
𝑡 𝑡𝑠
1+
−
1
𝑘
2
𝑝
NIAT𝑡 = 𝜃5 · 𝜃6 · 𝜃2 Sales𝑡
2
Then 𝜎NIAT
= 𝜃52 · 𝜃62 · 𝜃22 · 𝜃 2 p
salest
Where
𝑃𝑘
1
·𝜃
𝑃𝑡𝑠
𝛾𝑡
𝜃2 = 𝑃𝑡𝑠 𝛾𝑡 𝑐𝑡
𝜃𝑘 𝑃𝑘
1+
1− 2
1+
𝑘
𝜃4 =
1
1+
𝑘
𝜃5 = 1 − 𝑇𝑡
𝜃6 = 𝜃1 − 𝑖𝑡𝐴 𝜃4
And
𝜃1 = 1 − 𝛿2 − 𝛷
$𝑆𝑡𝑎 = 𝜃4 $𝑆𝑡
NIAT= 1 − 𝑇 𝜃1 · $𝑆𝑡𝑎 − 𝑖𝑡𝐴 𝜃4 · $𝑆𝑡𝑎
= 1 − 𝑇 𝜃1 − 𝑖𝑡𝐴 𝜃4 $𝑆𝑡𝑎
𝑝
= 1 − 𝑇 𝜃1 − 𝑖𝑡𝐴 𝜃4 𝜃2 Sales𝑡
𝑝
= 𝜃5 · 𝜃6 · 𝜃2 Sales𝑡
𝐶𝐴𝑡 =
1
· $𝑆𝑡𝑎
𝐷𝑡 = 𝛷FA𝑡
also, parameters are defined in the List of Equations (Table 26-10).
27
Sector Nine: Cost of Financing
28
•
Market factors enter into the determination of financing costs through the
slope (b1 and b2) and intercept (a1 and a2) coefficients of the risk–return
tradeoff functions — namely Equations (29) and (31) of Table 26.10.
•
At the present time, all four coefficients must be exogenously provided by
management.
•
Historical coefficients can be estimated empirically using simple linear
regression.
•
The regression coefficients would establish a plausible range of values that
might be used by management to determine the present or future coefficient
values.
Sector Ten: Common Stock Valuation
•
The valuation model used finds the present value of dividends, which are
presumed to grow perpetually at a constant rate.
•
Algebraically reduced to its simplest form, the single-share valuation model is
shown below:
Share price 
29
Cash dividend per year
(Equitycapitalization rate,its ) - (Growth rate,g ta )
•
Equation (33) of Table 26.10 differs slightly from the per-share valuation
model above because it values the firm's total equity outstanding.
•
This change was accomplished merely by multiplying both sides of the
valuation equation shown above by the number of shares outstanding.
26.4 Feltham-Ohlson Model for
Determining Equity Value
•
Ohlson Model introduced the clean surplus relations (CSR) assumption requiring
that income over a period equals net dividends and the change in book value of
equity.
•
CSR is an accounting system recognizing that the periodically value created is
distinguished from the value distributed.
•
Let NIAT𝑡 denote the earnings for period (t−1,t), TEV𝑡 denote the book value of
equity at time t, 𝑅𝑓 denote the risk-free rate plus one, CMDIV𝑡 denote common
𝑎
dividends, and NIAT𝑡
= NIAT𝑡 − 𝑅𝑓 − 1 TEV𝑡 denote the abnormal
earnings at time t.
•
The change in book value of equity between two days equals earnings plus
dividends, so the clean surplus relations (CSR) TEV𝑡 = TEV𝑡−1 + NIAT𝑡 −
CMDIV𝑡 implies that

Pts  TEVt   R f  Et  NIATta 
 1
30
(26.1)

