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After Trulia’s successful debut on the NYSE, its profits-revenues data were analyzed to predict both the profits and revenues for the fiscal year ending December 31, 2012. Trulia’s stock is being compared to Zillow, its main competition. Until Trulia, which has yet to report a profit, Zillow has reported quarterly profits for 4 out of 14 quarter, and a profits for three consecutive quarters starting Q42011. It has also reported a profit for the full year 2011. The profits and revenues data for Zillow (from 2006 to 2011, annual basis and Q1 2009 to Q2 20102, quarterly basis) is analyzed here to show that a simple linear law y = hx + c = h(x – x0) relates the revenues x and profits y, regardless of whether we consider the quarterly, cumulative quarterly, or the annual data. In all cases, as revenues increase, losses decrease and eventually turn into profits at higher revenues. Thus, the intercept x0 = - c/h made by the straight line on the x-axis (revenue axis) equals the cut-off or “breakeven” revenue, the minimum revenue needed before the company can report a profit. The slope h then gives the rate at which additional revenues are converted into profits. On a quarterly basis h = 0.518 and on an annual basis h = 0.574. In other words, Zillow has the potential to convert about 52% of its quarterly revenues into profits, or about 57% of its annual revenues into profits. However, costs (as revealed by the increasing values of x0) have also been increasing and consistent delivery of profits will require paying attention to three fundamental constants (a, b, p) which appear in the classical breakeven analysis for the profitability of any company. Here “a” is the fixed cost, “b” the unit variable cost and “p” the unit price.
Citation preview
Page 1 of 16
A Look at Zillow after Trulia’s IPO
Analysis of the Profits-Revenues Data
§ 1. Summary
After Trulia’s successful debut on the NYSE, its profits-revenues data were
analyzed to predict both the profits and revenues for the fiscal year ending
December 31, 2012. Trulia’s stock is being compared to Zillow, its main
competition. Unlike Trulia, which has yet to report a profit, Zillow has reported
quarterly profits for 4 out of 14 quarters and a profit for three consecutive quarters
starting Q42011. It has also reported a profit for the full year 2011.
The analysis of the profits and revenues data for Zillow (from 2006 to 2011, annual
basis and Q1 2009 to Q2 20102, quarterly basis) again reveals a simple linear law
y = hx + c = h(x – x0) relating the revenues x and profits y, regardless of whether
we consider the quarterly, cumulative quarterly, or the annual data. In all cases, as
revenues increase, losses decrease and eventually turn into profits at higher
revenues. Thus, the intercept x0 = - c/h made by the straight line on the x-axis
(revenue axis) equals the cut-off or “breakeven” revenue, the minimum revenue
needed before the company can report a profit. The slope h then gives the rate at
which additional revenues are converted into profits.
On a quarterly basis h = 0.518 and on an annual basis h = 0.574. In other words,
Zillow has the potential to convert about 52% of its quarterly revenues into profits,
or about 57% of its annual revenues into profits.
However, costs (as revealed by the increasing values of x0) have also been
increasing and consistent delivery of profits will require paying attention to three
fundamental constants (a, b, p) which appear in the classical breakeven analysis for
the profitability of any company. Here “a” is the fixed cost, “b” the unit variable
cost and “p” the unit price.
The two articles on Trulia and Zillow show that a simple approach based on the
analysis of the graphical trends in the profits-revenues diagram can serve as a
valuable tool for investors.
Page 2 of 16
Table of Contents
§
No.
Topic Page
No.
1. Summary 1
2. Introduction 3
3. Zillow’s Quarterly Profits-Revenue data 4
4. Zillow’s Annual Profits-Revenue data 7
Table 1: Annual Profits-Revenues data for Zillow 10
Table 2: Quarterly Profits-Revenues data for Zillow 11
5. List of References 13
Page 3 of 16
§ 2. Introduction
After the recent Facebook IPO, and some other disappointing IPOs, the news about
Trulia’s successful debut, on its first day of trading as a public company, caught
my attention, see Ref. [1], click here. The company sold six million shares at the
IPO price of $17 apiece, raising nearly $102 million in working capital. The stock
price went up from the IPO price of $17.00 to $24.00, a nice 40% boost, but was
down to $23.03 on Friday close, 9/21/2012, see Refs.[1-3].
