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Trying to look into the economics of SpaceX

Posted by: Ekkehard Augustin - Mon Aug 20, 2007 11:57 am
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Trying to look into the economics of SpaceX 
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Post Trying to look into the economics of SpaceX   Posted on: Mon Aug 20, 2007 11:57 am
Since long I delayed the initiation fo a thread like this - partially because waiting for data - partially because of priority of other threads in this section.

But because of the availability of estimated data about all Falcons under www.bernd-leitenberger.de (see a particular thread in the Technology section) I made up my mind to start it now although my ideas about how to do the look are still rudimentary only. There was another information this year triggering the earlier initiation of this thread - Elon Musk/SpaceX said that the launches are priced as if the Falcons would be expendable - a safety measure for loss of the reusable rocket(s)

What was available earlier was the information that SpaceX already had a positive Cash Flow in 2005 (2006? - I have to look for the date), that all launch prices included $ 1 mio in 2006 and that Elon Musk has said that he has invested $ 100 mio already when he told that he was investing another $ 100 mio.

In this initial post the only safe insight is enabled by www.bernd-leitenberger.de. That site is the first source I found about the relaltion between propellant weight and empty weight of the Falcons. I multiplied the amounts of propellant with the price of cerosene. Applying $ 0.65 as price of cerosene it turned out that - like for the russian Soyuz rocket - the propellant costs are below $ 200,000.

This means that the complete price seems to cover the complete investment into one rocket - the reusable part plus the non-reusable parts. I remeber that Falcon 5 and Falcon 9 are intended to be reuasbale completely but www.bernd-leitenberger doesn't quote that and on SpaceX's homepage this information isn't available no more now.

So what's left is the portion of the launch price(s) caused by an expendable upper stage.

This all is looking as if the main portion of SpaceX's investment has gone into development.

It turns out that the Falcon 1 economically is the right and correct first step for devlopment because the loss of less than $ 10 mio by failure or accident is easyly covered by the total investment.

An expendable upper stage is additional variable costs to be added to the propellant costs the amount of I should try to find out next.

The result could be made another detail of the Lunar Siyuz thread - it would enable to apply the launch price or costs under the aspect of reusability. At present only the expendability-prices listed by SpacX are available and applied there.

The informations also seem to mean that SpaceX will have depreciated the rocket hardware totally after significantly less than 10 launches. This of course does NOT hold for the total investment yet.



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Post    Posted on: Mon Aug 20, 2007 4:12 pm
I recommend you to use the euro, or even the yen, instead of the dollar calculating anything economicly. The dollar is simply way to unstable. Look at the prices spacex had to increase, because of fuel-price correction ánd inflation. Imo, talking in dollars is like tlaking of a bucket of water withouth knowing how many holes there are in the bottom.

But one thing worries me. Spacex is becoming very rapidly a middle to big company. Plus they are still hiring. The pricetag of the rockets will have to raise simply to pay personell alone. My question to you Ekkehard as a professional economist, how does spacex becoming a very large company effect or will effect the pricetag of the falcons in your opinion?


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Post    Posted on: Tue Aug 21, 2007 7:01 am
Hello Stefan,

you are correct regarding the Dollar.

I simply use it instead of the Euro because it is the major internationally used currency and because the most data about costs and prices available to me are listed in Dollars - like under www.astronautix.de for example. To enable comparability all costs and prices must or should be listed in the same currency and it would be painful to do permanent updates because of changes of exchange rates.

SpaceX and their evolution are very interesting - and positive from my point of view. I do not expect their prices to raise because of the hiring of lots of people. Their launch manifest is growing - their revenues a the actual prices are growing by this too and this will be the reason why they can hire so much additional people that they have grown from around 40 employees to more than 200.

The pricetag of the Falcons will be a factor that reduces the prices at the whole market. Mainly this will be so because the actual prices are significantly below the prices of others and because the actual Falcon-launch-prices are explicitly - I will look for the articles reporting the data and informations - expendability-price although the Falcons are reusable.

But there is a second important reason - SpaceX is a remarkable competitor of all the others and seem to be supported by potential customers (they have been quoting them in reports, interviews etc.).

