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ABSTRACT:
A new methodology for valuing common stocks utilizes unique features that are
consistent with economic theory and empirical evidence. The method is based on
a model into which fundamental factors such as estimates of the income
statement (such as earnings estimates) and balance sheet (book value) are used as
inputs,
and output can be considered reliable, proportional to the accuracy of the
estimated input parameters.
I. Background of the Diamond Hill Investment Model
(DHIM)
The standard definition for the intrinsic value of a financial asset is that it is
equal to the summation of the present value of cash flows associated with it.
This is illustrated below:
where 
represents the summation from period "0" to period "n." CF (sub "t")
represents the cash flows at time "t," and k represents the risk-adjusted
discount rate (required return).
A general formula for stocks (known as the Gordon Model) is:
where IV (sub "i") represents the theoretical intrinsic
value for stock "i", D (sub "1") represents the current indicated
dividend, k (sub "i") represents the risk-adjusted discount rate (required
return) and g (sub "i") represents the growth rate for stock "i". [This
model is a special case of (a) that assumes constant growth of dividends into
perpetuity, which is known in mathematics as a Taylor Series.]
The main shortcomings in this model are obvious. For one thing, forecasting the
future is difficult, and any attempt to go out into perpetuity (forever) is
highly speculative. Equally obvious is the dependence on a current dividend.
For companies where there is no current dividend, the Gordon Model calculates
an intrinsic Value
of $0, even though a company might be
reinvesting its earnings to grow its business, to pay out dividends at some
point in the future. Clearly there
is value in re-investing the earnings for profitable growth.
However the mechanics of the Gordon model does not capture this value.
Furthermore, this model cannot calculate the intrinsic value for companies where the
growth rate (g sub "i") exceeds the required return (k sub "i). This happens
in companies that are in the high growth phase for the next five years which eventually
slows down at some point of time in the future. In such cases
(and where a current dividend exists), some investors will use a rearranged
formula for the Gordon Model:
where k' (sub "i") is an estimated annual return, by using the
current price "P sub '0' " {with the estimated growth rate g (sub "i") }.
Although this lacks an explicit required return, it can be used to calculate a
risk-adjusted excess return by subtracting an explicit required return from the
estimated annual return. The risk-adjusted excess return is commonly referred
to as "alpha."
An alternative valuation technique that has become popular compares a stock's
current price ("P") divided by its current earnings per share ("E") (thus P/E
ratio, or simply "PE"), with its expected growth rate ("G") of E over the next
five years. This is sometimes called a PE to G, or "PEG ratio". The
idea is that the lower the ratio the better since an investor is paying a lower
valuation (numerator) for every single unit of growth (denominator). The problem with the PEG ratio is that it
simply provides an indication of relative valuation
(one stock compared to another), but gives no reasonable estimate of the intrinsic
value of a stock. Another issue with the PEG ratio
is that it does not differentiate between profitable growth and unprofitable growth. Companies sometimes may
take on projects that are not positive NPV to be able to depict a picture to the
street that they are still growing. However a zero NPV or a negative NPV project
does not create shareholder value. Clearly a company that invests in a positive
NPV project creates more value than a company that invests in a zero NPV project
even if both companies have the same valuation and growth rate. However the PEG
ratio will not distinguish one from the other. Therefore the PEG ratio does not provide a sufficient basis upon
which to make appropriate investment decisions. Furthermore, because the PEG
ratio does not explicitly consider risk (and required return), it is not useful
for comparing stocks having different risk characteristics.
II. Theoretical Basis for the Diamond Hill Investment Model
The idea for the DHIM resulted from understanding the
limitations of the above models, combined with familiarity with both general
economic theory and empirical evidence on various components of such models and
concepts.
First, the DHIM utilizes the current price of a stock as a dynamic
variable in the model.
Second, the DHIM incorporates
an important component of valuation that is typically ignored in most valuation
models, i.e. the tangible book value. The tangible value is important because it
determines the ability of the company to fund its growth prospects without needing
any external financing. For example,
the Gordon model uses earnings growth as one of the inputs without taking into consideration
whether the company has the capital to generate that earnings growth. To the degree
that accounting statements reflect economic reality, the tangible book value can
be also thought of as an estimate of the liquidation value of the company.
Hence a company that has no growth prospects or its future
earnings are not expected to be economic (return on equity equal to or lower than
cost of capital), then the company is at least worth its book value/liquidation
value.
