Overview of Financial Valuation Models - CFA Society Chicago · Prepared for the CFA Society...

Overview of Financial Valuation Models

Prepared for the CFA Society Chicago CFA Research Challenge

By: Larry A. Lonis, CFA

Index

Key Definitions The Valuation Process Earnings Quality – Accrual Ratios Beneish M-Score Model Streams of Expected Cash Flows - DDM Streams of Expected Cash Flows – FCFF & FCFE Residual Income Models Price Multiples Price and Enterprise Value Multiples in Valuation Rationales for and Drawbacks of P/E Ratios Summary of Price and Inverse Price Ratios Valuation Based on Comparables Peer Company Multiples Other Enterprise Valuation Multiples

2

Key Definitions

Valuation – the estimation of an asset’s value based either on variables perceived to be related to future investment returns or on comparisons with similar assets.

Intrinsic value – the value of the asset given a hypothetically complete understanding of the asset’s investment characteristics.

Rational efficient markets formulation – investors will not incur expenses of gathering information unless they expect to be rewarded by higher gross returns.

3Source: Equity Asset Valuation – 3rd Edition

The Valuation Process

Understanding the business – industry and competitive analysis, financial statement analysis.

Forecasting company performance – forecasts of sales, earnings, dividends, and financial position – provides inputs to models.

Selecting the appropriate valuation model – very important as not all models are effective on a universal basis.

Converting the forecasts to a valuation – this involves judgment in addition to entering the historical data.

Applying the valuation conclusions to:◦ A particular stock,◦ Providing an opinion about the price of a transaction, or◦ Evaluating the economic merits of a potential strategic investment.


Earnings Quality – Accrual Ratios

The purpose of this ratio analysis is to identify the cash component of earnings versus the accrual component5◦ These ratios are referred to as "scaled measures" that analysts can use as simple

measures they can readily compute and use in their evaluation of a firm's quality of earnings.

◦ Typically these calculations are completed using "standardized formats" (e.g., financial statements from Compustat, Thomson, FactSet, or other providers of financial data).

◦ A key advantage of using this standard data is that it facilitates cross-sectional comparisons across companies.

◦ Net operating assets (NOA) is the difference between operating assets (total assets less cash) and operating liabilities (total liabilities less total debt).

◦ Cash is excluded (defined as cash and short-term investments) and debt as they measures are essentially discretion free. ("t" refers to time period and "t - 1" is the prior year).

5

Source: International Financial Statement Analysis –2nd Edition

Earnings Quality – Accrual Ratios

The first scaled measure, the balance-sheet-based accruals ratio is defined as:

From a cash flow perspective, a measure of aggregate accruals can be defined as follows:

The ratio above is the cash-flow-statement aggregate accruals.

The scaled measure is called as the cash-flow statement-based accruals ratio. This ratio is defined as follows:

Definitions – NOA -= Net Operating Assets; NI = Net Income; CFO = Cash Flow from Operations;

CFI = Cash Flow from Investing; t = current period; and t – 1 equals prior period.

6

Source: International Financial Statement Analysis –2nd Edition

Accruals ratio, B/S (NOA (t ) - NOA (t-1) )(NOA (t ) + NOA (t-1) ) /2

Aggregate accruals - Cash Flow [NI t - (CFO t + CFI t)]

Accruals Ratio - Cash Flow [NI t - (CFO t + CFI t)](NOA (t ) + NOA (t-1) ) /2

Sample Template

Honeywell International

Time PeriodDefinitionsOperating AssetsOperating LiabilitiesNOA

Net Operating Assets (Equation 17-2)Total Assets Less CashMinusTotal Liabilities Less Total Debt

Total Assets$697,239Total Liabilities$577,347

Cash$14,275Total Debt$260,804

tSolution ------------------------------------->$682,964$316,543$366,421

2013





t - 1Solution ------------------------------------->$664,496$343,635$320,861

2012

Aggregate Accruals - Balance SheetNOA tMinusNOA t - 1

(Equation 17-3)$366,421$320,861$45,560

Accruals ratio, B/S(NOA (t) - NOA (t-1) )$45,560

(NOA (t) + NOA (t-1)) /2$343,64113.26%

Accruals Ratio - Cash Flow[NI t - (CFO t + CFI t)]$39,212

(NOA (t) + NOA (t-1)) /2$343,64111.41%

Net Income t$20,829

CFO t$33,019

CFI t($51,402)

Lockheed Martin

Lockheed Martin





tSolution ------------------------------------->$682,964$316,543$366,421

2013





t - 1Solution ------------------------------------->$664,496$343,635$320,861

2012


(Equation 17-3)$366,421$320,861$45,560


(NOA (t) + NOA (t-1)) /2$343,64113.26%


(NOA (t) + NOA (t-1)) /2$343,64111.41%

Net Income t$20,829

CFO t$33,019

CFI t($51,402)

Sheet1

Sample Template






tSolution ------------------------------------->$682,964$316,543$366,421

2013





t - 1Solution ------------------------------------->$664,496$343,635$320,861

2012


(Equation 17-3)$366,421$320,861$45,560


(NOA (t) + NOA (t-1)) /2$343,64113.26%


(NOA (t) + NOA (t-1)) /2$343,64111.41%

Net Income t$20,829

CFO t$33,019

CFI t($51,402)

Aggregate accruals - Cash Flow[NI t - (CFO t + CFI t)]

Lockheed Martin

Lockheed Martin





tSolution ------------------------------------->$682,964$316,543$366,421

2013





t - 1Solution ------------------------------------->$664,496$343,635$320,861

2012


(Equation 17-3)$366,421$320,861$45,560


(NOA (t) + NOA (t-1)) /2$343,64113.26%


(NOA (t) + NOA (t-1)) /2$343,64111.41%

Net Income t$20,829

CFO t$33,019

CFI t($51,402)

Sheet1

Sample Template






tSolution ------------------------------------->$682,964$316,543$366,421

2013





t - 1Solution ------------------------------------->$664,496$343,635$320,861

2012


(Equation 17-3)$366,421$320,861$45,560


(NOA (t) + NOA (t-1)) /2$343,64113.26%


(NOA (t) + NOA (t-1)) /2$343,64111.41%

Net Income t$20,829

CFO t$33,019

CFI t($51,402)

Accruals Ratio - Cash Flow[NI t - (CFO t + CFI t)]

Lockheed Martin

Lockheed Martin





tSolution ------------------------------------->$682,964$316,543$366,421

2013





t - 1Solution ------------------------------------->$664,496$343,635$320,861

2012


(Equation 17-3)$366,421$320,861$45,560


(NOA (t) + NOA (t-1)) /2$343,64113.26%


(NOA (t) + NOA (t-1)) /2$343,64111.41%

Net Income t$20,829

CFO t$33,019

CFI t($51,402)

Sheet1

Beneish M-Score Model – Ratio Definitions

Days Receivable Index (DSRI) is:DSRI = (Net Receivablest / Salest) / Net Receivablest-1 / Salest-1)

Gross Margin Index (GMI) is:GMI = [(Salest-1 - COGSt-1) / Salest-1] / [(Salest - COGSt) / Salest]

Asset Quality Index (AQI) is:AQI = [1 - (Current Assetst + PP&Et + Securitiest) / Total Assetst] / [1 - ((Current Assetst-1 + PP&Et-1 + Securitiest-1) / Total Assetst-1)]

Sales Growth Index (SGI) is: SGI = Salest / Salest-1 Depreciation Index (DEPI) is:

DEPI = (Depreciationt-1/ (PP&Et-1 + Depreciationt-1)) / (Depreciationt / (PP&Et + Depreciationt))

SG&A Expense Index (SGAI) is:SGAI = (SG&A Expenset / Salest) / (SG&A Expenset-1 / Salest-1)

Leverage index (LVGI) is:LVGI = [(Current Liabilitiest + Total Long Term Debtt) / Total Assetst] / [(Current Liabilitiest-1 + Total Long Term Debtt-1) / Total Assetst-1]

Total Accruals to Total Assets (TATA) is:TATA = (Income from Continuing Operationst - Cash Flows from Operationst) / Total Assetst

7

Beniesh M-Score Definitions

8

Definitions Acronym

Current Year CYPrevious year PYCash CAccounts Receivable ARCost of Goods sold COGSCurrent assets CACurrent Liabilities CLWorking Capital WCDepreciation and Amortization Expense D&ADepreciation Expense DEProperty Plant and equipment PPESales, General and Administrative Expense SGATotal Assets TAIncome taxes payable TPCurrent Portion of Long-term Debt CP LT DEBTLong-Term Debt LTD

Instruction Sheet

Step #Instruction

1Enter the financial data in the shaded portion to the "M-Score - Input and Graphs" worksheet in cells C1 - L19

2The portion below the input portion of the spreadsheet should automatically calculate and populate the specific ratios that are part of the model.

3Once you have entered the data and validated that the ratios have changed you will need to compare the ratios calculated to the numbers posted in the graphs.

4If the graphs do not automatically refresh with the correct numbers you will need to right click on each graph and click on "Select Data." This should then allow the graphs to refresh with the correct data.

5Complete step 4 for each graph if necessary.

6The graph portion of the spreadsheet is pre-formatted to print 4 graphs on each page on two pages in landscape mode.

7Review the "Ratio Interpretation Worksheet" to identify if any of the ratios are a cause for concern regarding earnings quality.

