**Tesla** (NASDAQ:TSLA) is continuing to ramp up their Model S deliveries, and the continued automotive reviews are now almost largely redundant (it's amazing, it's incredibly fast, it's groundbreaking... etc). However, the rate remains low - uncomfortably low if you're a Tesla investor (as I am) with a reasonable understanding of their cash burn rate.

Today's article is a short one - a prequel (if you will) to a longer analysis of the ramp-up that I'm sitting on until the next production numbers are available.

Today, the focus is: where does Tesla breakeven?

Not when - that's more speculative. But we can at least establish the conditions required for breakeven from an EBIT perspective based on the comments Musk has made over the last months, and what we see in Tesla's financials.

One statement Musk made that I think has been widely misinterpreted is:

Breakeven is 8,000 units/year [of the Model S]

Some SA commentators (which, I'm sure, means many others as well) seem to have understood this to mean that Tesla *the company* will break even at 8,000/year.

There is *no way on earth* that is possible. 8,000 units/year would give Tesla revenues (at average $70k/vehicle) of $560Mil/annum. If they maintain their Q2 R&D+SG&A of $111Mil/qtr (and, being a growth phase company, I think Tesla should if anything be looking to increase this spend), then covering these overheads alone would require an 80% Gross Margin. Which would mean they'd need to build a Model S60 for around $14k, including fixed line costs. No. They could maybe, barely, JUST buy the cells for the 60kWh pack for that money.

To be clear, I don't think Musk was being at all deceptive - I think he was just misunderstood. A breakeven point for the Model S *product line* of 8,000 units/annum is reasonable - but what's interesting is that this datapoint (8,000/annum = 0% Gross Margin) combined with the other widely discussed one (20,000/annum = 25% Gross Margin) allows us to take a (admittedly linearized and somewhat coarse) stab at the Model S cost structure, which is all kinds of useful in creating projections (as I'll do in my later article).

Basically, we want to know Tesla's Gross Margin (NYSE:GM) with the ModelS for any production rate. We know that:

ProducedCost = FixedCost + UnitCost

UnitCost is the incremental cost for every car that's made. FixedCost is the annual fixed cost of the line, divided by the number of vehicles that it can be amortized over.

To find out general equation for GM, we will use the two datapoints Musk gave us:

Price - UnitCost - FixedCost/20,000 = Price x 0.25

Price - UnitCost - FixedCost/8,000 = 0

To begin with, these look unsolvable - we know Price because we can fix it at the assumed average of $70k/vehicle, but we still have equations with two variables.

However, a bit of simple algebra combined with the wonder of simultaneous equations allows us to rewrite this as:

Price x 0.75 - FC/20,000 = Price - FC/8,000 ->

1.5FC/20,000 = Price x 0.25

FC = $70,000 x 0.25 x 20,000 / 1.5 = $233Mil/annum

Obviously Tesla's fixed costs will probably be slightly lower at 8,000/annum than at 20,000/annum; but over the range in question the linearization is fairly reasonable (plant won't change, factory space won't change, minimum labor to run the line won't change).

Now that we have the FixedCost, we can immediately substitute this back into one of our original equations, together with the average price of $70k/vehicle, to discover the approximate average unit cost (you'll find it doesn't matter which of the two equations you use - at least not to within a few bucks).

UnitCostAvg = Price($70k) x 0.75 - FixedCost($233M)/20,000 ->

UnitCostAvg = $40,875

Great - with these numbers we can calculate a reasonable estimate of Tesla's GM and GrossProfit for the Model S line at any production rate. Here are the results:

Assuming the existing overhead spend rate, around $110Mil/Qtr, we can see that at 8,000units/annum Tesla would run a loss of close to half a billion dollars in 2013. Not good!

Hitting breakeven as a company would require the ModelS line to generate a profit of around $110Mil/Qtr (a little less in reality - the profits from the drivetrain group help), which would occur at around 23,000 units/annum. If they hit the 30,000/annum mark, mentioned by Musk in the Q2 results call, they'd be seriously profitable (which would be nice considering the deep stockholders' equity hole they're currently in), but it is going to take that sort of number. Enterprise breakeven at 8,000/annum is dreaming.

I'm bullish on EVs, and I love Tesla as a company... but they're cutting it close. I totally agree with the sentiment Musk expressed regarding demand - as I've explained in previous articles, I think EVs have a very bright future and Tesla's product is exceptional. If they can build them, they will find buyers - at least within the range of production rates under discussion. However, they have to build them!

I'm sure none of this is news to the people working their butts off in Fremont - so I'll close with a motivational poster.

Go to it, guys and gals.

**Disclosure: **I am long TSLA. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.

**Additional disclosure:** In addition to my long position in TSLA, I'm actively trading put options to hedge. It could be a bumpy few months.