Interestingly, though, Trulia has not made one single dime in profits since it has
existed [4]. The recent passing of the JOBS Act has made it easier for companies,
with under $1 billion in revenue, to more easily raise money by doing the IPO.
Morning star, Ref.[5], notes the new, reduced, regulations as being somewhat
positive for qualifying companies to go public, modestly negative to the
investment community and neutral to investment banks, see also Ref. [6].
If there ever was a shining example of how tax cuts for the rich is supposed to help
create jobs, this IPO is it, folks! The rich can use their money that would otherwise
end up as tax paid for wasteful government expenditures, and invest it in IPOs of
companies like Trulia, Facebook, Groupon, Zynga, you name it, who will then start
hiring and create jobs – good, well-paying, jobs – in the financial sector. This
JOBS Act is such a pro-business, pro-free-enterprise, pro-risk-taker, pro-market,
anti-business, anti-regulation, initiative that it truly warms my heart. Now all we
need to do is to unleash the creative genius and go straight to the rich folks all over
this country to raise cash, millions of dollars in working capital, without ever
having made one red cent in profits! I am not the least bit sarcastic folks! This is
how capitalism is supposed to work.
Now, if we can only get that top tax rate down once again to like 7%! Yes, that
was the top tax rate back in 1913 before President Woodrow Wilson raised it to
77%, as the US entered World War I, see Refs.[7-10].
Nonetheless, as hinted by Morning Star, especially in the title to Ref. [5], the
burden is now upon the investor to study such companies carefully and make wise
investment decisions.
Page 4 of 16
And so, I have analyzed the profits-revenues data for Trulia and published it on
Sep 21, 2012 (click here and here). The analysis permits an estimate of both the
profits and the revenues for the fiscal year ending Dec 31, 2012. The reader is
referred to the article cited here for more details. The necessary background and all
the introductory material needed to understand the analysis (which is based on a
new, but very simple, methodology) may be found in there, see also Refs.[11,12]
for the links. In what follows here, we will consider the profits-revenues data for
Zillow Inc., Trulia’s main competition. Zillow went public in July 2011 and its
stock price has doubled since then. Trulia’s stock is considered to be a bargain
compared to Zillow’s [1].
§ 3. Zillow’s Quarterly Profits-Revenues Data
The annual (2006 to 2011) and quarterly (Q12009 to Q2 2012) profits and
revenues data for Zillow, can be readily obtained from the 2011 Annual Report and
the S-1 Registration filing and have been included here in Tables 1 and 2 for
convenience. A brief analysis of this data follows.
Consider first the quarterly data, for 14 consecutive quarters, which has been
plotted in Figure 1. We see nice a nice upward trend. As revenues increase, the
losses (the negative profits) decrease, which is mathematically equivalent to
increasing profits. Unlike Trulia, Zillow has reported a small profit for four out of
five recent quarters, starting Q22011 (a small loss for Q32011). However, as we
see from Figure 1, these five data points, at the highest revenues observed, deviate
from the nice linear upward trend for the earlier quarters and are scattered along
the x-axis, the horizontal y = 0 for ZERO profits (or losses).