A third factor is that Elon Musk has said that he is a supporter of cheap access to space and aims at very if not extremely low prices compared to the usual price level. He explicitly wants to bring down the prices. This will not reduce his revenues but cause their growth because he may achieve that much reductions that the expendables and their producers are out of the market because the reduced prices no longer will cover their costs - SpaceX then will experience a significant leap of the number of customers and achieve more economies of scale and scope than now. They still can reduce the prices then without too much risk to reduce their profits.

...

To me at present it looks as if their growth will have positive impacts.

What about it?



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Post    Posted on: Tue Aug 21, 2007 7:31 am
I hope you're right Ekkehard, but there will be a lower limit for the pricetag if they keep growing. Or the launch manifest has to grow exponentially also.

Also depends what Elon means by a 'competitive salary'. Is that in the order of 5k per month? So if we take 5k for one person, the cost for the company is somewhere at 5700-5800. 200 folks, so that makes 11,600,000 euro a month, just to pay the salaries. Plus everything else. Sure, not everyone wouldn earn that, but if they have personell working round the clock, i'm sure people would earn a lot more then 5 grand. Even if you drop the salary by 50%, it's still needs one falcon 1 launch every month to just pay the salaries. That's some flight rate.

Off course, this is a bit crude, but the costs are very likely to be much higher, so i would very much like to see any financial information from spacex or any other major aerospace company. Are there any aerospace companies which need to release their balance sheet and annual financial report to the public?


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Post    Posted on: Tue Aug 21, 2007 8:02 am
Hello, Stefan,

as far as I remember there is a long-term-contract getting them $ 100 mio. To this their COTS-success has to be added. At the flight rate to be expected they should be able to get the required revenues. The flight rate may be even higher than that of the Shuttle, Soyuz and Progress. And they will carry privates to the ISS because NASA plans to lease the ISS to them.

Of couse their are competitors like Kistler, t/Space and several others more but the cahnces are good that they can pay thos salaries. Each Falcon 9 S9 launch costs $ 78 mio actually - which would cover more than six months of salaries. And there are going to be much more than one Falcon-launches per year.

I have to have looks into their launch manifest and have decided how to conclude to the costs of the stages and engines in between - it again will be a sytem of linear equations made up of two equations in this case.



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Post    Posted on: Tue Aug 21, 2007 1:34 pm
In between I did initial calculations using SpaceX's data plus additional data got from Wikipedia and at least one additional source. It turned out that first calculations then do require only one equation because both the Falcon 9 and the Falcon 9 Heavy apply the same Merlin-engine in all stages.

The result is that the Merlin engine of the Falcon 9s cost between $ 1.9 mio and $ 3.5 mio.

These are only initial calculations and results and more are required - in particular it turned out that the two alternatives result in different Merlin-costs which seems to have to do with the prices listed by SpaceX and applied here.

I didn't find no prices of aluminum alloys and thus applied aluminum prices.

So these initial calculations would mean that the first stage of the Falcon 9s costs between $ 17.1 mio and $ 31.5 mio and the second stage costs between $ 1.9 mio and $ 3.5 mio.

The first of these stages will be reusable and thus is an investment - the larger portion of the expendability price.

The second stage would have to be taken as variable costs if it is expendable and a new one is produced for each flight but while looking into the informations available under www.bernd-leitenberger.de and www.spacex.com I had a look into SpaceX's data sheets and found there the information that BOTH Falcon 9-stages are intended to be reusable!

Under www.astronautix.com I did NOT find informations usable here.

But please keep in mind - further calculations are required before these numbers might be trusted in.

The calculations, numbers and source I will list later.



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Post    Posted on: Tue Aug 21, 2007 3:35 pm
Aluminum alloys are at about the same price as the expensive part with producing aluminum are the high energy requirements.

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Post    Posted on: Wed Aug 22, 2007 1:07 pm
Hello, Klaus,

Thank You Veryy Much for the information which seems to mean that errors involved are not caused by the aluminum price to a large degree.

There remain some problems however:

The calculations I did yesterday are based on SpaceX’s informations about the Falcon 9 and the Falcon 9 Heavy under www.spacex.com – from there I took the number of engines, the launch prices and the lengths and diameters of the Falcon 9 and Falcon 9 Heavy.

