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The New GM Analysis of the Revenue-Profits data for the five

consecutive quarters ending Q1 2011

by

Dr. V. Laxmanan

Email: vlaxmanan@hotmail.com ____________________________________________________________

The new General Motors, after emerging from bankruptcy, has just

reported it highest quarterly profits to date for the first quarter of 2011.

Profits have more than tripled, from $0.9 billion to $3.2 billion compared to

the same quarter in 2010. Also, revenues went up, to $36.2 billion from

$31.5 billion last year. Analysts had expected $35.59 billion; see link below

for the news release.

http://www.msnbc.msn.com/id/42896143/ns/business-autos

The following describes a simple approach to analyzing this financial data

using a somewhat unconventional methodology. For a household, the

simplest type of a financial entity, Income – Expenses = Savings. The

higher the income, or the lower the expenses, the higher will be the

savings. As income increases, expenses also increase but we also expect

the savings to increase. Likewise, the basic law that governs the operation

of any other financial entity, such as a corporation, can also be written quite

simply as follows:

Profits = Revenues – Costs

If revenues increase and/or costs go down, profits will increase. This is

supported by the quarterly earnings released by the new GM. Quarterly

profits tripled in 2011, compared to the same quarter in 2010, but revenues

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also increased. This is also obvious from the revenues-profits data for the

last five quarters, starting with first quarter of 2010, see Table 1. Notice that

revenues increased as profits increased in each of the quarters for which

data is available, the only exception being the fourth quarter of 2010 when

revenues increased without a concomitant increase in profits.

Table 1: Profits-Revenues data for GM

for the five most recent quarters

Quarter Revenues, $ billions Profits, $ billions

Q1 2011 36.2 3.2 Q1 2010 31.5 0.9 Q2 2010 33.2 1.3 Q3 2010 34.1 2.0 Q4 2010 36.9 0.5

Thus, it appears that the road to higher profits is paved by both revenue

enhancement and cost cutting strategies. Exclusive and/or excessive focus

on cost cutting will not grow a company since it means that the company is

not paying attention to enhancing its revenues, which is often accompanied

by increased market share. The higher the market share, the higher the

number of vehicles sold (as in the case of an automotive company such as

GM, see the GM annual reports), or other goods and services sold, and the

higher will be the profits.

Is there a simple and thus far unrecognized relationship between revenues

enhancements and increased profits? This can be explored by preparing a

x-y scatter graph, see Figure 1. As we see here, there is a remarkable

upward trend which can be described mathematically using a simple linear

equation y = hx + c, where x = revenues, y = profits, h = slope of the

straight line and c is the intercept made by the straight line on the y-axis.

When revenues increase, profits do not increase immediately. Revenues

must exceed a certain minimum value before any company can report a

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profit, since there are fixed costs associated with all operations. The linear

relation revealed here can be shown to be a consequence of the classical

breakeven analysis for determining the profitability of any operation. This

equivalence is shown in Appendix 1.

Figure 1: Graphical representation of the Profits-Revenues data for GM for

the five consecutive quarters ending first quarter of 2011. A remarkably

linear relationship is revealed here, if we take the Q4 2010 data as an

outlier. The regression coefficient r2 = 0.959 which indicates a high and

positive correlation between profits and revenues.

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Appendix 1

Linear Profit-Revenue Relationship and Classical Breakeven analysis

Let N denote the number of units sold and/or manufactured. The total cost

of producing these units, C = Fixed cost + Variable cost = a + bN. This is

the simplest mathematical relationship between C and N. If k is the unit

price, the revenue R generated by selling N units is R = kN. Here a, b, and

k are constants that depend on the type of units being sold/manufactured.

The breakeven quantity is the value of N for which R = C. The profits P will

increase as the number of units sold increases beyond this point.

