VALUATION
Terminology
Equity value
– Market value of shareholders’ equity (shares outstanding x
current stock price)
Enterprise value
– Market value of all capital invested in the firm
• Equity, debt (short-term and long-term), preferred stock, minority
interest
Assets
Liabilities
Equity
Enterprise
Value
=
Debt
Preferred Stock
Minority Interest
What is Value?
 In general, the value of an asset is the price that a willing and
able buyer pays to a willing and able seller
 Note that if either the buyer or seller is not both willing and
able, then an offer does not establish the value of the asset
 There are several types of value, of which we are concerned
with four:
– Book Value – The carrying value on the balance sheet of the firm’s
equity (Total Assets less Total Liabilities)
– Tangible Book Value – Book value minus intangible assets
(goodwill, patents, etc)
– Market Value - The price of an asset as determined in a competitive
marketplace
– Intrinsic Value - The present value of the expected future cash
flows discounted at the decision maker’s required rate of return
DIVIDEND DISCOUNT
MODELS
Common Stock Valuation
 As with any other security, the first step in valuing common
stocks is to determine the expected future cash flows.
 Finding the present values of these cash flows and adding
them together will give us the value:

CFt
VCS  
t
t 1 1  k 
 For a stock, there are two cash flows:
– Future dividend payments
– The future selling price
Common Stock Valuation: An Example
 Assume that you are considering the purchase of a stock
which will pay dividends of $2 (D1) next year, and $2.16 (D2)
the following year. After receiving the second dividend, you
plan on selling the stock for $33.33. What is the intrinsic
value of this stock if your required return is 15%?
?
VCS 
33.33
2.16
2.00
2.00
1.15
1

2.16  33.33
1.15
2
 28.57
The Dividend Discount Model (DDM)
 With these assumptions, we can derive a model that is
variously known as the Dividend Discount Model,
the Constant Growth Model, or the Gordon Model:
D 0 1  g
D1
VCS 

k CS  g
k CS  g
 This model gives us the present value of an infinite
stream of dividends that are growing at a constant
rate.
Estimating the DDM Inputs
 The DDM requires us to estimate the dividend growth rate
and the required rate of return.
 The dividend growth rate can be estimated in three ways:
– Use the historical growth rate and assume it will continue
– Use the equation: g = br
– Generate your own forecast with whatever method seems
appropriate
 The required return is often estimated by using the CAPM: ki
= krf + bi(km – krf) or some other asset pricing model.
The DDM: An Example
 Recall our previous example in which the dividends
were growing at 8% per year, and your required
return was 15%.
 The value of the stock must be (D0 = 1.85):
VCS 
185
. 1.08
.15.08
2.00

 28.57
015
. .08
 Note that this is exactly the same value that we got
earlier, but we didn’t have to use an assumed future
selling price.
The DDM Extended
 There is no reason that we can’t use the DDM at any
point in time.
 For example, we might want to calculate the price
that a stock should sell for in two years.
 To do this, we can simply generalize the DDM:
D N 1  g
D N 1
VN 

k CS  g
k CS  g
 For example, to value a stock at year 2, we simply use
the dividend for year 3 (D3).
The DDM Example (cont.)
 In the earlier example, how did we know that the
stock would be selling for $33.33 in two years?
 Note that the period 3 dividend must be 8% larger
than the period 2 dividend, so:
V2 
2.161.08
.15.08
2.33

 33.33
015
. .08
 Remember, the value at period 2 is simply the present
value of D3, D4, D5, …, D∞
What if Growth Isn’t Constant? (cont.)
 Let’s take our previous example, but assume that the
dividend will grow at a rate of 15% per year for the
next three years before settling down to a constant
8% per year. What’s the value of the stock now?
(Recall that D0 = 1.85)
0
2.1275
2.4466
2.8136
1
2
3
g = 15%
3.0387 …
4
g = 8%
What if Growth Isn’t Constant? (cont.)
 First, note that we can calculate the value of the stock at the
end of period 3 (using D4):
V3 
3.0387
 43 .41
.15  .08
 Now, find the present values of the future selling price and
D1, D2, and D3:
V0 
2.1275 2.4466 2.8136  43.41


