U.S. patent application number 10/676297 was filed with the patent office on 2004-09-09 for method and system for analyzing a capital structure for a company.
Invention is credited to Hakanoglu, Erol, Jones, Emerson P..
Application Number | 20040177016 10/676297 |
Document ID | / |
Family ID | 32043405 |
Filed Date | 2004-09-09 |
United States Patent
Application |
20040177016 |
Kind Code |
A1 |
Jones, Emerson P. ; et
al. |
September 9, 2004 |
Method and system for analyzing a capital structure for a
company
Abstract
Various embodiments of the present invention relate to methods
and systems for analyzing a capital structure for a company (e.g.,
a public corporation). More particularly, one embodiment of the
present invention relates to a decision making tool for analyzing a
company's capital structure, which decision making tool may
include: (1) Economic EPS, wherein Economic EPS and its volatility
may capture the cost/risk trade-off of all fixed income and
equity-related alternative capital structures; and (2) Capital
Structure Efficient Frontier, wherein a company should strive to
bring its capital structure to the efficient frontier of strategies
with the highest EPS for given levels of EPS risk. Of note, the
Economic EPS and the Capital Structure Efficient Frontier
methodologies of the present invention provide a unifying framework
in which to analyze a company's capital structure (e.g., for
identifying and implementing the economically optimal solutions to
a company's capital structure challenges). Apart from the global
view of the company's capital structure, this framework can be used
as a decision-making tool for analyzing and comparing specific
restructuring transactions (including, but not limited to): new
financing, share repurchase, liability management, bank capital
optimization, and/or tax-driven hybrid equity issuance.
Inventors: |
Jones, Emerson P.;
(Greenwich, CT) ; Hakanoglu, Erol; (New York,
NY) |
Correspondence
Address: |
GREENBERG TRAURIG, LLP
885 3RD AVENUE
NEW YORK
NY
10022
US
|
Family ID: |
32043405 |
Appl. No.: |
10/676297 |
Filed: |
September 30, 2003 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60414735 |
Sep 30, 2002 |
|
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Current U.S.
Class: |
705/35 |
Current CPC
Class: |
G06Q 40/00 20130101;
G06Q 40/12 20131203; G06Q 40/02 20130101; G06Q 40/04 20130101; G06Q
40/06 20130101; G06Q 40/10 20130101 |
Class at
Publication: |
705/035 |
International
Class: |
G06F 017/60 |
Claims
What is claimed is:
1. A method implemented by a programmed computer system for
characterizing a capital structure of an entity in connection with
a cost of a selected debt/equity ratio relative to a risk
associated with the selected debt/equity ratio, which method
comprises the steps of: iteratively changing a value of a
debt/equity ratio associated with the entity; calculating values of
earnings per share associated with the entity based at least in
part upon the iteratively changed values of the debt/equity ratio
associated with the entity; calculating values of earnings per
share risk associated with the entity based at least in part upon
the iteratively changed values of the debt/equity ratio associated
with the entity; and recording the calculated earnings per share
values associated with the entity and the calculated earnings per
share risk values associated with the entity.
2. The method of claim 1, wherein the entity is a public
corporation.
3. The method of claim 2, wherein at least one of the calculated
earnings per share values and the calculated earnings per share
risk values is applied to a financial presentation relating to at
least one of a balance sheet and an earnings per share metric.
4. The method of claim 1, wherein the iterations and calculations
are carried out at least in part using a Monte Carlo
simulation.
5. The method of claim 1, wherein the outputted calculated earnings
per share values and the outputted calculated earnings per share
risk values are plotted against one another.
6. The method of claim 5, wherein the plot of calculated earnings
per share values versus calculated earnings per share risk values
is credit adjusted.
7. The method of claim 1, further comprising: inputting data
associated with the entity including a number of common shares
outstanding, a value of earnings, a value of dividends per share, a
change in the effective number of common shares outstanding, which
change in the effective number of common shares outstanding
reflects the possibility, based upon an economically reasonable
analysis in light of market conditions, of conversion of a
convertible security; and a value of coupon payments; wherein each
value of earnings per share is calculated at least in part using
the formula 11 EPS = DPS 0 + Earnings 0 - N o .times. DPS 0 -
Coupon N o + N eff ,wherein Earnings.sub.0 equals the input value
of earnings, N.sub.o equals the input number of common shares
outstanding, DPS.sub.0 equals the input value of dividends per
share, Coupon equals the input value of coupon payments, and
.DELTA.N.sub.eff equals the input change in the effective number of
common shares outstanding.
8. The method of claim 7, wherein the economically reasonable
analysis in light of market conditions takes into account a
conversion premium associated with the convertible security.
9. The method of claim 1, further comprising: inputting data
associated with the entity including a number of existing shares, a
value of earnings, a value of an equity dividend, a value of an
attributed after-tax interest expense from a convertible security,
and a number of attributed shares from the convertible security,
which number of attributed shares reflects the possibility, based
upon an economically reasonable analysis in light of market
conditions, of conversion of the convertible security; wherein each
value of earnings per share is calculated at least in part using
the formula EPS=dividend per share+retained EPS; wherein dividend
per share=the value of the equity dividend/the number of existing
shares; and wherein retained EPS=(earnings without taking effect of
any interest expense from the convertible security minus attributed
after-tax interest expense from the convertible security)/(the
number of existing shares plus the number of attributed shares from
the convertible security).
10. The method of claim 9, wherein the economically reasonable
analysis in light of market conditions takes into account a
conversion premium associated with the convertible security.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit under 35 U.S.C. 119(e)
of U.S. Provisional Application Serial No. 60/414,735 filed Sep.
30, 2002.
FIELD OF THE INVENTION
[0002] Various embodiments of the present invention relate to
methods and systems for analyzing a capital structure for a company
(e.g., a public corporation).
[0003] More particularly, one embodiment of the present invention
relates to a decision making tool for analyzing a company's capital
structure, which decision making tool may include:
[0004] Economic EPS: Economic EPS (hereinafter sometimes referred
to as "Expected EPS" or "EEPS") and its volatility may capture the
cost/risk trade-off of all fixed income and equity-related
alternative capital structures, or securities (e.g., hybrid
securities such as, for example, convertible securities).
[0005] Capital Structure Efficient Frontier: A company should
strive to bring its capital structure to the efficient frontier of
strategies with the highest EPS for given levels of EPS risk.
[0006] In another embodiment, the present invention may aid in the
design and utilization of innovative financing products such as,
for example (which examples are intended to be illustrative and not
restrictive) Zero-put Contingent Convertibles (CUBZ/TUBZ/PLANZ) and
Zero-coupon Continent Convertibles (STARZ) that expand the capital
structure efficient frontier (e.g., by providing a better trade-off
between EPS and EPS risk).
[0007] Of note, the Economic EPS and the Capital Structure
Efficient Frontier framework/methodologies of the present invention
provide a unifying framework in which to analyze a company's
capital structure (e.g., for identifying and implementing the
economically optimal solutions to a company's capital structure
challenges). Apart from the global view of the company's capital
structure, this framework can be used as a decision-making tool for
analyzing and comparing specific restructuring transactions
(including, but not limited to): new financing, share repurchase,
liability management, bank capital optimization, and/or tax-driven
hybrid equity issuance.
[0008] For the purposes of the present application the term
"entity" is intended to refer to any type of company, organization,
or group.
[0009] Further, for the purposes of the present application the
term "security" is intended to refer to an instrument evidencing
debt and/or ownership of asset(s).
BACKGROUND OF THE INVENTION
[0010] Earnings per share has conventionally been used as a tool
for distinguishing the effective cost of debt versus equity.
[0011] However, hybrid securities pose a challenge for evaluating
earnings per share. For certain financing alternatives, such as
convertible bonds and stock options, for example, the impact on
earnings and shares outstanding may change over time. A convertible
bond, for example, generates tax-deductible interest expense until
it is converted into a fixed or variable number of shares. It would
seem that for the debt part of its life, a convertible bond reduces
earnings; and for the equity part of its life, it increases shares.
In an attempt to reconcile this dual nature of hybrid securities,
it is believed that the current required accounting treatment is
based upon "diluted EPS", which requires EPS to be calculated as
the worse of two alternatives (see SFAS No. 128, paragraphs
11-39):
[0012] 1) Basic EPS.
[0013] 2) Same as basic EPS, except (a) the denominator is
increased to reflect the potential number of additional shares, and
(b) the numerator is adjusted as if the dividends and interest on
the convertible had never been recognized.
[0014] In the case of convertible bonds, this corresponds to the
if-converted method of accounting. In the case of outstanding call
options on a company's stock, the increase in the denominator is
calculated based upon the treasury stock method, as the intrinsic
value of the option divided by the current market share price.
These accounting rules for calculating diluted EPS essentially
classify hybrids as either earnings-reducing (debt) or
share-increasing (equity), without any assessment of how likely it
is that the hybrid behaves as one or the other. Although it is a
calculable and unambiguous accounting quantity, it is clear that
diluted EPS does not accurately represent the economics for
existing shareholders, i.e., how much of a given period's earnings
each existing shareholder is entitled to.
[0015] Consider, for example, the impact of issuing a convertible
bond on existing shareholders. These shareholders realize that
earnings from the current year are not entirely their own. If some
of those earnings are retained, contracted future shareholders
(e.g., convertible bond holders) will be entitled to a piece of the
pie. Some complications arise in determining how much remains for
each existing shareholder. First, in many cases, it is unclear
whether the bond will ever be converted to equity. Second, even if
it is eventually converted, the number of shares may be uncertain
(it may be dependent, for example, on the share price). The
if-converted method assumes that convertible bond holders will
become shareholders regardless of the likelihood of such an event.
This accounting method does not capture the expected increase in
number of shares nor its uncertainty. Third, interest paid to
convertible bond holders is no longer available to distribute to
existing shareholders. It seems inaccurate, therefore, to add
interest payments back into the numerator as required by the
if-converted method. Fourth, and finally, equity dividends paid to
existing shareholders are not shared with future shareholders. Only
retained earnings are shared. If a company distributed all of its
earnings to existing shareholders through dividends, then future
shareholders would have no claim on the earnings and would
therefore not dilute earnings per share. Equity dividend policy
does matter (the initial pricing of the convertible bond issuance
would, of course, reflect a company's dividend policy).
[0016] These flaws make diluted EPS a poor tool for making
economically based decisions regarding hybrid securities. In order
to capture the economic consequences of hybrids more accurately, it
is necessary to depart from this accounting view and abandon
diluted EPS in favor of the Economic EPS methodology of the present
invention. Economic EPS is a better measure of existing
shareholders' probable economics. Specifically, it recognizes that:
(1) the interest paid to convertible bond holders reduces income
available to existing shareholders; (2) the equity dividend policy
affects the division of earnings between existing and future
shareholders; and (3) the number of shares (denominator) is
uncertain as well as the earnings themselves (numerator).
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] FIG. 1 shows a plot of a capital structure efficient
frontier according to an embodiment of the present invention;
[0018] FIG. 2 shows a plot of a credit-adjusted capital structure
efficient frontier according to an embodiment of the present
invention;
[0019] FIG. 3 shows a plot of capital structure efficient frontier
with hybrids (relating to share repurchase and debt replacement)
according to an embodiment of the present invention;
[0020] FIG. 4 shows plots of capital structure theory and earnings
per share according to an embodiment of the present invention;
[0021] FIG. 5 shows a plot of after-tax cash flows savings (TUBZ
vs. Equity) according to an embodiment of the present
invention;
[0022] FIG. 6 shows a plot of a capital structure efficient
frontier according to an embodiment of the present invention;
[0023] FIG. 7 shows a plot of distribution of EPS lift according to
an embodiment of the present invention;
[0024] FIG. 8 shows a plot of a capital structure efficient
frontier according to an embodiment of the present invention;
[0025] FIG. 9 shows a plot of sensitivity of tax credit to dividend
growth rate according to an embodiment of the present
invention;
[0026] FIG. 10 shows a plot of sensitivity of tax recapture to
growth rate according to an embodiment of the present
invention;
[0027] FIG. 11 shows a plot of STARZ value vs. tax rate according
to an embodiment of the present invention;
[0028] FIG. 12 shows a plot of life of STARZ according to an
embodiment of the present invention;
[0029] FIG. 13 shows a plot of after-tax cash flows vs. debt
according to an embodiment of the present invention;
[0030] FIG. 14 shows a plot of after-tax cash flow savings vs.
equity according to an embodiment of the present invention;
[0031] FIG. 15 shows a plot of STARZ tax recapture according to an
embodiment of the present invention;
[0032] FIG. 16 shows a plot of dilution according to an embodiment
of the present invention;
[0033] FIG. 17 shows a plot of a capital structure efficient
frontier according to an embodiment of the present invention;
and
[0034] FIG. 18 shows a plot of sensitivity to stock price growth
rate according to an embodiment of the present invention.
