20130519 第3回valuation勉強会
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Valuation in FED
2013/5/19(Sun) 1
自己紹介&Ice Break
• 名前
• 所属
• 勉強会に参加したきっかけ
2
3
Contents
• Part1 Foundations of Value
• Part2 Core Valuation Techniques
• Part3 Intrinsic Value and the Stock Market
• Part4 Managing for Value
• Part5 Advanced Valuations Issues
• Part6 Special Situations
4
Part2
6. Framework for Valuation 7. Reorganizing the Financial Statements 8. Analysand Performance and Competitive Position 9. Forecasting Performance 10. Estimating Continuing Value 11. Estimating the Cost of Capital 12. Moving from Enterprise Value to per Share 13. Calculating and Interpreting Results 14. Using Multiple
5
Part2
6. Framework for Valuation 7. Reorganizing the Financial Statements 8. Analysand Performance and Competitive Position 9. Forecasting Performance 10. Estimating Continuing Value 11. Estimating the Cost of Capital 12. Moving from Enterprise Value to per Share 13. Calculating and Interpreting Results 14. Using Multiple
6
Growth and ROIC:Drives of Value
Return on investment capital
Revenue growth
Cash flow
Cost of of Capital
Value
7
Home Depot:Enterprise DCF
Forcaset year Free cash flow($ million)
Discount factor(@ 8.5%)
Present value of FCF
(& million)2009 5,909 0.922 5,448
2010 2,368 0.850 2,013
2011 1,921 0.784 1,506
2012 2,261 0.723 1,634
2013 2,854 0.666 1,9022014 3,074 0.614 1,889
2015 3,308 0.567 1,874
2016 3,544 0.522 1,852
2017 3,783 0.482 1,822
2018 4,022 0.444 1,787Continuing value 92,239 0.444 40,966Present value of cash flow 62,694
Midyear adjustment factor 1.041 Value of operations 65,291
Value of excess cash -Value of long-term investments 361Value of tax loss carry-forwards 112Enterprise value 65,764
Less:Value of debt (11,434)Less:Value of capitalized operating leases (8,298)Equity value 46,032
Number of shares outstanding(December 2008) 1.7 Equity value per share 27.1
Forecasting performance
Can you predict the market which you belong to in business?
Let’s predict 5 years a?er in your market.
9
Determine length and detail of the forecast
• A detailed five-year to seven-year forecast,which develops complete balance sheets and income statements with as many links to real variables(e.g, unit volumes,cost per unit) as possible.
• A simplified forecast for the remaining years,focusing on a few important variables,such as revenue growth,margins,and capital turnover.
(P188)
10
Steady State
• The Company grows at a constant rate by reinvesting a constant propotion of its operating profits into the business each year
• The company earns a constant rate of return on both exsting capital and new capital invested.
(P188)
11
Non financial Companies:ROIC Decay Analysis
companies'rates of ROIC generally remain fairly stable over time.
(P77)
Exhibit4.8 (P77)
12
Revenue growth decay analysis
Growth decays very quickly;high is not sustainable for the typical company.
Exhibit5.10 (P97)
Five forces
13
Threat of new entry
Bargaining power of suppliers
The degree of rivalry among
existing competitors
Pressure from
substitute products
Bargaining power of buyers
Because the five forces differ by industry and because companies within the same industry can pursue different strategies, there can be significant variation in ROIC across and within industries.
Can companies keep their compeDDve advantages over Dme?
14
The image of traditional sustainable competitive advantage
The image of a succession of temporal competitive advantage
入山章栄(2012)『世界の経営学者はいま何を考えているのか』英治出版 P71
15
Future Cash Flow of steady state
revenue growth
margins
capital turnover
Value Driver
Past and
Future
P/L B/S
Finacials
A simplified forecast for the remaining years
16
Growth and ROIC:Drives of Value
Return on investment capital
Revenue growth
Cash flow
Cost of of Capital
Value
DCF approach to valuation
Value= FCFt=1
WACC-g
FCF=NOPLAT-Net Investment=NOPLAT-(NOPLAT× IR)=NOPLAT× (1-IR)
17
g=ROIC× IR
IR= gROIC
FCF=NOPLAT(1- gROIC
)
Value=NOPLATt=1 1-
gROIC
"
#$
%
&'
WACC-g
18
Company's earnings multiple
ValueNOPLATt=1
=1- g
ROIC!