 34.09
2
3
1.15
1.15
1.15
 So, the value of the stock is $34.09 and we didn’t even have
to assume a constant growth rate. Note also that the value is
higher than the original value because the average growth rate
is higher.
Two-Stage DDM Valuation Model
 The previous example showed one way to value a stock with
two (or more) growth rates. Typically, such a company can be
expected to have a period of supra-normal growth followed
by a slower growth rate that we can expect to last for a long
time.
 In these cases we can use the two-stage DDM:
D0 1  g1  1  g 2 
n

 1  g1  
D0 1  g1 
kCS  g 2
  
1  

n
kCS  g1   1  kCS  
1  kCS 


n
VCS
PV of the first N dividends + PV of stock price at period N
DDM Rationale
$
Earnings per share
Growth
Transition
Time
Maturity
Applying DDM Rationale
1. Growth stage: Rapidly expanding sales, high profit
margins, abnormally high growth in EPS. Payout
ratio is low.
2. Transition stage: Increased competition reduces
profit margins, and earnings growth slows. With
fewer investment opportunities, company begins to
pay out a larger percent of earnings.
3. Maturity stage: Earnings growth rate, payout ratio,
ad return on equity stabilize for the remainder of life.
Multistage model
Dt
Dt
Dt
 1  k t  Transition
 1  k t  Mature
 1  k t
V 0  Growth


 
Growth rates vary over time
Dt


t
G  T 1  k 
Constant growth
1
DT 1

T
kg

1 k 



Discount to time0
Mature stage
What would be the likely growth rate during the
mature stage?
EARNING AND FREE
CASH FLOW
MODELS
Other Valuation Methods
 Some companies do not pay dividends, or the
dividends are unpredictable.
 In these cases we have several other possible
valuation models:
– Earnings Model
– Free Cash Flow Model
The Earnings Model
 The earnings model separates a company’s earnings
(EPS) into two components:
– Current earnings, which are assumed to be repeated
forever with no growth and 100% payout.
– Growth of earnings which derives from future
investments.
 If the current earnings are a perpetuity with 100%
payout, then they are worth:
VCE
EPS 1

k
The Earnings Model (cont.)
 VCE is the value of the stock if the company does not grow,
but if it does grow in the future its value must be higher than
VCE so this represents the minimum value (assuming
profitable growth).
 If the company grows beyond their current EPS by
reinvesting a portion of their earnings, then the value of
these growth opportunities is the present value of the
additional earnings in future years.
 The growth in earnings will be equal to the ROE times the
retention ratio (1 – payout ratio):
 Where b = retention ratio and r = ROE (return on equity).
g  br
The Earnings Model (cont.)
 If the company can maintain this growth rate forever,
then the present value of their growth opportunities
is:

NPV
PVGO  
t 1
t
1  k t
 Which, since NPV is growing at a constant rate can
be rewritten as:
r 
r
RE1   RE1 RE1   1
NPV1
k 
k
PVGO 


kg
kg
kg
The Earnings Model (cont.)
 The value of the company today must be the sum of
the value of the company if it doesn’t grow and the
value of the future growth:
VCS
r 
RE1   1
EPS1 NPV1 EPS1
k 