P = R – C = kN – a – bN = (k – b)N – a .…….. A1

But, N = R/k. Therefore equation A1 can also be written as

P = [ (k – b)/k ] R – a ……….A2

Equation A2 is a linear relation between profits P and revenues R and can

be rewritten as y = hx + c where y is profits and x is revenues and

where h = (k – b)/k

and, c = - a

The simple linear relationship between profits and revenue, as revealed

here, by the GM financial data for five consecutive quarters is simply a

consequence of the classical breakeven analysis in a much more complex

situation (with more than one product stream each with its own value of the

constants a, b, and k, and with different N values).

The significance of the nonzero intercept c (which is the negative of the

constant a in the breakeven analysis) must also be appreciated. This is the

reason why profits more than tripled between Q1 2010 and Q1 2011 but

revenues went up only by about 15%. From equation A2, we can see that

the ratio P/R = [(k – b)/k] – a/R is not constant and keeps changing as

revenues increase or decrease. The ratio P/R is a constant if and only if

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a = 0 or c = 0, i.e., if the P-R graph passes through the origin. This is

impossible because of the nonzero fixed costs. Hence, a tripling or

doubling of revenues does not lead to a tripling or doubling of profits, or

vice versa.

Figures 2 and 3 illustrate the graphs of these relations for predetermined

values of the constants k, a, and b. In the real world, the constants h and c

can be deduced using a simple linear regression analysis as shown here.

Figure 2: Classical breakeven analysis. Revenues increase as units sold N

increases. Costs also increases as N increases. The breakeven quantity N0

(denoting zero profit) is obtained by setting R = C or kN = a + bN; thus N0 =

a/(k – b). For the values chosen here N0 = 1/(0.5 – 0.25) = 4, as seen from

the graph above. The minimum revenue for profitability R0 = ak/(k – b) =

kN0 and is deduced from equation A2 by setting profit P = 0.

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The classical breakeven analysis also implies a simple linear relationship

between profits and revenues, as illustrated in Figure 3.

The slope h = (k – b)/k = (0.5 – 0.25)/0.5 = 0.25/0.5 = 0.5

Intercept c = - a = - 1

These numerical values are confirmed by the graph prepared in Figure 3.

Figure 3: Linear relationship between profits and revenues implied by the

classical model for breakeven analysis. Profits increase linearly with

increasing revenue, beyond the breakeven value.

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Appendix 2

An example of forward predictions based on this methodology

Consider the profits-revenues data for the first and second quarters of

2010. Both revenues and profits increased. A straight line can obviously be

drawn between these two data points. The slope h of the straight line can

be readily calculated as follows.

The slope h = (1.3 – 0.9)/(33.2 – 31.5) = 0.235 Q12010 and Q22010

It is important to remember that this straight line does not pass through the

origin (0, 0). There is a finite intercept c, the significance of which has

already been discussed (it is related to the fixed costs). If the linear

relationship holds, the data point for the third quarter should fall on this

same straight line. Nonetheless, let’s recalculate the slope using the third

data point.

The slope h = (2 – 1.3)/(34.1 – 33.2) = 0.7/0.9 = 0.777 Q2 and Q3 data

The slope h = (2 – 0.9)/(34.1 – 31.5) = 1.1/2.6 = 0.423 Q1 and Q3 data

The average of the two slopes 0.235 and 0.777 equals 0.506 and the

average of the three slopes is 0.479. The slope of the best-fit line through

many (x, y) pairs, using standard statistical methods, is merely a “statistical

average” value of the slope when many data points are accumulated over

several quarters.

Thus, if future revenues can be predicted (using other market analysis

tools), the future profits can be predicted using the best-fit line and

the profits-revenues data for the immediate past quarters.

As an aside, this method, also known as the least squares method, or

simple linear regression analysis, was popularized by the French

mathematician Adrien Marie Legendre, in a famous paper published in

1805. For than 200 years, an incorrect side view portrait of this famous

mathematician has been used, as noted in a recent Wikipedia article.

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http://en.wikipedia.org/wiki/Adrien-Marie_Legendre

Legendre was interested in discovering methods to curve fit astronomical

data (the orbits of comets, notably). In the praise of his method, Legendre

noted that “of all the principles that can be proposed, there is none more

general, none more exact, and none more simple and easy to apply than

the method of minimizing the sum of the square of the errors”.