"#
$
%&
WACC-g
NOPLAT=Invested Capital×ROIC
Value=Invested Capital×ROIC× 1- g
ROIC!
"#
$
%&
WACC-g
ValueInvested Capital
=ROIC1- g
ROICWACC-g
!
"
###
$
%
&&&
Company‘s earnings multiple is driven by both its expected growth and its return on invested capital.
19
Components of a good model
i. Raw historical data
ii. Integrated financial statements
iii. Historical analysis and forecast ratios
iv. Market data and weighted average cost of capital
v. Reorganized financial statements
vi. ROIC and FCF
vii. Valuation summary
(P190)
20
Mechanics of forecasting
1. Prepare and analyse historical financials
2. Build the revenue forecast
3. Forecast the income statement
4. Forecast the balance sheet:invested capital and nonoperating assets
5. Forecast the balance sheet:investor funds
6. Calculate ROIC and FCF
21
Mechanics of forecasting
1. Prepare and analyze historical financials
2. Build the revenue forecast
3. Forecast the income statement
4. Forecast the balance sheet:invested capital and nonoperating assets
5. Forecast the balance sheet:investor funds
6. Calculate ROIC and FCF
22
Step1Prepare and analyze historical financials
• Collecting raw date on a separate worksheet
• Building the integrated financials,and deciding wether to aggregate immaterial line items.
• Making sure never to combine operating and nonoperating accounts into a single category.
23
Step1Prepare and analyze historical financials
2007 2008
Balance Sheet
Accounts payable and other liabilities 16,676 17,587
Advances in excess of related costs 13,847 12,737
Income taxes payable 253 41
Short-term debt and current portion of long-term debt 762 560
Current liability 31,538 30,925
From note11:Liabilities,commitments,and contingencies
Accounts payable 5,714 5,871
Accrued compensation and employee benefit costs 4,996 4,479
Product warranty liabilities 962 959
Environmental remediation 679 731
Forward loss recognition 607 1458
Other liabilities 3,718 4,089
Accounts payable and other liabilities 16,676 17,587
(P192 exhibit 9.2)
■Boeing Company: Current liabilities in Balance Sheet
24
Mechanics of forecasting
1. Prepare and analyze historical financials
2. Build the revenue forecast
3. Forecast the income statement
4. Forecast the balance sheet:invested capital and nonoperating assets
5. Forecast the balance sheet:investor funds
6. Calculate ROIC and FCF
25
Step2Build the revenue forecast
Using the company's own forecasts of demand from existing customers,customers turnover,and the potential bounds for the forecast.
Estimating revenues by sizing total market,determining market share,and forecasting prices.
bottom up approach
Top down forecast
26
Mechanics of forecasting
1. Prepare and analyze historical financials
2. Build the revenue forecast
3. Forecast the income statement
4. Forecast the balance sheet:invested capital and nonoperating assets
5. Forecast the balance sheet:investor funds
6. Calculate ROIC and FCF
27
Step3Forecast the income state
1st
2nd
3rd
Decide what economic relationship drive line item.