The equation of the “best-fit” line, labeled A, through the remaining eight (x, y)
pairs, which seem to lie very nearly on a perfect straight line, can be determined
using the well-known linear regression analysis. The data for Q1 2011 was
excluded from this analysis since it seems to deviate slightly from the nice upward
trend. Thus, the regression equation y = hx + c = h(x – x0) = 0.5179x – 5.559 =
0.52(x – 10.73). The cut-off, or breakeven, revenue x = x0 = - c/h, above which a
profit will be reported is obtained by setting y = 0 in this equation and equals x0 =
$10.73 million. This means that if the quarterly revenues exceed this cut-off level,
Page 5 of 16
a profit will be reported. This prediction is confirmed if we examine the data for all
the quarters for which a profit was reported, all of which are in excess of the cut-
off, or breakeven x0 = $10.73 million. Even so, we find that the data do not follow
the regression line A but are scattered along the horizontal. The deviation from line
A implies lower profits, which also implies higher costs.
Figure 1: Quarterly profits-revenue diagram for Zillow Inc. The data for 14
consecutive quarters, from Q12009 to Q22012, has been plotted here. The
revenues have been increasing consistently and correspondingly losses have also
been decreasing (mathematically equivalent to increasing profits).
Indeed, as discussed in the Trulia article, the linear law y = hx + c deduced here
from the empirical observations of profits and revenues can be shown to be a
consequence of the classical breakeven analysis for the profitability of a company.
According to this breakeven model, the relation between revenues x and profits y
is linear with the slope h = 1 – (b/p) and the intercept c = - a, and the breakeven
-8.00
-6.00
-4.00
-2.00
0.00
2.00
4.00
6.00
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00
Quarterly Revenues, x [$, millions]
Qu
art
erl
y P
rofi
ts,
y [
$,
millio
ns]
y = hx + c = h(x – x0) y = 0.518x – 5.56 = 0.52 (x – 10.73)
with r2 = 0.9669
A
x0
Page 6 of 16
revenue x0 = ap/(p – b). Here “a” is the fixed cost, “b” the unit variable cost and
“p” the unit price. For a company making and selling N units of a product, the
total costs C = a + bN is the sum of the fixed cost “a” and the variable cost “bN”.
The revenues R generated by selling the N units R = pN. Hence, the profits P = R =
C = pN – a – bN = (p – b)N – a = [(p – b)/p] R – a which means the P-R relation is
linear with a slope and intercept as just noted.
The deviation of the most recent quarterly data from the regression line A for
earlier quarters thus implies an increase in the total costs C associated with the
operation, or a changing cut-off revenue x0 = ap/(p –b) which reflects the complex
interaction of all the three constants (a, b, p) in the breakeven model.
This can also be appreciated if we take a careful look Figure 1. Notice that the two
(x, y) pairs for Q1 2011 (11.255, -0.830) and Q2 2011(15.85, 1.58), representing a
loss and a small profit, seem to fall on a line that is roughly parallel to the
regression line A. Likewise, the (x, y) pairs for Q3 2011 and Q1 2012, at even
higher revenues (another profit-loss pair), are also joined by a line segment that is
roughly parallel to line A. The equations of the line segments are given below. In
each case, as revenues increase, losses turn into profits with a higher and higher
cut-off, or breakeven, revenue x0; i.e., higher costs as revenues have increased.
Line B, y = 0.524x – 6.733 = 0.524 (x – 12.84) joins Q1 2011 and Q2 2011
Line C, y = 0.607x – 12.15 = 0.607 (x – 19.998) joins Q3 2011 and Q12012
The point marked by the red square on Line A in Figure 2, at the value of x =
27.77, the revenue for Q2 2012 is the projected profit if Zillow had continued to
operate along line A as its revenues increased. The vertical separation between the
red square and the actual profit for Q2 2012 represents the “lost” profits due to the
higher costs, or the higher value of x0 as revealed by the intercepts made by Lines
B, C, etc. at higher and higher values of the “cut-off”, or breakeven revenues.
The rather simple analysis presented here thus given us some invaluable insights
about the reasons for the “scatter” in the profits-revenues data. More importantly, it
also tells us what Zillow must do to increase its profits and return to line A, or
establish a new parallel to line A with increasing profits and increasing revenues,
following either lines B, or C, or a new parallel to line A in the near future.
