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
FRANCIS AND ROWELL MODEL
• 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
SUMMARY
• APPENDIX 26A: PROCEDURE OF USING MICROSOFT EXCEL TO RUN
FINPLAN PROGRAM
• APPENDIX 26B: PROGRAM OF FINPLAN WITH AN EXAMPLE

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.

4
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.
I.
Unknowns
1. SALES t
2. CA t
3. FA t
4. A t
5. CL t
6. NF t
7. EBIT t
8. NL t
9. NS t
10. L t
11. S t
12. R t
13. i t
14.
EAFCD
I
15.
CMDIV t
16.
NUMCS t
17.
NEWCS t
18.
P t
19.
EPS t
20.
DPS t
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

5
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.
SALES t −1
22.
GSALS t
23.
RCA t
24.
RFA t
25.
RCL t
26.
PFDSK t
27.PFDIV
t
28.
L t −1
29.
LR t
30.
S t
−1
31.
R t −1
32.
b t
33.
T t
34.
i t
−1
35.
i e t
36.
REBIT t
37.
U 1 t
38.
U s t
39.
K t
40.
NUMCS t
−1
41.
m t
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

6
Variable*
Number
34
35
36
37
38
39
40
41
27
28
29
30
31
32
33
21
22
23
24
25
26
Data**
61897.0
−0.2900
0.6388
0.8909
0.3109
0.0000
0.0000
8223.0
219.0
3120.0
67248.0
0.5657
0.2215
0.0671
0.0671
0.2710
0.0671
0.1053
0.1625
2754.3
14.5
Variable
SALEt−1
GCALSt
RCAt−1
RFAt−1
RCLt−1
PFDSKt−1
PFDIVt−1
Lt−1
LRt−1
St−1
Rt−1 bt−1
Tt−1 it−1 i e t
−
1
REBITt−1
U L
U E
Kt
NUMCSt−1 mt−1
Description
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
* Variable number as defined in Table 26-2.
***Variables can be found in Balance Sheet, Income
Statement, and Cash Flow
** Data obtained from JNJ Balance Sheets and Income Statements.
Table 26.3 FINPLAN Input Format

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.

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.

9
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
Manual
Calculation
43,946.87
11,909.60
502.39
11,372.53
2,519.02
8,853.52
3,868.53
219.00
Financial Plan
Model
43,946.87
11,909.60
502.39
11,372.53
2,519.02
8,853.52
3,845.08
219.00
Variance
(|(A − F)/A|) (%)
0.0
0.0
0.6
0.0
0.0
0.0
0.0
0.0
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)
28,073.26
39,152.27
67,225.53
13,663.08
7,487.22
(26,211.7)
72,286.98
67,225.53
58.79
4.05
1.76
28,073.26
39,152.27
67,225.53
13,663.24
7,487.20
(26,211.89)
72,286.98
67,225.53
58.51
4.04
1.75
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
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
29
30
31
32
25
26
27
28
Variable
Number*
1
21
22
23
24
37
38
39
40
41
33
34
35
36
0
1
1
0
1
0
1
1
Beginning
Period
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
4
4
0
4
0
4
4
Last
Period
0
4
4
0
4
4
4
4
0
4
4
4
4
0
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
10

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
28,073.26
39,152.27
67,225.53
2011
19,932.01
27,798.11
47,730.12
13,663.24
7,489.12
9,700.90
5,317.28
6,887.64
3,775.27
4,890.22
2,680.44
0.00
0.00
0.00
0.00
-26,214.00
-43,199.96
-55,258.11
-63,817.52
72,287.17
67,225.53
0.16
0.07
75,911.90
47,730.12
0.16
0.07
78,483.59
33,888.39
0.16
0.07
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 26.7
Pro forma Income Statement of JNJ:
2010- 2013
2012
14,151.73
19,736.66
33,888.39
2013
10,047.73
14,013.03
24,060.76
Table 26.6
Pro forma Balance Sheet of JNJ:
2010- 2013
Item/ Year 2010 2011 2012
Sales
Operating income
Interest expense
Underwriting commission -- debt
Income before taxes
43,946.87
11,909.60
502.74
34.56
11,372.30
31,202.28
8,455.82
356.94
131.09
7,967.78
22,153.62
6,003.63
253.43
88.81
5,661.39
Taxes
Net income
Preferred dividends
Available for common dividends
Common dividends
2,518.44
8,853.87
0.00
8,853.87
3,845.14
1,764.49
6,203.29
0.00
6,203.29
2,694.03
1,253.73
4,407.65
0.00
4,407.65
1,914.20
Debt repayments 219.00
219.00
219.00
Actual funds needed for investment -29,848.88
-18,938.80
-13,381.16
2013
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
11