The price of aluminium I took from www.taprofessional.de/charts/Aluminium-Line-Chart.htm - that site lists or shows the aluminum price as a chart including explicit numbers and data. I took the high and the low price and calculated the average which I used then to get the numbers posted yesterday – I also took the high and the low but didn’t list results here yet because the differences will be not that large and are not an essential point.

The charts are going to be updated – so the prices applied must be expected to be replaced later.

The thickness of the walls of the stages has been experimented – I tried 1 millimeter and 1 centimeter and thought the results for one centimeter to be more realistic using the density of aluminium of 2,700 kg/m^3 listed by Wikipedia. I tried to align the experiments to the drawings SpaceX provide regarding the fairing. There are differences between outer and inner diameters of 20 cm, 40 cm and 60 cm obviously. In relation to that 1 cm thickness in total appeared more realistic to me. The resulting weight should be considered to include the tops and bottoms of the stages also where the engines are mounted.

This enabled the equation “number of engines of first stage * investment per engine + number of identical engines of the second stage * investment per engine + total investment into aluminium of the first stage + total investment into aluminium of the second stage = priceâ€


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Post    Posted on: Thu Aug 23, 2007 11:39 am
In between I recognized a detail under www.spacex.com not incorporated into the considerations yet: they are listing the three alternative prices for GTO only – for LEO there is just one price only. It’s $ 35 mio for a Falcon 9-launch and $ 90 mio for the Falcon 9 Heavy-launch. So the $ 55 mio applied have to be replaced by the $ 90 mio which results in $ 3,211,213.32 per Merlin 1B at the Falcon 9 Heavy.

www.bernd-leitenberger.de shows a diagram that was on SpaceX’s website formerly. There one and the same price is listed for LEO and GTO – in so far the calculation applying those numbers don’t have to be redone.

Because of that diagram which includes a launch price of $ 35 mio for the Falcon 9 too I now think that the Falcon 9 Heavy is most similar to the Falcon 9 S 9. Then the factor for the launch price of that Falcon is 1.15384615 resulting in $ 3,090,901.84 per Merlin 1B.

Using that investment the Falcon 9 Heavy would be an investment of $ 83,520,149.20 into the three first stages plus $ 3,112,022.71 into the second stage - $ 86,632,171.92 in total. This leaves $ 3,367,828.07 to the price of $ 90 mio. Subtracting the propellant costs more than $ 3 mio are left. That seems to be sufficient. Leave away $ 1 mio earlier reported to be an insurance margin. Then there would be a profit of more than 2.22…% of the investment into the rocket per launch. This is a reasonable assumption under the aspect that more than one Falcon 9 Heavy launch per year is expected – in particular because of COTS and the Dragon.

The results based on SpaceX’s data for the Falcon 9 Heavy are very close tot the results I got based on Bernd Leitenberger and would mean no propellant and no profit – SpaceX doesn’t provide all informations interesting here or Virgin Galactic has published for their suborbital flights. So I at this point consider the calculations based on Leitenberger to be more correct or closer to the truth.

The factor applied yesterday to the Falcon 9 I don’t apply no more because it is the ratio between the present $ 35 mio and the former $ 27 mio. The $ 35 mio already existed earlier when the launch price for the Falcon 9 S 9 was $ 78 mio.

For the Falcon 9 the numbers are

    1. stage $ 27,840,049.74
    2. stage $ 3,112,022.71
    Total $ 30,952,072.45


To the price of $ 35 mio $ 4,047,927.55 are left. This means a profit of more than $ 3.5 mio per launch – more than 10 %.

If SpaceX suppose to have more business for the Falcon 9 than for the Falcon 9 Heavy then this is a very reasonable pricing because it would be according to the market.