k
kg
k
kg
 Where RE1 is the retained earnings in period 1, r is
the return on equity, k is the required return, and g is
the growth rate
Partitioning Value: Example
3
Vo 
 $42.86
(.15.08)
5
NGVo 
 $33.33
.15
PVGO  $42.86  $33.33  $9.52
DIV1=$3
EPS1=$5
K=15%
G=8%
Vo = value with growth
NGVo = no growth component value
PVGO = Present Value of Growth Opportunities
The Free Cash Flow Model - Concept
 Free cash flow is the cash flow that’s
FCF  NOPAT  Op Cap
left over after making all required
investments in operating assets:
 NOPAT is net operating profit after
V  VD  VP  VCS
tax
 The total value of the firm equals the
value of its debt plus preferred plus
common
FCF0 1  g
VOps 
 We can find the total value of the
kg
firm’s operations (not including nonoperating assets), by calculating the
present value of its future free cash
FCF0 1  g 
flows
V  VOps  VNonOps 
 VNonOps
kg
 Add in the value of its non-operating
assets to get the total value of the firm
 Then, subtract the value of the firm’s
debt and the value of its preferred
stock
 Divide by the number of shares
FCF0 1  g 
VCS 
 VNonOps  VD  VP
outstanding to get the per share value
kg
of the stock.


Discounted cash-flow
 DCF method entails estimating the free cash flow available to
debt and equity investors (i.e., the annual cash flows generated
by the business, and the terminal value of the business at the
end of the time horizon) and discounting these flows back to
the present using the weighted average cost of capital as the
discount rate to arrive at a present value of the assets
 DCF is often the primary valuation methodology in M&A
 DCF is the PV of 2 main types of free cash flows:
1. Free cash flows to all capital providers (debt and equity)
2. Free cash flows to equity capital providers
 Fundamental in nature, DCF allows for questioning all of the
assumptions and for performing sensitivity analysis
 One can easily estimate equity value from firm value by
subtracting the market value of debt today
DCF
1.
Project the free cash flows of a business over the forecast period
–
2.
3.
4.
5.

Use the weighted average cost of capital (WACC) to determine the appropriate
discount rate range
Estimate the terminal value of the business at the end of the forecast period
Determine the value for the enterprise by discounting the projected free cash flows
and terminal value to the present
Interpret the results and perform sensitivity analysis
Calculation of free cash flow begins with financial projections
–

Comprehensive projections (i.e., fully-integrated income statement, balance sheet and
statement of cash flows) typically provide all the necessary elements
Quality of DCF analysis is a function of the quality of projections
–
–