[0035] Of note, certain figures have legends with identification
numerals associated therewith. These identification numerals
correspond, of course, to various likewise labeled plot elements
included in respective ones of the figures.
[0036] Among those benefits and improvements that have been
disclosed, other objects and advantages of this invention will
become apparent from the following description taken in conjunction
with the accompanying figures. The figures constitute a part of
this specification and include illustrative embodiments of the
present invention and illustrate various objects and features
thereof.
DETAILED DESCRIPTION OF THE INVENTION
[0037] Detailed embodiments of the present invention are disclosed
herein; however, it is to be understood that the disclosed
embodiments are merely illustrative of the invention that may be
embodied in various forms. In addition, each of the examples given
in connection with the various embodiments of the invention are
intended to be illustrative, and not restrictive. Further, the
figures are not necessarily to scale, some features may be
exaggerated to show details of particular components. Therefore,
specific structural and functional details disclosed herein are not
to be interpreted as limiting, but merely as a representative basis
for teaching one skilled in the art to variously employ the present
invention.
[0038] In one embodiment the present invention provides a method
implemented by a programmed computer system for characterizing
earnings of an entity, which method comprises the steps of:
inputting data associated with the entity including a number of
common shares outstanding, a value of earnings, a value of
dividends per share, a change in the effective number of common
shares outstanding, which change in the effective number of common
shares outstanding reflects the possibility, based upon an
economically reasonable analysis in light of market conditions, of
conversion of a convertible security; and a value of coupon
payments; calculating at least one value of earnings per share
associated with the entity based upon at least some of the input
data, wherein each value of earnings per share is calculated at
least in part using the formula 1 EPS = DPS 0 + Earnings 0 - N o
.times. DPS 0 - Coupon N o + N eff ,
[0039] wherein Earnings.sub.0 equals the input value of earnings,
N.sub.o equals the input number of common shares outstanding,
DPS.sub.0 equals the input value of dividends per share, Coupon
equals the input value of coupon payments, and .DELTA.N.sub.eff
equals the input change in the effective number of common shares
outstanding; calculating values of earnings per share risk
associated with the entity based upon at least some of the input
data; and recording the calculated earnings per share values
associated with the entity and the calculated earnings per share
risk values associated with the entity.
[0040] In one example, the method may further comprise: iteratively
changing a value of a stock price associated with the entity;
iteratively changing the value of coupon payments associated with
the entity; iteratively calculating additional values of earnings
per share using the formula 2 EPS = DPS 0 + Earnings 0 - N o
.times. DPS 0 - Coupon N o + N eff .
[0041] In another example, the entity may be a public
corporation.
[0042] In another example, at least one of the calculated earnings
per share values and the calculated earnings per share risk values
may be applied to a financial presentation relating to at least one
of a balance sheet and an earnings per share metric.
[0043] In another example, the iterations and calculations may be
carried out at least in part using a Monte Carlo simulation.
[0044] In another example, the outputted calculated earnings per
share values and the outputted calculated earnings per share risk
values may be plotted against one another.
[0045] In another example, the plot of calculated earnings per
share values versus calculated earnings per share risk values may
be credit adjusted.
[0046] In another example, the economically reasonable analysis in
light of market conditions may take into account a conversion
premium associated with the convertible security.
[0047] In another embodiment the present invention provides a
method implemented by a programmed computer system for
characterizing earnings of an entity, which method comprises the
steps of: inputting data associated with the entity including a
number of existing shares, a value of earnings, a value of an
equity dividend, a value of an attributed after-tax interest
expense from a convertible security, and a number of attributed
shares from the convertible security, which number of attributed
shares reflects the possibility, based upon an economically
reasonable analysis in light of market conditions, of conversion of
the convertible security; calculating at least one value of
earnings per share associated with the entity based upon at least
some of the input data, wherein each value of earnings per share is
calculated at least in part using the formula
EPS=dividend per share+retained EPS;
[0048] wherein dividend per share=the value of the equity
dividend/the number of existing shares; and wherein retained
EPS=(earnings without taking effect of any interest expense from
the convertible security minus attributed after-tax interest
expense from the convertible security)/(the number of existing
shares plus the number of attributed shares from the convertible
security); calculating values of earnings per share risk associated
with the entity based upon at least some of the input data; and
[0049] recording the calculated earnings per share values
associated with the entity and the calculated earnings per share
risk values associated with the entity.
[0050] In one example, the method may further comprise: iteratively
changing a value of a stock price associated with the entity;
iteratively changing the value of coupon payments associated with
the entity; iteratively calculating additional values of earnings
per share using the formula
EPS=dividend per share+retained EPS;
[0051] wherein dividend per share=the value of the equity
dividend/the number of existing shares; and wherein retained
EPS=(earnings without taking effect of any interest expense from
the convertible security minus attributed after-tax interest
expense from the convertible security)/(the number of existing
shares plus the number of attributed shares from the convertible
security).
[0052] In another example, the entity may be a public
corporation.
[0053] In another example, at least one of the calculated earnings
per share values and the calculated earnings per share risk values
may be applied to a financial presentation relating to at least one
of a balance sheet and an earnings per share metric.
[0054] In another example, the iterations and calculations may be
carried out at least in part using a Monte Carlo simulation.
[0055] In another example, the outputted calculated earnings per
share values and the outputted calculated earnings per share risk
values may be plotted against one another.
[0056] In another example, the plot of calculated earnings per
share values versus calculated earnings per share risk values may
be credit adjusted.
[0057] In another example, the economically reasonable analysis in
light of market conditions may take into account a conversion
premium associated with the convertible security.
[0058] In another embodiment the present invention provides a
method implemented by a programmed computer system for
characterizing a capital structure of an entity in connection with
a cost of a selected debt/equity ratio relative to a risk
associated with the selected debt/equity ratio, which method
comprises the steps of: iteratively changing a value of a
debt/equity ratio associated with the entity; calculating values of
earnings per share associated with the entity based at least in
part upon the iteratively changed values of the debt/equity ratio
associated with the entity; calculating values of earnings per
share risk associated with the entity based at least in part upon
the iteratively changed values of the debt/equity ratio associated
with the entity; and recording the calculated earnings per share
values associated with the entity and the calculated earnings per
share risk values associated with the entity.
[0059] In one example, the entity may be a public corporation.
[0060] In another example, at least one of the calculated earnings
per share values and the calculated earnings per share risk values
may be applied to a financial presentation relating to at least one
of a balance sheet and an earnings per share metric.
[0061] In another example, the iterations and calculations may be
carried out at least in part using a Monte Carlo simulation.
[0062] In another example, the outputted calculated earnings per
share values and the outputted calculated earnings per share risk
values may be plotted against one another.
[0063] In another example, the plot of calculated earnings per
share values versus calculated earnings per share risk values may
be credit adjusted.
[0064] In another example, the method may further comprise:
inputting data associated with the entity including a number of
common shares outstanding, a value of earnings, a value of
dividends per share, a change in the effective number of common
shares outstanding, which change in the effective number of common
shares outstanding reflects the possibility, based upon an
economically reasonable analysis in light of market conditions, of
conversion of a convertible security; and a value of coupon
payments; wherein each value of earnings per share is calculated at
least in part using the formula 3 EPS = DPS 0 + Earnings 0 - N o
.times. DPS 0 - Coupon N o + N eff ,
[0065] wherein Earnings.sub.0 equals the input value of earnings,
N.sub.o equals the input number of common shares outstanding,
DPS.sub.0 equals the input value of dividends per share, Coupon
equals the input value of coupon payments, and .DELTA.N.sub.eff
equals the input change in the effective number of common shares
outstanding.
[0066] In another example, the economically reasonable analysis in
light of market conditions may take into account a conversion
premium associated with the convertible security.
[0067] In another example, the method may further comprise:
inputting data associated with the entity including a number of
existing shares, a value of earnings, a value of an equity
dividend, a value of an attributed after-tax interest expense from
a convertible security, and a number of attributed shares from the
convertible security, which number of attributed shares reflects
the possibility, based upon an economically reasonable analysis in
light of market conditions, of conversion of the convertible
security; wherein each value of earnings per share is calculated at
least in part using the formula
EPS=dividend per share+retained EPS;
[0068] wherein dividend per share=the value of the equity
dividend/the number of existing shares; and wherein retained
EPS=(earnings without taking effect of any interest expense from
the convertible security minus attributed after-tax interest
expense from the convertible security)/(the number of existing
shares plus the number of attributed shares from the convertible
security).
[0069] In another example, the economically reasonable analysis in
light of market conditions may take into account a conversion
premium associated with the convertible security.
[0070] The present invention provides an aid in answering the
following question. What is the optimal capital structure for a
given entity (e.g., a public corporation)? This puzzle of corporate
finance has typically remained in the realm of theoretical
speculation. Until now, actually applying the theory has typically
been hindered by the difficulty of evaluating and comparing the
economic cost and risk of debt, equity, and hybrid alternatives
along the debt/equity continuum. One embodiment of the present
invention is directed to a new quantitative framework for analyzing
a company's existing capital structure. Another embodiment of the
present invention is directed to suggesting more efficient
financing alternative(s). The model utilized in the present
invention is practical to implement, yet solidly grounded in modern
finance theory (e.g., with wide application of academic concepts:
firm value, Modigliani Miller Propositions I and II, tax shields,
financial distress, and CAPM. The model is practically
implementable, focusing on quantifiable numbers, such as earnings,
dividends and dilution). In general, the model is based upon four
basic ideas:
[0071] 1) Earnings per Share and the Capital Structure Efficient
Frontier: As utilized by the present invention, earnings per share
is a powerful metric that may be used to compare debt and equity on
the basis of both cost and risk, resulting in a "Capital Structure
Efficient Frontier". Although the Capital Structure Efficient
Frontier is neither generic nor static, it generally portrays a
trade-off where debt is less costly but more risky than equity.
[0072] 2) Credit Quality and Future Cost of Capital: Moving toward
the equity end of the Capital Structure Efficient Frontier
decreases leverage and therefore lowers the future cost of capital.
By taking this indirect benefit into account, the methodology of
the present invention can more accurately estimate the effective
cost of equity and hybrids with high equity credit.
[0073] 3) Economic Earnings per Share and Hybrids: "Economic EPS"
(as opposed to diluted EPS) captures risk in both earnings and
number of shares, allowing the broader set of hybrid alternatives,
including (but not limited to) convertible securities and stock
options, to be evaluated in the same framework. Hybrids can expand
the Capital Structure Efficient Frontier by offering a better cost
versus risk tradeoff than capital structures consisting of only
combinations of debt and equity.
[0074] 4) Taxes and Hybrids: Interest expense on debt is typically
tax-deductible, but dividends on equity and preferred securities
are typically not. The tax treatment of hybrids may be critical to
their economic performance and for determining whether they fall on
the Capital Structure Efficient Frontier. Several innovative hybrid
structures available in the marketplace today are highly
tax-advantaged (for example, trust preferred and Zero-put
Contingent Convertible securities). Various examples (which
examples are intended to be illustrative and not restrictive)
provided below illustrate how the framework of the present
invention may be used to analyze a wide range of capital structure
transactions, including (but not limited to) debt-financed share
repurchase, equity-financed debt repurchase, mandatory and
contingent convertible debt issuance, preferred and trust preferred
issuance, and stock option financing.
[0075] Referring now to earnings per share and the Capital
Structure Efficient Frontier, it is noted that modern finance
theory states that the capital structure of a firm should be chosen
to maximize the value of the firm's assets. According to theory, a
company can evaluate debt, equity and hybrid alternatives by
computing how much each alternative increases the value of the firm
and then choosing the most value-adding alternative. Unfortunately,
applying the theory is neither intuitive nor straightforward. One
embodiment of the present invention is directed to a framework
based upon earnings per share that is not only more intuitive and
more applicable, but also firmly grounded in finance theory.
[0076] Basic EPS is defined in SFAS No. 128, paragraphs 8-10
as:
EPS=Income available to common stockholders/Number of common shares
outstanding
[0077] where income available is equal to income from continuing
operations minus dividends on preferred stock. It measures how much
of each period's income each existing shareholder is entitled to.
In the context of EPS, adding debt lowers earnings (the numerator),
while adding equity raises the number of shares (the denominator).
EPS (the ratio) is lowered in either case, but through very
different mechanisms (the money raised by either form of financing
would presumably be deployed to increase EPS through investment,
liability management, or share repurchase).
[0078] As noted above, one embodiment of the present invention is
directed to a framework/methodology that can account for the
differences in risk between debt and equity (as well as for the
differences in cost). The management of a company interested in
maximizing shareholder value would do well to focus on optimizing
EPS: maximizing its level and minimizing its uncertainty.
[0079] Consider now the example (which example is intended to be
illustrative and not restrictive) of Company XYZ with the capital
structure and earnings profile shown in the "Before" column in
Table 1, below.