In the previous post I said I would think about including the Falcon 1 into the considerations. The problem is that it looked to me as if the Merlin of the Falcon 1 is another one than that in the Falcon 9 and Falcon 9 Heavy/S 9. The reason is that Bernd Leitenberger seems to be talking about different Merlins – Merlin and Merlin 1B and I remember also somewhere to have read of a Merlin 1A – and that there is the Kestrel engine. Because of two engines two equations are required – but there is no second rocket using the Kestrel nor a Merlin non-1B. So I had a look to www.spacex.com and didn’t find there different Merlins for the Falcons. So I continue to apply Leitenberger numbers but neglect the possibility that Falcon 1 might use another Merlin than the Falcon 9s.

The first stage of the Falcon 1 consumes 21,244 kg, the second 3,990 kg – based on Leitenbergers estimations. These means propellant costs of 13,808.60 of the first stage if the LOX would cost $ 0.65 instead of $ 0.08 or so and $ 2,593.50 of the second stage. Since the result for the mrlin is already known and the equations applied to get up to now did involve the Merlin solely the investment into the Kestrel can be got only. So the only check for the Merlin is the comparison to the Kestrel. Inserting the investment into the Merlin results in $ 3,998,755.34.

The question is i fit is reasonable to get an investment into he Kestrel that is higher than that into the Merlin – nad by that margin. The reusability of the Merlin might speak against it. The only aspect I found at SpaceX speaking for it is
Quote:
A highly reliable and proven TEA-TEB pyrophoric system is used to provide multiple restart capability on the upper stage.
. May be that also the niobium might justify the result.

In so far the result applied above will be kept.

Next I did not remove margins for insurance and the like – in contrary to what I intended. It’s due to not that overseeable or clear informations or data about that. I might do alternative calculations now or search in SpaceX-related articles first – which I prefer.

But there is something that can be considered now already.

Hello, Stefan,

you calculated salaries of 11,600,000 euro a month at 200 employees and 5700-5800 euros per month and employee. This seems to be a zero too much and thus I take 1,160,000 euro per month in total. At 1.3568 $/euro of today’s noon (according to www.welt.de) these are $ 1,573,888. So the profit got for one Falcon 9 Heavy-launch up to now could be used to cover the salaries of one month and a third while one launch of a Falcon 9 could cover the salaries of two months. The actual launch manifest includes 5 launches of a Falcon 9 from Q4/2008 to Q3/2009. Taking these as non-Heavy the salaries of 10 months would be covered. The Heavy would cover 7 months it seems.

If this would be true then the remaining salaries will be taken from the capital of $ 200 mio Elon Musk already invested into SpaceX. This will be no problem because the business is just starting.

But the prices are said to be expendability prices – so if the stages aren’t lost and thus expended but successfully recovered the margin of the price exceeding the costs is a value of several millions. This means that each single non-Heavy-launch where the first stage at least is recovered successfully covers the salaries of 17 months while a Heavy-launch would cover threee times that. SpaceX is going on very carefully and delays launches long after failures and thus don’t risk their reusable stages more than required.

But the truth is quite different. As a private entrepreneur Elon Musk will have calculated the prices so that the salaries are covered by all launches of one year regardless of the rocket launched – and that means that even SpaceX as a private company does so. So I did another calculation taking the salaries as if there were only one rocket instead of three different ones. Since the launch manifest at present lists five Falcon 9 launches within one year I divide the yearly salaries by five because all the launches together have to cover the salaries instead of each one the total salaries separatedly. The numbers for the investment into the stages drop by a few $ 100,000 per engine then, by $ 12 mio at the Falcon 9 Heavy and by $ 4.3 mio at the Falcon 9.

So the yearly salaries don't have that much an impact it seems.

I’ll go on later.

What about it all?



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Post    Posted on: Fri Aug 24, 2007 12:32 pm
Unexpectedly I didn't manage to find the article explicitly saying that Musk had been recommended to include third party insurance and thus add $ 1 mio to the former prices - which for example raised the Falcon 1 launch price from $ 5.7 mio to $ 6.7 mio.

I still will have to look for the article which I suppose to have downloaded also.