The “error” that Legendre is referring to is the “vertical” deviation of an

individual data point from the best-fit line. The slope h of the best-fit line is

fixed by minimizing the squares of the vertical deviations, since some data

points will fall above the best-fit line (positive deviation) and some data

points will fall below the best-fit line (negative deviation). If there is no

“error” all the data points will fall exactly on the best-fit line.

The formulae for determining the slope h and intercept c, along with a

worked example, may be found in the link given below.

http://phoenix.phys.clemson.edu/tutorials/excel/regression.html

Unfortunately, although the method of least squares is well known to

financial analysts it is rarely employed, as done here, to analyze financial

data accumulated each quarter for literally hundreds and thousands of

companies all over the world, operating in different sectors, and in different

economic, political, and social (read “tax” ! ) environments. Instead, it is

common to use % changes and various ratios, such as the profit margin

(ratio of profits to revenues), or earnings per share (ratio of earnings to total

number of shares), etc. to assess the financial performance of various

companies and rank them, for example, in the annual Fortune and Forbes

magazine lists.

The significance of the non-zero intercept c and its fundamental and

far-reaching implications for the validity of various ratio analyses cannot be

overlooked and will be discussed separately.

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Finally, in addition to considering quarterly data for the individual quarters,

we can create additional (x, y) pairs by considering 6-month, 9-month, and

annual profits and revenues data to refine the estimates of the slope h and

the intercept c. The best-fit line determined in this fashion becomes the

“operating line” for GM, at least for the near future. GM’s future

performance can thus be assessed on the basis of its immediate

performance in the last few quarters.

Over the last nearly 10+ years, the author has studied the financial data for

several companies, in several sectors of the economy, using exactly similar

methodology. It is sufficient to note that the simple linear relation observed

here holds for all companies.

Indeed, it appears that the linear law y = hx + c can be elevated to the

status of a universal law that describes the behavior of all companies, in

any given sector of the economy, each with slightly different values of the

constants h and c. Analysis across sectors and between companies within

a single sector can therefore be performed using this remarkably simple

approach – going back more than 200+ years to Legendre’s most famous

contribution to statistics.

Finally, here’s an interesting example of what Legendre’s least squares

method, or linear regression analysis, or “best-fit” line can do. A few years

ago, when the present author was discussing the efficacy of such an

analysis, he was posed the following question by a clearly skeptical golf

enthusiast. “Ok, in my last three rounds, I posted 72, 66, 74. Tell me what I

scored in my final round?”

These are not the exact numbers given to the author, but the general

nature of the question should be appreciated. Yes, one can use the least

squares method to determine the best-fit line through these three data

points (1, 72), (2, 66), (3, 74) and get the value (4, y). Or the analysis can

be done differently, and more accurately, as (1, 72), (2, 138), (3, 212), or

even as (18, 72), (36, 138), (54, 212), since 18 holes are played during

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each round of golf. The y values for the second and third sets are obtained

by adding the scores for all the previous rounds.

Indeed, the prediction made for the fourth round using this method proved

to be resoundingly correct and was so acknowledged by the (honest)

golfer! Of course, true golf enthusiasts know that this method might not

apply to the fourth round of star golfers like Rory McIlroy, Phil Mickelson, or

even the new Tiger Woods of the year 2011! As we see in Figure 1, there

are always outliers.

*************************************************************************************

About the author:

The author obtained his Master’s (S. M.) and Doctoral (Sc. D.) degrees in

Materials Engineering from the Massachusetts Institute of Technology,

Cambridge, USA. He then spent his entire professional career at leading US

research institutions (MIT, NASA, Case Western Reserve University, and General

Motors R & D Center, in Warren, MI). He holds four patents in advanced

materials processing, has co-authored two books, and has published several

scientific papers in leading peer-reviewed international journals. His expertise

includes developing simple mathematical models to explain the behavior of

complex systems. He can be reached by email at vlaxmanan@hotmail.com

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Appendix 3

Some comments and discussion

The following are some comments received from some friends and

colleagues with whom I shared this analysis prior to uploading it as a public

document.