1TABLE 1 Company XYZ Capital Structure and Earnings per Share
Before and After $200 Million Debt-Financed Share Repurchase Before
After Change Capital Structure Number of Shares 100 MM 95 MM (5 MM)
Share Price $40 $40 -- Equity $4000 MM $3800 MM ($200 MM) Debt
$2000 MM $2200 MM $200 MM Debt/Total Cap. 33% 37% 4% Year 1
Earnings Earnings $500 MM $492 MM ($8 MM) Earnings Risk $50 MM $52
MM $2 MM EPS $5.00 $5.18 $0.18 EPS Risk $0.50 $0.55 $0.05 P/E Ratio
8.0 7.7 (0.3)
[0080] Company XYZ is considering issuing debt to repurchase $200
mm of equity and would like to quantify the cost versus risk
trade-off of this change in capital structure. The actual impact of
this transaction on Company XYZ's capital structure and earnings
per share are calculated and shown in the "After" and "Change"
columns of Table 1. The added after-tax interest expense associated
with $200 mm of additional debt depresses earnings and increases
its volatility. Using the proceeds to buy back 5 mm common shares
at $40 per share reduces the number of common shares outstanding
from 100 mm to 95 mm. This antidilution is enough to offset the
increase in interest expense and raise the expected EPS by 3.5%,
from $5.00 per share to $5.18. Replacing equity with debt is
cheaper, but it is also riskier. This is because a larger amount of
earnings volatility is shared by a smaller number of shareholders.
EPS risk rises by 10%, from $0.50 per share to $0.55.
[0081] Referring now to FIG. 1, this Fig. depicts a graphical
representation of the cost versus risk tradeoff of this $200 mm
transaction in a more global context. Increasing the amount of the
transaction traces out a Capital Structure Efficient Frontier
representing the lower cost but higher risk associated with an
increasingly levered capital structure. Issuing shares and
repurchasing debt moves in the opposite direction along the Capital
Structure Efficient Frontier, corresponding to more costly, yet
less risky, unlevered capital structures.
[0082] Although it was the case for Company XYZ, equity will not
necessarily always be more costly than debt. For example (which
example is intended to be illustrative and not restrictive), again
assuming the same facts as used for Company XYZ above, Table 2,
below, shows the sensitivity of the EPS economics of the share
repurchase transaction to the share price.
2TABLE 2 Sensitivity of EPS Impact of Share Repurchase to Share
Price Share Price $40 $100 $200 Shares Existing 100 MM 100 MM 100
MM Repurchased 5 MM 2 MM 1 MM Remaining 95 MM 98 MM 99 MM Year 1
EPS EPS $5.18 $5.02 $4.97 EPS Risk $0.55 $0.53 $0.53 P/E Ratio 7.7
19.9 40.2
[0083] For growth companies with very high P/E ratios it is
inefficient to replace equity with debt. A company with a P/E ratio
of 40 would actually reduce EPS rather than increase it by
repurchasing shares at an elevated price of $200 per share. This
conclusion is consistent with a traditionally accepted doctrine:
Companies that are still in the high growth phase of development
should maintain a more equity-intensive capital structure, while
more-established companies can afford to have higher levels of
debt. Likewise, debt may not always be more risky than equity. If a
company's earnings are positively correlated with interest rates,
as is the case for many financial companies, replacing equity with
debt would potentially reduce both cost and risk. In line with
intuition, financial companies would be expected to favor highly
levered capital structures.
[0084] Thus, the optimal capital structure is neither generic nor
static. Rather, it depends upon the characteristics of the specific
company and its industry, as well as changing market
conditions.
[0085] Referring now to credit quality and future cost of capital,
it is believed that while growth companies with 100% equity capital
structures do in fact exist, there are essentially no financial
companies with 100% debt capital structures. There are a number of
reasons for this. For one thing, industry specific regulations,
such as the Basel Accord minimum capital ratios for banks, may put
absolute constraints on a company's leverage. Another softer
constraint that actually affects essentially all companies is the
impact of leverage on a company's credit ratings and therefore its
future cost of capital. The more leveraged a firm, the greater its
risk of default. Future bondholders and shareholders will demand a
higher risk premium before investing to compensate for this higher
risk. This raises the company's future cost of capital. As the
company refinances maturing debt and the debt portfolio is repriced
at higher and more volatile spreads, interest expense and risk both
rise, resulting in a decrease in EPS and an increase in its
volatility.
[0086] Referring now to the question of how much are credit spreads
affected by changes in a company's leverage, this question is
broken into two parts:
[0087] 1) How much do credit ratings change with changes in
leverage and coverage ratios?
[0088] 2) How much do credit spreads change with changes in credit
ratings?
[0089] In Table 3, below, the relationship among financial ratios,
ratings and credit spreads is estimated for this example.
3TABLE 3 Relating Leverage to Credit Spreads S&P(1) Credit
Spreads(2) Debt/Cap. EBIT/Int. Mean Std. Dev. AAA 20% 21.4 97 16 AA
25% 10.1 120 19 A 40% 6.1 156 28 BBB 50% 3.7 211 32 BB 60% 2.1 NA
NA Notes on Table 3: (1)From S&P's 2002 Corporate Ratings
Criteria. Debt/Capitalization based upon ratio guidelines for
"above average" US industrials. EBIT/Interest based upon three year
medians for US industrials; (2)From the Goldman Sachs USD
Investment Grade Index for the past three years.
[0090] These estimates can be used to adjust Company XYZ's Capital
Structure Efficient Frontier for changes in credit quality. FIG. 2
shows both the unadjusted and the credit-adjusted Capital Structure
Efficient Frontiers. As seen in this FIG. 2, adjusting for credit
flattens the Capital Structure Efficient Frontier by narrowing the
difference in effective cost between debt and equity and widening
the difference in effective risk. The Capital Structure Efficient
Frontier flattens more at higher leverage levels, so that
increasing leverage tends to further produce diminishing returns--a
smaller marginal gain in EPS and a larger marginal gain in risk. In
part, this can explain a company's reluctance to maximize its
leverage.
[0091] Referring now to equity hybrids, it is noted that these are
neither debt nor equity, so they do not fit easily into typical
financial ratio calculations. Recognizing this, both S&P and
Moody's have provided guidance regarding their methodology for
evaluating the impact of hybrids on leverage ratios. These methods
include: (1) assigning hybrids 100% equity credit but limiting
hybrids to a fraction of the total equity (S&P); (2) assigning
hybrids fractional equity credit depending upon where they are
deemed to fall on the debt/equity continuum (Moody's); and (3)
calculating and considering several alternative sets of ratios.
[0092] It is believed that subordinated and secured debt should
also be viewed in this context. While subordinated debt is more
expensive than senior debt for the issuer owing to its lower claim
on assets, it makes more assets available to future bondholders,
thereby making future borrowing less costly. Similarly, secured
debt is cheaper than ordinary senior debt, but it reduces the
amount of assets available to future bondholders and shareholders,
making the future cost of capital higher.
[0093] Still referring to hybrids, it is noted, as discussed above,
that hybrids also pose a challenge for evaluating EPS.
[0094] The flaws discussed above make diluted EPS a poor tool for
making economically based decisions regarding hybrid securities. In
order to capture the economic consequences of hybrids more
accurately, it is necessary to depart from the traditional
accounting view and abandon diluted EPS in favor of the Economic
EPS methodology of the present invention. Economic EPS is a better
measure of existing shareholders' probable economics. Specifically,
it recognizes that (1) the interest paid to convertible bond
holders reduces income available to existing shareholders; (2) the
equity dividend policy affects the division of earnings between
existing and future shareholders; and (3) the number of shares
(denominator) is uncertain as well as the earnings themselves
(numerator). Economic EPS can be calculated as the sum of two
pieces:
Economic EPS=Dividend per share+Retained EPS
[0095] 1) Each existing shareholder is entitled to a share of the
current dividend (income). Of note, convertible shareholders may,
in some cases, be entitled to dividends on the underlying shares.
In those cases, no separation is necessary and all income, whether
dividend or retained, is shared between current and future
shareholders.
Dividend per share=Equity dividend/Number of existing shares
[0096] 2) Each existing shareholder must share the rest of the
earnings with other existing shareholders and potential future
shareholders (capital gain).
Retained EPS=Remaining income/Number of existing and future
shares
[0097] The number of new shares can be estimated based upon all
available information at the time, for example, how far the
conversion option is in or out of the money. Rather than a single
fixed number, the estimate may include an estimate of uncertainty,
e.g., 5.0 mm expected shares with a standard deviation of 1.2 mm
shares. Of note, these estimates may be made by simulating the
market as well as the issuer's and investors' actions on a
scenario-by-scenario basis to determine the actual number of future
shares created under the scenario; the results from each scenario
may then be collected to form a probability distribution of
outcomes.
[0098] To illustrate this methodology, consider again Company XYZ.
In this example Company XYZ is thinking about raising $400 mm of
additional capital through issuance of either: 1) 10 mm shares of
equity; or 2) $400 mm of a convertible bond that pays a 4% coupon
after taxes for three years, then mandatorily converts into between
8.3 mm and 10 mm shares, depending upon the share price (This is
similar to Goldman Sachs' ACES structure. For example, when the
share price is below its current value of $40, the bond converts to
10 MM shares. If it is 20% or above (i.e., $48), it converts to 8.3
MM shares. In between, it converts to $400 MM/price shares).
[0099] Company XYZ pays a $1 dividend to any shareholder, but pays
no dividend to convertible bond holders until they convert.
Assuming earnings in the upcoming year are unchanged, Table 4,
below, illustrates the dilution of Economic EPS for the two
issuance alternatives.
4TABLE 4 Dilution of Year 1 Economic EPS Under Alternative Issuance
Scenarios Issue Issue Current Equity Convert Year 1 Earnings
Earnings $500 MM $500 MM $484 MM Dividend $100 MM $110 MM $100 MM
Retained $400 MM $390 MM $384 MM Shares Existing Shares 100 MM 110
MM 100 MM Future Shares 0 MM 0 MM 9 MM Uncertainty 0 MM 0 MM 1 MM
Year 1 EPS Dividends Per Share $1.00 $1.00 $1.00 Retained EPS $4.00
$3.55 $3.53 EPS $5.00 $4.55 $4.53 EPS Risk $0.00 $0.00 $0.03
[0100] In the case of equity issuance, Economic EPS in this example
is simply diluted by the addition of 10 MM shares, resulting in a
year 1 EPS of $4.55. It is not affected by the dividend policy at
all. For the convert, overall earnings available to existing
shareholders are reduced by the interest expense of $16 mm.
Existing shareholders still receive a $1 per share dividend, but
the retained earnings must be shared with 9 mm (plus or minus 1 mm)
future shareholders, resulting in retained EPS of $3.53. Overall
the convertible dilutes year 1 EPS to $4.53. Based upon this
analysis, the convertible would appear to be less attractive than
pure equity issuance. However, it would be shortsighted to focus
only on year 1 Economic EPS. After the conversion, there may be
fewer shares outstanding with the convertible than with the equity
issuance. In fact, issuing the convertible rather than equity may
result in smaller dilution of future earnings.
[0101] Referring now to stock options, it is noted that these can
also be considered a hybrid form of financing. The issuer receives
the option premium in exchange for later repayment of the option
payoff (in the form of cash or stock). One way to think about
employee stock options is as two transactions: (1) The company pays
the employee in cash; (2) The company finances that expense by
selling an equivalent value of stock options to the same employee
(This perspective is consistent with the current movement pursued
by legislators and regulators, and adopted by more and more
forward-looking corporations, to expense stock options. Separating
the transaction into two makes it clear that the expense occurs in
the first (operating) transaction, and not in the second
(financing) transaction. It is also clear that the transaction
involves two types of cash flows: operating cash flow in the first
transaction and financing cash flow in the second transaction. This
cash flow distinction is especially poignant in light of recent
corporate accounting irregularities). Stock options can be analyzed
similarly in the Economic EPS framework. Existing shareholders need
not share dividends with option holders, but any retained earnings
would be shared with an uncertain number of future shareholders.
The expected number of potential future shareholders, and its
uncertainty, can be estimated based upon all available information
at the time.
[0102] As an example, again consider Company XYZ, but assume that
there are 5 mm exercisable call options outstanding with a strike
price of $40 and which expire in five years. In Table 5, below,
several share price scenarios are considered, and both the expected
number of shares to be issued in the future to pay off option
holders and the uncertainty in that number is determined.