Typical forecast period is 10 years. However, the range can vary from five to 20 years
Confirm and validate key assumptions underlying projections
Sensitize variables that drive projections
Sources of projections include
–
–
–
–
Target company’s management
Acquiring company’s management
Research analysts
Bankers
FCF: What is it?
Free cash flow is un-levered cash available to creditors
and owners after taxes and reinvestment
– Un-levered means free from financing considerations
– Contrast with Cash Flow from Operations (which consists
of Net Income plus Depreciation and Amortization plus
Deferred Taxes and Non-Cash charges)
– Free cash flows can be forecast from a firm’s financial
projections, even if those projections include the effects of
debt
FCF: How to calculate it?
Net Sales (Revenue)
- Cost of goods sold (COGS)
- Selling, general, and administrative (SG&A)
=Earnings before interest, taxes, depreciation and amortization (EBITDA)
- Depreciation & Amortization (D&A)
= Earnings before interest and taxes (EBIT)
- Taxes (tax rate*EBIT)
=Net operating profit/loss after taxes (NOPLAT)
+ Depreciation & Amortization (D&A)
- Capital Expenditure (Capex)
- Change in Net working capital (NWC)
=Free cash flow (FCF)
FCF: How to forecast?
 Project growth in Net Sales by basing assumptions on
– Research reports
– Client forecasts (if available)
– Industry trends
– percent growth is usually an input; aggregate sales is derived from
this input
 Estimate the following by percent of sales
– Cost of Goods Sold (COGS)
– Selling, General and Administrative (SG&A) Expenses
 Determine Interest Expense
– Refer to the debt schedule and calculate the weighted average interest
rate.
– If no debt schedule is available, then compute Interest Expense as a
percent of average Long-Term Debt= (Beginning LTD + Ending
LTD)/2
 Assess tax rate based on the marginal tax rate (federal, state and local)
and current tax regulation
FCF: How to forecast? (contd..)
 Depreciation
– Sometimes expressed as % of Property, Plant and Equipment
(PP&E)
 Capital Expenditures (Capex)
– Expenditures necessary to maintain the required capital intensity
 Working Capital excluding cash and cash equivalents and STD
– WC = (Current Assets–Cash and Cash Equivalents)–(Current
Liabilities–STD)
– Estimate WC as a percent of sales
– Possible to squeeze cash from WC by operating more efficiently
– Three major components of working capital are: inventories,
receivables and payables
 Property, Plant and Equipment (PP&E):
– Project by capital intensity/efficiency: sales divided by (PP&E)
– Beginning PP&E–Depreciation+ CapEx = Ending PP&E
DCF – WACC
Weighted Average Cost Of Capital (WACC)
– Ascertain the costs of the various sources of capital for the
company, with a given capital structure
• Debt
• Equity
– The after-tax costs of the various sources are then averaged
to arrive at an appropriate discount rate to value unlevered
cash flows
– Debt and equity market values used should represent the
“target” capital structure (the capital structure that includes
planned debt and equity financings, if any)
DCF – WACC (contd..)
Cost of debt
Consult with the debt capital markets group for a 10year maturity all-in new issue rate at the credit rating
corresponding to the targeted capital structure. As
part of this process, you should look at the yield on
new issues of comparable companies since the cost of
debt is a function of the risks associated with a given
business/industry
If the company has public debt outstanding and you
do not intend to change its capital structure, find the
debt rating
DCF – WACC (contd..)
Cost of equity
Use the Capital Asset Pricing Model (CAPM)
requity  Risk - freeraterf  b  Equity risk premium
The risk-free rate can be taken as the interest rate on a
generic 10-year government note
– Roughly matches the maturity of projections
b = cov(r,rM)/var(rM), usually estimated using a
regression
rt  rf ,t    b rM ,t  rf ,t   t
Estimation issues
– Betas may change over time
– Don’t use data from too long ago
– Five years of monthly data is reasonable
ROIC
 Used to assess a company's efficiency at allocating the capital
under its control to profitable investments. The return on
invested capital measure gives a sense of how well a company
is using its money to generate returns. Comparing a company's
ROIC with its cost of capital (WACC) reveals whether
invested capital was used effectively.
The general equation for ROIC is as follows:
Total capital includes long-term debt, and common and
preferred shares. Because some companies receive income
from other sources or have other conflicting items in their net
income, net operating profit after tax (NOPAT) may be used
instead.
DCF – Terminal value
Terminal value is the value of all future cash flows
after the explicit forecast period of 10 years
g 