Impressive analysis. We are still not back to even a recession level of

sales. We are about 2 million units below what would be a recession

sales level. Dave

Thanks for the encouragement. The remarkable thing about the new GM, which

comes out of this analysis, and the linear law y = hx + c, is that once the

breakeven revenue level is achieved, nearly 50% of the additional revenue (from

the increased sales, once we reach higher post-recession levels) is turning into

profits. The slope h is like the marginal tax rate in economics, the tax paid on each

additional dollar earned. Likewise, the slope h = dy/dx is the derivative of the

profits-revenue curve and is different from the familiar profit margin, which is the

ratio y/x. The slope h tells us about the profit made on each additional dollar of

revenue, past the breakeven revenue level. In my earlier analysis of the financial

data for the old GM, the slope h had a much smaller value.

It definitely is an interesting angle to the whole earnings game.

Thought provoking, to say the least. Please publish it and let's see

what kind of response you get. Ramesh

Thanks. What is new is that the slope h is now very high for GM, which means that

almost 50% of the additional revenues will translate into profits, once the

breakeven revenue has been achieved.

But, this will not last for very long. As the new GM gets older, the slope will

change (actually reduce) and the intercept c will go from the negative value today

to a positive value. This is what happens with what I call "mature" companies.

There is another universal mathematical curve that can be fitted to such a

situation. Hopefully, we will discuss this in a later write up.

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Your analysis is correct, though I see the following 2 issues affecting

profitability in near future:

1) Part production from Japan is reduced, so finding alternate

sources may be expensive in the short term or even not possible.

This will reduce the revenue very soon. So, don’t know when $40

billion level will be reached.

2) With less no. of vehicles produced and good demand, incentives

will be lower, so higher profit will be made. So, we may get

same/relatively more profit without increase in revenue in the near

future.

Let’s see how it goes. Sudhir

The above response was prompted by the following message from the author.

Here's a problem for you. The following is taken from the news on GM quarterly

profits this morning. It has more than tripled according to the report - from 0.9 B

to 3.2 B. Also says revenues went up, see below what I have pasted from the

article. http://www.msnbc.msn.com/id/42896143/ns/business-autos

Net income in the first quarter rose to $3.2 billion, or $1.77 a share, compared

with $900 million, or 55 cents a share, in the year earlier quarter. Revenue rose to

$36.2 billion from $31.5 billion last year. Analysts had expected $35.59 billion.

Now, I have a problem for you to think about. Let’s say, in the near future, the

quarterly revenues increase to $40.2 billion from the current value of $36.2 billion.

What will be the profit in that quarter?

I predict a profit of $5.16 Billion in that quarter based on the info currently

available. Do you agree? Anyway, if GM gets to $5 billion in quarterly profits, it

would be a mind boggling quarterly profit by an auto company. Before the

bankruptcy, they could not show $5 billion profit annually with more than $200

billion in revenues.

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Sounds good. But here we are only talking about P&L (profit and loss). Where is the analysis on the B/S (balance of sheet), pipeline of cars, international growth and all that. Also, create an account on blogspot and post it there as well. LN.

Hi LN: To me their detailed balance sheet per se is NOT important. The bottom

line is their profits and revenues. Everything else follows. Hence, what I have

done. We cannot look at the trees and forget the forest. That is what everyone

seems to do. Then they don’t get the BIG picture. (Some analysts have already

stated that GM is nowhere doing as well as Ford. Give me a break, that is stating

the obvious and that is really not the issue. The issue is how well GM is doing.) We

can do a similar analysis for Ford and only then compare GM and Ford but even

then it would be comparing two very different situations. One company is emerging

from bankruptcy while the other has avoided it in the worst crisis faced by the US

economy and the automotive industry since the days of Henry Ford. A mature

company cannot be fairly compared to an emerging and nascent company.