But I found the article "Pentagon Could Face Big Cost Increases for Future TacSats" ( www.space.com/spacenews/archive06/Response-022706.html ) which reported that
Quote:
...SpaceX currently offers Falcon 1 launches for $6.7 million including range expenses, but that figure could rise as the company's insurance costs for launches from Vandenberg Air Force Base in California go up. According to the GAO report, the insurance on Falcon rockets could rise from $40,000 to as much as $500,000.
SpaceX President Elon Musk said he had been notified that his premiums would go up after the Air Force commissioned Lockheed Martin Corp. of Bethesda, Md., to build a launch pad at Vandenberg for its Atlas 5 rockets, but said that he hoped that the cost would be lower than the numbers contained in the GAO report. ...


At present I cannot but take this as the hint that the $ 6.7 already include third party insurance range costs etc. - all that which will NOT be removed by depreciations.

I also randomly found one article which included the information that the present Falcon launch-prices are expendability prices: The article "SpaceX to Tackle Fully Reusable Heavy Lift Launch Vehicle" ( www.space.com/news/050908_spacex_falcon.html ) is quoting Elon Musk saying that
Quote:
The prices we are showing do not account for reusability, so I'm hopeful that we will be able to reduce costs significantly over time. Also, this is still the first generation of our propulsion technology," Musk said. The SpaceX Merlin 2 engine will benefit from a very significant thrust upgrade and also be considerably cheaper per pound of thrust than Merlin 1, he said.


Another randomly found information regards the revenues: The article "Briefs" ( www.space.com/spacenews/archive05/Briefs_112105.html ) reports that
Quote:
The company has taken in a total of $200 million in contracts to date, Musk said in a Nov. 18 press conference. Musk said he needs to raise another $100 million to complete Falcon 9 and will approach outside investors early in 2006.
.

So there are revenues of $ 200 mio already (to be claimed after succesful launches at least) and the required additional $ 100 mio are more than covered by the COTS-contract.

In so far no problems regarding salaries are to be expected.

Calculations will go on later as far as required - the impact of the $ 1 mio for insurance costs etc. is felt below the $ 1 nio border only.



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Post    Posted on: Mon Aug 27, 2007 1:42 pm
In between I included $ 1 mio third party insurance and other costs into the calculations and it turned out that the results for both the Falcon 9 and the Falcon 9 heavy approach $ 3 mio and – in particular – each other.

The Kestrel engine now seems to cost less than $ 3 mio by less than $ 2,000.

But there still is a component of the price which no data or informations are available about – the profit SpaceX or Elon Musk are assuming to get. I might try three assumptions of Return On Investment – but there is another aspect I prefer to try to look into because there is an information about it: the Cash Flow.

According to the article “Elon Musk: SpaceX Rocket Plans Outlinedâ€


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Post    Posted on: Wed Aug 29, 2007 12:34 pm
Of course there may have been much more new provisions been in SpaceX’s balance sheet than assumed in the calculations or considerations of the previous post. But to apply this assumptions would be much more speculative than what has been done there. The information that they had contracts of $ 200 mio that time doesn’t mean that they have got those $ 200 mio in total already. How much they have got already depends on the conditions of those contract and those conditions may include an agreement on how long before a launch the price has to be paid. If this time is three months for example they will NOT have got the price for a launch in April 2007 before August 2006 but in February 2007 earliest. If in difference to that the time is one year the price for a launch in April 2007 would have to be paid in May 2006 latest in SpaceX would have the money before August 2006 – then this money would have been accounted under provisions and it would be new provisions and thus involved into the Cash Flow.

In the previous post I assumed that the conditions of the contracts are so that launches in 2007 didn’t have to be paid before August 2006

The revenues below the Falcon 1 launch price might be interpreted as if SpaceX could claim a portion of the price only because it was a test flight or/and because it failed – for example.

I announced to include ealier calculations. Here I do that using their results. These were profits of $ 2,367,828.07 in the case of the Falcon 9 Heavy and $ 3,047,927.55 in the case of the Falcon 9. The profits in the case of the Falcon 1 seem to be negligible or losses.

This would mean that a portion of the surplus of $ 13.7 mio is costs really. These costs may be the $ 3.8 mio got as revenues left after the failed test launch of March 2006. Then $ 9.9 mio would be left of the surplus – they may the remainder of the Falcon 5 launch price delayed and in between cancelled. Then the costs involved in that launch price would be $ 6.8 mio after subtraction of $ 1 mio third party insurance, range costs etc..