NoplatT 1  1 

FCFT 1
ROIC 

T VT 

(WACC  g )
(WACC  g )
Key value drivers
•Growth rate of NOPLAT (g)
•Return on invested capital ROIC
•Value is higher if ROIC is higher than WACC;
•Higher growth rate is good because our projects have a ROIC
greater
•than the cost of capital.
•Value is lower if ROIC is higher than WACC
•Higher growth rate is bad because our projects have a ROIC lower
DCF – Terminal value (contd..)
Can also estimate terminal value using an exit multiple
Terminal value = Statistic x Multiple
Forecast 10 explicit years of FCF, EBITDA, Net
Income
Use a multiple of any relevant figure: Book Value, Net
Income, Cash Flow from Operations, EBIT,
EBITDA, Sales, etc.
– Terminal Value should be an Enterprise Value; NOT ALL
multiples produce an Enterprise Value (e.g., P/Es)
Multiply and estimate Terminal Value
DCF – Terminal value: exit multiple
DCF – Terminal value: perpetuity growth
DCF
Validate and test projection assumptions
Carefully consider all variables in the calculation of
the discount rate
Consistency of assumptions concerning interest rates,
inflation rates, tax rates and the cost of capital is
critical
Thoughtfully consider terminal value methodology
Do sensitivity analysis (base projection variables,
synergies, discount rates, terminal values, etc.)
DCF – Walmart example
December 2007 Treasury rates
3-month
1-year
5-year
20-year
3.00%
3.26%
3.49%
4.57%
December 2007 AAA yield
5.49%
Risk premium for AA rate bonds
2.2%
Equity risk premium
Tax Rate
Beta
Cost of debt (rd )
5.0%
33%
0.71
6.80%
=rf+risk premium
Cost of equity (re)
8.13%
=rf+ *(rm-rf)
Net debt (D)
Market cap (E)
Total Value (V=D+E)
D/V
E/V
WACC
=rd (1-tax) D/V + re E/V
37.00
192.00
229.00
16.2%
83.8%
7.56%
Walmart FCF assumptions
 The sales at the end of 2007 were $370 billion. They are
projected to grow by 10% during the next year. The growth
rate of sales will decline by 0.5% each year for the next 10
years
 COGS is currently 76% of sales and is expected to decline by
0.1% during the next 10 years
 SG&A is currently 17% of sales and is expected to increase by
0.1% during the next 10 years
 D&A are currently 1.7% of sales and are expected to remain
at the same level
 Capex is currently 3.5% of sales and is expected to remain at
the same level
 NWC is 0.5% of sales and is expected to remain at the same
level
Walmart FCF’s
Sales
Sales growth
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
370,000
407,000
10.0%
445,665
9.5%
485,775
9.0%
527,066
8.5%
569,231
8.0%
611,923
7.5%
654,758
7.0%
697,317
6.5%
739,156
6.0%
779,810
5.5%
308,913
337,814
367,732
398,462
429,769
461,390
493,033
524,383
555,106
584,857
75.9%
75.8%
75.7%
75.6%
75.5%
75.4%
75.3%
75.2%
75.1%
75.0%
69,597
76,654
84,039
91,709
99,615
107,698
115,892
124,122
132,309
140,366
17.1%
17.2%
17.3%
17.4%
17.5%
17.6%
17.7%
17.8%
17.9%
18.0%
6,919
7,576
8,258
8,960
9,677
10,403
11,131
11,854
12,566
13,257
1.7%
1.7%
1.7%
1.7%
1.7%
1.7%
1.7%
1.7%
1.7%
1.7%
14,245
15,598
17,002
18,447
19,923
21,417
22,917
24,406
25,870
27,293
3.5%
3.5%
3.5%
3.5%
3.5%
3.5%
3.5%
3.5%
3.5%
3.5%
3.5%
1,850
2,035
2,228
2,429
2,635
2,846
3,060
3,274
3,487
3,696
3,899
0.5%
0.5%
0.5%
0.5%
0.5%
0.5%
0.5%
0.5%
0.5%
0.5%
0.5%
21,571
7,118
14,453
6,919
185
14,245
6,942
0.930
6,454
23,620
7,795
15,826
7,576
193
15,598
7,610
0.864
6,579
25,746
8,496
17,250
8,258
201
17,002
8,305
0.804
6,675
27,934
9,218
18,716
8,960
206
18,447
9,022
0.747
6,742
30,169
9,956
20,213
9,677
211
19,923
9,756
0.695
6,778
32,432
10,703
21,729
10,403
213
21,417
10,501
0.646
6,783
34,702
11,452
23,250
11,131
214
22,917
11,251
0.601
6,757
36,958
12,196
24,762
11,854
213
24,406
11,997
0.558
6,699
39,175
12,928
26,247
12,566
209
25,870
12,733
0.519
6,610
41,330
13,639
27,691
13,257
203
27,293
13,451
0.483
6,492
COGS
% of Sales
76.0%
SGA
% of Sales
17.0%
D&A
% of Sales
1.7%
Capex
% of Sales
NWC
% of Sales
EBIT
Tax
NOPLAT
+D&A
- NWC
-Capex
FCF
Discount factor
Discounted cash flows
Total (excl Cont Value)