Estimate
the forecast ratio
Multiply
the forecast ratio by an estimate of its driver
Partial Forecast of Income Statement
28
Exhibit9.3 (P195)
29
Typical forecast drivers for the income statement
Line item Typical
forecast driver Typical forecast ratio
Operating
Costs of goods and sold(COGS)
Revenue COGS/revenue
Selling,general,and administrative(SG&A)
Revenue SG&A/revenue
Depreciation Prior-year net PP&E Depreciation_t/net PP&E_t-1
Nonoperating
Nonoperating income Appropriate nonoperating asset,if any
Nonoperating income/nonoperating asset or growth in nonoperating income
interest expense Prior-year total debt Interest expense_t/total debt_t-1
interest income Prior-year excess cash Interest income_t/excess cash_t-1
(P196 exhibit 9.4)
30
Completed Forecast of the Income Statement
Forecast Forecast
percent 2009 2010 $million 2009 2010
Revenue growth 20 20 Revenues 240 288
COGS/revenues 37.5 37.5 COGS -90 -108
S&GE/revenues 18.8 18.8 S&GE -45 -54
Depreciation_t/net PP&E_t-1 9.5 9.5 Depreciation -19 -24
EBITA/revenue 35.8 35.8 EBITA 86 102
Interest rate Interest expense -23 -22.2
Interest expense 7.6 7.6 Interest income 5 3.0
Interest income 5 5 Nonoperating income 4 5.3
Earnings before taxes 72 88.2
Nonoperating items
Nonoperating income growth 33.3 33.3 Provision for income taxes -24 -29.7
Net income 48 58.8
Taxes
Operating tax rate 34.4 34.4
Statutory tax rate 40 40
Average tax rate 33.3 33.6
(P197 exhibit9.5)
31
Mechanics of forecasting
1. Prepare and analyze historical financials
2. Build the revenue forecast
3. Forecast the income statement
4. Forecast the balance sheet:invested capital and nonoperating assets
5. Forecast the balance sheet:investor funds
6. Calculate ROIC and FCF
Stock versus flow example
32
Year1 Year2 Year3 Year4
Revenue(dollars) 1,000 1,100 1,200 1,300
Accounts receivable(dollars) 100 105 117 135
Stock method
Accounts receivable as % of revenues(%) 10 9.5 9.8 10.4
Flow method
Change in accounts receivable as % of the change in revenues(%) - 5 12 18
Exhibit9.8 P201
• When you forecast the balance sheet, one of the first issues you face is whether to forecast the line items in the balance sheet directly(in stocks) or indirectly by forecasting changes(in flows)
• The relationship between the balance sheet accounts and revenues is more stable than that between balance sheet changes and changes in revenues.
33
Typical forecast drivers for the balance sheet
Line item Typical forecast driver Typical forecast ratio
Operating line items
Accounts receivable Revenues Accounts receivable/Revenues
Inventories Cost of goods sold Inventories/COGS
Accounts payable Cost of goods sold Accounts payable/COGS
Accrued expense Revenues Accrued expense/Revenues
Net PP&E Revenues Net PP&E/Revenues
Goodwill and acquired intangibles
Acquired revenues Goodwill and acquired intangibles/Acquired revenues
Nonoperating line items
Nonoperating assets None Growth in nonoperating assets
Pension assets or liabilities
None Trend toward zero
Deferred taxes Operating taxes or corresponding balance sheet item
Change in operating deferred taxes/operating taxes, or deferred taxes/corresponding balance sheet item
(P202 exhibit 9.9)
34
Typical forecast drivers for the balance sheet
• Nonoperating assets
• Operating working capital
– estimating most line items as a percentage of revenues or in day's sales.
• Property,plant,and equipment
• Goodwill and acquired intangibles
• Nonoperating assets,debt and equity equivalents
35
Forecast balance sheet Sources of financing (P206 exhibit 9.12)
Assets 2008 2009 2010 2010
Operating cash 5 5 6 6
Excess cash 100 60 35.8
Inventory 35 45 54 54
Current assets 140 110 95.8
Net PP&E 200 250 300 300
Equity investments 100 100 100 100
Total Assets 300 350 400
Liabillity
Accounts payable 15 20 24 24
Short-term debt 224 213 213 213
Current liabilities 239 233 237 237
Long term debt 80 80 80 80
Newly issued debt 0 0 0 0
Common stock 65 65 65 65
Retained earnings 56 82 113.8 113.8
Total liabilities and equity 440 460 495.8
Completed
Forcast Balance Sheet:Sources of Financing
Step1
• Determine retained earnings using the clean surplus relationship,forecast exsiting debt using contractual terms,and keep common stock constant.
Step2 • Test which is higher,assets excluding excess cash,or
liabilities and equity excluding newly issued debt.
Step3
• If assets excluding excess cash are higher,set excess cash equal to zero,and plug the difference with newly issued debt.Otherwise,plug with excess cash.