Year
GSALS t= b t−1=
−0.2900
EPS =
0.5657
DPS =
PPS =
GSALS t= b t−1=
−0.4
0.5657
EPS =
DPS =
PPS =
GSALS t= b t−1=
0.09
EPS =
0.5657
DPS =
PPS =
GSALS t= b t−1=
−0.2900
0.3
EPS =
DPS =
PPS =
GSALS t= b t−1=
−0.2900
EPS =
0.7
DPS =
PPS =
GSALS t= b t−1=
−0.2900
0.5657
EPS =
DPS =
PPS =
GSALS t= b t−1=
−0.2900
EPS =
0.5657
DPS =
PPS =
K t=
0.1625
K t=
0.1625
K t=
0.1625
K t=
0.1625
K t=
0.1625
K
K t= t=
0.1
0.5
12
2010
4.04
1.75
58.42
3.69
1.60
53.47
5.09
2.21
73.61
3.97
2.78
57.46
4.07
1.22
58.90
3.97
1.72
57.42
3.94
1.71
56.97
3.46
1.50
50.02
3.39
1.47
49.01
3.31
2.32
47.92
3.49
1.05
50.44
2011
3.43
1.49
49.59
2.88
1.25
41.71
5.65
2.46
81.81
2012
2.95
1.28
42.68
2013
2.54
1.10
36.74
2.29
0.99
33.10
1.82
0.79
26.27
6.23
2.70
90.11
6.86
2.98
99.26
2.80
1.96
40.52
2.37
1.66
34.27
3.03
0.91
43.80
2.63
0.79
38.03
2.99
1.30
43.23
2.58
1.12
37.37
2.86
1.24
41.40
2.42
1.05
34.98
Table 26.8
Results of Sensitivity Analysis
• 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.

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 ).

14
Sales 𝐏 𝐭
S 𝐅𝐂 𝐭
S 𝐚 𝐭
S 𝐏 𝐭 𝛄
𝟏𝐭 𝛄
𝟐𝐭
𝐊 𝐭
𝐍𝐊 𝐭
FA 𝐭
NF 𝐭
𝐏 𝐭𝐬
$ 𝐒 𝐭
𝐂𝐎𝐆 𝐭
𝐎𝐂 𝐭
𝐎𝐂𝟐 𝐭
Table 26.9
List of Variables for FR Model
Endogenous
Potential industry sales (units)
Full capacity unit output (company)
Actual company unit output
Potential company unit output
Measure of necessary new investment (based on units)
Measure of slack due to underutilization of existing resources
Units of capital stock
Desired new capital (capital units)
Fixed assets (current $)
Desired new investment (current $)
Output price
Sales dollars (current $)
Cost of goods (current $)
Overhead, selling, cost of goods (current $)
Nonoperating income (current $) 𝛄 𝐭 𝐜 𝐭 𝛉
P 𝐤𝐭
P 𝛅
𝟐
Φ
N
LR 𝐭
𝐓 𝐭
GSALS 𝐭
Sales 𝐏 𝐭−𝟏
S 𝐅𝐂 𝐭−𝟏
INV 𝐭−𝟏
FA 𝐭−𝟏
Exogenous
Growth rate in potential industry sales
Previous period potential industry sales (units)
Previous period company full capacity unit output
Previous period company finished goods inventory
Previous period company fixed asset base ($)
Capacity utilization index
Desire market share
Proportionality coefficient of to
GNP component index for capital equipment
Percentage markup of output price over ratio of
/
Proportionality coefficient of to $
Proportionality coefficient of to
Proportionality coefficient of to $
Repayment of long-term debt
Corporate tax rate