&"Geneva,Bold"&14DePaul University - Finance 524Beneish M-Score Model Instruction Sheet

&"Geneva,Bold"&14&ACreated by: Larry A. Lonis, CFA

M-Score- Input and Graphs

M-score for Jean Phillippe Fragrances Inc.

The Full Beneish model for earnings manipulation detection

(Based on Eight Variables)

Step 3 - compare data in table in Step 2 to data posted in the graphs below and refresh data in each graph if needed.

(Students posts numbers in yellow shaded columns.)Step 1 - Input Data

INPUT VARIABLES2016201520142013201220112010200920082007

Net Sales$93,281$91,000$90,000$89,000$88,000$87,000$86,000$85,000$84,000$83,000

CGS$51,355$48,703$46,000$45,000$44,000$43,000$42,000$41,000$40,000$39,000

Net Receivables$1,124$970$970$970$970$970$970$970$970$970

Current Assets (CA)$72,726$67,539$67,539$67,539$67,539$67,539$67,539$67,539$67,539$67,539

PPE (Net)$1,734$1,970$1,970$1,970$1,970$1,970$1,970$1,970$1,970$1,970

Depreciation$1,597$1,322$1,322$1,322$1,322$1,322$1,322$1,322$1,322$1,322

Total Assets$85,585$84,000$83,000$82,000$81,000$80,000$79,000$78,000$77,000$76,000

SGA Expense$32,416$31,000$30,000$29,000$28,000$27,000$26,000$25,000$24,000$23,000

Net Income (before Extraordinary items)$5,658$9,038$8,500$8,000$7,500$7,000$6,500$6,000$5,500$5,000

CFO (Cash flow from operations)$7,975$2,836$2,836$2,836$2,836$2,836$2,836$2,836$2,836$2,836

Current Liabilities$26,158$22,000$21,000$25,000$26,000$20,000$19,000$18,500$18,000$17,500

Long-term Debt$485$596$596$596$596$596$596$596$596$596

Step 2 - Validate Ratios

DERIVED VARIABLES

Other L/T Assets [TA-(CA+PPE)]$11,125$14,491$13,491$12,491$11,491$10,491$9,491$8,491$7,491$6,491

2016201520142013201220112010200920082007

Days Sales in Receivables IndexDSRI1.1300.9890.9890.9890.9890.9890.9880.9880.988

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.0001.000

2016201520142013201220112010200920082007

Gross Margin IndexGMI1.0341.0521.0111.0111.0111.0121.0121.0121.012

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.0001.000

2016201520142013201220112010200920082007

Asset Quality IndexAQI0.7541.0611.0671.0741.0821.0921.1041.1191.139

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.0001.000

2016201520142013201220112010200920082007

Sales Growth IndexSGI1.0251.0111.0111.0111.0111.0121.0121.0121.012

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.0001.000

2016201520142013201220112010200920082007

Depreciation IndexDEPI0.8381.0001.0001.0001.0001.0001.0001.0001.000

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.0001.000

2016201520142013201220112010200920082007

Sales, General and Administrative Expenses IndexSGAI1.02011.02201.02301.02411.02531.02651.02791.02941.0311

YoY Change(0.0019)(0.0010)(0.0011)(0.0012)(0.0013)(0.0014)(0.0015)(0.0016)

2016201520142013201220112010200920082007

Total Accruals to Total Assets IndexTotal Accruals/Total Assets(0.0271)0.07380.06820.06300.05760.05210.04640.04060.03460.0285

YoY Change(0.1009)0.08200.08360.09370.10620.12230.14340.17250.2151

2016201420132012201120102009200820072006

Leverage IndexLVGI1.1571.0340.8340.9511.2751.0381.0131.0141.014

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.000

M = -6.065+ .823 DSRI + .906 GMI + .593 AQI + .717 SGI + .107 DEPI

M-score (5-variable model)-2.93

M = -4.84 + .920 DSRI + .528 GMI + .404 AQI + .892 SGI + .115 DEPI

-.172 SGAI + 4.679 Accrual to TA - .327 Leverage


Note: if M > -2.22, firm is likely to be a manipulator

&"Chicago,Bold"&14Beneish M-Score ModelEarnings Quality Assessment

&"Geneva,Bold"&12&A&PCreated by: Larry a. Lonis, CFA

Days Sales In Receivables Index

DSRI2016201520142013201220112010200920081.13042766137168730.989010989010989050.988888888888888930.988764044943820310.988636363636363650.98850574712643680.98837209302325590.988235294117646990.98809523809523814Upper Limit201620152014201320122011201020092008111111111

Gross Margin Index

GMI2016201520142013201220112010200920081.03413666491405841.0518213795041941.01123595505617981.01136363636363651.01149425287356331.01162790697674421.01176470588235291.01190476190476191.0120481927710843Upper Limit201620152014201320122011201020092008111111111

Asset Quality Index

AQI2016201520142013201220112010200920080.753500065252944441.06133630533230261.0670448988331841.07376823006764571.08179733128101591.09154593825729631.10362274873320821.11896155728754861.1390716816691242Upper Limit201620152014201320122011201020092008111111111

Sales Growth Index

SGI2016201520142013201220112010200920081.0250659340659341.01111111111111111.01123595505617981.01136363636363651.01149425287356331.01162790697674421.01176470588235291.01190476190476191.0120481927710843Upper Limit201620152014201320122011201020092008111111111

Depreciation Index

DEPI2016201520142013201220112010200920080.8376090193413987511111111Upper Limit201620152014201320122011201020092008111111111

Sales, General & Administrative Index

SGAI2016201520142013201220112010200920081.02010747270387661.02197802197802211.02298850574712641.02407704654895681.02525252525252531.02652519893899211.0279069767441861.02941176470588251.031055900621118YoY Change201620152014201320122011201020092008-1.8705492741455387E-3-1.0104837691042867E-3-1.0885408018304066E-3-1.1754787035684888E-3-1.2726736864667743E-3-1.3817778051938845E-3-1.5047879616965076E-3-1.6441359152354895E-30

Total Assets to Total Assets Index

Total Accruals/Total Assets201620152014201320122011201020092008-2.7072501022375416E-27.3833333333333334E-26.8240963855421694E-26.2975609756097561E-25.7580246913580248E-25.2049999999999999E-24.6379746835443041E-24.0564102564102561E-23.4597402597402599E-2YoY Change201620152014201320122011201020092008-0.100905834355708758.1950329566854899E-28.3609418308400241E-29.3701627410785249E-20.106248739934298730.122257096069868910.143369232985005510.172460922460922320.21506589528770687

Leverage Index

LVGI2016201420132012201120102009200820071.15726598896334051.03384886090016680.833560213662902890.950663771188772211.27537649645502291.03789293733414991.01319382944536061.01372227829530481.0142845660087039Upper Limit201620142013201220112010200920082007111111111

Ratio Interpretation Worksheet

Ratio DescriptionsAcronymAnalysis Observations

1Days Sales in Receivables IndexDSRIGreater than 1 indicates inflated revenue

2Gross Margin IndexGMIGreater than 1 indicates a deterioration in the margin

3Asset Quality IndexAQIGreat than 1 indicates cost deferral and a reduction in asset quality

4Sales Growth IndexSGIGreater than 1 indicates fast growth that induces manipulation

5Depreciation IndexDEPIGreater than 1 indicates upward revision of a companies PPE which increases income

6Sales, General and Administrative Expenses IndexSGAIA large increase in sales growth to SGAI indicates negative indication

7Total Accruals to Total Assets IndexTATALarge accruals are associated with earnings manipulation

8Leverage IndexLVGIGreater than 1 indicates too much leverage

DefinitionsAcronym

Current YearCY

Previous yearPY

CashC

Accounts ReceivableAR

Cost of Goods soldCOGS

Current assetsCA

Current LiabilitiesCL

Working CapitalWC

Depreciation and Amortization ExpenseD&A

Depreciation ExpenseDE

Property Plant and equipmentPPE

Sales, General and Administrative ExpenseSGA

Total AssetsTA

Income taxes payableTP

Current Portion of Long-term DebtCP LT DEBT

Long-Term DebtLTD

&"Geneva,Bold"&14M-Score AnalysisRatio Descriptions, and Analysis Observation Guidance

&"Geneva,Bold"&12&A

Ratio for PPT










DefinitionsAcronym

Current YearCY

Previous yearPY

CashC



Current assetsCA


Working CapitalWC





Total AssetsTA



Long-Term DebtLTD

Beneish M-Score Ratio Interpretation

FormulaBased on an eight factor model that gives a score.

M Score = -4.840 + 0.920 x DSRI + 0.528 x GMI + 0.404 x AQ + 0.892 x SGI + 0.115 x DEPI - 0.172 x SGAI - 0.327 x LVGI + 4.697 x TATA


9

Ratio Descriptions Acronym Analysis Observations

1 Days Sales in Receivables Index DSRI Greater than 1 indicates inflated revenue

2 Gross Margin Index GMI Greater than 1 indicates a deterioration in the margin

3 Asset Quality Index AQI Great than 1 indicates cost deferral and a reduction in asset quality

4 Sales Growth Index SGI Greater than 1 indicates fast growth that induces manipulation

5 Depreciation Index DEPI Greater than 1 indicates upward revision of a companies PPE which increases income

6 Sales, General and Administrative Expenses Index

SGAI A large increase in sales growth to SGAI indicates negative indication

7 Total Accruals to Total Assets Index TATA Large accruals are associated with earnings manipulation

8 Leverage Index LVGI Greater than 1 indicates too much leverage

Instruction Sheet

Step #Instruction

1Enter the financial data in the shaded portion to the "M-Score - Input and Graphs" worksheet in cells C1 - L19

2The portion below the input portion of the spreadsheet should automatically calculate and populate the specific ratios that are part of the model.