Page 7 of 16
Figure 2: A set of parallels (or nearly parallel lines) are revealed as shown here
by a careful consideration of the profits-revenue data that do not lie along Line A.
Each of these lines, with a more negative value of the intercept c, or equivalently
higher cut-off, or breakeven, revenue x0, implies higher costs and therefore
decreased profits for the company.
§ 4. Zillow’s Annual Profits-Revenues Data
As we know, the. quarterly observations plotted in Figures 1 and 2 are combined
into six-month, nine-month and yearly revenues and profits and revenues and
reported in the 10-Q filings for each quarters. The cumulative revenues and profits
reveal the same linear behavior, see Figure 3, where we consider the four
consecutive quarters starting with Q32011 (with a small loss) to Q2 2012. As
revenues increased, the losses decreased and turned into a profit and the company
moves into the positive territory. (As an aside, this is similar to the situation
observed during the Clinton years with the US budget Surplus-Receipts data. As
-15.00
-10.00
-5.00
0.00
5.00
10.00
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00
Quarterly Revenues, x [$, millions]
Qu
art
erl
y P
rofi
ts,
y [
$,
millio
ns]
A B
C
Q2 2012 x0
x0
A
Page 8 of 16
the government’s receipts increased, the deficits decreased and turned into a nice
surplus, for four consecutive years, see discussion in Refs. [13-16], click here to
see the graph for the Clinton years. )
Thus, based on its current “cost structure”, we expect Zillow to report a profit, on a
quarterly basis, as long as the revenues exceed the cut-off, or breakeven, value of
x0 = $29.18 million. This is higher the cut-off estimated from Line C of Figure 2.
Figure 3: The cumulative profits, obtained by combining the quarterly values,
increase as the cumulative revenues increase. Starting with the data for Q3 2011,
when a small loss was reported, we see the company moving into the positive
territory as it started reported a profit for each quarter. Again, the same linear law
y = hx + c is observed. The cut-off revenue x0 = $29.18 million.
Finally, the annual data (where the four quarterly points for each year are collapsed
into one single point), for the years 2006 to 2011, is plotted in Figure 4. Once
again, we see the same linear trends and also what appears to be a movement of the
data along parallel lines, as discussed earlier with the quarterly data (in Figure 2).
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
6.00
0 20 40 60 80 100 120 140
Cumulative Revenues, x [$, millions]
Cu
mu
lati
ve
Pro
fits
, y [
$, m
illi
on
s]
y = 0.056x – 1.643 = 0.056 (x – 29.18)
x0
Cumulative Values Q32011 to Q2 2012
Page 9 of 16
For 2006, Zillow reported a loss. As revenue increased, between 2006 and 2007,
the loss actually increased. However, as revenues increased further, Zillow started
reported lower and lower losses each year. A small profit, on an annualized basis,
was finally reported in 2011. However, as with the quarterly data, the (x, y) pair for
2011 does not fall on the line, labeled A in Figure 5. Instead, we can imagine a
parallel B to line A through the 2011 data point, which would intersect the x-axis
at a much higher value of x0, the cut-off revenue (on an annualized basis).
The cut-off, or “breakeven”, revenue given by x0 = ap/(p – b) = -c/h, has increased
between 2010 and 2011 and this explains the reduced profits compared to the
projected value (given by the red square on Line A).
Figure 4: The annualized profits, obtained by combining the quarterly values,
increase as the annualized revenues increase. Line A is the best-fit line through the
2007-2010 data. Again, the same linear law y = hx + c is observed. The cut-off
revenue x0 = $41.53 million on an annualized basis. The data for 2011 falls on the
parallel B with a higher intercept x0 which means the costs have increased between
2010 and 2011.