66,569
Walmart continuation value
Continuation Value
PV(Continuation Value)
Firm value
Less Debt value
Equity value
Number of shares
Equity value per share
NOPLATT+1 (1-g/ROIC)/(WACC-g)
381,123
183,953 73%
250,522
37,000
213,522
4,170
51.20
WACC = ROIC
Terminal ROIC
Walmart sensitivity analysis
51.20
6.0%
6.4%
6.8%
7.2%
7.6%
8.0%
8.4%
8.8%
2.0%
46.32
47.54
48.62
49.59
50.45
51.22
51.92
52.56
2.4%
45.28
46.87
48.28
49.53
50.64
51.65
52.56
53.38
2.8%
44.04
46.06
47.84
49.43
50.84
52.12
53.27
54.32
3.2%
42.52
45.06
47.29
49.27
51.05
52.65
54.09
55.41
Terminal growth rate
3.6%
4.0%
40.66
38.33
43.81
42.24
46.59
45.69
49.06
48.75
51.26
51.49
53.25
53.96
55.05
56.19
56.69
58.22
4.4%
35.36
40.22
44.51
48.32
51.73
54.80
57.57
60.10
4.8%
31.46
37.56
42.93
47.71
51.99
55.84
59.32
62.48
5.2%
26.17
33.92
40.76
46.84
52.28
57.18
61.60
65.63
5.6%
18.63
28.72
37.62
45.54
52.62
58.99
64.76
70.00
6.0%
7.09
20.73
32.77
43.48
53.05
61.67
69.46
76.55
51.20
6.0%
6.4%
6.8%
7.2%
7.6%
8.0%
8.4%
8.8%
2.0%
71.48
64.99
59.32
54.32
49.90
45.95
42.42
39.24
2.4%
71.72
65.21
59.52
54.51
50.06
46.11
42.56
39.37
2.8%
71.97
65.44
59.72
54.69
50.23
46.26
42.70
39.49
3.2%
72.22
65.66
59.93
54.88
50.40
46.41
42.84
39.62
Terminal growth rate
3.6%
4.0%
72.47
72.71
65.88
66.11
60.13
60.33
55.06
55.24
50.57
50.74
46.57
46.72
42.98
43.12
39.75
39.88
4.4%
72.96
66.33
60.53
55.43
50.90
46.87
43.26
40.01
4.8%
73.21
66.55
60.73
55.61
51.07
47.03
43.40
40.14
5.2%
73.45
66.78
60.94
55.80
51.24
47.18
43.55
40.27
5.6%
73.70
67.00
61.14
55.98
51.41
47.34
43.69
40.40
6.0%
71.33
67.22
61.34
56.16
51.58
47.49
43.83
40.53
RELATIVE VALUATION
MODELS
Terminology
Equity value
– Market value of shareholders’ equity (shares outstanding x
current stock price)
Enterprise value
– Market value of all capital invested in the firm
• Equity, debt (short-term and long-term), preferred stock, minority
interest
Assets
Liabilities
Equity
Enterprise
Value
=
Debt
Preferred Stock
Minority Interest
Terminology (contd..)
Equity Value Multiples
 Certain flows or values apply to
equity holders only—these
include net income and book
value of equity. Since each of
these values is after debt and
preferred financing is taken into
account, multiples of these flows
or values should be based on the
value of the equity only
 Relevant ratios are Equity Value
to: Net Income to Common
Shareholders, Book Value and
Cash Flow
Enterprise Value Multiples
 Other flows apply to all
capital providers (i.e., debt
and equity), and therefore
Enterprise Value should be
used
 Relevant ratios are:
Enterprise Value to: Sales,
EBITDA and EBIT
Relative Value Models
 Professional analysts often value stocks relative to one another.
 For example, an analyst might say that XYZ is undervalued relative to
ABC (which is in the same industry) because it has a lower P/E ratio,
but a higher earnings growth rate.
 These models are popular, but they do have problems:
–
–
–
–
Even within an industry, companies are rarely perfectly comparable.
There is no way to know for sure what the “correct” price multiple is.
There is no easy, linear relationship between earnings growth and price multiples
(i.e., we can’t say that because XYZ is growing 2% faster that it’s P/E should be 3
points higher than ABC’s – there are just too many additional factors).
A company’s (or industry’s) historical multiples may not be relevant today due to
changes in earnings growth over time.
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
 As a rule of thumb, or simplified model, analysts often
assume that a stock is worth some “justified” P/E ratio times
the firm’s expected earnings.
 This justified P/E may be based on the industry average P/E,
the company’s own historical P/E, or some other P/E that
the analyst feels is justified.
 To calculate the value of the stock, we merely multiply its next
years’ earnings by this justified P/E:
P
VCS 
E
 EPS1
P/E Ratio: No Expected Growth
E1
P0 
k
P0 1