5TABLE 5 Sensitivity of Stock Option Dilution to Share Price Share
Price Scenario $40 $70 $100 Shares Existing Shares 100 MM 100 MM
100 MM Future Shares 1.5 MM 3.5 MM 4.5 MM Uncertainty 1.0 MM 1.3 MM
0.5 MM Year 1 EPS EPS $4.93 $4.83 $4.78 EPS Risk $0.05 $0.06
$0.02
[0103] When the share price is at the money ($40 per share),
diluted EPS calculated using the treasury stock method would
register no change, because it is based upon the intrinsic value of
the option. Economic EPS, on the other hand, recognizes that there
is an appreciable probability that these options will in fact be
exercised in the future, and that each option would convert to
about 1.5 shares with an uncertainty of 1.0 share. For options that
are well in the money, there is a higher likelihood of exercise and
less uncertainty regarding the outcome. The Economic EPS method is
actually similar in this example to the diluted EPS method. Instead
of fixing the number of shares by assuming exercise today, however,
Economic EPS estimates the number of shares and its uncertainty by
assuming exercise in the future.
[0104] Referring now to taxes and hybrids, it is noted that taxes
are a fundamental and essential element of the capital structure
decision (In fact, Modigliani and Miller's famous Proposition I
concludes that a firm's capital structure is irrelevant in the
absence of taxes and costs of financial distress. See F. Modigliani
and M. H. Miller, "The Cost of Capital, Corporation Finance and the
Theory of Investment", American Economic Review, 48:261-297 (June
1958), or R. A. Brealey and S. C. Myers, Principles of Corporate
Finance, 5th Edition, McGraw-Hill, New York, 1996).
[0105] The tax treatment of debt and equity is straightforward:
Interest expense on debt is typically tax-deductible while
dividends on equity typically are not. The tax treatment of equity
hybrids must clearly lie somewhere between debt and equity. An
important question is, where?
[0106] Preferred securities fall essentially in the middle of the
debt/equity continuum since they have properties that are
intermediate between debt and equity: (1) maturities that are
typically long or perpetual, (2) fixed dividend payments that are
deferrable without triggering default, (3) investor claim on assets
that is between debt and equity, and (4) partial ratings and
regulatory equity credit. The tax treatment on preferred
securities, however, is essentially identical to equity: Dividends
are not tax-deductible. For this reason, plain-vanilla preferred
securities have largely been replaced by trust preferred securities
(e.g., MIPS, QUIPS, and Capital Securities), which have all the
above desired equity properties of plain-vanilla preferred
securities but also have what are effectively tax-deductible
dividends. This is accomplished by issuing the preferred securities
through a wholly owned trust, which then loans the proceeds to the
parent. The interest payments on the loan are exactly matched to
the dividend payments on the preferred security. However, the
interest paid by the parent is tax-deductible and is not offset by
tax paid on interest received by the trust. On consolidation, the
net effect is a tax-deductible preferred security. This tax
deduction allows trust preferreds to jockey for a better position
on the Capital Structure Efficient Frontier than that of
plain-vanilla preferreds (see FIG. 3).
[0107] Convertible bonds offer a different challenge since they
change character from debt to equity over time. Until they are
converted, convertible bonds generate tax-deductible interest
expense. Generally, however, because of the conversion option, the
coupon on convertible bonds is lower than the coupon on comparable
non-convertible bonds, so the tax deduction is correspondingly
smaller. For this reason, ordinary convertibles, including
mandatory convertibles such as ACES, may take their place on the
Capital Structure Efficient Frontier, but are not been expected to
expand the frontier (see FIG. 3).
[0108] A recent ruling by the IRS changes the landscape for
convertibles, creating an opportunity to significantly enhance the
interest tax deductions on variants of convertibles known as
contingent convertibles (see Revenue Ruling 2002-31; see also
.sctn. 1.1275-4 of the Income Tax Regulations on contingent payment
debt instruments). Contingent convertibles differ from ordinary
convertibles by the addition of one or more features that make the
periodic payments dependent (or contingent) upon another factor.
For example, coupon payments on the convertible bond may be
structured to include the dividend on the underlying shares. If the
contingencies are neither remote nor incidental, then the issuer
may take interest tax deductions based upon interest accrued at a
much higher straight debt rate. The appropriate rate would
correspond to the yield on non-convertible debt with essentially
the same terms (maturity, payment dates, seniority) as the
convertible bond. The enhanced tax deductibility of contingent
convertible debt has the potential to expand the Capital Structure
Efficient Frontier significantly (see FIG. 3).
[0109] In practice, structuring contingent convertibles requires a
delicate balance of many considerations: satisfying conditions
required for contingent payment debt treatment, maximizing tax
deductions, minimizing accounting interest expense, avoiding
if-converted EPS accounting, and creating investor demand. Examples
of such securities developed at Goldman Sachs include Contingent
Accretion Rate Securities (CARZ) and Zero-put Contingent
Convertible Securities (CUBZ, TUBZ, and PLANZ).
[0110] In addition, it is noted that there may be tax advantages
associated with adding employee stock options to a company's
capital structure.
[0111] Taxes are fundamental to the determination of optimal
capital structure. While many of the complexities arise from the
tax treatment of hybrid securities, certain additional tax effects
should be considered under all circumstances. Although companies
are generally free to choose their capital structure, the IRS may
treat debt as stock for tax purposes if it deems the debt/equity
ratio to be unreasonably high. This would result in a loss of the
interest tax deduction. Another deterrent to overly leveraged
capital structures is the potential for interest expense to be so
high that it generates a net operating loss. In this case, the
value of the tax deduction would be reduced, since a portion may
have to be deferred (carried forward), if possible, or otherwise
forfeited.
[0112] Referring now to restructuring, as an application of the
framework/methodology of the present invention discussed above,
strategies for realigning Company XYZ's capital structure will now
be considered. FIG. 3 shows the impact of modifying 10% of Company
XYZ's capital structure by issuing debt, equity, or hybrids and
using the proceeds to repurchase equity or pay down debt. For
comparison, the debt/equity Capital Structure Efficient Frontier is
also indicated. Moving toward the debt end of the spectrum by
replacing equity with other alternatives generally increases
Expected EPS as well as EPS volatility; meanwhile, replacing debt
generally decreases both Expected EPS and its volatility. Most of
the hybrid strategies fall near the debt/equity Capital Structure
Efficient Frontier, although trust preferred securities have
slightly higher Expected EPS because of their favorable tax
treatment. Zero-put Contingent Convertibles are an exception.
Replacing equity with these structures boosts Expected EPS by more
than 10% while only marginally increasing volatility. Replacing
debt with Zero-put securities reduces risk by 20% and increases
Expected EPS slightly. Zero-put Contingent Convertibles greatly
expand the Capital Structure Efficient Frontier. The overwhelming
tax benefits of contingent convertibles are clearly illuminated by
this framework.
[0113] These results are summarized in Table 6, below, where the
Economic EPS shortfall risk is also calculated.
6TABLE 6 Comparison of Restructuring Alternatives Economic EPS
Statistics Shortfall Strategy Average STD Risk Current $5.00 $0.50
$0.40 Debt Replacement -10% Debt/+10% Equity 4.58 0.39 1.15 -10%
Debt/+10% Preferred 4.87 0.48 0.55 -10% Debt/+10% Trust Preferred
5.03 0.48 0.37 -10% Debt/+10% ACES 4.66 0.41 0.94 -10% Debt/+10%
Zero-put Contingent 5.13 0.40 0.26 Share Repurchase -10%
Equity/+10% Debt 5.53 0.67 0.12 -10% Equity/+10% Preferred 5.42
0.66 0.16 -10% Equity/+10% Trust Preferred 5.58 0.66 0.10 -10%
Equity/+10% ACES 5.10 0.50 0.31 -10% Equity/+10% Zero-put
Contingent 5.60 0.52 0.06
[0114] Shortfall risk is a one-sided risk measure that quantifies
the risk of performing worse than some benchmark, in this case, the
current capital structure (Shortfall risk is technically defined
here as the probability of falling short of the benchmark
multiplied by the average shortfall). On a shortfall basis, moving
toward the debt end of the spectrum appears more appropriate for
Company XYZ, since shifting out of equity and into other
alternatives both increases Expected EPS and decreases its
shortfall risk. Still, shifting out of debt may be appropriate if
it is replaced, for example, with trust preferreds or Zero-put
Contingent Convertible securities.
[0115] Of note, decisions regarding a company's capital structure
should generally be based upon a detailed analysis of the economic
cost versus risk trade-off of financing alternatives. Nevertheless,
other considerations may place constraints on the capital structure
alternatives that a company is able to or is willing to consider.
For example:
[0116] Regulations: For many financial entities, federal and
industry regulations may limit leverage through minimum capital
ratios, and deter excessive use of hybrids by limiting equity
credit associated with the instruments.
[0117] Accounting. Many companies may be sensitive to reported EPS
in addition to Economic EPS. This can lead companies to make
capital structure decisions that are not necessarily optimal
economically, but that do balance economic and accounting
considerations.
[0118] Referring now to an additional discussion of Economic EPS
under an embodiment of the present invention, it is noted, as
discussed above, that Economic EPS measures value for existing
common shareholders. More particularly, existing common
shareholders are entitled to any common dividend that is paid.
Shareholders are also entitled to a share of the earnings retained
in the business (capital gains). However, these capital gains will
also be shared with future shareholders (e.g. convertible bond
holders, equity option holders). Thus: 4 Economic EPS = Common
Dividend Per Share + Retained Earnings Expected Number of Shares or
Income + Capital Gains
[0119] For a base capital structure consisting of debt and equity
only, this would amount to 5 EPS 0 = DPS 0 + Earnings 0 - N 0
.times. DPS 0 N 0 = Earnings 0 N 0
[0120] where N.sub.0 is the existing number of shares, EPS.sub.0,
DPS.sub.0, Earnings.sub.0 are the base case earnings per share,
dividends per share and earnings, respectively. As expected,
dividend policy does not affect shareholder's value.
[0121] Accordingly, the Economic EPS framework/methodology of the
present invention can help with capital structure decisions such as
(but not limited to):
[0122] Evaluating the economics of alternative financing
instruments including debt, equity, and equity hybrids.
[0123] Evaluating capital restructuring ideas, such as debt, equity
and hybrid repurchase or retirement.
[0124] Of note, Economic EPS.noteq.accounting EPS. More
particularly, accounting EPS (diluted EPS) does not accurately
capture the economic consequences of equity hybrids such as
convertibles (e.g. dilution does not depend upon likelihood of
conversion). Economic EPS recognizes that both earnings and
expected number of shares are uncertain. Economic EPS also
recognizes the impact of dividend policy.
[0125] Of further note, Economic EPS unifies debt, equity and
hybrids. More particularly, issuing each reduces capital gains by
either lowering retained earnings, raising expected number of
shares, or both:
[0126] Debt: Reduces retained earnings through interest payments
(Dividend policy does not matter) 6 EPS = DPS 0 + Earnings 0 -
Interest - N 0 .times. DPS 0 N 0 = Earnings 0 - Interest N 0
[0127] Equity: Increases number of shares (Dividend policy does not
matter). 7 EPS = DPS 0 + Earnings 0 - N 0 .times. DPS 0 - N .times.
DPS 0 N 0 + N = Earnings 0 N 0 + N
[0128] Convertibles. Reduces retained earnings through interest and
dividend payments.
[0129] Increases expected number of shares (e.g., depending upon
conversion premium and estimated likelihood of conversion). 8 EPS =
DPS 0 + Earnings 0 - N 0 .times. DPS 0 - Coupon N 0 + N eff
[0130] where .DELTA.N.sub.eff is the effective number of shares,
which reflects the possibility that a convertible may convert into
the underlying shares .DELTA.N.sub.und or no shares at all. In
certain cases, EPS for convertibles can be simplified. If for
example, conversion is a certainty
(.DELTA.N.sub.eff=.DELTA.N.sub.und), and the coupon on the
structure is equal to a non-contingent coupon plus dividends on the
underlying shares (Coupon=Non-contingent
coupon+DPS.sub.0.times..DELTA.N.- sub.und) this simplifies to: 9
EPS = Earnings 0 - Non - Contingent Coupon N 0 + N und
[0131] The following discussion will now characterize the Economic
EPS framework/methodology of the present invention in the context
of modern finance theory.
[0132] Value of the Firm Framework
[0133] Modern finance theory states that the capital structure of a
firm should be chosen to maximize the value of the firm's assets.
On the other hand, Modigliani and Miller's famous Proposition I
makes the following assertion:
[0134] MM I: In the absence of taxes and financial distress, firm
value is independent of capital structure.
[0135] The MM I argument is simply that the total value of the firm
cannot be changed by slicing up its ownership between different
stakeholders. In the real world, adding debt introduces two new
third parties: (1) the government, which contributes value to the
firm equal to the tax shield on interest payments, and (2) lawyers,
who take away value from the firm equal to the potential costs of
financial distress. For this reason, changing the capital structure
can change the overall value of the firm for stakeholders. The
traditional trade-off theory asserts that a firm can maximize its
value by increasing its leverage until the incremental value of the
tax shield is offset, at the margin, by the incremental cost of
financial distress (or, a firm should increase leverage until the
increase in EPS due to the tax shield is offset by the increase in
EPS risk due to risk of financial distress). But, even after
choosing the optimal capital structure possible with existing
financing alternatives, firm's needn't be satisfied. The challenge
of financial innovation is to design value-adding hybrid financing
products that raise the Capital Structure Efficient Frontier by
providing a better trade-off between tax shield benefits and costs
of financial distress than that offered by debt and equity
alone.