36
37
Mechanics of forecasting
1. Prepare and analyze historical financials
2. Build the revenue forecast
3. Forecast the income statement
4. Forecast the balance sheet:invested capital and nonoperating assets
5. Forecast the balance sheet:investor funds
6. Calculate ROIC and FCF
38
Calculate ROIC and FCF
• Once you have completed your income statement and balance sheet forecasts,calculate ROIC and FCF.
• For companies that are creating value,futures ROICs should fit one of three general patterns:
– ROIC should either remain near current levels,trend toward an industry or economic median,or trend to the cost of capital.
Additonal Issues
39
Nonfinancial Operating Drivers
Fixed versus Variiables
Costs
In industries where prices are changing or technology is advancing,forecasts should incorporate nonfinancial ratios,such as volume and productivity
Inflation
Since corporate valuation is about long-run profitability and growth,nearly every cost should be treated as variables.
When inflation exceeds 5% annuallyhistorical analysis,historical financials should be adjusted to reflect operating performance independent of inflation.
40
Part2
6. Framework for Valuation 7. Reorganizing the Financial Statements 8. Analysand Performance and Competitive Position 9. Forecasting Performance 10. Estimating Continuing Value 11. Estamting the Cost of Capital 12. Moving from Enterprise Value to per Share 13. Calculating and Interpreting Results 14. Using Multiple
41
Mechanics of forecasting
1. Prepare and analyse historical financials
2. Build the revenue forecast
3. Forecast the income statement
4. Forecast the balance sheet:invested capital and nonoperating assets
5. Forecast the balance sheet:investor funds
6. Calculate ROIC and FCF
What is the reason for high PER?
42
Home Depot:Enterprise DCF
Forcaset year Free cash flow($ million)
Discount factor(@ 8.5%)
Present value of FCF
(& million)2009 5,909 0.922 5,448
2010 2,368 0.850 2,013
2011 1,921 0.784 1,506
2012 2,261 0.723 1,634
2013 2,854 0.666 1,9022014 3,074 0.614 1,889
2015 3,308 0.567 1,874
2016 3,544 0.522 1,852
2017 3,783 0.482 1,822
2018 4,022 0.444 1,787Continuing value 92,239 0.444 40,966Present value of cash flow 62,694
Midyear adjustment factor 1.041 Value of operations 65,291
Value of excess cash -Value of long-term investments 361Value of tax loss carry-forwards 112Enterprise value 65,764
Less:Value of debt (11,434)Less:Value of capitalized operating leases (8,298)Equity value 46,032
Number of shares outstanding(December 2008) 1.7 Equity value per share 27.1
Estimating Continuing Value
43
Defining company's value
Value=
Present Value of Cash Flow during Explicit Forecast Period
Present Value of Cash Flow after Explicit Forecast Period
+
• To estimate a company's value,separate a company's expected cash flow into two period.
• A thoughtful estimate of continuing value is essential to any valuation,because continuing value often accounts for a large percentage of a continuing value.
44
Continuing Value as a Percentage of total value
• Continuing value accounts for 56% to 125% of total value. • These large percentage do not necessarily mean that most of a company's value will be created in the continuing-value period.
56
81
0
-25
44
19
100
125
Tabaco Sporting goods Skin care High tech
Forecast period cash flow Continuing value
45
Continuing value by using the value driver formula in Chapter2
• NOPLAT_t+1=net operating profit less adjusted taxes in the first year after the explicit forecast period
• g=expected growth rate in NOPLAT in perpetuity
• RONIC=expected rate of return on new invested capital
• WACC=weighted average cost of capital
gWACCRONIC
g1NOPLATValue Continuing
1t
−
⎟⎠
⎞⎜⎝
⎛ −=
+
DCF approach to valuation
Value= FCFt=1
WACC-g
FCF=NOPLAT-Net Investment=NOPLAT-(NOPLAT× IR)=NOPLAT× (1-IR)
46
g=ROIC× IR
IR= gROIC
FCF=NOPLAT(1- gROIC
)
Value=NOPLATt=1 1-
gROIC
"
#$
%
&'
WACC-g
47
CV = 501.11
+531.11( )2
+561.11( )3
++50(1.06)149(1.11)150
CV = 999
000,1CV%6%11
50CV
=−
=
000,1CV%6%11%12%61100
CV
=−
⎟⎠
⎞⎜⎝
⎛ −=
Comparing the methods of computingcontinuing value
Discounting a long forecast(150 years)
Using the growth free cash flow(FCF) perpetuity formula
Using the value driver formula
48
Tehnical considerations
NOPLAT
RONIC
Growth rate
WACC
The level of NOPLAT should be based on a normalized level of revenuews and sustainabel margin and ROIC.