-50.00
-40.00
-30.00
-20.00
-10.00
0.00
10.00
20.00
0 10 20 30 40 50 60 70 80
Annual Revenues, x [$, millions]
An
nu
al P
rofi
ts,
y [
$, m
illio
ns]
y = 0.574x – 23.84 = 0.574 (x – 41.53)
r2 = 0.9348
y = 0.574x – 36.81 = 0.574 (x – 64.13)
A
B
Page 10 of 16
The equation for line A was determined using linear regression analysis. At first
five data points (2007, 2008, 2009, 2010) were considered with 2006 and 2011
being excluded for obvious reason. However, the final equation was determined by
eliminating the 2008 data as well from the regression analysis. This yields the
“best” fit to the data for 2007, 2009 and 2010. The straight line joining the 2007
and 2010 has the slope h = ∆y/∆x = 13.516/23.361 = 0.5786, which is very nearly
the same as the slope h = 0.574 from the regression analysis.
The vertical separation between the parallels is equal to the differences in the
values of the intercepts. The line A has the equation yA = hx + cA where yA means
the value of y on Line A for any x and cA is the intercept made by Line A. The
equation for line B is yB = hx + cB . The vertical separation between the parallels A
and B is therefore given by (yA – yB) = (cA – cB). In other words, the difference in
the profits on line A and B (for any fixed revenues x) is equal to the difference in
the values of the intercepts.
Table 1: Annual Profits-Revenues Data for Zillow
Year Revenues, x [$, millions] Profits, y [$, millions]
2011 66.053 1.102
2010 30.467 -6.774
2009 17.491 -12.855
2008 10.593 -21.217
2007 7.106 -20.29
2006 4.289 -12.589
Source: http://investors.zillow.com/secfiling.cfm?filingID=1193125-11-
100697&CIK=1334814
Page 11 of 16
Table 2: Quarterly Profits-Revenues Data for Zillow
Quarter Revenues, x [$, millions] Profits, y [$, millions]
Q22012 27.77 1.33
Q12012 22.83 1.72
Q42011 19.89 0.92
Q32011 19.06 -0.57
Q22011 15.85 1.58
Q12011 11.255 -0.830
Q42010 9.573 -0.486
Q32010 8.229 -1.510
Q22010 7.334 -1.972
Q12010 5.331 -2.806
Q42009 4.704 -2.932
Q32009 5.541 -2.425
Q22009 4.504 -3.069
Q12009 2.742 -4.429
Let us consider the data for 2009, which reveals an interesting trend. Since a loss
(negative profits) was reported for all four quarters in 2009, the cumulative losses
just keep on increasing as revenues increase (when we combine the data for each
consecutive quarter to arrive at the annual profits-revenues figures). Hence, the
slope of the graph h is negative.
This would be similar to the case of profits decreasing with increasing revenues,
which would also yield a negative slope. This too is observed when we analyze
financial data, some companies do report decreasing profits with increasing
revenues, for example, General Motors before its bankruptcy, see Refs.[17-19].
Struggling companies usually have this pattern (negative slope h) but with graph
being entirely in the first quadrant. With Zillow, however, the graph is
entirely in the fourth quadrant. Notice that the intercept made with the y-axis is
also negative, c = - 2.863. Hence, the extrapolation of this line will cut the x-axis at
a a negative value, which means x0 = - c/h = - 5.01. Such a trend is obviously not
desirable. The cumulative profits-revenue graph for the year must have a positive
slope, as we see for successful companies like Microsoft, Google, Apple, etc. This
has been discussed in other articles, see Refs. [20-23]. It is also of interest to note
Page 12 of 16
that the absolute magnitude of the (without the negative sign) is very close to the
numerical value of the slope h = 0.574 for the annual data (Figure 4).
Figure 5: The Cumulative Profits-Revenues graph for the year 2009. Notice again
the nearly perfectly linear trend.