3Once you have entered the data and validated that the ratios have changed you will need to compare the ratios calculated to the numbers posted in the graphs.

4If the graphs do not automatically refresh with the correct numbers you will need to right click on each graph and click on "Select Data." This should then allow the graphs to refresh with the correct data.

5Complete step 4 for each graph if necessary.

6The graph portion of the spreadsheet is pre-formatted to print 4 graphs on each page on two pages in landscape mode.

7Review the "Ratio Interpretation Worksheet" to identify if any of the ratios are a cause for concern regarding earnings quality.

&"Geneva,Bold"&14DePaul University - Finance 524Beneish M-Score Model Instruction Sheet

&"Geneva,Bold"&14&ACreated by: Larry A. Lonis, CFA

M-Score- Input and Graphs

M-score for Jean Phillippe Fragrances Inc.

The Full Beneish model for earnings manipulation detection

(Based on Eight Variables)

Step 3 - compare data in table in Step 2 to data posted in the graphs below and refresh data in each graph if needed.

(Students posts numbers in yellow shaded columns.)Step 1 - Input Data

INPUT VARIABLES2016201520142013201220112010200920082007

Net Sales$93,281$91,000$90,000$89,000$88,000$87,000$86,000$85,000$84,000$83,000

CGS$51,355$48,703$46,000$45,000$44,000$43,000$42,000$41,000$40,000$39,000

Net Receivables$1,124$970$970$970$970$970$970$970$970$970

Current Assets (CA)$72,726$67,539$67,539$67,539$67,539$67,539$67,539$67,539$67,539$67,539

PPE (Net)$1,734$1,970$1,970$1,970$1,970$1,970$1,970$1,970$1,970$1,970

Depreciation$1,597$1,322$1,322$1,322$1,322$1,322$1,322$1,322$1,322$1,322

Total Assets$85,585$84,000$83,000$82,000$81,000$80,000$79,000$78,000$77,000$76,000

SGA Expense$32,416$31,000$30,000$29,000$28,000$27,000$26,000$25,000$24,000$23,000

Net Income (before Extraordinary items)$5,658$9,038$8,500$8,000$7,500$7,000$6,500$6,000$5,500$5,000

CFO (Cash flow from operations)$7,975$2,836$2,836$2,836$2,836$2,836$2,836$2,836$2,836$2,836

Current Liabilities$26,158$22,000$21,000$25,000$26,000$20,000$19,000$18,500$18,000$17,500

Long-term Debt$485$596$596$596$596$596$596$596$596$596

Step 2 - Validate Ratios

DERIVED VARIABLES

Other L/T Assets [TA-(CA+PPE)]$11,125$14,491$13,491$12,491$11,491$10,491$9,491$8,491$7,491$6,491

2016201520142013201220112010200920082007

Days Sales in Receivables IndexDSRI1.1300.9890.9890.9890.9890.9890.9880.9880.988

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.0001.000

2016201520142013201220112010200920082007

Gross Margin IndexGMI1.0341.0521.0111.0111.0111.0121.0121.0121.012

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.0001.000

2016201520142013201220112010200920082007

Asset Quality IndexAQI0.7541.0611.0671.0741.0821.0921.1041.1191.139

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.0001.000

2016201520142013201220112010200920082007

Sales Growth IndexSGI1.0251.0111.0111.0111.0111.0121.0121.0121.012

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.0001.000

2016201520142013201220112010200920082007

Depreciation IndexDEPI0.8381.0001.0001.0001.0001.0001.0001.0001.000

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.0001.000

2016201520142013201220112010200920082007

Sales, General and Administrative Expenses IndexSGAI1.02011.02201.02301.02411.02531.02651.02791.02941.0311

YoY Change(0.0019)(0.0010)(0.0011)(0.0012)(0.0013)(0.0014)(0.0015)(0.0016)

2016201520142013201220112010200920082007

Total Accruals to Total Assets IndexTotal Accruals/Total Assets(0.0271)0.07380.06820.06300.05760.05210.04640.04060.03460.0285

YoY Change(0.1009)0.08200.08360.09370.10620.12230.14340.17250.2151

2016201420132012201120102009200820072006

Leverage IndexLVGI1.1571.0340.8340.9511.2751.0381.0131.0141.014

Upper Limit1.0001.0001.0001.0001.0001.0001.0001.0001.000

M = -6.065+ .823 DSRI + .906 GMI + .593 AQI + .717 SGI + .107 DEPI


M = -4.84 + .920 DSRI + .528 GMI + .404 AQI + .892 SGI + .115 DEPI

-.172 SGAI + 4.679 Accrual to TA - .327 Leverage



&"Chicago,Bold"&14Beneish M-Score ModelEarnings Quality Assessment

&"Geneva,Bold"&12&A&PCreated by: Larry a. Lonis, CFA

Days Sales In Receivables Index

DSRI2016201520142013201220112010200920081.13042766137168730.989010989010989050.988888888888888930.988764044943820310.988636363636363650.98850574712643680.98837209302325590.988235294117646990.98809523809523814Upper Limit201620152014201320122011201020092008111111111

Gross Margin Index

GMI2016201520142013201220112010200920081.03413666491405841.0518213795041941.01123595505617981.01136363636363651.01149425287356331.01162790697674421.01176470588235291.01190476190476191.0120481927710843Upper Limit201620152014201320122011201020092008111111111

Asset Quality Index

AQI2016201520142013201220112010200920080.753500065252944441.06133630533230261.0670448988331841.07376823006764571.08179733128101591.09154593825729631.10362274873320821.11896155728754861.1390716816691242Upper Limit201620152014201320122011201020092008111111111

Sales Growth Index

SGI2016201520142013201220112010200920081.0250659340659341.01111111111111111.01123595505617981.01136363636363651.01149425287356331.01162790697674421.01176470588235291.01190476190476191.0120481927710843Upper Limit201620152014201320122011201020092008111111111

Depreciation Index

DEPI2016201520142013201220112010200920080.8376090193413987511111111Upper Limit201620152014201320122011201020092008111111111

Sales, General & Administrative Index

SGAI2016201520142013201220112010200920081.02010747270387661.02197802197802211.02298850574712641.02407704654895681.02525252525252531.02652519893899211.0279069767441861.02941176470588251.031055900621118YoY Change201620152014201320122011201020092008-1.8705492741455387E-3-1.0104837691042867E-3-1.0885408018304066E-3-1.1754787035684888E-3-1.2726736864667743E-3-1.3817778051938845E-3-1.5047879616965076E-3-1.6441359152354895E-30

Total Assets to Total Assets Index

Total Accruals/Total Assets201620152014201320122011201020092008-2.7072501022375416E-27.3833333333333334E-26.8240963855421694E-26.2975609756097561E-25.7580246913580248E-25.2049999999999999E-24.6379746835443041E-24.0564102564102561E-23.4597402597402599E-2YoY Change201620152014201320122011201020092008-0.100905834355708758.1950329566854899E-28.3609418308400241E-29.3701627410785249E-20.106248739934298730.122257096069868910.143369232985005510.172460922460922320.21506589528770687

Leverage Index

LVGI2016201420132012201120102009200820071.15726598896334051.03384886090016680.833560213662902890.950663771188772211.27537649645502291.03789293733414991.01319382944536061.01372227829530481.0142845660087039Upper Limit201620142013201220112010200920082007111111111

Ratio Interpretation Worksheet










DefinitionsAcronym

Current YearCY

Previous yearPY

CashC



Current assetsCA


Working CapitalWC





Total AssetsTA



Long-Term DebtLTD

&"Geneva,Bold"&14M-Score AnalysisRatio Descriptions, and Analysis Observation Guidance

&"Geneva,Bold"&12&A

Ratio for PPT










DefinitionsAcronym

Current YearCY

Previous yearPY

CashC



Current assetsCA


Working CapitalWC





Total AssetsTA



Long-Term DebtLTD

Streams of Expected Cash Flows - DDM

Differences in cash flow may be caused by differences in:◦ Business risk,◦ Operating risk (use of fixed assets in production), or◦ Financial risk or leverage (use of debt in the capital structure).

Three alternative definitions of cash flow:◦ Dividend discount model◦ Free cash flow model◦ Residual income model

The dividend discount model (DDM) accounts for reinvested earnings when it takes all future dividends into account.

The relative stability of dividends makes the DDM less volatile than alternative DCF models.

Dividend policy practices have international differences, and change through time even in one market.

A lower percentage of U.S. companies pay dividends. For non-dividend paying companies – analysts usually prefer a model that

defines returns at the company level (free cash flow or residual income) rather than at the stockholder level.

10

Source: Equity Asset Valuation – 3rd Edition

Streams of Expected Cash Flows - DDM

Using stylized growth patterns◦ Constant growth forever (the Gordon growth model)◦ Two-distinct stages of growth (the two-stage growth model and the H model)◦ Three distinct stages of growth (the three-stage growth model)

Forecast dividends for a visible time horizon, and then handle the value of the remaining future dividends either by:◦ Assigning a stylized growth pattern to dividends after the terminal point◦ Estimate a stock price at the terminal point using some method such as a

multiple of forecasted book value or earnings per share

The stock’s DDM value is then found by discounting the dividends (and forecasted price, if any) back to the present.