15 𝒗 NIAT
TEV 𝒕 𝒈 𝒂 𝒕
EAFCD 𝒕
CMDIV 𝒕
𝜟 RE 𝒕
GPO 𝒕
RE 𝒕
EBIT 𝒕 𝒊 𝑨 𝒕 𝒗 EBIT 𝒊 𝒔 𝒕
𝑫 𝒕
INV 𝒕
𝑳 𝒕 𝒊 𝑳 𝒕
NL 𝒕
NS 𝒕
NIAT 𝒕
Endogenous
Depreciation expense (current $)
Inventory (current $)
Long-term debt
Cost of new debt (%)
New long-term debt needed ($)
New common stock (equity) needed ($)
Net income after tax (current $)
Retained earnings
Earnings before interest and taxes
Weighted average cost of long term debt
Coefficient of variation of EBIT
Cost of new stock issue 𝒃 𝒕
U 𝑳 𝒕
PFDIV 𝒕 𝒊 𝑨 𝐭−𝟏
𝑳 𝐭−𝟏 k 𝜶
𝑳
, 𝜷
𝑳 𝜶 𝒔
, 𝜷 𝒔
GOP 𝒕−𝟏 𝜹
𝟏 𝜹
𝟑 𝜶
𝟏
, 𝜶
𝟐
, 𝜶
𝟑
Coefficient of variation of NIAT
Total equity value
Growth rate in $
Earnings available for common dividend
Common dividend
Contributions to RE made in the period
Gross operating profit (current $)
Exogenous
Retention rate
Underwriting cost of new debt
Preferred dividend
Previous period weighted average cost of long-term debt
Previous period long-term debt
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
Ratio of to actual net sales
Ratio of OC2 to net sales
Production function coefficients
Ratio of to net sales
𝟏
𝟐 𝝈
2
Sale 𝜹 𝝆
𝑷
Ratio of to net sales
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
(1) = Sales 𝑡 𝑝
= Sales 𝑝 𝑡−1
(1 + GSALS 𝑡
2. Company Production Sector
(2) 𝛼
3
FA 𝑡−1
S 𝐹𝐶 𝑡
= 𝛼
1
𝑆
𝐹𝐶 𝑡−1
+ 𝛼
2
INV 𝑡−1
+
(3)
𝑆
𝑆 𝑎 𝑡
𝐹𝐶 𝑡
(4) 𝑆 𝑡 𝑝
(9) 𝑁𝐾 𝑡
(10) 𝑃
𝐾𝑡
= 𝛾 𝑡
· 𝐾 𝑡
→ 𝑆 𝑡 𝑎
= 𝑐 𝑡