Pts  TEVt   R f  Et  NIATta 
(26.1)
 1
•
The price of firm's equity ( 𝑃𝑡𝑠 ) is equal to its book value of equity adjusted
for the present value of expected future abnormal earnings.
•
The variables on the right-hand side of (26.1) are still forecasts, not past
realizations.
•
. To deal with this problem, Ohlson Model introduced the information
dynamics to link the value to the contemporaneous accounting data.
•
Assume NIAT𝑡
𝑎
𝜏≥1
follows the stochastic process
NIAT
vt 1 
•
31
a
t 1
  NIATta  vt  1,t 1
  vt   2,t 1
(26.2)
where 𝑣𝑡 is value relevant information other than abnormal earnings and 0 ≤
ω, γ ≤ 1.
•
Based on Equations (26.1) and (26.2), Ohlson Model demonstrated that the
value of the equity is a function of contemporaneous accounting variables as
follows.
Pts  TEVt  ˆ1NIATta  ˆ2vt
•
Where 𝛼1 = 𝜔
𝑅𝑓 − 𝜔 and 𝛼2 = 𝑅𝑓
𝑅𝑓 − 𝜔
(26.3)
𝑅𝑓 − 𝛾 . Or equivalently,
Pts    xt  dt   1   TEVt  2vt
32
𝑅𝑓 − 𝜔 and 𝜑 = 𝑅𝑓
(26.4)
•
where 𝜅 = 𝑅𝑓 − 1 𝜔
𝑅𝑓 − 1
•
Equations (26.3) and (26.4) imply that the market value of the equity is equal
to the book value adjusted for (i) the current profitability as measured by
abnormal earnings and (ii) other information that modifies the prediction of
future profitability.
•
One major limitation of the Ohlson Model is that it assumed unbiased accounting.
•
. Feltham and Ohlson (1995) (hereafter FO) introduce additional dynamics to deal
with the issue of biased (conservative) accounting data.
•
The information dynamics in the FO Model is
ox
a
t 1
 10  11oxta  12oat  13v1t  1t 1
oa t 1  20  22 oxta  24 v2t   2t 1
v1t 1  30  33v1t   3t 1
(26.5)
v 2t 1  40  44 v2t   4t 1
•
33
where 𝑜𝑥𝑡𝑎 is the abnormal operating earnings, 𝑜𝑎𝑡 is the operating assets, 𝑣1𝑡
and 𝑣2𝑡 are the other value relevant information variables for firm at time t,
respectively.
•
The derived implied pricing function is
Pt  yt  ˆ0  ˆ1oxta  ˆ2oat  ˆ3v1t  ˆ4v2t
•
Where
ˆ0 
ˆ1 
ˆ10 1  r  ˆ 22 1  r  ˆ 33 1  r  ˆ 44  


ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
1

r



1

r





1

r


   12 20 
33 
13 30 
22  
 ˆ ˆ

ˆ



1

r




44
 14 40

r 1  r  ˆ11 1  r  ˆ 22 1  r  ˆ 33 1  r  ˆ 44 
ˆ11
r 1  r  ˆ11 
1  r  ˆ12
1  r  ˆ11 1  r  ˆ 22 
1  r  ˆ13
ˆ3 
1  r  ˆ11 1  r  ˆ33 
1  r  ˆ14
ˆ4 
1  r  ˆ11 1  r  ˆ 44 
ˆ2 
34
(26.6)
(26.7)
•
Which is same as
Pt  k  xt  dt   1    yt  ˆ 2oat  ˆ3v1t  ˆ4v2t
35
(26.8)
•
where 𝜅 = 𝑅𝑓 − 1 𝜔11
𝑅𝑓 − 𝜔11 and 𝜙 = 𝑅𝑓 ( 𝑅𝑓 − 1 .
•
The implied valuation function in Equations (26.6) and (26.8) is a weighted
average of firm's operating earnings, firm's book value, and the other valuerelevant information with an adjustment for the understatement of the
operating assets resulting from accrual accounting.
•
The major contribution of the FO Model is that it considered the accounting
conservatism in the equity valuation.
26.5 Combined Forecasting Method to
Determine Equity Value
36
•
Lee et al. (2011) investigate the stock price forecast ability of Ohlson (1995)
model FO (1995) model, and WS (1971) Model.
•
They use simultaneous equation estimation approach to estimate the
information dynamics for Ohlson model and FO model and forecast future
stock prices.
•
Empirical results show that the simultaneous equation estimation of the
information dynamics improves the ability of the Ohlson Model and FO
model in capturing the dynaic of the abnormal earnings process.
•
The evidence shows that combined forecast method can reduce the prediction
errors.
26.6 Summary
37
•
Two simultaneous-equation financial planning models were discussed in
detail in this chapter.
•
There are 20 equations and 20 unknowns in the WS model.
•
A computer program of the WS model is presented in Appendix 26B.
•
The FR model is a generalized WS financial-planning model.
•
There are 36 equation and 36 unknown in the FR model.
•
In this chapter, we have also briefly discussed Felthan-Ohlson model for
determining equity value.
•
In addition, we have explored the usefulness of integrating WS model and
Felthan-Ohlson model to improve the determination of equity value.