The challenge is to:◦ Choose an appropriate model for the stock’s future dividends, and ◦ Develop quality inputs to that model.

11


Streams of Expected Cash Flows – FCFF & FCFE

Free Cash Flow to the Firm (FCFF) is cash flow from operations minus capital expenditures.

Capital expenditures are defined as reinvestment in new assets and includes both fixed assets (FCI) and working capital (WCI) investment.

The value of common equity (FCFE) is the present value of FCFF (total value of the company) minus the market value of outstanding debt.

Free Cash Flow to Equity (FCFE) is cash flow from operations minus capital expenditures.

The FCFF model may be easier to apply when the company’s debt structure is expected to change significantly over time.

FCFF or FCFE can be calculated for any company. FCFE can be:◦ Used with non-dividend paying companies ◦ Viewed as what a company can afford to pay in dividends◦ Appropriate for investors who want to take a control perspective.


Streams of Expected Cash Flows – FCFF & FCFE

Defining returns as free cash flows and using the FCFE (and FCFF) models are most suitable when:◦ The company is not dividend paying◦ The company is dividend paying, but dividends significantly exceed or fall short of

free cash flow to equity.

◦ The company’s free cash flows align with the company’s profitability within a forecast horizon with which the analyst is comfortable.

◦ The investor takes a control perspective.

FCFF is a pre-debt cash flow concept FCFE is a post-debt cash flow concept

13


Forecasting Free Cash Flow – FCFF from Net Income

Free cash flow to the firm (FCFF) is the cash flow available to the firm’s suppliers of capital after all operating expenses (including taxes) have been paid and operating investments have been made. The firm’s suppliers of capital include creditors, bondholders and common stockholders (and occasionally preferred stockholders that we will ignore until later).

Free cash flow to the firm is:FCFF = Net income available to common shareholders

Plus: Net Non-Cash Charges (NCC aka DDA) (1)

Plus: Interest Expense times (1 – Tax rate)

Less: Investment in Fixed Capital (FCI)Less: Investment in Working Capital (WCI)

(1) Common non-cash charges represent depreciation, depletion, and amortization expenses, but see slide 21 for other examples.

14


Forecasting Free Cash Flow – FCFF from Net Income

This equation can be written more compactly as: (Where Inv(FC) = FCI and Inv(WC) = WCI)

FCFF = NI + NCC + Int(1 – Tax rate) – Inv(FC) – Inv(WC)or

FCFF = NI + NCC + Int(1 – Tax rate) – FCI – WCI Discussion on adjustments◦ Add back preferred stock dividends to arrive at FCFF◦ FCI can also include items such as intangible assets; e.g., trademarks◦ FCI is adjusted for cash proceeds when assets acquired in a transaction are

subsequently sold.◦ FCI – non-cash transactions (stock or debt exchanges) do not affect historical

FCFF, the analyst needs to consider this in forecasting future FCFF.◦ Working capital excludes cash, short-term debt, notes payable, and the current

portion of long-term debt. (Excluding cash this represents net borrowing.)◦ Typically changes in working capital occur in A/R, inventory, A/P and accrued

expenses.◦ Cash and Cash equivalents are excluded because the change in cash is what is

being explained.

15


FCFF and FCFE - Non-Cash Charges

The best place to find historical non-cash charges is to review the firm’s statement of cash flows.

Some common non-cash charges and the adjustments to net income to get cash flow are:


Non-Cash Item Adjustment to NI to arrive at CF Depreciation Added Back Amortization of intangibles Added Back Restructuring Charges (expense) Added Back Restructuring Charges (income resulting from reversal)

Subtracted

Losses Added Back Gains Subtracted Amortization of long-term bond discounts Added Back Amortization of long-term bond premium Subtracted Deferred taxes Added back, but calls for special attention

Non-Cash Item

Adjustment to NI to arrive at CF

Depreciation

Added Back

Amortization of intangibles

Added Back

Restructuring Charges (expense)

Added Back

Restructuring Charges (income resulting from reversal)

Subtracted

Losses

Added Back

Gains

Subtracted

Amortization of long-term bond discounts

Added Back

Amortization of long-term bond premium

Subtracted

Deferred taxes

Added back, but calls for special attention

Residual Income Models

The third definition of returns is residual income – the earnings for a given period in excess of the investor’s required rate of return on beginning-of-period investment (stockholder’s equity).

Opportunity cost for investing in the stock is the required rate of return for the highest expected rate of return investors forgo when investing in the stock.

Residual income contrasts to accounting income:◦ Attempts to match profits to the time period in which they are earned, not

necessarily realized as cash.◦ Attempts to measure the value added in excess of opportunity costs.

Residual income values a firm based on:◦ Its book value per share plus;◦ The present value of future expected earnings.

Book value per share = common stockholder’s equity divided by the number of common shares outstanding.

The residual income model can be viewed as a restatement of the dividend discount model using a company-level return concept.

17


Residual Income Models

Analyst’s can use a residual income approach for companies with negative expected free cash flows within their comfortable forecast horizon.

A detailed knowledge of accrual accounting is required in order to use the residual income model, so this is frequently the reason that analysts use the DDM’s if they can.

A high quality of earnings makes it easier to calculate residual income by making the appropriate adjustments.

The definition of returns and use of the residual income model is most suitable when:◦ The company is not paying dividends – an alternative to FCFF or FCFE◦ The company’s expected free cash flows are negative within the analyst’s forecast

horizon.

18


Price Multiples

Price multiples are ratios of a stock’s market price to some measure of fundamental value per share.

Enterprise value multiples relate the total market value of all sources of a company’s capital to a measure of fundamental value for the entire company.

The intuition behind a multiple is to determine whether a stock is:◦ Fairly valued,◦ Overvalued, or◦ Undervalued

Multiples are simple in use and ease of communication.

A multiple summarizes in a single number the relationships between the market value of a company’s stock (or its total capital) and some fundamental quantity, such as sales, earnings, or book value (owner’s equity based on accounting values).

19


Price Multiples - Key Questions to be Answered

Questions to consider in making the correct use of multiples as valuation tools:◦ What accounting issues affect particular price and enterprise value multiples, and

how can analysts address them?

◦ How do price multiples relate to fundamentals, such as earnings growth rates, and how can analysts use this information when making valuation comparisons among stocks?

◦ For which types of valuation problems is a particular price or enterprise value multiple appropriate or inappropriate?

◦ What challenges arise in applying price and enterprise value multiples internationally?

Momentum indicators typically relate either price or fundamentals (such as earnings) to the time series of its own past values or in come cases, to its expected value.

These types of indicators may provide some information on future patterns of return.

20


Price and Enterprise Value Multiples in Valuation

The method of comparables

Valuation of an asset based on multiples of comparable or similar assets.

Alternative terms for similar assets:◦ Comparables,◦ Guideline assets, or◦ Guideline companies

Choices for the benchmark value of a multiple include the multiple of a closely matched individual stock, and the average or median value of the multiple for the stock’s peer group of companies or industry.

The economic rationale underlying the method of comparables is the law of one price — the economic principle that two identical assets should sell at the same price.


Rationales for and Drawbacks of P/E ratios

Rationales which support the use of P/E multiples in valuation: Earning power is a chief driver of investment value. Earnings per share

(EPS), the denominator of the price/earnings ratio, is perhaps the chief focus of security analysts’ attention.

The price/earnings ratio is widely recognized and used by investors. Differences in price/earnings ratios may be related to differences in

long-run average returns, according to empirical research.

Drawbacks based on nature of EPS: EPS can be negative. The P/E ratio does not make economic sense

with a negative denominator. The components of earnings that are on-going or recurrent are most

important in determining intrinsic value. However, earnings often have volatile, transient components, making the analyst’s task difficult.

Management can exercise its discretion within allowable accounting practices to distort earnings per share as an accurate reflection of economic performance.

Distortions can affect the comparability of P/E ratios across companies.

22


Summary of Price and Inverse Price Ratios

23


Exhibit 3

Price Ratio Inverse price Ratio Comments

Price-to-earnings (P/E) Earnings yield (E/P) Both forms commonly used.

Price-to-book (P/B) Book-to-market (B/P)*

Book value is less commonly negative than EPS. Book-to-market is favored in research but not common in practitioner usage.(book-to-market (B/M) is more commonly used than B/P)

Price-to-sales (P/S) Sales-to-price (S/P)S/P is rarely used except when all other ratios are being stated in the form of inverse price ratios; sales is not zero or negative in practice for going concerns.

Price-to-cash flow (P/CF) Cash flow yield (CF/P) Both forms are commonly used.

Price-to-dividends (P/D) Dividend yield (D/P)

Dividend yield is much more commonly used because P/D is not calculable for non-dividend paying stocks, but both D/P and P/D are used in discussing index valuation.