The expected rate of return on RONIC should be consistent with expected competitive conditions.
Few companies can be expected to grow faseter than the economy for long periods.
WACC should incorporate a sustainable capital structure.
49
Economic Profit approach
( )
WACC
WACCRONICRONIC
NOPLAT)Profits cPV(Economi
such thatgWACC
)2tProfits csPV(Economi
WACCWACC)-IC(ROIC
1]Year t beyond ofitsEconomicPr1Year tin Profits EconomicCV
1t
2t
t
−⎟⎠
⎞⎜⎝
⎛
=
−++=
+++=
+
+
g
Value= Invested Capital at Beginning of Forecast
Present Value of Forecast Economic Profit during Explicit Forecast Period
+
Present Value of Forecast Economic Profit after Explicit Forecast Period
+
50
Comparison of Total-valueEstimates using different forecast horizons
Years 1-5 Years 6+
Growth 9 6
RONIC 16 12
WACC -12 -12
Spread 4 0
Modeling assumptions
As the explicit forecast horizon grows longer,value shifts from the continuing value to the explicit forecast period, but the total value always remain the same.
100% = $893 $893 $893 $893 $893
Continuing value
value of exlplict free cash flow
21 33
40
54 65
79 67
60
46 35
5 8 10 15 20
Exhibit10.3 (P219)
185
358 364
1050
877
104
767
Free Cash flow model Business components approach Economic profit approach
51
Comparison of Continuing value approaches
(15%)
Value of years 1-9 free cash flow
(71%)
Base business Present value of continuing value
(85%)
(29%) New product line Economic-profit
continuing value (30%)
Present value of years 1-9 economic profit (8%)
Invested capital (62%)
52
Common Piatfalls
• Naive Base year extrapolation
• Naive Overconservatism
• Purposeful Overconservatism
53
Evaluating other approachesto continuing value
• Other DCF Approaches – convergence formula
• Non Cash flow Approaches
– multiples,liquidation value,Replacement cost
• Advanced formulas for continuing value
– two periods with different growth and ROIC assumption
54
Technique Assumptions Continuing value
Book value Per accounting records 268
Liquidation value 80% of working capital 186
70% of net fixed assets
Price to earnings ratio Industry average of 15× 624
Market to book ratio Industry average of 1.4× 375
Replacement cost Book value adjusted for inflation 275
Perpetuity based on final year's cash flow
Normalized FCF growing at inflation rate 428
Continuing value estimatesfor a Sporting goods company
55
Part2
6. Framework for Valuation 7. Reorganizing the Financial Statements 8. Analysand Performance and Competitive Position 9. Forecasting Performance 10. Estimating Continuing Value 11. Estamting the Cost of Capital 12. Moving from Enterprise Value to per Share 13. Calculating and Interpreting Results 14. Using Multiple
56
Growth and ROIC:Drives of Value
Return on investment capital
Revenue growth
Cash flow
Cost of of Capital
Value
57
Mechanics of forecasting
1. Prepare and analyse historical financials
2. Build the revenue forecast
3. Forecast the income statement
4. Forecast the balance sheet:invested capital and nonoperating assets
5. Forecast the balance sheet:investor funds
6. Calculate ROIC and FCF
How do you justify the relationship of high risk and high return?
58
Weighted Average Capital Cost
The opportunity cost that investors face for investing their funds in one particular business instead of others with similar risk.
59
Criteria of cost of capital
• It must include the opportunity costs of all investors-debt,equity,and so on-since free cash flow is available to all investors,who expect compenstion for the risks they take.
• It must weight each security's required return by its target marked-based weight,not by its historical book value.
• Any financing-related benefits or costs,such as interest tax shields,not included in free cash flow must be incorporated into the cost of capital or valued separately using adjusted present value.