[0136] While theoretically elegant, the value of the firm framework
for optimizing capital structure is difficult to use as an analysis
and decision-making tool. In contrast, the Economic EPS
framework/methodology provides the ability to discriminate between
capital structure alternatives based upon easily quantifiable
criteria. The discussion which follows demonstrates that the
Economic EPS framework is both solidly grounded in modern finance
theory and theoretically equivalent to the value of the firm
framework (see FIG. 4 for a road map of this discussion).
[0137] Moving to the Shareholders' Perspective
[0138] The value of the firm framework challenges the management of
a firm to maximize the total value of the firm, yet in practice,
management acts to maximize only the value of common shareholders'
stake and not the value of other stakeholders such as creditors,
debt holders, and convertible holders. As seen below, the total
value of the firm is:
Value of the Firm=Common Shareholders' Value+Other Stakeholders'
Value
[0139] Common Shareholders' Value=Number of Common
Shares.times.Share Value
[0140] Other Stakeholders' Value=Value of obligations to creditors
and bond, preferred and convertible holders.
[0141] The first step in moving toward a practical framework is to
adopt the shareholders' perspective by restating the objective:
Capital structure should be chosen to maximize the share value. MM
I can be restated from the shareholders' perspective as: In the
absence of taxes and financial distress, share value is independent
of capital structure as long as transactions are executed at fair
market value. In the real world, markets will determine how much of
the value of tax shields and the costs of financial distress are
distributed between common shareholders and other stakeholders.
Mispricing of instruments may also redistribute value between
stakeholders.
[0142] Moving to an Explicit Tradeoff Perspective
[0143] The value of the firm framework implicitly involves a
complex cost/benefit/risk tradeoff between the benefits of the tax
shield, and the costs and risks of financial distress. In practice,
few companies will have developed enough intuition regarding these
abstract quantities. The shareholders' perspective is more
intuitive. The value of the share can be written as a product of
EPS and the P/E ratio:
Price=P/E.times.EPS
[0144] Maximizing share value involves an implicit tradeoff between
P/E and EPS. Generally, trying to increase one decreases the other.
The next step in moving toward a practical framework is to recast
the objective in terms of an explicit tradeoff: Capital structure
should be chosen to optimize the tradeoff between EPS and P/E. MM I
can be restated from the explicit tradeoff perspective as: In the
absence of taxes and financial distress, although both EPS and the
P/E ratio depend upon leverage, the changes are exactly inversely
proportional so that share price is unchanged (or, in absence of
taxes and financial distress, Modigliani and Miller conclude that
EPS is linearly related to EPS risk). In the real world, if
shareholders receive some value from tax shields, are not charged
too much by creditors for the cost of financial distress, or
benefit from market mispricing, then EPS can be raised with a
smaller decrease in P/E than that predicted by MM I.
[0145] Moving to the EPS Framework
[0146] While P/E is an intuitive measure, it is not easy to see how
to calculate how it changes when the capital structure is changed.
Intuitively, certain companies have high P/E ratios because their
earnings are less risky than those of companies with low P/E
ratios. There exists the following relationship: 10 EPS Risk = a P
/ E - b
[0147] where a and b are constants. Maximizing share value involves
a tradeoff between EPS and EPS risk. Generally, trying to increase
EPS also increases EPS risk. The final step arrives at the Economic
EPS Framework: Capital structure should be chosen to optimize the
tradeoff between EPS and EPS risk. MM I can be restated in this
framework as: In the absence of taxes and financial distress,
although both EPS and EPS risk depend upon leverage, the changes
are linearly related in such a way that share price is unchanged.
(This is, in fact, a paraphrase of MM's Proposition II). In the
real world, if shareholders receive some value from tax shields,
are not charged too much by creditors for the cost of financial
distress, or benefit from market mispricing, then EPS can be raised
with a smaller decrease in P/E than predicted by MM I.
[0148] Of note, the above formula for EPS risk is derived from
these four relationships:
[0149] 1) Perpetuity: The P/E ratio of a perpetually growing
company is inversely proportional to its return on equity,
R.sub.E.
P/E=1/R.sub.E
[0150] 2) CAPM: Return on equity is equal to the risk free rate,
R.sub.F, plus beta times the market risk premium.
R.sub.E=R.sub.F+.beta..times.Market Risk Premium
[0151] 3) Beta: Equity beta is proportional to the equity return
risk, .sigma..sub.E.
.beta.=Constant.times..sigma..sub.E
[0152] 4) EPS Risk: EPS risk is proportional to equity return
risk
EPS Risk=Constant.times..sigma..sub.E
[0153] In another embodiment of the present invention simulation
analysis is utilized. That is, in order to accurately measure risk,
the Economic EPS impact of capital structure decisions may be
calculated using Monte Carlo simulation. Of note, this simulation
methodology is ideally suited for handling complexities of, for
example, Zero-put contingent convertible securities: fluctuating
dividends, path dependent tax basis, share price dependent tax
recapture, and uncertain call/convert/mature outcome. In any case,
in one example (which example is intended to be illustrative and
not restrictive), Economic EPS may be calculated using Monte Carlo
simulation as follows:
[0154] Generate Scenarios Generate numerous (e.g., thousands) of
realistic scenarios for future interest rates and stock prices
based upon current market conditions and historical experience.
[0155] Simulate Company Simulate behavior of the company's earnings
and behavior of each financing alternative over the market
scenarios, including (but not limited to) coupon, dividend, tax,
and principal cash flows; as well as shares outstanding. As
mentioned above, this methodology is ideally suited for handling
complexities of, for example, Zero-put contingent convertible
securities: fluctuating dividends, path dependent tax basis, share
price dependent tax recapture, and uncertain call/convert/mature
outcome.
[0156] Analyze Alternatives Analyze and compare financing
alternatives based upon stand-alone after-tax cash flow
characteristics. Analyze and compare how alternative restructuring
strategies change the company's EPS and EPS risk.
[0157] Analyze Strategies Perform optimization analysis to
determine the strategies that maximize EPS while minimizing EPS
risk. Determine the Capital Structure Efficient Frontier of
restructuring strategies.
[0158] Test Conclusions Rigorously test conclusions and recommended
strategies under adverse and contrarian scenarios. Discard
strategies that perform poorly under sensitivity scenarios.
[0159] Reference will now be made to a detailed example share
repurchase analysis (of course, this example is intended to be
illustrative and not restrictive). More particularly, we analyze a
$1 BN share repurchase transaction, financed with two competing
products: Call-monetized trust preferred securities (e.g. QUIPS)
and CUBZ/TUBZ/PLANZ. To summarize the results of this example share
repurchase analysis:
[0160] EPS: Call-monetized trust preferred securities lift expected
EPS marginally more than CUBZ/TUBZ/PLANZ.
[0161] EPS Risk: Call-monetized trust preferred securities increase
EPS risk significantly more than CUBZ/TUBZ/PLANZ.
[0162] Efficiency: CUBZ/TUBZ/PLANZ are more efficient than
call-monetized trust preferred securities because they have a
better trade-off between EPS and EPS risk.
[0163] More particularly, this example share repurchase analysis
may be carried out as follows:
[0164] Simulating The Company
[0165] Horizon: In order to fully capture the impact of long-dated
instruments, the simulation time horizon may encompass their
behavior over essentially their entire lives. For this reason the
analysis may simulate the company and the instruments over a
30-year horizon and compute the cumulative average behavior over
the horizon.
[0166] Common investing decisions: In order to fairly compare one
financing alternative to another over a time horizon, the analysis
may assume that the company makes the same investing decisions
throughout the horizon (identical assets) regardless of its capital
structure. Because different strategies use different amounts of
cash (an asset) over time, assets will begin to build up
differently from one strategy to another.
[0167] Using excess earnings to repurchase equity: Assets can be
kept the same between strategies by assuming that if an alternative
requires less cash than another (say a base case), the company uses
that excess cash to repurchase equity, bringing assets back in
line. As an added benefit, using earnings to repurchase equity also
prevents equity from building up differently from one strategy to
another.
[0168] Summary of Assumptions
[0169] Analysis Concept: In order to accurately measure EPS risk,
the Economic EPS impact of capital structure decisions may be
calculated using Monte Carlo simulation. Of note, this simulation
methodology is ideally suited for handling complexities, for
example, of TUBZ/CUBZ/PLANZ: fluctuating dividends, path dependent
tax basis, share price dependent tax recapture, and uncertain
call/convert/mature outcome.
[0170] Assumptions for the Analysis: In this example analysis
(which example is intended to be illustrative and not restrictive)
the following assumptions are made regarding Company XYZ's capital
structure, earnings, and dividends:
[0171] 3.4 BN shares with market value of $85.5 BN, or $25 share
price
[0172] EPS in line with 2002 I/B/E/S estimates of $1.65 per share,
annual uncertainty going forward of $0.15 per share
[0173] 2% dividend yield growing at an average rate of 7% per
year
[0174] 35% corporate tax rate
[0175] Analysis of After-Tax Cash Flows
[0176] The Capital Structure Efficient Frontier Model according to
the present invention is used to analyze $1 BN share repurchase
strategies, financed with alternatives including debt, equity,
trust preferred securities, or Zero-put Contingent Convertibles
(TUBZ/CUBZ/PLANZ).
[0177] The analysis begins by looking at each alternative from a
debt perspective, by focusing on the after-tax cash flows.
After-tax cash flows consist of all coupons, dividends, tax
credits, and tax recapture.
[0178] Neither a final principal payment nor share delivery is
included in the cash flow picture. The Economic EPS framework of
the invention is better suited to handle this complexity.
[0179] A calculation is performed regarding after-tax cash flows of
TUBZ/CUBZ/PLANZ versus equity and trust preferred on a bond
equivalent basis (see FIG. 5 and Table 7, below).
7TABLE 7 After-Tax Cash Flows Expected After-Tax Instrument Cash
Flow (%) TUBZ 2.76 CUBZ 3.69 PLANZ 3.67 Call-monetized QUIPS 3.66
Equity 5.56
[0180] Analysis of Share Repurchase Strategies
[0181] The cash flows above do not fully capture the "all-in" cost
and risk of strategy, since cash flows neither capture dilution nor
properly distinguish dividend cash flows. Economic earnings per
share provide a single metric for comparing both the cost and risk
of debt, equity and hybrid equity alternatives all in the same
unifying framework.
[0182] In this regard, the percentage change ("lift") in Company
XYZ's Expected EPS versus EPS risk resulting from each share
repurchase funding strategy is calculated. The strategies that form
the Capital Structure Efficient Frontier by maximizing Expected EPS
and minimizing EPS risk are then identified.
[0183] Of note, repurchasing shares with TUBZ/CUBZ/PLANZ increases
the lift in Economic EPS with only a small increase in EPS risk. In
this regard, TUBZ/CUBZ/PLANZ are superior to equity.
[0184] Of further note, repurchasing shares with Call-monetized
Trust Preferred Securities increases the lift in Economic EPS
slightly more, but increases EPS risk. From an EPS perspective,
TUBZ/CUBZ/PLANZ are superior to call-monetized trust
preferreds.
[0185] Referring now to simulation results, Table 8, below,
summarizes the results of this example (showing the impact of $1 BN
share repurchase on economic EPS); FIG. 6 shows the Capital
Structure Efficient Frontier; and FIG. 7 shows the Distribution of
Economic EPS lift).
8TABLE 8 (Impact of $1BN share repurchase on Economic EPS)
Percentage Percentage Change (Lift) Change (Lift) in Expected in
EPS Instrument EPS (bps) Risk (bps) TUBZ 57 15 CUBZ 46 31 PLANZ 46
30 30 Year Senior Debt 76 179 30 Year Subordinated Debt 75 172 Call
Monetized Trust Preferred 80 164
[0186] Sensitivity Analysis of Share Repurchase Strategies
[0187] The economics of the TUBZ/CUBZ/PLANZ financed share
repurchase transaction depends upon the assumed growth rate of the
share price. In general, at higher growth rates the economics are
expected to erode. A sensitivity analysis may be performed to
determine at what growth rate TUBZ/CUBZ/PLANZ become unattractive
relative to other alternatives.
[0188] Even at very high growth rates, TUBZ/CUBZ/PLANZ outperform
the behavior of the underlying shares on risk-adjusted EPS basis.
In this case, one benefit of the repurchase is just a free decrease
in shares outstanding. A second benefit is the large tax deduction
on the dividends. These benefits ensure that the TUBZ/CUBZ/PLANZ
financed repurchase outperforms other strategies on the Capital
Structure Efficient Frontier.