Chapter 2 Slide 8

Chapter 2 slide # 8

(V0 - P0)

E(Rt)=r t +P0

Chapter 2 slide # 10


11

β U=1 + D/Eβ E=1 + (40/60)1.20.6 x 1.2 = 0.72

&"Arial,Bold"&Z&F

IBM example 3-12

Exhibit 12 IBM Corporation

YearROE %Profit Margin %Asset TurnoverFinancial Leverage

201287.515.890.886.28

201178.414.830.925.75

201064.014.850.884.90

200959.014.020.884.79

200890.811.900.958.06

200736.610.550.824.23

200633.310.380.893.62

200524.08.710.863.19

200423.67.710.873.50

200322.27.360.843.59

&"Arial,Bold"&Z&F

Sensitivty Analysis

PAGE 186

Exhibit 4-14 Sensitivity Analysis for Petrobas Valuation

VariableBase-Case EstimateLow EstimateHigh EstimateValuation with Low EstimateValuation with High Estimate

Beta1.000.751.25BRL 96.69BRL 68.92

Risk-free rate10.00%8.00%12.00%BRL 106.43BRL 64.70

Equity risk premium5.50%4.50%6.50%BRL 91.65BRL 71.73

FCFE growth rate7.30%5.00%9.00%BRL 61.50BRL 103.13

&"Arial,Bold"&Z&F

3rd Ed - Chapter 5

Page 250 - 3rd Edition Sensitivity AnalysisPage 251 Problem

Sample Problem:

Current dividend (D0)= $0.74V o = DoV o = $4.25

Expected Dividend Growth Rate (g) = 3.5%r - g[0.09 - (-0.04)]

Required Rate of Return (r)= 7.00%

Varying r and g by 25 bps results in alternate valuesInputV o = $4.25V o = $32.69

0.130

Exhibit 3Estimated Price Given Uncertain InputsBoxes

g = 3.25%g = 3.50%g = 3.75%

r =0.090

r = 6.75%$21.83$23.57$25.59g =-0.040

r = 7.00%$20.37$21.88$23.62D o4.25

r = 7.25%$19.10$20.42$21.94

p 275

2nd Edition Problem

3rd Edition Problem

Exhibit11 - Johnson & Johnson

Inputs

D 0 = $2.40g L = 6%

g s = 7.5% first 6 yearsCurrent price = $86.97

TimeD tPresent value of D t and V 6 at r = 9%Present value of D t and V 6 at r = 10%

12.58002.36702.3455

22.77352.33442.2921

32.98152.30232.2401

43.20512.27062.1891

53.44552.23932.1394

63.70392.20852.0908

73.9262

Subtotal 1(t = 1 to 6)$13.7221$13.2970

Subtotal 2(t = 7 to Infinity)$78.0347$55.4054

Total$91.76$68.70

Market Price$86.97$86.97

P 275 Term Value Calc

14Valuing a Non-Dividend-Paying Stock (First-Stage Dividend = 0)14Valuing a Non-Dividend-Paying Stock (First-Stage Dividend = 0)

Definitions:Definitions:

AD oCurrent dividend at Time = t (time period)AD oCurrent dividend at Time = t (time period)

BD n +1Current dividend at Time = t + 1 (time period)BD n +1Current dividend at Time = t + 1 (time period)

CgThe expected constant growth rateCgThe expected constant growth rate

Dr Required rate of return or cost of equityDr Required rate of return or cost of equity

EV nCurrent price of the stock, based on next year's dividend amountEV nCurrent price of the stock, based on next year's dividend amount

Assumptions:Input BoxesAssumptions:Input Boxes

ACurrent dividend (D o)$0.00ACurrent dividend (D o)$0.00

BInitial dividend at time n$3.9262BInitial dividend at time n$3.9262

CTime period in which dividend will start (years forward).7CTime period in which dividend will start (years forward).7

DTime period prior to payment of anticipated dividend payment.6DTime period prior to payment of anticipated dividend payment.6

EGrowth rate in the dividend amount (percent).0.06EGrowth rate in the dividend amount (percent).0.06

FAnnual growth rate factor 1.06FAnnual growth rate factor 1.06

GThe required rate of return is known (percent).0.09GThe required rate of return is known (percent).0.10

HRequired rate of return factor1.09HRequired rate of return factor1.10

Formula:Formula:

D n +1D n +1

V n =r -g V n =r -g

Sample Problem:Sample Problem:

D 7D 7

V 6 =r - gV 6 =r - g

$3.93$3.93

V 6 =.09 - .06V 6 =.09 - .06

$3.93$3.93

V 6 =3.00%=$130.87V 6 =4.00%=$98.16

Today's' Stock Value where r = 9%Today's' Stock Value where r = 10%

V 6V 6

V 0 =(1 + r) e 6V 0 =(1 + r) e 6

V 0 =$130.87V 0 =$98.16

(1 +.09) e 6(1 +.10) e 6

$130.87$98.16

V 0 =1.68=$78.04V 0 =1.77=$55.41

Two Stage Dividend Discount

13Valuing a Stock Using the Two-Stage Dividend Discount Model

Definitions:

AD oCurrent dividend at Time = t (time period)

BD 1Current dividend at Time = t + 1 (time period)

CgThe expected constant growth rate

Dr Required rate of return or cost of equity

EP oCurrent price of the stock

Assumptions:Input Boxes

ACurrent dividend (D o)$1.10

BGrowth rate for first 5 years (G S)11.00%

CAnnual growth rate factor 1.11

DGrowth rate long-term (G L)8.00%

ERequired rate of return ( r )10.7%

FTerminal value of the stock (T).$5.00

GPresent value discount factor1.107

Sample Problem:

Calculate the terminal value of the stock using the long-term growth rate

D o (1 + G S) exp n X (1 + G L)

V 5 =r - G L

V 5 =1.10(1.11) exp. 5 X (1.08)

0.107 - .08

V 5 =1.101.6851.08

0.027

V 5 =2.002

0.027=74.976

PV of

GrowthDiscountPresent

Time ValueDividendCalculationD t or V tFactorValues

1D 11.101.1071.2211.103

2D 21.101.2321.3551.2251.106

3D 31.101.3681.5041.3571.109

4D 41.101.5181.6701.5021.112

5D 51.101.6851.8541.6621.115

5D 574.9761.66245.101

Total$50.645

Interest-Dividend Treatment

Exhibit 4-4 IFRS versus U.S. GAAP Treatment of Interest and Dividends

IFRSU.S. GAAP

Interest ReceivedOperating or InvestingOperating

Interest PaidOperating or InvestingOperating

Dividends ReceivedOperating or InvestingOperating

Dividends PaidOperating or InvestingFinancing

Page 183Country Return (real) 7.30%

+/- Industry adjustment0.80%

+/- Size adjustment-0.33%

+/- Leverage adjustment-0.12%

Required rate of return7.65%

&"Arial,Bold"&Z&F

Chp 6 p 335

PAGE 335

Exhibit 14 Sensitivity Analysis for Petrobas Valuation


Beta1.201.001.40BRL23.68BRL16.13

Risk-free rate5.20%4.20%6.20%BRL23.19BRL16.37

Equity risk premium5.50%4.50%6.50%BRL24.20BRL15.90

FCFE growth rate6.00%4.00%8.00%BRL14.00BRL29.84

Chapter 4 Tables

Exhibit 15 FCFE Estimates for Technocrat (in Euros)

Year

1234560.9001.0801.29654.55

Sales growth rate20.00%20.00%20.00%6.00%6.00%6.00%V 0=1.124+(1.124) 2+(1.124) 3+(1.124) 3

Sales per share

Net profit margin10.00%10.00%10.00%10.00%10.00%10.00%V 0=0.801+0.855+0.913+38.415

EPS3.0003.6004.3204.5794.8545.140

lessNet FCInv per share2.5003.0003.6001.2961.7401.456V 0=40.98

lessWCInv per share1.0001.2001.4400.5180.5500.582

plusDebt financing per share1.4001.6802.0160.7260.7690.815

equalsFCFE per share0.9001.0801.2963.4913.7003.922

Growth rate of FCFE20.00%20.00%169.00%6.00%6.00%

Example 16 FCFE Estimates for Sindhuh Enterprises (per share in US dollars)

Year

20132014201520162017

Growth rate for EPS30.00%18.00%12.00%9.00%7.00%

EPS3.1203.6824.1234.4944.809

lessNet FCInv per share3.0002.5002.0001.5001.000

lessWCInv per share1.5001.2501.0000.7500.500

plusDebt financing per share1.3501.1250.9000.6750.450

equalsFCFE per share-0.0301.0572.0232.9193.759

PV of FCFE discounted at 10.4%-0.0270.8671.5041.965

Example 17 FCFE Estimates for Medina Werks (C$ in millions)

Year

123456

Sales growth rate20%16%12%10%8%7%

Net profit margin14%13%12%11%10.50%10%

Sales720.000835.200935.4241,028.9661,111.2841,189.074

Net profit100.800108.576112.251113.186116.685118.907

lessNet FCInv72.00069.12060.13456.12549.39046.674

lessWCInv30.00028.80025.05623.38620.57919.447

plusDebt financing40.80039.16834.07631.80427.98826.449

equalsFCFE39.60049.82461.13765.48074.70379.235

PV of FCFE discounted at 10.95%35.69240.47544.76343.21144.433

Exhibit 18 Forecasted FCFF for Reliant Home Furnishings

Year

12345678

Growth rate8.80%8.80%8.80%8.80%7.40%6.00%4.60%3.20%

FCFF8118829591,0441,1211,1881,2431,283

PV of FCFF discounted at 8.93%7447437427417317116835,095

&"Arial,Bold"&14&Z&F

Chapter 7

Page 370

Example 3

MeasureFull Year 2012 (a )Less First Quarter 2012(b)Three Quarters of 2012 (c = a - b)Plus First Quarter 2013 (d )Trailing 12 Months EPS ( e = c + d)