Third, the DHIM assumes mean reversion for equity valuations
(in this case the adjusted PE ratio which will be explained in detail below). Competition theory suggests that excess returns allowing for growth will be
competed away over time. This implies a mean reversion assumption for the adjusted PE
ratios. Empirical evidence (Beaver and Morse, 1978) also suggests that the mean reversion process for valuations
take place in as few as four years.
The DHIM is a tool that calculates the DH Value (estimate of intrinsic value)
of a stock and the alpha. For a
share of common stock not held forever, the DH Value is equal to the sum of all the future cash flows discounted at a risk adjusted required
return, which includes both
dividends and the proceeds received when the stock is ultimately sold.
The
challenge for the security analyst is estimating these future cash flows and
the return investors require to compensate for the risk of the stock. DHIM
assumes that the current dividend and earnings grow at some rate during the
holding period and that the stock is ultimately sold for an estimate of tangible book value plus the adjusted multiple of the
earnings at the end of the holding period. A required return k (sub "i") is
estimated by the user (such as one derived from the use of some conventional
method, like the Capital Asset Pricing Model).
The DHIM then, is a special form
of the dividend discount model with a pre-determined holding period. A
preferred implementation due to industry convention and empirical evidence uses
a period of five years, and can thus be written mathematically as follows:
where IV (sub "i") represents the theoretical DH Value for stock "i", D (sub
"t") defined as dividends received at time(s) "t" over the five years, and P
(sub "5") representing the price of the stock at the end of year 5.
Estimated annual return (k'i)
can be solved by substituting P0 for IVi in Equation
c. This can be written mathematically as Equation c1.
The estimated P (sub "5") is calculated as the sum of two
components. The first component is
the tangible
book value at the end of year 5. This
is calculated by adding the tangible book value at year 0 to the sum of all earnings
from year 1 thru 5 and deducting the sum of all dividends from year 1 thru 5. Thus tangible book value for year 5
is calculated by adding all retained earnings for the holding period to the current
tangible book value. This can
be written mathematically as Equation d.
The second component is called the “excess earnings value” of the stock. To understand
this concept it is essential to understand that the excess earnings value of any
company depends on the extent to which the earnings are economic.
So for example if the company
earned a return on equity equal to the required rate of return, no excess value
is created and the value of the business/ stock would be the tangible book value. So in this case, the excess value would
be 0. However if the company does earn
excess returns (over its required rate) the excess value would be positive. Another
way of thinking about this excess value is that, the higher the tangible book value
and the higher the future profitable growth prospects of the company, the higher
the excess value will be since the company can profitably grow its business without
much need for any external financing. Either
in the form of debt (which increases interest expense) or equity (which leads to
dilution in share count) both ultimately lead to lower earnings per share growth.
This excess value
is calculated by multiplying the earnings per share at year 5 and the adjusted PE. The earnings per share in year 5 is calculated by growing current earnings E at an annualized rate
for five years, resulting in EPS (sub "5"). (For cyclical companies, a
normalization of earnings is preferred.) Next, EPS (sub "5") is multiplied by a
terminal adjusted PE ratio (adjusted PE at
year 5). This can be written mathematically as equation e.
The adjusted PE5
can be calculated by equation f and g.
The adjusted
current PE(sub "0" at year 0) is calculated by deducting the tangible book value from the current market
price and then dividing the result by current normalized earnings per share. Conceptually the
adjusted PE ratio just like the PE ratio is a measure of equity valuation with the
main difference being that the adjusted PE ratio measures the excess earnings power
of the company. A high adjusted PE
equates to high earnings power. The
calculation of adjusted current PE(sub "0") can be written mathematically as equation f.
The DHIM is unique in that it incorporates one of the key basic rules of economics. It is that excess returns earned by
companies will be competed away over a period of time.
In case of the mechanics of the model, this key point is captured in the
adjusted PE, which we earlier described as a measure of earnings power.
The adjusted PE reverts half way to its long term average of 12 over five
years. Hence the terminal adjusted
PE is equal to the average of the adjusted current PE and 12 as equation g.
The calculation of P(sub "5") can be written mathematically as equation h.
III. Practical Aspects of the Diamond Hill Investment Model
The DHIM provides a framework in which to analyze the valuation
of a stock, and allows the analyst flexibility to input earnings and the
expected growth rate of those earnings, as well as the necessary risk-adjusted
discount rate. In addition, the user estimates the adjusted terminal market P/E, and
thus different users with different macro-economic outlooks are accommodated.