-16.00
-14.00
-12.00
-10.00
-8.00
-6.00
-4.00
-2.00
0.00
0.00 5.00 10.00 15.00 20.00 25.00
Cumulative Revenues, x [$, millions]
Cu
mu
lati
ve
Pro
fits
, y [
$, m
illi
on
s]
y = -0.5714x – 2.863 = -0.571 (x – 5.01)
Page 13 of 16
§ 5. List of References
1. Trulia stock soars in debut, By Maureen Farrell, cnn.com, Sep 20, 2012,
http://buzz.money.cnn.com/2012/09/20/trulia-ipo-stock/
2. Real Estate Wave Helps an IPO Avoid a Tech Wipeout, by Robert Cyram,
slate.com, Sep 20, 2012,
http://www.slate.com/blogs/breakingviews/2012/09/20/real_estate_wave_help
s_an_ipo_avoid_a_tech_wipeout_.html
3. Trulia Soars in Trading After IPO Prices Above Range, by Dan Levy and
Lee Spears, Sep 20, 2012, http://www.businessweek.com/news/2012-09-
20/trulia-surges-in-trading-debut-after-pricing-ipo-above-range
4. Trulia IPO: With no profits, who will invest? By Erik Sherman,
cbsnews.com http://www.cbsnews.com/8301-505124_162-57496310/trulia-
ipo-with-no-profits-who-will-invest/
5. JOBS Act Resulting in Easier IPO Roadmap but at Investor’s Cost, http://news.morningstar.com/articlenet/article.aspx?id=568389
6. The IPO Quandry, By Atmabus, Sep 23, 2012, seekingalpha.com,
http://seekingalpha.com/article/883021-the-ipo-
quandary?source=marketwatch
7. Sixteenth Amendment to the United States Constitution, Wikipedia article,
http://en.wikipedia.org/wiki/Sixteenth_Amendment_to_the_United_States_Co
nstitution http://www.shmoop.com/constitution/16th-amendment.html
8. Woodrow Wilson, Congress and the Income Tax, March 16, 2004,
wilsoncenter.org http://www.wilsoncenter.org/sites/default/files/ACF18.pdf
9. Top Tax rates, Historical facts, taxpolicycenter.org
http://www.taxpolicycenter.org/taxfacts/displayafact.cfm?Docid=213
10. Top Federal Income tax rates, 1916-2013, findthedata.org, http://top-
federal-tax-rates.findthedata.org/
11. Trulia After its IPO, Analysis of Profits-Revenues Data, Published Sep 21,
2012, http://www.scribd.com/doc/106573459/The-Trulia-IPO-Analysis-of-
Profits-Revenues-Data
12. The Trulia IPO: Analysis of Profits-Revenues Data, vlaxmanan’s
Instablog, Published Sep 21, 2012, http://seekingalpha.com/instablog/958073-
vlaxmanan/1096481-the-trulia-ipo-analysis-of-profits-revenues-data
13. The Amazing US Government Surplus (Deficits)-Receipts Relation
during the Clinton Presidency, http://www.scribd.com/doc/105821230/The-
Page 14 of 16
Amazing-US-Government-Receipts-Surplus-Relation-during-the-Clinton-
Presidency, Published Sep 13, 2012.
14. A Brief Review of the Historical US Government Receipts-Surplus
(Deficit) Relation, http://www.scribd.com/doc/106003088/A-Brief-Review-of-
the-Historical-US-Government-Surplus-Receipts-Relation , Published Sep 15, 2012.
15. The Clinton Budget Surpluses, http://www.scribd.com/doc/105819500/The-
Clinton-Budget-Surpluses-Treating-Government-like-a-Business, Published
Sep 13, 2012 , Google financial data for early years may be found in Table 2.
16. The Efficiency of Government Compared to the Thermal Efficiency of a
Heat Engine, Sep 18, 2012, http://www.scribd.com/doc/106220758/The-
Efficency-of-Government-Compared-to-Thermal-Efficiency-of-a-Heat-Engine
17. GM Before the Bankruptcy:Maximum point on the profits-revenues graph,
http://www.scribd.com/doc/103938349/GM-Before-the-Bankruptcy-
Maximum-Point-on-Profits-Revenue-Graph , Published August 25, 2012.