…

Does anyone have the correct, complete and original launch manifest valid for 2006 before the failed test launch?



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Post    Posted on: Wed Aug 29, 2007 4:25 pm
Do you search that one?

Code:
Customer    Launch Date   Vehicle   Departure Point   Status
US Defense Dept   Q4 2004   Falcon I   Vandenberg   Contracted
US Defense Dept   Q2 2005   Falcon I   Marshall Islands   Tentative
International Government   Q4 2005   Falcon I   Marshall Islands   Contracted
Bigelow Aerospace   Q4 2005   Falcon V   Vandenberg   Contracted
International Commercial   Q3 2006   Falcon V   Cape Canaveral   Tentative


or that one?

Code:
Customer   Launch Date   Vehicle   Departure Point
US Defense Dept (DARPA)   Q1 2006   Falcon 1   Kwajalein
US Defense Dept (DARPA)   Q4 2006   Falcon 1   Kwajalein
US Defense Dept (OSD/NRL)   Q4 2006   Falcon 1   Kwajalein
Malaysia (ATSB)   Q3 2007   Falcon 1   Kwajalein
US Government   Q1 2008   Falcon 9   Kwajalein
SpaceDev   Q2 2008   Falcon 1   Vandenberg
MDA Corp.   Q2 2008   Falcon 9   Kwajalein
MDA Corp.   Q3 2008   Falcon 1    Vandenberg
Bigelow Aerospace   Q4 2008   Falcon 9    Kwajalein
Swedish Space Corp.    Q4 2009    Falcon 1    Vandenberg
US Air Force    $100 million contract thru 2010    Falcon 1    TBD


Or perhaps you'll be please by a third one?

Code:
US Defense Dept (DARPA)   Q4 2005   Falcon 1   Kwajalein
US Defense Dept (OSD/NRL)   Q4 2005   Falcon 1   Vandenberg
Malaysia (ATSB)   Q2 2006   Falcon1   Kwajalein
US Government    Q2 2007   Falcon 9   Kwajalein
Bigelow Aerospace   Q1 2008   Falcon 9   Kwajalein
US Commercial    Q2 2008   Falcon 1   Vandenberg
MDA Corp.    Q3 2008   Falcon 1   Vandenberg
Swedish Space Corp.    Q4 2008   Falcon 1   Vandenberg
US Air Force    $100 million contract thru 2010   Falcon 1   TBD


In case that doesn't help you, let me know...

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Post    Posted on: Thu Aug 30, 2007 1:04 pm
Hello, Klaus,

Thank You Very Much for those tables – they will be of much help and they already seem to show that I remembered wrong and would have to correct earlier calculations.

The price of a Falcon 5 launch applied is aged of course and would have been to be multiplied by 1.15 to get correct numbers – but this wouldn’t change the circumstance that a portion of that price would be a portion of the surplus. This can’t be correct since the engines of the Falcon 5 – in both stages – are Merlin 1Bs which means that the investment into the Falcon 5 would be a bit more than $ 18 mio. Of course these wouldn’t be costs if the Falcon 5 comes back intact but what should the difference be between this investment and the surplus left of it?

Here the looks into the Cash Flow and the combination with the earlier calculations seem to show that additional costs or even profit margins have to be included to get the correct results for the engines, stages, costs, profits etc.

At this point now it’s time to put it all together as an equation system including the Cash Flow and to apply all the numbers available either updated to now – by the factor 1.15 if no actual numbers available – or adjusted to 2006 by the factor of 1.15.

Let’s call the investment into one Merlin 1B X, that into one Kestrel Y and that into one Merlin non-1B Z. Next let’s call the known value of the investments into aluminium of the first Stage of the Falcon 9 a, of the second stage of that rocket b, of the first stage of the Falcon 5 c, of it’s second stage d, of the first stage of the Falcon 1 e and of its second stage f and the prices F1, F9, F9H and F5. To this let’s add portions of the labor costs L Stefan calculated and call the factors g, h, i and j. Finally there are additional unknown values u9, u9h, u1 and u5 at present unknown costs and p9, p9h, p1 and p5 of at present unknown profits.