Reported EPS$4.98$1.27$3.71$0.81$4.52

Core EPS$6.41$1.81$4.60$1.41$6.01

EPS excluding 2012 legal provisions$5.07$1.28$3.79$0.81$4.60

Chapter 5 Tables

Value using the residual income model is:

Exhibit 5-1 Carrefour SAExhibit 5-2 - Bugg Properties$1.40$1.80$3.175

V 0=$6.00+($1.10)+(1.10) 2+(1.10) 3

Forecasting Book Value per share20072008Year123

Beginning book value ( B t -1)13.4615.14Beginning book value per share (B t - 1)$6.00$7.00$8.25V 0=$6.00+1.2727+1.4876+2.3854

Earnings per share forecast (E t)2.712.86Net income per-share (EPS)$2.00$2.50$4.00

Less dividend forecast (D t)(1.03)(1.06)Less Dividends per share (d)$1.00$1.25$12.25V 0=$11.15

Add change in retained earnings ( E t - D t)1.681.80Change in retained earnings (EPS - D)$1.00$1.25($8.25)

Forecast ending book value per share [(B t - 1) + (E t - D t)]15.1416.94Ending book value per share ( B t-1) + (EPS - D)$7.00$8.25$0.00

Net income per share (EPS)$2.00$2.50$4.00

Calculating the equity chargeLess per-share equity charge (r B t - 1)$0.60$0.70$0.825

Beginning ending book value per share13.4615.14Residual income (EPS - Equity charge)$1.40$1.80$3.175Value using the discounted dividend growth model is:V 0=$1.00$1.25$12.25

Multiply by cost of equity0.0930.093($1.10)+(1.10) 2+(1.10) 3

Per-share equity charge (r X B t - 1)1.251.41

V 0=$0.9091+$1.0331+$9.2036

Estimating per-share residual income

EPS forecast2.712.86V 0=$11.15

Less: equity charge1.251.41

Per-share residual income1.461.45

Page 471 3rd EditionPage 223

P 0ROE - g

Exhibit 1 Silver Wheaton CorporationB 0=r - g

Forecasting Book Value per share20132014

Beginning book value ( B t -1)8.779.65

Earnings per share forecast (E t)1.401.60

Less dividend forecast (D t)0.520.60P 0ROE - r

Add change in retained earnings ( E t - D t)0.881.00B 0=1+r - g

Forecast ending book value per share [(B t - 1) + (E t - D t)]9.6510.65

Calculating the equity charge

Beginning ending book value per share8.779.65

Multiply by cost of equity0.0910.091(ROE - r)

Per-share equity charge (r X B t - 1)0.800.88V o= B o+r - gX B o


EPS forecast1.401.60



&"Arial,Bold"&14&Z&F

Exhibit 5.7

Exhibit 5-7 Final-Stage Residual Income Persistence

Lower Residual Income PersistenceHigher Residual Income Persistence

Extreme accounting rates of return (ROE)Lower dividend payout

Extreme levels of special items (e.g., nonrecurring items)High historical persistence in the industry

Extreme levels of accounting accruals

&Z&F

Exhibit 5-11

Exhibit 11ActualForecast AForecast BForecast C

Yeart - 1tt + 1tt + 1tt + 1

Beginning Balance Sheet

Assets1,000.001,020.001,142.401,020.001,042.401,020.001,242.40

Liabilities------------------------------------------

Common stock1,000.001,000.001,000.001,000.001,000.001,000.001,000.00

Retained earnings120.00242.40120.00242.40120.00242.40

AOCI(100.00)(100.00)(100.00)(200.00)(100.00)------

Total equity1,000.001,020.001,142.401,020.001,042.401,020.001,242.40

Total liabilities and total equity1,000.001,020.001,142.40 1,020.001,042.401,020.001,242.40

Net income120.00122.40137.09122.40125.09122.40149.09

Dividends------------------------------------------

Other comprehensive income(100.00)------------(100.00)(100.00)100.00------

Exhibit 11 (Continued)ActualForecast AForecast BForecast C

Yeart - 1tt + 1tt + 1tt + 1

Ending Balance Sheet

Assets1,020.001,142.401,279.491,042.401,067.491,242.401,391.49

Liabilities------------------------------------------

Common stock1,000.001,000.001,000.001,000.001,000.001,000.001,000.00

Retained earnings120.00242.40379.49242.40367.49242.40391.49

AOCI(100.00)(100.00)(100.00)(200.00)(300.00)------------

Total equity1,020.001,142.401,279.491,042.401,067.491,242.401,391.49

Total liabilities and total equity1,020.001,142.401,279.491,042.401,067.491,242.401,391.49

Residual income calculation based on beginning total equity

Net income120.00122.40137.09122.40125.09122.40149.09

Equity charge at 10%100.00102.40114.24102.00104.24102.00124.24

Residual income20.0020.4022.8520.4020.8520.4024.85

Yearly Change in Residual Income2.450.454.45

Growth in residual income12.0%2.2%21.8%

&Z&F

Exhibit 5-12

Exhibit 12 - Forecast for Mannistore, Inc.Solution 1 - DDM

Year$0.26$0.29$0.29$0.29$0.38$68.40

Variable12345V 0=(1.10)+(1.10) 2+(1.10) 3+(1.10) 4+(1.10) 5+(1.10) 5

Shareholders' equity (t - 1)$8.58$10.32$11.51$14.68$17.86V 0$43.59

Plus: net income2.002.483.463.474.56

Less: dividends(0.26)(0.29)(0.29)(0.29)(0.38)

Less: other comprehensive income0.00(1.00)0.000.000.00

Equals: shareholders' equity$10.32$11.51$14.68$17.86$22.04Solution 2 - Part A

Net Income$2.00$2.48$3.46$3.47$4.56BV$1.14$1.45 $2.30$2.00$2.77$68.40 - $22.04

Less: (SE t - 1 X r) (where r = 10%)$0.86$1.03$1.15$1.47$1.79V 0=$8.58+(1.10)+(1.10) 2+(1.10) 3+(1.10) 4+(1.10) 5+(1.10) 5

Residual Income$1.14$1.45$2.31$2.00$2.77

V 0=$8.58+$35.84=$44.42

Solution 2A - Residual income calculationSolution 2 - Part B

Year

12345BV$1.14$0.45 $2.30$2.00$2.77$68.40 - $22.04

V 0=$8.58(1.10)+(1.10) 2+(1.10) 3+(1.10) 4+(1.10) 5+(1.10) 5

RI = NI - (Se t - 1 X r)1.141.452.302.002.77

V 0=$8.58+$35.01=$43.59

Solution 2B - Residual income calculation - adjusted for OCI

Year

12345

RI before adjustment1.141.452.302.002.77

OCI(1.00)

RI = (NI + OCI ) - (SE t - 1 X r)1.140.452.302.002.77

&Z&F

Intangible Assets

AlphaBeta

(ROE - r)

Cash1,600100V o= B o+r - gX B o

Property, plant and equipment3,400900

Total assets5,0001,000

Equity5,0001,000

Net income600150Value of Alpha

0.12 - 0.10

V o=5,000+0.10 - 0.00X5,000

V o=6,000

Alpha acquires Beta by paying Beta's shareholders 1,500 in cash

AlphaValue of Beta

Cash200

Property, plant and equipment4,3000.15 - 0.10

Lcense500V o=1,000+0.10 - 0.00X1,000

Total assets5,000

Equity5,000V o=1,500

Alpha acquires Beta by issuing stockValue of Alpha - license amortized over 10 years

Alpha0.14 - 0.10

V o=5,000+0.10 - 0.00X5,000

Cash1,700

Property, plant and equipment4,300V o=7,000

License500

Total assets6,500

Equity6,500

Value of Alpha - no amortization

0.15 - 0.10

V o=5,000+0.10 - 0.00X5,000

V o=7,500

Value of Alpha - Beta acquired for stock

0.15 - 0.10

V o=5,000+0.10 - 0.00X5,000

V o=7,500

Value of Alpha acquired with 1,500 in new stock - no amortization

0.11538 - 0.10

V o=6,500+0.10 - 0.00X6,500

V o=7,500

&Z&F

Page 242

Year

12345

RI = NI - (SE t - 1 X r)1.141.452.302.002.77

&Z&F

Exhibit 5-13

Exhibit 5-13 - 2nd Edition

International Application of Residual Income Models

Explanatory PowerCountry

40 - 50 percentGermany

Japan (Parent company reporting)

60 - 70 percentAustralia

Canada

Japan (Consolidated reporting)

United Kingdom

More than 70%France

United States

&Z&F&A

CH 7 - Example 3

Page 3703rd EditionPage 375

Example 3Exhibit 2 P/E and E/P for Five Beer Companies (as of 9/5/13 in US Dollars)

MeasureFull Year 2012 (a )Less First Quarter 2012 (b)Three Quarters of 2012 (c = a - b)Plus First Quarter 2013 (d )Trailing 12 Months EPS ( e = c + d)CompanyCurrent PriceDiluted EPS TMP/E TTME/P (%)

Molson Coors Brewing Co49.193.1415.76.38

Reported EPS$4.98$1.27$3.71$0.81$4.52

Anheuser Busch Cos.94.738.0411.88.49

Core EPS$6.41$1.81$4.60$1.41$6.01

Boston Beer Co223.574.7347.32.12

EPS excluding 2012 legal provisions$5.07$1.28$3.79$0.81$4.60

Craft Brew Alliance, Inc.12.300.02615.00.16

Mendocino Brewing Company, Inc.0.29(0.02)NM(6.90)

Example 6-3

MeasureFull Year 2008 (a )Less First Quarter 2007(b)Three Quarters of 2007 (c = a - b)Plus First Quarter 2008 (d )Trailing 12 Months EPS ( e = c + d)

Reported EPS$3.74$1.02$2.72$1.03$3.75

Core EPS$4.38$1.07$3.31$1.28$4.59

EPS excluding first quarter 2008 impairment$3.74$1.02$2.72$1.15$3.87

Page 374

Exhibit 1Taiwan Semiconductor Manufacturing Company (Currency in US Dollars)

Measure2006200720082009201020112012Avg.