E1 k
 E1 - expected earnings for next year
– E1 is equal to D1 under no growth
 k - required rate of return
P/E Ratio with Constant Growth
D1
E1 1  b 
P0 

r  g r  b  ROE
P0
1 b
1 b


E1 r  b  ROE r  g
 ROE: Higher ROE implies
higher P/E
 Growth rate, g: Higher
growth rate implies higher
P/E
 Market capitalization rate, r:
Higher r implies lower P/E
 Retention ratio, b: Higher b
implies higher P/E
No Growth:
Numerical Example:
E0 = $2.50 g = 0 k = 12.5%
P0 = D/k = $2.50/.125 = $20.00
PE = 1/k = 1/.125 = 8
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
How to compare P/E’s
Comparison across time
– If the PE ratio of a firm is high today relative to the
average PE ratio over time, is the stock overvalued?
Comparison across firms
– If the PE ratio of a firm is high today relative to the
average PE ratio of other comparable firms, is the stock
overvalued?
Pitfalls in P/E Analysis
 Use of accounting earnings
– Earnings Management
– Choices on GAAP
 Inflation
 Reported earnings fluctuate around the
business cycle.
 Examine the time series of P/E ratios (for
that matter, any valuation ratio) to examine if
there are any abnormal changes across time
– P/E ratio may be small if any large increase
earnings are expected to be temporary.
– P/E ratio may be large if any large decline in
earnings is expected to be temporary
P/E Ratios for Different Industries, 2006
Forecasting PE
TIME SERIES APPROACH
PE ratios depend on the current economic conditions
One can use a regression model to predict PE
PEt = a + b*Tbond-ratet + c*Expected Inflationt
Then plug in the current/predicted values for interest
rates to get the PE for the firm
CROSS-SECTIONAL APPROACH
One can use a regression model to predict PE
PEi = a + b*FirmSizei + c*Leveragei +
d*ExpectedGrowthi + e*Betai
Then plug in the characteristics for the firm to get it’s
PE
Example (cross sectional)
1987 PE = 7.1839 + 13.05 PAYOUT - 0.6259 BETA + 6.5659 EGR
1988 PE = 2.5848 + 29.91 PAYOUT - 4.5157 BETA + 19.9143 EGR
1989 PE = 4.6122 + 59.74 PAYOUT - 0.7546 BETA + 9.0072 EGR
1990 PE = 3.5955 + 10.88 PAYOUT - 0.2801 BETA + 5.4573 EGR
1991 PE = 2.7711 + 22.89 PAYOUT - 0.1326 BETA + 13.8653 EGR
where,
PE = Price-Earnings ratio at the end of the year
PAYOUT = Dividend Payout ratio at the end of the year
BETA = Beta of the stock, using returns from prior five years
EGR = Earnings growth rate over the previous five years
Regression
P/E
 The basic regression
assumes a linear relationship
between PE ratios and
independent variables
 The basic relationship
between PE ratios and
independent variables itself
might not be stable, and if
it shifts from year to year
 It is always useful to
supplement with the
analysis of what should be
the PE based on
fundamentals (growth,
ROE etc.)
100
90
80
70
y = 192.8x + 3.7131
60
R2 = 0.1437
50
40
30
20
10
0
0%
5%
10%
15%
Growth Rate
20%
25%
30%
Price to book ratio
Price-to-Book
ROE P Payoutratio  ROE ROE  g
P
 