The engines and stages of the Falcon 9 Heavy will be taken from the Falcon 9 because the Falcon 9 Heavy simply is a Falcon 9 with three identical first stages two of which are boosters simply.

Then the equations are as follows:

Falcon 9: 9 * X + a + 1 * X + b + g * L + u9 + p9 = F9
Falcon 9 Heavy: 3 * 9 * X + 3 * a + 1 * X + b + h * L + u9h + p9h = F9H
Falcon 1: 1 * Z + e + 1 * Y + f + i * L + u1 + p1 = F1
Falcon 5: 5 * X + c + 1 * X + d + j * L + u5 + p5 = F5

These equations then can be calculated to:

Falcon 9: 10 * X + a + b + g * L + u9 + p9 = F9
Falcon 9 Heavy: 28 * X + 3 * a + b + h * L + u9h + p9h = F9H
Falcon 1: 1 * Z + e + 1 * Y + f + i * L + u1 + p1 = F1
Falcon 5: 6 * X + c + d + j * L + u5 + p5 = F5

Gathering known values on one side of the equations:

Falcon 9: 10 * X + g * L + u9 + p9 = F9 – (a + b)
Falcon 9 Heavy: 28 * X + h * L + u9h + p9h = F9H – (3 * a + b)
Falcon 1: 1 * Z + 1 * Y + i * L + u1 + p1 = F1 – (e + f)
Falcon 5: 6 * X + j * L + u5 + p5 = F5 - (c + d)

What’s left at this point are the factors of the labor costs. For these an additional equation can be added:

g * L + h * L + i * L + j * L = L

because L is known and only spread over the equations by the factors. So L can be removed from the additional equation by division by L:

g + h + i + j = 1.

Then the equation system is:

Falcon 9: 10 * X + g * L + u9 + p9 = F9 – (a + b)
Falcon 9 Heavy: 28 * X + h * L + u9h + p9h = F9H – (3 * a + b)
Falcon 1: 1 * Z + 1 * Y + i * L + u1 + p1 = F1 – (e + f)
Falcon 5: 6 * X + j * L + u5 + p5 = F5 - (c + d)
labor costs share: g + h + i + j = 1.

So at this point there are 5 equations but 15 unknowns (g, h, i, j, u9, u9h, u1, u5, p9, p9h, p1, p5, X, Y and Z) – so to get one and only one result the values of 10 of the unknowns had to be set by me or other while to get a set of results represented by function the values of 9 unknowns only need to be selected.

One more unknown might be handled by assuming a 6th equation Z = X which would express what has been done in an earlier post already – the assumption that Merlin 1 B is very similar to the Merlin of the Falcon 1. Now 8 unknowns only would be left. There are two sets of them that might make sense - either g, h, i, j, p9, p9h, p1 and p5 are selected artificially or arbitrarily or g, h, i, j, u9, u9h, u1 and u5 or u9, u9h, u1, u5, p9, p9h, p1 and p5. The first both alternatives would make sense - g to j are arbitrary economically nonetheless to a very high degree.

But there is a 7th equation to be added – the Cash Flow. Because of the surplus/deficit additional factors are required – the number of launches for each of the rockets n9, n9h, n1 and n5. And two more unknowns are added now – the depreciation r of the total investment I (which is known) and the new provisions np. Then the 7th equation.is the Cash Flow. Really this equation should be an inequation here because Musk said that the Cash Flow is positive in 2006 and thus is greater than zero:

n9 * F9 + n9h * F9H + n1 * F1 + n5 * F5 – L - u9 - u9h - u1 - u5 + r * I + np > 0

Gathering the known values on one side again results in

u9 + u9h + u1 + u5 - r * I - np < n9 * F9 + n9h * F9H + n1 * F1 + n5 * F5 – L

The complete system then is:

Falcon 9: 10 * X + g * L + u9 + p9 = F9 – (a + b)
Falcon 9 Heavy: 28 * X + h * L + u9h + p9h = F9H – (3 * a + b)
Falcon 1: 1 * Z + 1 * Y + i * L + u1 + p1 = F1 – (e + f)
Falcon 5: 6 * X + j * L + u5 + p5 = F5 - (c + d)
labor costs share: g + h + i + j = 1
Similarity: Z = X
Cash Flow: u9 + u9h + u1 + u5 - r * I - np < n9 * F9 + n9h * F9H + n1 * F1 + n5 * F5 – L