EPS (ADR)$0.74$0.63$0.61$0.54$1.07$0.88$1.08$0.79

BVPS (ADR)$3.00$2.93$2.85$2.99$3.80$4.03$4.82$3.49

ROE24.7%21.5%21.4%18.1%28.2%21.8%22.4%22.6%

&Z&F&A

Exhibit 7-3

Exhibit 3

Price RatioInverse price RatioComments

Price-to-earnings (P/E)Earnings yield (E/P)Both forms commonly used.

Price-to-book (P/B)Book-to-market (B/P)*Book value is less commonly negative than EPS. Book-to-market is favored in research but not common in practitioner usage.(book-to-market (B/M) is more commonly used than B/P)

Price-to-sales (P/S)Sales-to-price (S/P)S/P is rarely used except when all other ratios are being stated in the form of inverse price ratios; sales is not zero or negative in practice for going concerns.

Price-to-cash flow (P/CF)Cash flow yield (CF/P)Both forms are commonly used.

Price-to-dividends (P/D)Dividend yield (D/P)Dividend yield is much more commonly used because P/D is not calculable for non-dividend paying stocks, but both D/P and P/D are used in discussing index valuation.

&Z&F

Ch 6 -Slide 47

&Z&F

Chapter 7 - Exhibit 20

Exhibit 20Alternative Denominators in Enterprise Value Multiples

Free Cash Flow to the Firm=Net IncomePlus interest expenseMinus tax savings on interestPlus depreciationPlus amortizationLess investment in working capital (WCI)Less investment in fixed capital (FCI)

EBITDANet IncomePlus interest expensePlus taxesPlus depreciationPlus amortization

EBITA=Net IncomePlus interest expensePlus taxesPlus amortization

EBIT=Net IncomePlus interest expensePlus taxes

Chpater 7 - Exhibit 28

Page 443

Exhibit 28 - Alternative Mean P/Es

Market CapEarningsStock(1)(2)(3)(4)

Security€ MillionsPercent€ MillionsP/EArithmetic MeanWeighted MeanHarmonic MeanWeighted Harmonic Mean

Stock 17155571.50100.5100.55100.50.10.550.1

Stock 25854529.25200.5200.45200.50.050.450.05

15 14.50.0750.0775

Arithmetic Mean15

Weighted Mean14.5(1/0.75)

Harmonic Mean13.33(1/0.775)

Weighted harmonic Mean12.90

g = 3.45%

g = 3.70%

g = 3.95%

r = 5.95%

$33.20

$36.89

$41.50

r = 6.20%

$30.18

$33.20

$36.89

r = 6.45%

$27.67

$30.18

$33.20

g = 3.45%

g = 3.70%

g = 3.95%

r = 5.95% $33.20 $36.89 $41.50

r = 6.20%

$30.18

$33.20

$36.89

r = 6.45% $27.67 $30.18 $33.20

Time t

Dt

Present Value of Dt and V6

at r = 9.5%

Present Value of Dt and V6

at r = 10.0%

1

$0.8015

$0.7320

$0.7286

2

$0.9177

$0.7654

$0.7584

3

$1.0508

$0.8003

$0.7895

4

$1.2032

$0.8369

$0.8218

5

$1.3776

$0.8751

$0.8554

6

$1.5774

$0.9151

$0.8904

7

$1.7035

6

$65.8838

$48.0805

Total

$70.8085

$52.9245

Time t D

t

Present Value of D

t

and V

6

at r = 9.5%

Present Value of D

t

and V

6

at r = 10.0%

1 $0.8015 $0.7320 $0.7286

2 $0.9177 $0.7654 $0.7584

3 $1.0508 $0.8003 $0.7895

4 $1.2032 $0.8369 $0.8218

5 $1.3776 $0.8751 $0.8554

6 $1.5774 $0.9151 $0.8904

7 $1.7035

6 $65.8838 $48.0805

Total $70.8085 $52.9245

Sheet1

Chapter 2 slide # 8

(V0 - P0)

E(Rt)=r t +P0



11

β U=1 + D/Eβ E=1 + (40/60)1.20.6 x 1.2 =0.72

IBM example 3-12

Exhibit 3-12 IBM Corporation


200630.6%10.30%0.82103.62

200524.7%8.77%0.88003.20

200429.3%8.77%0.91003.67

200330.1%8.54%0.94003.75

Sensitivty Analysis

PAGE 186



Beta1.000.751.25BRL 96.69BRL 68.92






IFRSU.S. GAAP





Page 183Country Return (real)7.30%





Chapter 4 Tables

Exhibit 4-15 FCFE Estimates for Technocrat (in Euro)

Year

1234560.9001.0801.29654.55


Sales per share


EPS3.0003.60044.3204.5794.8545.140






Example 4-17 FCFE Estimates for Sindhuh Enterprises (per share in US dollars)

Year

20082009201020112012


EPS3.1203.6824.1234.4944.809






Example 4-18 FCFE Estimates for Medina Werks (C$ in millions)

Year

123456



Sales720.000835.200935.4241,028.9661,111.2841,189.074

Net profit100.800108.576112.251113.186116.685118.907

lessNet FCInv72.00069.12060.13456.12549.39046.674

lessWCInv30.00028.80025.05623.38620.57919.447


equalsFCFE39.60049.82461.13765.48074.70379.235


Exhibit-4-19 Forecasted FCFF for Reliant Home Furnishings

Year

12345678

Growth rate8.80%8.80%8.80%8.80%7.40%6.00%4.60%3.20%

FCFF8118829591,0441,1211,1881,2431,283


Chapter 5 Tables



V 0=$6.00+($1.10)+(1.10) 2+(1.10) 3




Less dividend forecast (D t)(1.03)(1.06)Less Dividends per share (D)$1.00$1.25$12.25V 0=$11.15








V 0=$0.9091+$1.0331+$9.2036





Page 223

P 0ROE - g

B 0=r - g

P 0ROE - r

B 0=1+r - g

(ROE - r)

V 0=B 0+r - gXB 0

Exhibit 5.7






Exhibit 5-11

Exhibit 5-11ActualForecast AForecast BForecast C

Yeartt + 1tt + 1tt + 1


Assets1,000.001,020.001,142.401,020.001,042.401,020.001,242.40

Liabilities

Common stock1,000.001,000.001,000.001,000.001,000.001,000.001,000.00


AOCI(100.00)(100.00)(100.00)(200.00)(100.00)

Total equity1,000.001,020.001,142.401,020.001,042.401,020.001,242.40

Total liabilities and total equity

Net income120.00122.40137.09122.40125.09122.40149.09

Dividends

Other comprehensive income(100.00)(100.00)(100.00)100.00




Assets1,020.001,142.40

Liabilities

Common stock1,000.001,000.001,000.001,000.001,000.001,000.001,000.00


AOCI(100.00)(100.00)(100.00)(200.00)(300.00)

Total equity1,020.001,142.401,279.491,042.401,067.491,242.401,391.49



Net income120.00122.40137.09122.40125.09122.40149.09

Equity charge at 10%100.00102.40114.24102.00104.24102.00124.24

Residual income20.0020.0022.8520.4020.8520.4024.85


Exhibit 5-12

Exhibit 5-12 - Forecast for Mannistore, Inc.Solution 1 - DDM

Year$0.26$0.29$0.29$0.29$0.38$68.40

Variable12345V 0=(1.10)+(1.10) 2+(1.10) 3+(1.10) 4+(1.10) 5+(1.10) 5


Plus: net income2.002.483.463.474.56

Less: dividends(0.26)(0.29)(0.29)(0.29)(0.38)

Less: other comprehensive income0.00(1.00)0.000.000.00

Equals: shareholders' equity$10.32$11.51$14.68$17.86$22.04Solution 2 - Part A

$1.14$1.45$2.30$2.00$2.77$68.40 - $22.04

V 0=(1.10)+(1.10) 2+(1.10) 3+(1.10) 4+(1.10) 5+(1.10) 5

Solution 2A - Residual income calculationV 0=$8.58+$35.84=$44.42

Year

12345

RI = NI - (Se t - 1 X r)1.141.452.302.002.77

Solution 2 - Part B

$1.14$0.45$2.30$2.00$2.77$68.40 - $22.04

Solution 2B - Residual income calculation - adjusted for OCIV 0=(1.10)+(1.10) 2+(1.10) 3+(1.10) 4+(1.10) 5+(1.10) 5

Year

12345V 0=$8.58+$35.01=$43.59

RI = (NI + OCI )- (Se t - 1 X r)1.140.052.302.002.77

Intangible Assets

AlphaBeta

(ROE - r)