E B
rg
rg

( 1 / B )
– P/B is bigger when cost of capital is lower
– P/B is bigger when growth rate is higher
– P/B is bigger when ROE is higher
P/B and ROE
Firms which have high ROE usually sell for well
above book value and firms which have low ROE sell
at or below book value
The firms which should draw attention from investors
are those which provide mismatches of price-book
value ratios and returns on equity
– low P/BV ratios and high ROE or high P/BV ratios and
low ROE
PB ratios versus ROE
10
9
8
y = 11.132x + 2.4981
7
R2 = 0.1103
P/B
6
5
4
3
2
1
0
0%
5%
10%
15%
20%
ROE
25%
30%
35%
40%
P/B ratios caution
P/B ratio could be difficult to interpret when there
are unusual write-offs, or negative book values
Several commercial services including Standard and
Poor’s provide balance sheet numbers that adjust book
values for any large and unusual write offs
Book value is an application of arbitrary accounting
rules
The P/S Approach
 In some cases, companies aren’t currently earning any money
and this makes the P/E approach impossible to use (because
there are no earnings).
 In these cases, analysts often estimate the value of the stock
as some multiple of sales (Price/Sales ratio).
 The justified P/S ratio may be based on historical P/S for the
company, P/S for the industry, or some other estimate:
VCS  P  Sales1
S
Comparative Value Approaches
Using multiples
1. Determine the peer group (your comps universe)
2. Gather the appropriate financial information
3. Enter the financial information into your spreadsheet
– normalize for non-recurring items (why?)
4. Calculate relevant historical or forward multiples
(P/E; EV/EBITDA)
– Medians are better than means (why?)
– Forward multiples are better than historical multiples (why?)
5. Forecast your company’s future financial performance
(EBITDA, EPS, Cash Flow, etc.)
6. Apply appropriate multiples to your company’s financial stats
and derive implied valuation range
Using Multiples
A comparable peer group should embody the same
operational and financial attributes so that their public
trading values represent a reasonable proxy for those
of the company under consideration
Operational
 Industry
 Product
 Markets
Financial
 Size (revenues, assets, market
cap)
 Leverage
 Distribution channels
 Customers
 Margins
 Dividend yield
 Seasonality
 Cyclicality
 Shareholder base
 Growth prospects
Using Multiples
Even with standard metrics, certain multiples are more
relevant for some industries than others
– For many industries, EV/EBITDA multiples are the most
common trading metric (e.g. Industrials, Transportation,
Distribution, etc.)
– For other industries, P/E multiples are more widely
followed (Pharmaceuticals, Restaurants, Biotech, etc.)
– Financials usually trade on P/B (price-to-book)
Reading analyst reports will help you understand the
metrics analysts use to value the sector and the
industry
Using Multiples
Certain sectors have unique metrics
– Telecommunications: Enterprise value to
• Number of subscribers
• Route miles, fiber miles
• Access lines
– Natural resources: Enterprise value to
• EBITDAX (Earnings Before Interest, Taxes, Depreciation,
Amortization and Exploration Expenses)
• Reserves
• Production
– Retail/Real estate: Enterprise value to
• Square footage
• EBITDAR (Earnings Before Interest, Taxes, Depreciation,
Using Multiples
Using Multiples
 Getting the correct numbers
– Ensure you have correctly captured the equity and net debt
components
• Diluted shares (includes options and convertibles if in the money)
• Net debt includes preferreds, out of the money converts, capital leases, etc.
– Ensure your income statement projections are uniform across your
comps
• Adjust for extraordinary items and one time charges
• Calendarize so that projections reflect the same time periods
• Check analyst projections to make sure they are treating all expense
components the same across the comps (e.g., amortization of intangibles)
 Determining a value range
– Thoughtfully consider the multiple range—using the mean/median is
not thoughtful
– Calculate the value correctly (Firm value versus Equity value issue)