[0189] Of note, in this example, TUBZ dominate the Capital
Structure Efficient Frontier under all equity growth assumptions
(see FIG. 8).
[0190] As discussed above, one embodiment of the present invention
relates to a quantitative framework/methodology for analyzing a
company's existing capital structure and suggesting more efficient
financing alternatives. By showing the equivalence between the
dictum of modern finance theory that suggests that a company choose
the capital structure that maximizes the value of the firm with the
objective of optimizing the trade-off between economic earnings per
share and its volatility, the framework/methodology marries sound
theoretical foundation with an easily observable, measurable and
implementable process.
[0191] Economic EPS (EEPS) and its volatility captures the
cost/risk trade-off of all fixed income and equity-related
alternative capital structures. A company should strive to bring
its capital structure to the Capital Structure Efficient Frontier
of strategies with the highest EEPS for given levels of EEPS risk.
New financing alternatives claiming to be adding value to the
existing capital structure only do so if they expand this Capital
Structure Efficient Frontier. The Capital Structure Efficient
Frontier of the present invention concludes that innovative
financing products/strategies should be considered seriously if and
only if they improve EEPS per unit risk more than what can be
achieved by combining existing debt and equity strategies and
therefore expand the Capital Structure Efficient Frontier.
[0192] Contingent convertible securities that are described and
analyzed in detail below are examples (which examples are intended
to be illustrative and not restrictive) of financial innovation
that meet the criteria outlined above. By providing higher level of
EEPS per unit of risk than other available strategies that combine
debt and equity products helps to optimize corporate capital
structures in current markets.
[0193] The examples below will focus on two main classes of
contingent convertible securities: 1) Zero-put Convertibles (e.g.,
TUBZ, CUBZ and PLANZ); and 2) Zero-coupon Convertibles (e.g.,
STARZ, CARZ). After describing the basic features of the securities
their behavior over time will be analyzed, highlighting the
critical properties stemming from embedded options in their
structure with respect to economic, accounting and tax-related
variables. The rigorous simulation and optimization based analytic
framework of the present invention is the appropriate microscope to
get to the level of granularity that is needed to understand the
pros and cons of any structure that claims to have superior
properties to existing and well understood financial products.
[0194] Of note, Zero-put Convertibles are characterized by the
absence of an investor put option. The TUBZ structure typifies this
class and has the following features (CUBZ and PLANZ are variations
on the TUBZ structure with modifications in the coupon cash flows,
call/conversion schedule, and conversion premium):
[0195] Long maturity (e.g., 30 years).
[0196] Low non-contingent coupon (e.g., 3%).
[0197] Contingent coupon equal to dividend on underlying shares
minus a spread (e.g., 1.0%), floored at zero.
[0198] Convertible at a conversion premium (e.g., 10%), provided
the value of underlying shares is above a threshold (e.g., 110% of
the conversion price).
[0199] Callable at par on or after a non-call period (e.g., year
5).
[0200] Not putable by investor.
[0201] Zero-coupon Convertibles are characterized by a low coupon.
The CARZ structure typifies this class and has the following
features:
[0202] Long maturity (e.g., 30 years).
[0203] Zero non-contingent coupon.
[0204] Proceeds may be less than principal (e.g. 10% discount,
accreting at 2% interest rate).
[0205] Contingent coupon equal to zero until first put date, and
equal to dividend on underlying shares thereafter, provided the
trading price of the CARZ exceeds a threshold (e.g., 120% of
principal amount).
[0206] Convertible at a conversion premium (e.g., 25%) on or after
a non-convert period (e.g., 5 years) provided value of underlying
shares is above a threshold (e.g., 110% of conversion price).
[0207] Callable at par on or after a non-call period (e.g., 5
years).
[0208] Putable at par on discrete put dates (e.g., every 5
years).
[0209] Interest adjustment provision. On each put date, if the
value of underlying shares is below the conversion price, interest
adjustment is triggered: (1) on the first adjustment, the
conversion price is permanently elevated (e.g., tripled); (2) the
contingent coupon is reset to an interest rate so that CARZ are
judged to be worth, for example, 102% of principal value; (3) the
dividend pass through is turned off until the next put date; and
(4) the issuer's call is turned off until the next put date.
[0210] STARZ is a strategy that combines a CARZ structure with a
purchased variable share repurchase contract. The CARZ underlying a
STARZ strategy is issued typically at par (0% discount, 0% interest
rate) by reducing the conversion premium (e.g. 12.5%). The variable
share contract of this example has the following features:
[0211] Purchased by company for a premium (e.g., for 10% of CARZ
principal). The net proceeds are therefore less than the principal
of the CARZ (e.g., 90% of CARZ principal).
[0212] Maturity matching the first put/call date of the CARZ (e.g.,
5 years).
[0213] Company receives payment in the form of shares. The number
of shares delivered varies within a limited range depending upon
the share price at maturity (e.g. 0 shares if share
price<=112.5% of current share price, 2.6 shares if share
price>=147% of current share price, and varying in between).
[0214] Since, in this example, STARZ turn out to be the most
attractive economically, the following discussion will center
around an analysis of this structure. The framework/methodology of
the present invention, however, is applicable to any of these
structures (as well as other financing mechanisms), and throughout
the discussion certain results for other alternatives and certain
differences therebetween will be noted.
[0215] As a general outline, the key features of these contingent
convertibles will be discussed below first and the factors driving
their economics will be discussed (including their intricate tax
treatment). Next the instruments will be analyzed in a
probabilistic simulation framework according to the present
invention, comparing their cash flows and dilution impact with both
debt and equity. Finally, cash flow and dilution effects will be
combined in an Economic EPS framework embodiment according to the
present invention (which allows comparison of capital structure
alternatives including contingent convertibles, debt, and equity
using a single unifying economic metric).
[0216] As will be seen below, for most tax-paying issuers,
economically, contingent convertibles are lower cost, less dilutive
alternatives to combinations of debt and equity (Contingent
convertibles may or may not be suitable as a replacement for equity
from a ratings perspective. While Zero-put structures receive some
rating agency equity credit due to the absence of an investor put,
Zero-coupon structures receive no equity credit). With their
favorable cost/risk trade-off, these structures broaden the range
of financing alternatives and significantly expand the Capital
Structure Efficient Frontier.
[0217] Referring now to tax treatment, it is noted that interest on
convertible bonds is generally tax deductible, but since the
coupons are typically lower than on straight debt, the tax
deduction has limited economic value. This discussion assumes that
contingent convertibles will meet the requirements for contingent
payment debt treatment, which allows the issuer to take tax
deductions based upon interest accrued at the issuer's higher
straight debt rate rather than at the lower stated coupon rate (see
IRS Revenue Ruling 2002-31; See also .sctn. 1.1275-4 of the Income
Tax Regulations regarding contingent payment debt instruments).
This tax treatment greatly enhances the attractiveness of these
structures as low cost alternatives to ordinary equity.
[0218] Deducting interest based upon the straight debt rate does
not mean that the tax deduction is equal to that of straight debt
with the same principal. Rather, the tax deduction is calculated
based upon a level yield methodology. Each year the tax-deductible
interest expense is equal to the level yield multiplied by a tax
basis, in much the same way that GAAP interest expense for a fixed
rate bond is equal to the level yield multiplied by bonds payable.
In both cases, the calculation of the basis is based upon
projections of the coupon cash flows (The evolution of the tax
basis can be calculated when the instrument is issued, by
estimating expected future (perhaps, probability weighted)
contingent cash flows and tax deductions, assuming a constant stock
growth rate. The stock growth rate is chosen so that the IRR of the
projected pre-tax cash flows is equal to the straight debt rate).
But, whereas the coupon cash flows can be projected for the fixed
rate bond, they will differ from projections for the contingent
convertible. As a result, for the purposes of calculating taxes on
contingent convertibles, the tax deductible interest expense is
adjusted each period for any difference between actual and
projected cash flows.
[0219] Generally speaking, under GAAP, if the actual interest paid
in cash or interest payable accrued on a fixed rate bond in a year
is less than the interest expense, bonds payable is adjusted upward
to account for the difference. Similarly for the tax treatment of
contingent convertibles, if the actual cash paid or payable is less
than the tax deductible interest expense, the tax basis is
increased. Applying the same level yield to this new tax basis
results in a higher tax deduction in the next year, which in turn
increases the tax basis for the following year. As long as the
actual cash flow remains below the deductible expense, the tax
basis continues to accrete over time, producing a chain reaction of
increasing tax deductions.
[0220] Under GAAP, if at maturity, the amount paid to retire the
bond is less than bonds payable, then the excess amount is
recognized as a gain. Similarly, if at termination, the amount paid
to retire a contingent convertible is less than the tax basis, then
the excess amount is recognized as a taxable gain, subject to tax
recapture. If the contingent convertible terminates with the
delivery of the principal, then tax is based upon the difference
between the tax basis and the principal. If, however, it terminates
with the delivery of shares, then tax is based upon the difference
between the tax basis and the value of the shares. As long as the
value of the shares exceeds the projected tax basis, there will be
no tax recapture.
[0221] As an example (which example is intended to be illustrative
and not restrictive), Company XYZ raises $90 through a STARZ
strategy with the properties described above. The underlying CARZ
has a principal of $100 and the variable share repurchase contract
has a premium of $10. We assume that interest on the CARZ is
deductible based upon a 7.00% straight bond yield and that the
corporate tax rate is 35%. Table 9, below, shows the cash flows and
tax calculations under a scenario in which Company XYZ initially
pays dividends based upon a 1.50% dividend yield and dividends grow
at 7% per year.
9TABLE 9 STARZ Cash Flows for a Single Scenario Pre-Tax Cash Flow
Tax Credit Calculation Underlying Coupon Projected Projected
Deductible End of After-Tax Year Share Value Cash Flow Cash Flow
Expense Expense Year Basis Credit Cash Flow 1 93.51 0.00 0.00 7.00
7.00 107.12 2.45 -2.45 2 98.37 0.00 0.00 7.50 7.50 114.75 2.62
-2.62 3 103.49 0.00 0.00 8.03 8.03 122.93 2.81 -2.81 4 108.87 0.00
0.00 8.60 8.60 131.68 3.01 -3.01 5 114.53 0.00 0.00 9.22 9.22
141.06 3.23 -3.23 6 120.49 1.81 4.02 9.87 7.66 147.02 2.68 -0.87 7
126.75 1.90 4.50 10.29 7.69 152.91 2.69 -0.79 8 133.34 2.00 4.55
10.70 8.15 159.17 2.85 -0.85 . . . 29 386.64 5.80 6.94 26.45 25.32
397.76 8.86 -3.06 30 406.74 6.10 6.96 27.84 26.98 419.00 9.44
-3.34
[0222] In year 1, Company XYZ pays $0.00, while deducting interest
expense of $7.00 (=7.00% times a tax basis of $100). No adjustment
is necessary since the actual cash flow is equal to the projected
cash flow. The tax basis grows to $107.12
(=$100+$7.00-$0.00+semi-annual compounding). This sets the chain
reaction in motion. In year 2, Company XYZ pays $0.00 while
deducting $7.50 (=7.00%.times.$107.12), and the tax basis grows
further to $114.75 (=$107.12+$7.50-$0.00+semi-annual
compounding).
[0223] Over time this is how the cash flows evolve. In year 1, the
tax credit is 2.45 (=.times.7.00.times.35%) and the after-tax cash
flow is -2.45 (=$0.00-$2.45). In year 2, the tax credit is 2.62
(=7.50.times.35%) and the after-tax cash flow is -2.62
(=$0.00-$2.62).
[0224] A number of factors affect the tax credit enjoyed by Company
XYZ:
[0225] Through year 5, projected and actual cash flows are
identical and equal to zero. As a result, projected and actual
tax-deductible expense are the same. In this particular scenario,
starting in year 6, the contingent coupon is payable, and actual
and projected cash flow differ. Actual cash flows fall short of
projections, and the tax deductible expense needs to be adjusted
downward. The actual tax credit appears to depend sensitively on
the growth rate of dividends (See FIG. 9). Tax credits would be
lower for lower growth rates. From the table, however, it is
apparent that even in the worst case, in which dividends are zero,
the actual tax credit would remain high.
[0226] In fact however, if low dividends are due to low stock
prices, the interest adjustment provision in the underlying CARZ
would be triggered at the first put date, essentially converting
the security into a bond. Actual payments would then likely be
higher than projected payments. (See the low growth scenario in
FIG. 9).
[0227] Company XYZ may have to pay tax recapture if the underlying
CARZ is converted to shares that are worth less than the projected
tax basis. FIG. 10 illustrates how the tax recapture depends upon
the stock growth rate (assuming that the STARZ is not called
early). In this example, as long as the stock price grows at an
average rate of 5.24% or higher per year over 30 years, the
underlying shares will exceed the $419.00 projected tax basis, and
there would be no tax recapture. Company XYZ keeps fully all
accumulated tax credits (net tax credit=cumulative tax credit in
FIG. 10). Even if the growth rate is slower than this threshold,
however, the accumulated tax credits will be larger than the tax
recapture. The interpretation is that Company XYZ is simply
returning a portion of the excess tax credits that it has enjoyed
through the life of the instrument. The worst case outcome is that
the price of the underlying CARZ falls below par, triggering the
interest adjustment, and tax recapture is based upon the difference
between the projected tax basis and par.