Sales 𝑝 𝑡
3. Capital Stock Requirements Sector
(5) 𝑆 𝑡 𝑝
− 𝑆 𝑡 𝑎
= 𝑆 𝑡
𝐹𝐶
− 𝑆 𝑡 𝑎
𝑆 𝑡 𝑝
− 𝑆 𝑡
𝐹𝐶
(6) 𝑆 𝑡
𝐹𝐶
− 𝑆 𝑡 𝑎
= 𝛾
2𝑡
(7) 𝑆 𝑡 𝑝
− 𝑆 𝑡
𝐹𝐶
= 𝛾
1𝑡
(8) 𝐾
1
= 𝜃𝑆 𝑡
𝐹𝐶
= 𝜃𝛾
1𝑡
4. Pricing Sector
= 𝐹𝐴
(11) 𝑃
𝐾𝑡
· 𝑁𝐾 𝑡
(12) 𝑃 𝑠𝑡
· 𝑆 𝑡 𝑎
(13) 𝑃 𝑡𝑠
= 𝑝 𝑡
= 𝛾 𝑡
𝑆 𝑡
𝐹𝐶 or 𝐹 𝐴 𝑡
= 𝑁𝐹 𝑡
= $𝑆 𝑡 𝑎
GOP 𝑡−1
(0 ≤ 𝛾
𝐾 𝑡
INV 𝑡−1
1𝑡
= 𝑃
+
𝐾𝑡
5. Production Cost Sector
(14) OC 𝑡
= 𝛿
2
(15) COG 𝑡
= 𝛿
1
$𝑆 𝑡 𝑎
$𝑆 𝑡 𝑎
(16) GOP 𝑡
= $𝑆 𝑡 𝑎
− COG 𝑡
(17) OC2 𝑡
= 𝛿
3
$𝑆 𝑡 𝑎
6. Income Sector
(18) INV 𝑡
= 𝑁($𝑆 𝑡 𝑎
(19) EBIT 𝑡
= $𝑆 𝑡 𝑎
− OCt + OC2 𝑡
− 𝐷 𝑡
(20) NIAT 𝑡
= ( EBIT2 − 𝑖 𝑡
𝐴 𝐿 𝑡
(1 − 𝑇
(20′) CL 𝑡
=
2
( $𝑆 𝑡 𝑎
7. New Financing Required Sector
8. Risk Sector
(27)
(28) 𝜎
2
= 𝜃
2
5
· 𝜃
2
6
· 𝜃
2
2
· 𝜎
2
Sales 𝑝 𝑡
9. Costs of Financing Sector
(29)
(30) 𝑖 𝜎 𝑣
𝐿 𝑡
2 ebit
= 𝛼
𝐿
EBIT
= 𝜃
2
1
· 𝜃
2
2
+ 𝛽
𝐿 𝑣 EBIT
= 𝜎 EBIT
𝑅 EBIT
· 𝜎
2
Sales 𝑝 𝑡
(31) 𝑖 𝑡 𝑎
= 𝛼 𝑠
+ 𝛽 𝑠 𝑣 NIAT
(32) 𝑣 NIAT = 𝜎 NIAT
𝑅 NIAT
10. Valuation of Equity Sector
(21) NF
(23) 𝑡
= NLS 𝑡
+ 𝛥 RE 𝑡
(22) NLS 𝑡
+ 𝑏 𝑡
= NS
1 − 𝑇 [𝑖 𝑡
𝐿 NL 𝑡
+ 𝑈 𝑡
𝐿 NL 𝑡 𝑡
+ CL
+ NL 𝑡 𝑡
− CL 𝑡−1
𝛥 RE 𝑡
= 𝑏 𝑡
1 − 𝑇 [ EBIT 𝑡
− 𝑖 𝑡
𝐴
𝐿 𝑡
− 𝑈 𝑡
𝐿 NL 𝑡
] −
(33) TEV 𝑡
=
CMDIV 𝑡 𝑖 𝑠 𝑡
−𝑔 𝑠 𝑡
(34) EAFCD 𝑡
= (1 − 𝑇 𝑡
× [ EBIT 𝑡
− 𝑖 𝑡
𝐴
𝐿 𝑡
− 𝑈 𝑡
𝐿 NLt ] − PFDIV 𝑡
PFDIV 𝑡
(35) CMDIV 𝑡
= (1 − 𝑏 𝑡
EAFCD 𝑡
(24) 𝑖 𝑡
𝐴
= 𝑖
𝐴 𝑡−1
𝐿 𝑡−1
−
LR 𝑡
𝐿 𝑡
+ 𝑖 𝑡
𝐿
NL
𝐿𝑡 𝑡
(36) 𝑔 𝑡 𝑎
=
$𝑆 𝑡
−$𝑆 𝑡−1
$𝑆 𝑡−1
(25)
NS
NL 𝑡 𝑡
+𝛥
RE 𝑡
= 𝑘
(26) 𝐿 𝑡
= 𝐿 𝑡−1
− LR 𝑡
+ NL 𝑡
16