• It must be computed after corporate taxes(since free cash flow is calculated in after-tax terms)
• It must be based on the same expectations of inflation as those embedded in forecasts of free cash flow.
• The duration of the securities used to estimate the cost of capital must match the duration cash flows.
60
Weighted Average Capital Cost
=
=
=
=
=
+−=
m
e
d
emd
TkkVEVD
kKETk
VDWACC
//
)1(
target level of debt to enterprise value using market-based(not book)values
target level of equity to enterprise value using market-based values
cost of debt
cost of equity
company's marginal income tax rate
61
Weighted Average Capital Cost
Components Methodology Data requirements
Cost of equity CAPM
Risk Free Use a long-term government rate denominated in same currency as cash flows.
Market risk premium
The market risk premium is difficult to measure.Various models point to risk premium between 4.5% and 5.5%
Company beta To estimate beta, lever the company's industry beta to company's target debt-equity ratio.
After tax cost of debt
Expected return proxied by yield to maturity on long- term debt
Risk Free Use a long-term government rate denominated in same currency as cash flows.
Default spread Default spread is determined by company's bond rating and amount of physical collateral
Marginal tax rate
In most situations,use company's statutory tax rate.The marginal tax rate should match marginal tax rate used to forecast net operating profit less adjusted taxes(NOPLAT)
Capital structure Proportion of debt and equity to enterprise value
Measure debt and equity on a market,not book,basis.
Use a forward-looking target capital structure
(exhibit11.1 P237)
62
Source of capital
Proportion of total capital
Cost of capital
Marginal tax rate
After-tax opportunity
cost
Contribution to weighted
average
Debt 31.5 6.8 37.6 4.2 1.3
Equity 68.5 10.4 10.4 7.1
WACC 100 8.5
Home Depot: Weighted Average Cost of Capital
・The company's cost of equity was estimated using the CAPM,which led to a cost of equity of 10.4%.
63
Estimating the cost of equity
• Capital Asset Pricing model
• Fama-French three factor model
• The arbitrage pricing theory(APT)
64
Estimating the cost of equity
• Capital Asset Pricing model
• Fama-French three factor model
• The arbitrage pricing theory(APT)
65
Capital Asset Pricing model
[ ]fmifi rRErRE −+= )()( β
market theofreturn expected)( themarkety tosensitivit sstock'
rate freerisk security ofreturn expected)(
=
=
=
m
i
f
i
RE
riRE
=β
66
General conclusion regarding CAPM
• To estimate the risk-free rate in developed economies,use highly liquid,long term government securities,such as the 10 year zero-coupon STRIPS.
• Based on historical averages and forward-looking estimates,the appropriate market risk premium is between 4.5% and 5.5%.
• To estimate a company's target capital structure.Company-specific betas vary too widely over time to be used reliable.
67
[CAPM]Estimating the risk free rate
• Ideally,each cash flow should be discounted using a government bond with the same matuirty.
• In reality,few practitioners discount each cash flow using a matched maturity.
• For US based corporate valuation,the most common proxy is 10 year government STRIPS.
68
[CAPM]Estimating the market risk premium
• Estimating the future risk premium by measuring and extrapolating historical returns.
• Using regression analysis to link current market variables,such as the aggregate dividend-to-price ratio,to project the expected market risk premium.
• Using DCF valuation,along with estimates of return on investment and growth,to reverse engineer the markets cost of capital.
69
[CAPM]Estimating beta
εβα ++= mRRi
• In the market model, the stock's return(Ri) ,not, price regressed against the market's return. • The measurement period for raw regressions should include at least 60 data point. • Raw regressios should be on monthly returns. • Company stock returns should be regressed against a value-weighted,well-diversified market portfolio.
70
Estimating the cost of equity
• Capital Asset Pricing model
• Fama-French three factor model
• The arbitrage pricing theory(APT)
71
Fama-French Three factor model
• Given the strength of Fama French's empirical results,the academic community now measures risk with a model commonly known as the Fama-French three-factor model.
• With this model, a stock's excess returns are regressed on – excess market returns(similar to the CAPM), – the excess returns of small stocks over big stocks(SMB), – excess returns of high book to market stocks over low
book to market stocks(HML).