[0228] If Company XYZ's tax rate were lower, the corresponding tax
credits would be lower and the after-tax cash flows would be less
favorable. A company with a low tax rate would benefit less by
tax-advantaged structures such as STARZ.
[0229] Of note, the tax treatment of other Zero-coupon and Zero-put
contingent convertibles is essentially the same as for STARZ.
[0230] Referring now to an investor conversion option, it is noted
that in this example the investor has the right to convert the
underlying CARZ to shares on or after year five if the share price
is 10% or higher than the conversion price. However, the investor
receives no immediate benefit by doing so because it would then
simply receive the same dividends that it would be receiving
already, and would simply be giving up its put option to receive
par should the share value fall below par. While the investor would
never convert early, converting at maturity may be very beneficial.
The investor would convert at maturity as long as the share price
exceeds the conversion threshold at maturity. With reasonable
conversion premium and annual share appreciation, this scenario is
very likely.
[0231] Likewise an investor is unlikely to convert a Zero-put
Contingent Convertible early. In the TUBZ structure, the investor
has the right to convert to shares at any time if the share price
is 10% or higher than the conversion premium. But, by converting,
the investor would simply be giving up a spread (e.g., 2%) and a
floor (e.g., 1%) on the dividend. CUBZ typically have a higher
conversion premium (e.g., 20%) than TUBZ, while PLANZ typically
have a conversion premium that is determined at the end of a
non-convert period (e.g., 10%-30%, depending upon the stock price
at year 3).
[0232] Referring now to an investor put option, it is noted that
the investor also has the right to put the underlying CARZ at par
(e.g., every five years). However, the CARZ is structured to deter
the investor from doing so by providing the investor with the
economic benefits of putting the security without returning capital
to the investor. When the investor would want to put the security
to receive par, the interest adjustment essentially delivers to the
investor a bond that is worth a small premium above par. This
interest adjustment makes the security a more permanent form of
capital. However, it also makes the cash flows highly sensitive to
the stock price on the put dates (Zero-put Contingent Convertibles
are not putable by the investor).
[0233] Referring now to an issuer call option, it is noted that the
issuer has the right to call the STARZ at par (e.g., on or after
year 5). If the issuer does call the bond, the investor would most
likely exercise its conversion option, resulting in a forced
conversion. As a result, by calling, the issuer trades the
after-tax cash flows of the underlying CARZ for the dividends on
the underlying shares. Given the tax benefits of the CARZ, it seems
unlikely that the issuer would have any incentive to do this.
[0234] The issuer would similarly have little incentive to give up
its tax deduction by calling and forcing conversion of a Zero-put
Contingent Convertible security early.
[0235] Referring now to an issuer variable share repurchase
contract, it is noted that in the STARZ strategy, the issuer pays
investors in advance for the delivery of a number of shares at the
first put/call date of the underlying CARZ, with the number of
shares depending upon the share price on that date. Economically,
this transaction is unrelated to the rest of the structure (the
CARZ portion), and is simply a hedging transaction on the side
designed to increase the effective conversion premium. The purchase
of this stock option is essentially a nontaxable equity
transaction.
[0236] Referring bow to other issuer options, it is noted that
Zero-put securities may have other modifications. For example, in
the TUBZ structure, the dividend is typically floored at some
minimum level (e.g., 1.0% of par value). This option gives the
investor a small measure of protection against a deterioration in
the company's dividends. However, by increasing the guaranteed
portion (non-contingent) of the coupon, the floor ensures that the
pre-tax debt content of the TUBZ is over 50%. Debt content greater
than 50% is a guideline for receiving contingent payment debt
treatment. By comparison, the CUBZ structure does not include a
dividend floor option. To compensate for the reduction in debt
content, the CUBZ is structured with a higher non-contingent coupon
(e.g., for the first three years).
[0237] This discussion will now turn to valuation analysis. More
particularly, it is noted that valuing Zero-put Contingent
Convertibles is not straightforward, particularly since the value
for both the issuer and investor depends upon the decisions of the
issuer, which take into account tax considerations. To build some
intuition regarding the factors driving the economics, this portion
of the discussion will be directed to estimating the net
theoretical value of the STARZ package to both the investor and the
issuer.
[0238] Referring now to a value to investor, it is noted that from
the investor's perspective, the STARZ package looks a lot like
equity, with enhancements (see Table 10, below).
10TABLE 10 STARZ Valuation Analysis (35% Tax Rate) Investor Issuer
Total Underlying Stock 88.89 -88.89 0.00 Adjustment -16.67 16.67
0.00 Investor Put 19.29 -19.29 0.00 Issuer Call -0.60 0.60 0.00 Tax
Credit 0.00 51.27 51.27 Value 90.92 -39.65 51.27 Proceeds -90.00
90.00 0.00 Net Theoretical Value 0.92 50.35 51.27
[0239] Underlying each $100 principal (of the underlying CARZ) are
shares worth, in this example, $88.89 (=$100/(1+12.5% Conversion
Premium)). For the most part, the investor receives dividends on
these shares and also participates in the appreciation of these
shares, just like common shares. However, some adjustments are
necessary. For the first 5 years, for example, the investor
receives no dividends and thereafter receives dividends only if the
value of the shares exceeds a threshold. Also, the investor may
have to deliver some shares (e.g., at year 5) because of the
variable share repurchase contract. The value to the investor must
be adjusted downward by, for example, $16.67 for these effects.
This is compensated for by the investor's put option, or
equivalently the interest adjustment, which is worth, in this
example, $19.29. The investor is also short the issuer's call
option. If the STARZ is called early, the investor loses the
remaining benefits of the put option. However, when the tax rate is
sufficiently high, the issuer is unlikely to exercise early. For
the purposes of this discussion, the effective cost of the call
option is estimated to be only $0.60, resulting in total value to
the investor of $90.92 (=$88.89-16.67+19.29-1.52). The net
theoretical value of $0.92 (=$90.92-90.00) is defined as the
difference between the value of the STARZ and the price paid for
it. For the investor, the net theoretical value is relatively
insensitive to the issuer's tax rate. At low tax rates, the call
option is more likely to be exercised very early, since the issuer
would no longer be accruing valuable tax benefits. The cost of the
call option increases slightly, and the value of the STARZ for the
investor decreases, as the tax rate is decreased and the issuer has
less incentive to keep the STARZ outstanding (see FIG. 11). In
fact, at zero tax rates the net theoretical value to the investor
falls to zero. Referring now to value to issuer, it is noted that
if the STARZ has positive net value to the investor, it might seem
that it should have negative net value to the issuer. Indeed it
would, if the transaction were a zero-sum game, as it is when tax
rates are zero. At zero tax rates, STARZ has zero net theoretical
value to the issuer. Non-zero tax rates, however, introduce a third
party, the government, that changes the economics for the issuer
and the investor. The issuer receives tax credits from the
government that increase with the tax rate. For example, at a 35%
tax rate, the issuer receives a tax credit of $51.27, so that the
net theoretical value of the STARZ issuance to the issuer is
$50.35, equal to the proceeds of the issuance plus the tax credit
minus the value of the liability (=$90.00+51.27-90.92).
[0240] The transaction between the issuer and the investor is no
longer a "zero-sum" transaction because the government contributes
value equal to the tax credits on the STARZ. The terms of the
STARZ, or pricing, determine how this added value is shared between
the investor and issuer. The pricing clearly favors the issuer,
with the issuer accruing almost all the benefits of the tax
credits. With appropriate pricing, the STARZ can have positive net
theoretical value for both the issuer and the investor (The
government may also tax the investor's income. As long as this tax
liability is smaller than the issuer's tax credit, there is a net
tax credit that can be shared between the issuer and the
investor).
[0241] A similar analysis applies to Zero-put convertibles. Table
11, below, shows an example for the TUBZ structure.
11TABLE 11 TUBZ Valuation Analysis (35% Tax Rate) Investor Issuer
Total Underlying Stock 90.91 -90.91 0.00 Adjustment -1.64 1.64 0.00
Interest 24.93 -24.93 0.00 Issuer Call 1.53 -1.53 0.00 Tax Credit
0.00 42.72 42.72 Value 118.01 -75.29 42.72 Proceeds -100.00 100.00
0.00 Net Theoretical Value 18.01 24.71 42.72
[0242] The investor put and the adjustment play a much smaller (or
no) role in these securities. In their place, the interest
component associated with the non-contingent coupon has significant
value to the investor.
[0243] The discussion will now turn to EEPS Framework and
Simulation Analysis. More particularly, because of their hybrid
nature, a meaningful analysis of contingent convertibles must
include both debt and equity-related factors. From the debt
perspective, coupon cash flows are paid out during the life of the
instrument, incurring a negative impact on the issuer's earnings.
From the equity perspective, contingent convertibles immediately
reduce the earnings participation for existing shareholders,
because these convertible holders are entitled to a share of
earnings paid out in the form contingent coupons related to the
dividend, as well as retained earnings. In order to contextualize
hybrids and be able to compare them with both pure debt and pure
equity instruments, under an embodiment of the EEPS Framework of
the present invention earnings and dilution are included and
combined to achieve a unified measure that can be employed as an
effective tool to aid with capital structure decisions.
[0244] In order to accurately measure and analyze the cash flows,
dilution effects, and risk characteristics of contingent
convertibles, an embodiment of the present invention may utilize a
Monte Carlo simulation methodology. Within such simulation model, a
large number (e.g., 10,000) stock price and interest rate paths may
be generated using historical volatilities and correlations as well
as the current term structure of interest rates. Along each path,
the behavior of the instrument may be computed given the behavior
of stock prices and interest rates along that path. Through this
methodology, the after-tax cash flows over each path may be
calculated and the resulting economics may be measured against
alternative strategies for the issuer. The expected economics of
the instrument may be based upon the average behavior of the
instrument across all (e.g., 10,000) paths. Meanwhile, the full
distribution gives a perspective on how much the actual economics
may differ from its expected value and the probability of this
occurring.
[0245] Continuing now with the example in which Company XYZ raises
money through a STARZ issuance strategy, the discussion will
further assume that Company XYZ's stock price is $80.0 per
share.
[0246] In order to fully capture the impact of long-dated
instruments, the simulation should use a time horizon that
encompasses their behavior over their entire lives. For this
reason, the company and the instruments may be simulated over a
30-year horizon and the cumulative average behavior may be computed
over the horizon. In order to fairly compare one financing
alternative to another over such an extended time horizon, the
simulation may need to make the assumption that the company makes
the same investing decisions throughout the horizon (identical
assets) regardless of its capital structure. Because different
strategies use different amounts of cash (an asset) over time,
assets will begin to build up differently from one strategy to
another. Assets may be kept the same between strategies by assuming
that if an alternative requires less cash than another (say the
do-nothing strategy), the company uses that excess cash to
repurchase equity, bringing assets back in line. As an added
benefit, using earnings to repurchase equity also prevents equity
from building up differently from one strategy to another.
[0247] Referring now to expected life, it is noted that before
entering into a detailed analysis of the earnings and dilution
impact of the STARZ, it is useful to enumerate the possible ways in
which the underlying CARZ can terminate and to assess the
probability of each (see FIG. 12, for example):
[0248] Called/Forced Conversion: The security is called by the
issuer before the final maturity date, forcing the investor to
convert. The issuer delivers the underlying shares to the
investor.
[0249] Put: The security is put by the investor before the final
maturity date and terminates early.
[0250] Converted: The security is converted by the investor at
maturity. The issuer delivers the underlying shares to the
investor. This includes scenarios in which the conversion price has
tripled as a result of an interest adjustment and the share price
recovers enough so that the conversion option is in the money.
[0251] Matured: The security is retired at maturity. The issuer
repays the principal to the investor. This includes scenarios in
which the interest adjustment is in effect until maturity.
[0252] From the simulation results of this example, it is clear
that for Company XYZ, the CARZ underlying a STARZ strategy behaves
much like equity, ultimately converting 94% of the time into the
underlying shares, and paying a contingent coupon economically
equivalent to the dividend for much of the time. This may be
surprising given the potential for the conversion price to triple
as a result of the interest adjustment provision. But even at the
elevated conversion price, at reasonable growth rates, most of the
time there is sufficient time for the stock price to recover and
drive the conversion option in-the-money. From a tax perspective,
the STARZ behaves much like debt, since most of the time--more than
99% of all outcomes--it survives until final maturity, allowing the
issuer to enjoy a full 30 years of enhanced tax deductions. The
likelihood of the STARZ being put or called early in this example
is less than 1%.
