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Tesla Motors: Linear And Nonlinear Analysis For Profitability

|Includes: Tesla, Inc. (TSLA)


Couldn't help it folks, had to post this!

Like many others, after the recent negative press received by Tesla Motors Inc. (as a result of the negative review of the Model S performance by a NYT reporter), I took interest in the company for the first time and started analyzing its financial data using a new methodology that I have described in several articles uploaded at At least on my computer, I can adjust the three parameters, "m", "n", and "a", in the mathematical equation, y = m*(x^n)*exp (-ax), which describes the costs-revenues data for Tesla Motors and extrapolate to produce any desired level of profits! Here x is revenues and y is costs and x^n means x raised to the exponent n. If n = 1/2, we have the square root of x, for n = 2, we have square of x, if n = 3, we have the cube and so on for any general value of n.

If we consider the cumulative revenues and costs for 2012 (these are the 3 month, 6 month, 9 month, and full year values), we find that costs have decreased dramatically in the fourth quarter of 2012, see Figure 1, although the company has not yet reported a profit since it became a public company in 2012. This nonlinear decrease in the costs, with increasing revenues, can be modeled using the mathematical equation give above, where the numerical values of the constants m, n, and a can be deduced, as I have shown, from the financial data. This is discussed in detail in two articles that interested readers can find, see links given below (or click here and here).

  1. Linear analysis and introduction to the model for breakeven analysis.
  2. Nonlinear model and breakeven revenue calculations.

I have posted several short posts on my Facebook page describing these findings. The simpler power-law model, y = m(x^n) is seen to offer an adequate description for the costs-revenues data. Although costs exceed revenues and the company has not reported a profit, the power-law tells us that the rate of increase of costs, with increasing revenues, is actually decreasing. Also, if we examine the data carefully, we see that the data at the higher revenues begins to deviate from the power-law. The power-exponential law, with the exponential term exp (-ax), then becomes a more appropriate model.

I have also found the value of the parameter "a", holding m and n constant (to match with 2012 cumulative quarterly data) so that Tesla Motors could start making a profit once they exceed sales (or deliveries as they put it, a car is made only after there is a commitment by the customer by advanced reservations) of 15,000 units per year.

Current production capability is 20,000 units per year. This means the last 5000 units produce a profit. The first 15,000 units help them breakeven (recover fixed costs and the variable costs which increase as N, the number of units sold, increases). After that it is all profits. So, one plant can produce a profit of 5000 times $100,000 per unit (the current average price for Tesla's Model S) or $500 million in profits. The profits per plant could potentially even go up to $ 1 billion --- at least on my computer!

That's good news Tesla Motors can use, I think, after some of the beating they have received from other experts here who have been dealing with such problems for much longer than I have been.

Figure 1: The dramatic change in the slope of the cumulative costs versus cumulative revenues in 2012 for Tesla Motors, Inc. The rate of increase of costs, as measured by the slope of the graph has decreased.

Finally, the meaning of the term "costs" is clarified in both the articles above. The "breakeven" analysis can only be performed if all the costs of operation are properly accounted for. The reader is urged to review this point. Also, although this might all seem academic to many here who are interested in more practical matters such as making money, even the ideas such as fixed costs and variable costs, and the three constants (a, b, p) which appear in the classical breakeven analysis (see discussion in Ref.[1]) are academic concepts. To date, I am not aware of any attempts to quantify the three constants (a, b, p) in the classical breakeven analysis. As discussed in the articles cited, Tesla Motors offers a unique test case to study the meaning of these real "fundamentals" about a company. As new operational data on revenues, profits, and costs become available in the near future, we will be able to gain deeper insights into the meanings of these theoretical concepts. More importantly, we might actually start "designing" companies, like scientists and engineers design our cars, airplanes, rockets, cell phones, computers, washing machines, refrigerators, etc. Call me a fool, if you like. Cheers. :)

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.