17
• The FR model is composed of 10 sectors:
(1) industry sales
(2)
(3)
(4)
(5) production sector fixed capital-stock requirements
Pricing production costs
(6)
(7)
(8)
(9)
Income new financing required
Risk 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 seven in the variable interdependence table shown below.
Table 26.12
Variable Interdependence within Sector Seven
Explained
Variables
RE 𝑡
L 𝑡
NL
NS 𝑖 𝐴 𝑡
NLS 𝑡 𝑡 𝑡
RE 𝑡
X
Explained
Sector
7
8
9
10
Explaining Variables
L 𝑡
X
X
X
NL
X 𝑡
X
X
X
X
3
4
1
2
5
6
Table 26.11
Sector Interdependence
Earning Sector
1 2 3 4 5 6 7 8 9 10
X
X
X
X
X
X X
X X X X X X X
NS 𝑡
X 𝑖 𝐴 𝑡
X
X
X
NLS 𝑡
X
X
X
18

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.

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.

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.

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).

23
• 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.
• 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).

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.

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.

26
Table 26.13
Transformation of Industry Sales Moments to Company
NIAT and EBIT Moments
EBIT 𝑡
= $𝑆 𝑡 𝑎 − OC 𝑡
− 𝐷 𝑡
= $𝑆 𝑎 𝑡
− 𝛿
2
$𝑆 𝑡 𝑎 − 𝛷 FA 𝑡
= $𝑆 𝑎 𝑡
− 𝛿
2
$𝑆 𝑡 𝑎
1
− 𝛷𝑃 𝑘𝑡 𝜃 · 𝛾 𝑡
∴
$𝑆 𝑡 𝑎
𝑃 𝑠𝑡
EBIT
If 𝑆 𝑡 𝑝
= 𝑆 𝑡
𝐹𝐶 then 𝑆 𝑡
𝐹𝐶 = 𝑐 𝑡
Sales 𝑝 𝑡
∴ 𝑆 𝑡 𝑝
= 𝑐 𝑡
Sales 𝑝 𝑡
Since: 𝑆 𝑎 𝑡
= 𝛾 𝑡
𝑆 𝑡
𝐹𝐶 = 𝛾 𝑡 𝑐 𝑡
Sales 𝑎 𝑡
So: 𝑃 𝑡𝑠
𝑆 𝑡 𝑎 = $𝑆 𝑡
= 𝑃 𝑡𝑠 𝛾 𝑡 𝑐 𝑡
Sales 𝑝 𝑡
And: $𝑆 𝑎 𝑡
= 𝜃
2
Sales 𝑝 𝑡
= 1 − 𝛿
2
− 𝛷
𝑃 𝑘𝑡
𝑃 𝑡𝑠
· 𝜃
1 𝛾 𝑡
= 𝜃
1
$𝑆 𝑡
$𝑆 𝑡 𝑎
Hence: EBIT 𝑡
= 𝜃 2
1
· 𝜃 2
2 𝜎
2
Sales 𝑝 𝑡
Then: 𝜎
2
EBIT
= 𝜃 2
1
· 𝜃 2
2 𝜎
2
Sales 𝑝 𝑡

27
Table 26.13
Transformation of Industry Sales Moments to Company
NIAT and EBIT Moments (Cont.)
NIAT 𝑡
= 1 − 𝑇 EBIT 𝑡
If 𝑈 𝐼 = 0
− 𝑖 also:
𝐴 𝐿 𝑡
− 𝑈 𝐿 NL 𝑡
𝐿 𝑡
=
1
+
𝑃 𝑘 𝛾 𝑡 𝜃 𝑡
𝑃 𝑡𝑠
−
1 +
1 𝑘
2
$𝑆 𝑡 𝑎 = 𝜃
4
$𝑆 𝑡
NIAT= 1 − 𝑇 𝜃
1
· $𝑆 𝑡 𝑎 − 𝑖 𝐴 𝑡 𝜃
4
· $𝑆 𝑡 𝑎
= 1 − 𝑇 𝜃
1
− 𝑖 𝑡
𝐴 𝜃
4
$𝑆 𝑡 𝑎
= 1 − 𝑇 𝜃
1
− 𝑖 𝑡
𝐴 𝜃
4 𝜃
2
Sales 𝑝 𝑡
= 𝜃
5
· 𝜃
6
· 𝜃
2
Sales 𝑡 𝑝
NIAT NIAT 𝑡
Then 𝜎
2
NIAT
= 𝜃
5
· 𝜃
6
= 𝜃 2
5
· 𝜃
· 𝜃
2
6
2
Sales 𝑡
· 𝜃 2
2 𝑝
· 𝜃
2 salest p
Where 𝜃 1 𝜃
4
𝑃 𝑘
= 1 − 𝛿
2
=
− 𝛷 · 𝜃
𝑃 𝑡𝑠 𝜃
2
= 𝑃 𝑡𝑠 𝛾 𝑡 𝑐 𝑡
1
+ 𝜃 𝑘
𝑃 𝑘
1 +
1 𝑘
−
1 +
1 𝑘 𝜃
6 𝜃
5
= 1 − 𝑇
= 𝜃
1
− 𝑖 𝑡
𝐴 𝑡 𝜃
4
2
1 𝛾 𝑡
And
𝐶𝐴 𝑡
𝐷 𝑡
= · $𝑆 𝑡 𝑎
1
= 𝛷 FA 𝑡 also, parameters are defined in the List of Equations (Table 26-10).

