chapter 18 equity valuation. mcgraw-hill/irwin © 2004 the mcgraw-hill companies, inc., all rights...
TRANSCRIPT
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Fundamental Stock Analysis: Models of Equity
Valuation
• Basic Types of Models• Balance Sheet Models• Dividend Discount Models• Price/Earning Ratios
• Estimating Growth Rates and Opportunities
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Dividend Discount Models:General Model
VD
ko
t
tt
( )11
VD
ko
t
tt
( )11
• V0 = Value of Stock• Dt = Dividend• k = required return
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
No Growth Model
VD
ko
• Stocks that have earnings and dividends that are expected to remain constant
• Preferred Stock
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
No Growth Model: Example
E1 = D1 = $5.00
k = .15
V0 = $5.00 / .15 = $33.33
VD
ko
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Constant Growth Model
VoD g
k g
o
( )1Vo
D g
k g
o
( )1
• g = constant perpetual growth rate
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Constant Growth Model: Example
VoD g
k g
o
( )1Vo
D g
k g
o
( )1
E1 = $5.00b = 40% k = 15%
(1-b) = 60% D1 = $3.00 g = 8%
V0 = 3.00 / (.15 - .08) = $42.86
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Estimating Dividend Growth Rates
g ROE b g ROE b
• g = growth rate in dividends
• ROE = Return on Equity for the firm
• b = plowback or retention percentage rate• (1- dividend payout percentage rate)
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Estimating Growth via historical info.
• Dividend in 2000 was $1.
• Dividend in 2006 was $1.80
• Growth is (1.80/1)^(1/6)-1 = 10.29%
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Specified Holding Period Model
01
12
2
1 1 1V D
kDk
D Pk
N NN
( ) ( ) ( )...
• PN = the expected sales price for the stock at time N
• N = the specified number of years the stock is expected to be held
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Partitioning Value: Growth and No Growth Components
VE
kPVGO
PVGOD g
k g
E
k
o
o
1
11( )
( )
VE
kPVGO
PVGOD g
k g
E
k
o
o
1
11( )
( )
• PVGO = Present Value of Growth Opportunities
• E1 = Earnings Per Share for period 1
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Partitioning Value: Example
• ROE = 20% d = 60% b = 40%
• E1 = $5.00 D1 = $3.00 k = 15%
• g = .20 x .40 = .08 or 8%
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
V
NGV
PVGO
o
o
3
15 0886
5
1533
86 33 52
(. . )$42.
.$33.
$42. $33. $9.
V
NGV
PVGO
o
o
3
15 0886
5
1533
86 33 52
(. . )$42.
.$33.
$42. $33. $9.
Partitioning Value: Example
VVoo = value with growth = value with growth
NGVNGVoo = no growth component value = no growth component value
PVGO = Present Value of Growth OpportunitiesPVGO = Present Value of Growth Opportunities
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
A much better model is to apply discount models to FCFE which may more accurately reflect a firms value.
FCFE = Net Income + depreciation – Cap. Expend. – change in working capital – principal debt repayments + new debt issues.
Apply model as per usual.
Free Cash Flow to Equity
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
• If the firm finances a fixed percentage of its capital spending and investments in working capital with debt, the calculation of FCFE is simplified. Let DR be the debt ratio, debt as a percentage of assets. In this case, FCFE can be written as
• FCFE = NI – (1 – DR)(Capital Spending + change in Working Capital – Depreciation)
• When building FCFE valuation models, the logic, that debt financing is used to finance a constant fraction of investments, is very useful. This equation is pretty common.
Free Cash Flow to Equity
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
http://faculty.etsu.edu/trainor/FNCE%203300/Lowes.doc
Another interesting site you may want to use:
http://caps.fool.com/Ticker.aspx?source=icaedilnk9950012&ticker=LOW
Let’s look at an example
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
• FCFF = EBIT(1-tax rate) + Dep. – Cap. Expenditures – Change in WC – Change in other assets.
• Again, proceed as normal(replace dividends with FCFF) but discount at firms cost of capital.
• You find value of firm. To find value of equity, simply subtract off debt.
Free Cash flow to the Firm
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Price Earnings Ratios
• P/E Ratios are a function of two factors• Required Rates of Return (k)• Expected growth in Dividends
• Uses• Relative valuation• Extensive Use in industry
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
P/E Ratio: No expected growth
PE
kP
E k
01
0
1
1
PE
kP
E k
01
0
1
1
• E1 - expected earnings for next year
• E1 is equal to D1 under no growth
• k - required rate of return
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
P/E Ratio with Constant Growth
)(
1
)(
)1(
1
0
110
ROEbk
b
E
P
ROEbk
bE
gk
DP
)(
1
)(
)1(
1
0
110
ROEbk
b
E
P
ROEbk
bE
gk
DP
• b = retention ration• ROE = Return on Equity
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Numerical Example: No Growth
E0 = $2.50 g = 0 k = 12.5%
P0 = D/k = $2.50/.125 = $20.00
PE = 1/k = 1/.125 = 8
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Numerical Example with Growth
b = 60% ROE = 15% (1-b) = 40%
E1 = $2.50 (1 + (.6)(.15)) = $2.73
D1 = $2.73 (1-.6) = $1.09
k = 12.5% g = 9%
P0 = 1.09/(.125-.09) = $31.14
PE = 31.14/2.73 = 11.4
PE = (1 - .60) / (.125 - .09) = 11.4
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Pitfalls in Using PE Ratios
• Flexibility in reporting makes choice of earnings difficult
• Pro forma earnings may give a better measure of operating earnings
• Problem of too much flexibility
McGraw-Hill/Irwin © 2004 The McGraw-Hill Companies, Inc., All Rights Reserved.
Other types of Valuation
• Use Price/sales
• Price/Cash flow
• All relative valuation models rely on the market to be fairly valued. What is a good Price/Sales ratio? Relies on comparisons which may or may not be valued accurately.