72
Home Depot: Weighted Average Cost of Capital
Factor Average monthly
premium (percent)
Average annual
premium (percent)
Regression coefficient
Contribution to expected
return (percent)
Market portfolio 5.4 1.39 7.5
SMB portfolio 0.23 2.8 (0.09) (0.3)
HML portfolio 0.4 5.0 (0.14) (0.7)
Premium over risk-free rate 6.6
Risk free rate 3.9
Cost of equity 10.5
1 SMB and HML premiums based on average monthly returns date, 1926-2009. 2 Based on monthly returns date, 2002-2006. 3 Summation rounded to one decimal point.
73
Estimating the cost of equity
• Capital Asset Pricing model
• Fama-French three factor model
• The arbitrage pricing theory(APT)
74
Arbitrage Pricing Theory
• In the APT,a security's actual returns are generated by k factors and random noise.
• On paper,the theory is extremely powerful.
• In practice,implementation of the model has been tricky,as there is little agreement about how many factors there are,what the factors represent,or how to measure the factors.
kkft rRE λβλ+・・・+βλβλβλβ +++++= 4321)(
75
Estimating the after tax cost of debt
• To estimatet,the cost of debt for investment-grade companies,use the yeild to maturity of company's long-term,option-free bonds.
• Technically speaking,yield to maturity is only a proxy for expected return,because the yield is actually a promised rate of return on company's debt.
• For companies with below investment grade debt,we recommend using adjusted present value(AVP) based on the unlevered cost of equity rather than the WACC to value the company.
76
Adjusted present value model(APV)
Adjusted
Present Value
Enterprise Value
as if company was
All-equity-Financed
Present Value of
Tax Shields
= +
The APV valuation model follows directly from the teachings of economists Franco Modigliani and Merton Miller,who proposed that in a market with no taxes, a company choice of financial structure will not affect the value of its economic assets.
77
Process of AVP in detail
1. Valuing free cash flow at unlevered cost of capital
2. Determining the unlevered cost of capital with market data
3. Choosing the appropriate formula.
4. Valuing tax shields and other capital structure effects.
78
Bond Ratings and Yield to Maturity
N)YTM1(CouponFace
)YTM1(Coupon
)YTM1(CouponPrice 2 +
++
++
+= ・・・
• To solve for yeild to maturity,reverse enginieer the discount rate required to set the present value of bond's promised cash flow equal to its price.
• To determine a company's bond rating,a rating agency will examine the company's most recent financial ratios,analyze the company's competitive environment,and interview senior management.
• Using the company's bond ratings to detemine the yield to maturity is a good alternative to calculating the yeild to maturity directly.
79
Trade time Trade volume ($thousand) Bond Price (dollars) Yield (percemt)
16:15:51 29 78.75 7.75
16:15:51 29 78.75 7.75
14:48:00 5 78.00 7.83
14:03:19 110 81.85 7.43
12:08:43 2,000 80.06 7.62
12:08:00 2,000 80.06 7.62
12:08:00 2,000 80.00 7.62
12:08:00 2,000 80.06 7.62
12:06:22 2,000 80.25 7.60
Home Depot bond yield 7.62
30-year U.S. Treasury yield (4.39)
Home Depot default premium 3.23
Home Depot: Trading Data on Corporate Debt
80
Maturity(years)
Rating 1 2 3 5 7 10 30
Aaa/AAA 36 59 55 69 82 58 139
Aa2/AA 154 140 150 160 168 139 179
A1/A+ 159 153 166 169 168 139 182
A2/A 183 178 192 193 189 152 190
A3/A- 195 194 213 210 210 177 199
Baa1/BBB+ 324 310 336 333 325 288 320
Baa2/BBB 332 315 340 338 328 292 324
Baa3/BBB- 402 408 425 433 421 380 416
Ba2/BB 559 583 586 590 578 545 577
B2/B 870 916 913 925 909 878 904
Yield Spread over U.S. Treasuries by Bond Rating, May 2009
Basis points
81
Using target weights to determine the cost of capital
• Estimate the company's current market-value-based capital structure.
• Review the capital structure of comparable companies.
• Review management's implicit or explicit approach to financing the business and its implications for the target capital structure.
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