18. The New GM: A Brief Analysis of the Profits-Revenues Data,
http://www.scribd.com/doc/103600274/The-New-GM-A-Brief-Analysis-of-
the-Profits-Revenues-Data-through-1Q2011, Published May 9, 2011 and again
on August 22, 2012, Discussion of the new GM data from 1Q2010 to 1Q2011.
19. Why Can’t GM be more like Microsoft? The New GM Just May be.
http://www.scribd.com/doc/103607023/Why-Can-t-General-Motors-be-more-
like-Microsoft-The-new-GM-may-just-be Published August 22, 2012.
20. A Fresh Look at Microsoft after its Historic Quarterly Loss,
http://www.scribd.com/doc/101062823/A-Fresh-Look-at-Microsoft-After-its-
Historic-Quarterly-Loss , Published July 25, 2012.
21. A Second Look at Microsoft after its Quarterly loss,
http://www.scribd.com/doc/101518117/A-Second-Look-at-Microsoft-After-
the-Historic-Quarterly-Loss , Published July 30, 2012.
22. Google Inc. A Lovable One-Trick Pony Another Single-product Company
Analyzed using the New Methodology.
http://www.scribd.com/doc/98825141/Google-A-Lovable-One-Trick-Pony-
Another-Single-Product-Company-Analyzed-Using-the-New-Methodology,
Published July 1, 2012.
23. The Perfect Apple-II: Taking A Second Bite: A Simple Methodology for
Revenues Predictions (Completed July 8, 2012, To be Published)
http://www.scribd.com/doc/101503988/The-Perfect-Apple-II, Published July
30, 2012.
Page 15 of 16
About the author
V. Laxmanan, Sc. D.
Email: [email protected]
The author obtained his Bachelor’s degree (B. E.) in Mechanical Engineering from
the University of Poona and his Master’s degree (M. E.), also in Mechanical
Engineering, from the Indian Institute of Science, Bangalore, followed by a
Master’s (S. M.) and Doctoral (Sc. D.) degrees in Materials Engineering from the
Massachusetts Institute of Technology, Cambridge, MA, USA. He then spent his
entire professional career at leading US research institutions (MIT, Allied
Chemical Corporate R & D, now part of Honeywell, NASA, Case Western Reserve
University (CWRU), and General Motors Research and Development Center in
Warren, MI). He holds four patents in materials processing, has co-authored two
books and published several scientific papers in leading peer-reviewed
international journals. His expertise includes developing simple mathematical
models to explain the behavior of complex systems.
While at NASA and CWRU, he was responsible for developing material processing
experiments to be performed aboard the space shuttle and developed a simple
mathematical model to explain the growth Christmas-tree, or snowflake, like
structures (called dendrites) widely observed in many types of liquid-to-solid phase
transformations (e.g., freezing of all commercial metals and alloys, freezing of
water, and, yes, production of snowflakes!). This led to a simple model to explain
the growth of dendritic structures in both the ground-based experiments and in the
space shuttle experiments.
More recently, he has been interested in the analysis of the large volumes of data
from financial and economic systems and has developed what may be called the
Quantum Business Model (QBM). This extends (to financial and economic
systems) the mathematical arguments used by Max Planck to develop quantum
physics using the analogy Energy = Money, i.e., energy in physics is like money in
economics. Einstein applied Planck’s ideas to describe the photoelectric effect (by
treating light as being composed of particles called photons, each with the fixed
quantum of energy conceived by Planck). The mathematical law deduced by
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Planck, referred to here as the generalized power-exponential law, might actually
have many applications far beyond blackbody radiation studies where it was first
conceived.
Einstein’s photoelectric law is a simple linear law, as we see here, and was
deduced from Planck’s non-linear law for describing blackbody radiation. It
appears that financial and economic systems can be modeled using a similar
approach. Finance, business, economics and management sciences now essentially
seem to operate like astronomy and physics before the advent of Kepler and
Newton.
Cover page of AirTran 2000 Annual