Of course the known values L and I are still on the wrong side but this is justified by there factors not selected yet. Now there are 7 equations and 17 unknowns – but it seems that of the two alternatives making sense found above one can be preferred. The alternatives were two different sets of unknowns the values for would have to be selected artificially or arbitrarily. The Cash Flow-equation results in a preference for setting u9 etc. because turning the inequation-sign into an equation-sign determines the maximum value of the sum of 6 unknowns. The results based on this maximum is outside the set of valid values for other unknowns.

Next there are two unknowns that are automatically and inescapably are set by selecting the other 9 ones. So then there are 7 equations and 8 unknowns which will result in a function describing a set of values.

The knowns will be inserted into the equations in the next post. There also it will be considered what the most proper values to be selected for g to j and u9 to u5 may be.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)


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Post    Posted on: Fri Aug 31, 2007 11:39 am
Since I recognized in between that I didn’t include the propellant costs explicitly into the equation system got in the previous post I consider them now.

In principle the propellant costs are part of the unknown called u9 to u5. Of course the propellant costs are knowns here – let’s call them pr9, pr9h, pr1 and pr5. Then the other portions of the unknowns can be called npr9, npr9h, npr1 and npr5:

u9 = pr9 + npr9
u9h = pr9h + npr9h
u1 = pr1 + npr1
u5 = pr5 + npr5

So the properly detailed equation system is:

Falcon 9: 10 * X + g * L + pr9 + npr9 + p9 = F9 – (a + b)
Falcon 9 Heavy: 28 * X + h * L + pr9h + npr9h + p9h = F9H – (3 * a + b)
Falcon 1: 1 * Z + 1 * Y + i * L + pr1 + npr1 + p1 = F1 – (e + f)
Falcon 5: 6 * X + j * L + pr5 + npr5 + p5 = F5 - (c + d)
labor costs share: g + h + i + j = 1
Similarity: Z = X
Cash Flow: pr9 + npr9 + pr9h + npr9h + pr1 + npr1 + pr5 + npr5 - r * I - np < n9 * F9 + n9h * F9H + n1 * F1 + n5 * F5 – L

The equation system is designed this way because the launch prices are the starting point – later the equation system will be modified so that at least two groups of unknowns will be removed and/or consolidated.

Now the launch prices are to be looked at systematically. The informations available are listed in the following table

Code:
                     2006         2007       factor
Falcon 1             $  6.7 mio   $  7 mio   1.045
Falcon 5             $ 18   mio       -        -
Falcon 9             $ 35   mio   $ 35 mio   1
Falcon 9 Heavy/S 9   $ 78   mio   $ 90 mio   1.154


So there is a complete set of prices for 2006 while for 2007 a Falcon 5 launch price would have to be got by applying one of the factors – which then needs to be thought about. The prices of aluminium I got could be applied to 2006 also – in particular since I calculated the average of the two prices I found. The propellant price applied I found much earlier and is applied in the Lunar Siyuz-thread and the CXV-costs-thread also – so this price should be applied to 2006 also. The error will not be that large since it’s clear already that the propellant costs aren’t that large. But the number of employees has been smaller – so this number will be looked at again.

So what about g to j? They are percentages of the labor costs – what percentages might be correct? What factors determine how the labor is spread over the launches etc.? First there is the question if there are several launches at one time. Because there informations about quarters of a year only more than one launch per quarter could be treated as more than one launch at one time.

In principle I have problems to imagine that launches of different rockets might require different numbers of employees – because of computers, tools and the like. Also all the employees having tasks of administration can’t be distributed unevenly regarding the costs they mean. An aspect speaking for inequally distributed costs may be different weights or shapes or properties of payloads. Regarding this I prefer less labor costs for smaller rockets.

According to articles under www.space.com the employees are structured so that the structure can be applied here.

The article “SpaceX Rocket Readied For Maiden Flightâ€


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