The flexibility to overlay individual judgment regarding such issues as
translating accounting earnings into economic earnings, incorporating recent
developments, and factoring in qualitative information, leads each user to a
conclusion based upon his or her own scenarios. Given the
possibility for imprecision in these estimates, being able to conduct scenario
analysis to investigate the sensitivity of the calculated DH Value to the
various estimates is also useful.
IV. Examples
Table A summarizes various exemplary data used to compare the intrinsic
value of a stock, determined by an embodiment of the present invention, to other
methods.
Table A
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Companies Ticker Symbols
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Parameter
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WMT
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LOW
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AMZN
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Current Price (P0)
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$45.94
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$27.77
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$84.04
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Tangible Book Value (TBV0)
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$11.03 |
$10.44 |
$0.81 |
Current EPS (EPS0)
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$3.09
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$ 1.99
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$ 0.98
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Current PE ratio (PE0)
|
14.9
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14
|
85.8
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Adjusted PE Ratio (Adjusted PE0
= (P0-TBV0)/ EPS0) |
11.3 |
8.7 |
84.9 |
| Current Dividend
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$ 0.88
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$ 0.32
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$ 0
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Required Return  |
8.0%
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9.0%
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9.0%
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Estimated Growth
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13.0%
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15.0%
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24.0%
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Where, in the adjusted PE Ratio, the adjusted terminal market PE assumption is 12 |
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Example A: Comparison of the DHIM model with the
Gordon Model
Gordon Model (Using equation [b (sub "1") ] results is shown is Table B.
Table B
Parameter
|
WMT
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LOW
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AMZN
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For each company,  |
14.9%
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16.2%
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24.0%
|
|
Required return |
8.0%
|
9.0%
|
9.0%
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| yields alpha |
6.9%
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7.2%
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15.0%
|
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|
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As can be seen from the results of the Dividend Discount Model, AMZN comes up as
the most attractive stock since it has the highest alpha, followed by LOW and WMT
in that order. This is because the assumptions of constant growth till perpetuity
results in a wide variance in estimated returns between AMZN and the other two stocks.
DHIM (Using equations [c1] and [g]) results is shown is Table C.
Table C
Parameter
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WMT
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LOW
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AMZN
|
|
TBV5 |
$27.21 |
$23.39 |
$10.59 |
 |
$5.69
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$4.00
|
$2.87
|
|
Adjusted P/E5 |
11.6
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10.4
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48.5
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$93.5
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$64.8
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$149.8
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| Annualized Price Appreciation |
15.3%
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18.5%
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12.3%
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Annualized Dividend Return |
1.9%
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1.2%
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0.0%
|
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Annual Return
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17.2%
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19.6%
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12.3%
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Required return |
8.0%
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9.0%
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9.0%
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Alpha |
9.2%
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10.6%
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3.3%
|
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As per the results above, LOW seems to be the most attractive stock followed by
WMT and AMZN comes up as least attractive. This is in contrast with the results
of the DDM but more reasonable since the DHIM does not extrapolate the growth rate
into perpetuity and also because it assumes that excess returns get competed away
in the long run.
Table D presents an analysis obtained using Equations [c] and [g]
of the DHIM model.
Table D
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WMT
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LOW
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AMZN
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| Intrinsic Value ("IV") |
$68.71
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$44.02
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$97.38
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| Current Price / IV |
.67
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0.63
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0.86
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With the lower ratio of Current Price divided by Intrinsic Value
preferable, LOW
is considered more attractive, which is consistent with the
alpha calculation.
Example B: Comparison of the DHIM model with the PEG
ratio
Table E presents an analysis obtained using the
PEG model.
Table E
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WMT
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LOW
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AMZN
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| PE / G (i.e. Price/EPS0/Growth rate) |
1.1
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0.9
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3.6
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The PEG ratio model also suggest similar results as the DHIM i.e. LOW being the
most attractive stock followed by WMT and AMZN being the least attractive.
However, the relative attractiveness of LOW and WMT compared to AMZN is significantly
magnified by the PEG ratio model. This model does not give AMZN enough credit
for its unique business model that generates significantly high returns on equity
as compared to LOW or WMT. Another shortcoming of the PEG model is that it
does not explicitly consider a required rate of return/ hurdle rate. Hence
of two companies have the same valuation and growth rate but different required
return the PEG ratio model will not differentiate between the two.
V. Holding Period
It will be appreciated, of course, that the DHIM is not limited
to a holding period of five years. Equations [c], [c1], and [d] can thus be
represented as Equations
[c'], [c1'], and [d'] for a generalized holding period of "n" years:
Preferably "n" would be chosen in correspondence with the period
required for PE mean reversion in a particular industry of interest.
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