28
• Market factors enter into the determination of financing costs through the slope ( b 1 and b 2) and intercept ( a 1 and a 2) 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.

29
• 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

Cash
(Equity capitaliza dividend tion per year rate, i t s
) (Growth rate, g t a
)
• 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.

30
• 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 NIAT 𝑡 denote the earnings for period ( t
−1
,t ), TEV 𝑡 denote the book value of equity at time t , 𝑅 𝑓 denote the risk-free rate plus one, CMDIV dividends, and NIAT 𝑡 𝑎
= NIAT 𝑡
− 𝑅 𝑓
− 1 TEV 𝑡 𝑡 denote common 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) TEV
CMDIV 𝑡 implies that
P ts

TEV t





1
R E f t 𝑡
=
NIAT
TEV t a
  𝑡−1
+ NIAT 𝑡
−
(26.1)

31
P ts

TEV t





1
R E f t
NIAT t a
 
(26.1)
• The price of firm's equity ( 𝑃 𝑡𝑠
) 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 NIAT 𝑎 𝑡 𝜏≥1 follows the stochastic process
NIAT a t

1 v t

1

 
NIAT t a   t

1, t

1
  v t
 
2, t

1
(26.2)
• where 𝑣 𝑡
ω, γ ≤ 1. is value relevant information other than abnormal earnings and 0 ≤

32
• 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.
P ts

t
 
1
t a  
2 v t
(26.3)
• Where 𝛼
1
= 𝜔 𝑅 𝑓
− and 𝛼
2
= 𝑅 𝑓
𝑅 𝑓
− 𝑅 𝑓
− . Or equivalently,
P ts
 x t
 d t
   
TEV t
 
2 v t
(26.4)
• where 𝜅 = 𝑅 𝑓
− 1 𝜔 𝑅 𝑓
− and 𝜑 = 𝑅 𝑓
𝑅 𝑓
− 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.

33
• 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 t a

1
 
10
 
11 ox t a
 
12 oa t
  v
13 1 t
  oa t

1 v 
 
20
 
22 ox t a
 
30
  v t
 
 
3 t

1 t
 
2 t

1

(26.5) v
2 t

1
 
40
  t
 
4 t

1
• where 𝑜𝑥 𝑡 𝑎 and 𝑣
2𝑡 is the abnormal operating earnings, 𝑜𝑎 𝑡 is the operating assets, are the other value relevant information variables for firm at time t 𝑣
,
1𝑡 respectively.

34
• The derived implied pricing function is
P t y t
 
0
ˆ
1 ox t a
  ˆ
2 oa t
  ˆ v
3 1 t
  ˆ v
4 2 t
• Where
 ˆ
0
 ˆ
1
 ˆ
2
 ˆ
3
 ˆ
4





 r
1


1 r
 r








ˆ
10

ˆ ˆ
12 20
ˆ ˆ
14 40
11

1
 
 

1

1

1


 r

1
 ˆ
11 r
1

11


1

 ˆ
11 r


1
 ˆ
12
1
1

1

 ˆ
11 r


1
 ˆ
13

1

 ˆ
11 r


1
 ˆ
14
 ˆ
22

1
 ˆ
33
 r
 ˆ
33
   
13 30
1

1
 ˆ
22
 ˆ
44

1

 ˆ
33

1
 ˆ
22
 ˆ
33
 ˆ
44




44
 ˆ
22

 ˆ
44







(26.6)
(26.7)

35
• Which is same as
P t
 k
  x t
 d t
 
1
  y t
  ˆ
2 oa t
  ˆ v
3 1 t
  ˆ v
4 2 t
• where 𝜅 = 𝑅 𝑓
− 1 𝜔
11
𝑅 𝑓 𝜔
11 and 𝜙 = 𝑅 𝑓
( 𝑅 𝑓
− 1 .
(26.8)
• 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.

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.

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.