[0253] Referring now to debt perspective and after-tax cash flows,
it is noted that the STARZ strategy will be tackled first from a
debt perspective, and will focus initially on the cash flows (The
focus will be on the coupon and tax cash flows, and will set aside
for the moment the termination "cash flows" associated with
repaying the principal or delivering shares). The after-tax cash
flows of contingent convertibles are not straightforward for
several reasons:
[0254] The pre-tax cash flow may depend upon the dividends paid on
underlying shares or on the interest adjustment.
[0255] The tax recapture cash flow may depend upon the share price
at termination.
[0256] The maturity of the instrument is uncertain.
[0257] The simulation framework of an embodiment of the present
invention is well suited to handle these complexities, generate a
realistic distribution of the after-tax cash flows of these
instruments, and compare these cash flows with debt and equity. In
order to capture the full spectrum of possible outcomes, the
simulation framework may compare the after-tax cash flows of
contingent convertibles with debt and equity over a 30-year
analysis horizon.
[0258] FIG. 13 shows the distribution of average annual after-tax
cash flows for the STARZ of this example over the 30-year horizon.
The STARZ are compared with 30-year senior debt. On a cash flow
basis STARZ compares favorably with 30-year debt, with an expected
average annual aftertax cash flow of -1.18% compared with 4.55%
(=7.00% pre-tax coupon.times.65% tax effect) for senior debt. For
Company XYZ, the STARZ cash flows exceed the debt cash flows only
1% of the time and has a shortfall risk relative to debt of only 1
bps (Shortfall risk relative to a benchmark is defined here as the
probability that the cash flow exceeds the benchmark multiplied by
the expected excess).
[0259] Unlike the cash flows of senior debt, which are fixed, the
cash flows of equity are equal to the dividends on the shares,
which differ depending upon the scenario. To compare STARZ with
equity, it is necessary to compare their cash flows on a
scenario-by-scenario basis. FIG. 14 shows the distribution of
average annual after-tax cash flows savings that STARZ offer
compared with equity. The after-tax cash flow savings compared with
equity is striking, averaging 487 bps and falling below zero less
than 3% of the time. The shortfall risk is less only 4 bps. The
after-tax cash flows for debt, equity, and some Contingent
Convertibles are summarized in Table 12, below.
12TABLE 12 After-Tax Cash Flows Instrument Mean Std Debt 4.55%
0.00% Equity 3.69% 1.31% STARZ -1.18% 1.33% CARZ -0.72% 1.25% TUBZ
1.13% 0.74% CUBZ 2.43% 0.68% PLANZ 2.45% 0.62%
[0260] By focusing on average annual cash flows, this methodology
has captured the average behavior over time, but has not fully
represented the potential lumpiness of those cash flows over time.
Cash flows may in fact be lumpy because some of the tax savings
accrued over the life of a contingent convertible may have to be
returned, in the form of tax recapture, upon termination. The
effect of tax recapture has been incorporated in computing the
average annual cash flows. In order to provide more detail on the
timing of the STARZ cash flows, its tax recapture cash flows are
broken out in FIG. 15. In most cases, the stock price is higher
than the projected tax basis and no tax recapture is warranted.
[0261] After-tax cash flows capture only part of the economics of
debt, equity and convertibles and should not be misinterpreted as
cost. Cash flows do not capture the distinction between the payment
of principal at maturity and the conversion into shares.
[0262] The discussion will now turn to equity perspective and
dilution. Addressing contingent structures next from the equity
perspective, the discussion will focus on dilution. As noted above,
in this example there is a very high probability that CARZ holders
ultimately become shareholders, and will therefore own a share of
the equity of the company, including any accumulated retained
earnings. Due to the contingent coupon, CARZ holders also receive a
share of any earnings distributed in the form of contingent coupons
that are economically equivalent to dividends. Debt, equity and
STARZ have significantly different dilution effects. Assuming the
facts for Company XYZ, raising $1000 of each has the following
dilution effect (To raise $1000 through the STARZ strategy, XYZ
must issue a CARZ with $1111 (=$1000/90%) principal):
[0263] Debt does not dilute.
[0264] Equity dilutes by 12.5 shares (=$1000/$80).
[0265] The STARZ strategy has two elements of dilution. The
underlying CARZ dilutes by zero shares if not converted, by 12.3
shares (=$1111/[112.5%.times.$80]) if converted without intervening
interest adjustment, and by 4.1 shares
(=$1111/[3.times.112.5%.times.$80]) if converted after interest
adjustment. The variable share repurchase contract reduces the
dilution by up to 2.9 shares (=$l 111.times.2.6/$1000) when the
share price in year 5 is greater than the conversion price on the
CARZ.
[0266] While the dilution impact of debt and equity is fixed and
certain, the impact of STARZ is not. FIG. 16 shows the distribution
of the increase in shares for each instrument. STARZ behave very
much like equity but result in not only smaller expected after-tax
cash flows but also less dilution. Compared with debt, the extra
dilution of STARZ should be regarded as an additional cost, which
could outweigh the after-tax cash flow savings of the
instrument.
[0267] The discussion will now turn to combined perspective and
EEPS. More particularly, cash flows and dilution offer two
perspectives on the contingent structures that yield insight into
their properties in comparison to debt and equity. However, with
two metrics, it remains difficult to rank these alternatives based
upon their "all-in" cost/risk trade-off. One embodiment of the
present invention relates to a quantitative framework based upon
EEPS that is both intuitive and implementable, and yet firmly
grounded in modern finance theory. EEPS provides a single metric
for comparing both the cost and risk of debt, equity, and hybrid
equity alternatives all in the same unifying framework. EEPS
measures how much of each period's income each existing shareholder
is entitled to. For simple capital structures, the EEPS calculation
of an embodiment of the present invention is essentially no
different than the basic EPS calculation: adding debt lowers
earnings, the numerator in the calculation; while adding equity
raises the number of shares, the denominator. EEPS is lowered in
either case, but through very different mechanisms (The money
raised by either form of financing would presumably be deployed to
increase EEPS through investment, liability management, or share
repurchase).
[0268] With hybrids, it is important to make a distinction between
EEPS and reported EPS. For financial reporting, it is believed
that, depending upon the structure, issuers determine dilution
caused by contingent convertibles using either the "treasury stock"
method or the "if-converted" method. For the purposes of evaluating
economics, the EEPS metric of the present invention recognizes that
contingent convertibles: (1) reduce the income that is available to
shareholders, like debt; and (2) increase the number of claims on
that income, like equity.
[0269] To illustrate this framework, the discussion will again
consider Company XYZ, making the additional assumptions shown in
Table 13
13TABLE 13 Company XYZ Capital Structure and EEPS Before
Restructuring Capital Structure Number of Shares 50 MM Share Price
$80 Equity $4000 MM Debt $2000 MM Average Annual Earnings Earnings
$250 MM Earnings Risk $35 MM EEPS $5.00 EEPS Risk $0.70
[0270] Strategies are compared in which Company XYZ restructures
10% of its capital by raising $600 million and using the proceeds
to repurchase existing equity or debt. FIG. 17 shows EEPS and EEPS
risk of STARZ, CARZ, TUBZ and CUBZ, and compares these with debt
and equity issuance. Except for the Zero-coupon and Zero-put
securities, restructuring alternatives essentially fall along a
line that defines the debt/equity Capital Structure Efficient
Frontier. Along this Capital Structure Efficient Frontier the
trade-off between EEPS and EEPS risk is roughly constant. Both
Zero-coupon and Zero-put convertibles expand the Capital Structure
Efficient Frontier, offering a trade-off superior to those on the
debt/equity Capital Structure Efficient Frontier. Compared with the
current capital structure in this example, replacing a combination
of debt and equity with contingent convertibles boosts EEPS
essentially without increasing EEPS risk. Compared with equity,
these instruments result in much higher EEPS and only slightly
higher EEPS risk, while compared with debt, they result in lower
EEPS risk and only slightly lower EEPS. These quantitative EEPS
findings confirm the qualitative intuition developed when viewing
the structure from the debt and equity perspectives. The results
are summarized in Table 14, below, where the EEPS shortfall risk is
also calculated.
14TABLE 14 Company XYZ's EEPS After Restructuring EEPS Statistics
($) Shortfall Strategy Average STD Risk CURRENT CAPITAL STRUCTURE
5.00 0.70 0.24 + 10% EQUITY - 10% DEBT 4.82 0.61 0.34 + 10% DEBT -
10% EQUITY 5.24 0.82 0.22 + 10% STARZ - 10% CURRENT 5.59 0.72 0.08
+ 10% STARZ - 10% DEBT 5.41 0.65 0.10 + 10% STARZ - 10% EQUITY 5.69
0.76 0.07 + 10% CARZ - 10% CURRENT 5.50 0.70 0.10 + 10% TUBZ - 10%
CURRENT 5.18 0.68 0.19 + 10% PLANZ - 10% CURRENT 5.00 0.69 0.28 +
10% CUBZ - 10% CURRENT 5.11 0.69 0.23
[0271] The economics of financing share repurchase with contingent
convertibles depends upon the assumed growth rate of the share
price. Sensitivity analyses were performed to determine whether, at
certain growth rates, STARZ become unattractive relative to other
alternatives (see FIG. 18). As expected, that even at very high
growth rates, STARZ simply behave asymptotically like the
underlying shares, but with tax-deductible dividends. The net
result of the repurchase is a slight reduction in shares
outstanding and an increase in income available to common
shareholders. This combination essentially guarantees that at any
growth rate, STARZ-financed share repurchase outperforms any
strategy based upon debt and equity alone.
[0272] Accordingly, as discussed above, contingent convertibles
offer a tremendous opportunity for issuers to raise funds in a way
that is more attractive from an economic cost/risk perspective than
combinations of debt and equity. These securities are not only
attractive on a cash flow basis in comparison to senior debt and
equity, but also significantly expand the Capital Structure
Efficient Frontier when viewed in an economic EPS perspective. They
provide advantages of both debt and equity and provide corporate
CFO's and treasurers with the means of truly optimizing their
capital structure.
[0273] In another embodiment, the Economic EPS
framework/methodology can account for the differences in risk
between debt and equity as well as provide a unifying framework for
analyzing and comparing the broader set of hybrid alternatives
along the debt/equity continuum.
[0274] In another embodiment, P/E Ratio is a measure of EPS risk:
lower P/E means higher EPS risk.
[0275] Perpetuity: P/E ratio=1/Return on Equity
[0276] CAPM: Return on Equity=Risk Free Return+Equity
Beta.times.Market Risk Premium
[0277] Beta=Correlation.times.Equity Return Risk/Market Return
Risk
[0278] EPS Risk=Equity Return Risk.times.Price
[0279] In another embodiment, if shareholders receive some value
from tax shields, are not charged too much by creditors for the
cost of financial distress, or benefit from market mispricing, then
EPS can be increased with a smaller increase in EPS risk than
predicted by Modigliani Miller.
[0280] In another embodiment, the Monte Carlo simulation may
propogate a random variable over time, may create and/or utilize a
probability distribution of Economic EPS, and/or may be utilized in
the context of determining which scenario will give the highest EPS
(e.g., Economic EPS) per unit risk of EPS (e.g., Economic EPS).
[0281] In another embodiment, the present invention relates to a
methodology for decomposing an instrument (e.g., a security) into a
debt component and an equity component (e.g., in the context of
EPS).
[0282] In another embodiment, the retained EPS component of
Economic EPS may equal: (earnings without taking effect of any
interest expense from the equity-related security minus attributed
after-tax interest expense from the equity-related security)
divided by (the number of common shares plus the number of
attributed shares from the equity related security).
[0283] In another embodiment, Economic EPS may result in net
accretion from a purchased variable share repurchase contract
(e.g., for a low P/E issuer).
[0284] Of note, the method embodiments described herein may, of
course, be implemented using any appropriate computer hardware
and/or computer software. In this regard, those of ordinary skill
in the art are well versed in the type of computer hardware that
may be used (e.g., a mainframe, a mini-computer, a personal
computer ("PC"), a network (e.g., an intranet and/or the
Internet)), the type of computer programming techniques that may be
used (e.g., object oriented programming), and the type of computer
programming languages that may be used (e.g., C++, Basic). The
aforementioned examples are, of course, illustrative and not
restrictive.
[0285] While a number of embodiments of the present invention have
been described, it is understood that these embodiments are
illustrative only, and not restrictive, and that many modifications
may become apparent to those of ordinary skill in the art. For
example, certain methods have been described herein as being
"computer implementable". In this regard it is noted that while
such methods can be implemented using a computer, the methods do
not necessarily have to be implemented using a computer. Also, to
the extent that such methods are implemented using a computer, not
every step must necessarily be implemented using a computer.
Further, the specific dates, time spans, rates, prices, values and
the like described with reference to the various examples are, of
course, illustrative and not restrictive.
* * * * *