Cash1,600100V o=B o+r - gXB o

Property, plant and equipment3,400900

Total assets5,0001,000

Equity5,0001,000

Net income600150Value of Alpha

0.12 - 0.10

V o=5,000+0.10 - 0.00X5,000

V o=6,000

Alpha acquires Beta by paying Beta's shareholders 1,500 in cash

AlphaValue of Beta

Cash200

Property, plant and equipment4,3000.15 - 0.10

Lcense500V o=1,000+0.10 - 0.00X1,000

Total assets5,000

Equity5,000V o=1,000

Alpha acquires Beta by issuing stockValue of Alpha - license amortized over 10 years

Alpha0.14 - 0.10

V o=5,000+0.10 - 0.00X5,000

Cash1,700

Property, plant and equipment4,300V o=7,000

Lcense500

Total assets6,500

Equity6,500

Value of Alpha - no amortization

0.15 - 0.10

V o=5,000+0.10 - 0.00X5,000

V o=7,500

Value of Alpha - Beta acquired for stock

0.15 - 0.10

V o=5,000+0.10 - 0.00X5,000

V o=7,500

Exhibit 5-13

Exhibit 5-13

International Application of Residual Income Models

Explanatory PowerCountry

40 - 50 percentGermany

Japan (Parent company reporting)

60 - 70 percentAustralia

Canada

Japan (Consolidated reporting)

United Kingdom

More tan 70%France

United States

Chapter 6

Example 6-3

MeasureFull Year 2008 (a )Less First Quarter 2001 (b)Three Quarters of 2007 (c = a - b)Plus First Quarter 2008 (d )Trailing 12 Months EPS ( e = c + d)

Reported EPS$3.74$1.02$2.72$1.03$3.75

Core EPS$4.38$1.07$3.31$1.28$4.59

EPS excluding first quarter 2008 impairment$3.74$1.02$2.72$1.15$3.87

Exhibit 6-1

Measure2001200220032004200520062007Average

EPS (ADR)$0.08$0.12$0.28$0.58$0.59$0.74$0.63$0.43

BVPS (ADR)$1.58$1.64$1.94$2.50$2.67$3.03$3.34

ROE5.2%7.3%14.4%23.1%21.0%24.7%19.0%16.39%

Exhibit 6-2

CompanyCurrent PriceDiluted EPS (TTM)Trailing P/EE/P

Molson Coors Brewing Co.$57.72$2.9019.95.02%

Anheuser Busch Cos.$61.12$2.8321.64.63%

Boston Beer Co$40.34$0.9044.82.23%

Redhook Ale Brewery$4.50($0.14)N/M-3.11%

Pyramid Breweries$2.57($0.42)N/M-16.34%

Exhibit 6-3

Price RatioInverse price RatioComments

Price-to-earnings (P/E)Earnings yield (E/P)Both forms commonly used.

Price-to-book (P/B)Book-to-market (B/P)*Book value is less commonly negative than EPS. Book-to-market is favored in research but not common in practitioner usage.(book-to-market (B/M) is more commonly used then B/P)

Price-to-sales (P/S)Sales-to-price (S/P)S/P is rarely used except when all other ratios are being stated in the form of inverse price ratios; sales is not zero or negative in practice for going concerns.

Price-to-cash flow (P/CF)Cash flow yield (CF/P)Both forms are commonly used.

Price-to-dividends (P/D)Dividend yield (D/P)Dividend yield is much more commonly used because P/D is not calculable for non-dividend paying stocks, but both D/P and P/D are used in discussing index valuation.

Sheet8

Example 6-16

An Analysis of P/Es and Inflation

SalesTotal Assets

P 0=E 0 (1 + I)g=b X PM 0XTotal AssetsXShareholders Equity

r - I

P 0=E 0 (1 + ∂ I )=E 1

r - ∂ Ir - ∂ IExhibit 6-20Alternative Denominators in Enterprise Value Multiples

Free Cash Flow to the Firm=Net IncomePlus interest expenseMinus tax savings on interestPlus depreciationPlus amortizationLess investment in working capitalLess investment in fixed capital

P 0=E 1

(p - (1 - ∂ ) IEBITDANet IncomePlus interest expensePlus taxesPlus depreciationPlus amortization

andEBITANet IncomePlus interest expensePlus taxesPlus amortization

P 0=E 1EBITNet IncomePlus interest expensePlus taxes

E 1p + (1 - ∂ ) I

Solution 1

For Company M,1

0.03 + (1 - 0.75)0.06=22.2

For Company P,1

0.03 + (1 - 0.75)0.02=28.6

Solution 2

For Company M,1

0.03 + (1 - 0.90)0.06=27.8

For Company P,1

0.03 + (1 - 0.70)0.02=20.8

Chapte 7

MethodBasis of ValuationDLOC Expected?

GTMControlYes

(Guideline Transaction Method)

GPCMTypically minorityNo

(Guideline Public Company Method)

CCM/FCFControl or minorityDepends on cash flows

(Capitalized Cash Flow Method or Free Cash Flow Method)

Sheet6

Sheet5

Sheet4

Sheet2

Sheet3

g = 3.45%

g = 3.70%

g = 3.95%

r = 5.95% $33.20 $36.89 $41.50

r = 6.20%

$30.18

$33.20

$36.89

r = 6.45% $27.67 $30.18 $33.20

MBD000870E2.doc

g = 3.45%

g = 3.70%

g = 3.95%

r = 5.95%

$33.20

$36.89

$41.50

r = 6.20%

$30.18

$33.20

$36.89

r = 6.45%

$27.67

$30.18

$33.20

Exhibit 6-2

Company

Current Price

Diluted EPS

(TTM)Trailing P/EE/P

Molson Coors Brewing Co. $57.72$2.9019.95.02%

Anheuser Busch Cos. $61.12$2.8321.64.63%

Boston Beer Co $40.34$0.9044.82.23%

Redhook Ale Brewery $4.50($0.14)N/M-3.11%

Pyramid Breweries $2.57($0.42)N/M-16.34%

Sheet1

Chapter 2 slide # 8

(V0 - P0)

E(Rt)=r t +P0



11

β U=1 + D/Eβ E=1 + (40/60)1.20.6 x 1.2 =0.72

IBM example 3-12

Exhibit 3-12 IBM Corporation


200630.6%10.30%0.82103.62

200524.7%8.77%0.88003.20

200429.3%8.77%0.91003.67

200330.1%8.54%0.94003.75

Sensitivty Analysis

PAGE 186



Beta1.000.751.25BRL 96.69BRL 68.92






IFRSU.S. GAAP





Page 183Country Return (real)7.30%





Chapter 4 Tables

Exhibit 4-15 FCFE Estimates for Technocrat (in Euro)

Year

1234560.9001.0801.29654.55


Sales per share


EPS3.0003.60044.3204.5794.8545.140






Example 4-17 FCFE Estimates for Sindhuh Enterprises (per share in US dollars)

Year

20082009201020112012


EPS3.1203.6824.1234.4944.809






Example 4-18 FCFE Estimates for Medina Werks (C$ in millions)

Year

123456



Sales720.000835.200935.4241,028.9661,111.2841,189.074

Net profit100.800108.576112.251113.186116.685118.907

lessNet FCInv72.00069.12060.13456.12549.39046.674

lessWCInv30.00028.80025.05623.38620.57919.447


equalsFCFE39.60049.82461.13765.48074.70379.235


Exhibit-4-19 Forecasted FCFF for Reliant Home Furnishings

Year

12345678

Growth rate8.80%8.80%8.80%8.80%7.40%6.00%4.60%3.20%

FCFF8118829591,0441,1211,1881,2431,283


Chapter 5 Tables



V 0=$6.00+($1.10)+(1.10) 2+(1.10) 3




Less dividend forecast (D t)(1.03)(1.06)Less Dividends per share (d)$1.00$1.25$12.25V 0=$11.15








V 0=$0.9091+$1.0331+$9.2036





Page 223

P 0ROE - g

B 0=r - g

P 0ROE - r

B 0=1+r - g

(ROE - r)

V o=B o+r - gXB o

Exhibit 5.7






Exhibit 5-11




Assets1,000.001,020.001,142.401,020.001,042.401,020.001,242.40

Liabilities

Common stock1,000.001,000.001,000.001,000.001,000.001,000.001,000.00


AOCI(100.00)(100.00)(100.00)(200.00)(100.00)

Total equity1,000.001,020.001,142.401,020.001,042.401,020.001,242.40


Net income120.00122.40137.09122.40125.09122.40149.09

Dividends

Other comprehensive income(100.00)(100.00)(100.00)100.00




Assets1,020.001,142.40

Liabilities

Common stock1,000.001,000.001,000.001,000.001,000.001,000.001,000.00


AOCI(100.00)(100.00)(100.00)(200.00)(300.00)

Total equity1,020.001,142.401,279.491,042.401,067.491,242.401,391.49



Net income120.00122.40137.09122.40125.09122.40149.09

Equity charge at 10%100.00102.40114.24102.00104.24102.00124.24

Residual income20.0020.0022.8520.4020.8520.4024.85


Exhibit 5-12

Exhibit 5-12 - Forecast for Mannistore, Inc.Solution 1 - DDM

Year$0.26$0.29$0.29$0.29$0.38$68.40

Variable12345V 0=(1.10)+(1.10) 2+(1.10) 3+(1.10) 4+(1.10) 5+(1.10) 5


Plus: net income2.002.483.463.474.56

Less: dividends(0.26)(0.29)(0.29)(0.29)(0.38)

Less: other comprehensive

Overview of Financial Valuation Models - CFA Society Chicago · Prepared for the CFA Society...

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