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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    Posted on: Mon Sep 03, 2007 11:22 am
I detected an error in the equation system – in the Cash Flow equation the numbers of launches are missing in the left side. The correct 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: n9 * pr9 + n9 * npr9 + n9h * pr9h + n9h * npr9h + n1 * pr1 + n1 * npr1 + n5 * pr5 + n5 * npr5 - r * I - np < n9 * F9 + n9h * F9H + n1 * F1 + n5 * F5 – L

So let’s insert numbers now that are reported or the bases for are provided by SpaceX and Bernd Leitenberger:

Falcon 9: 10 * X + g * L + 169130 + npr9 + p9 = 35 mio – (20958.4082353887 + 23151.7300274643)
Falcon 9 Heavy: 28 * X + h * L + 465530 + npr9h + p9h = 78 mio – (3 * 20958.4082353887 + 23151.7300274643)
Falcon 1: 1 * Z + 1 * Y + i * L + 16402,1 + npr1 + p1 = 6.7 mio – (5754,08494834638 + 306,884530578474)
Falcon 5: 6 * X + j * L + 91780 + npr5 + p5 = 18 mio - (26807.2663 + 11372.7797)
labor costs share: g + h + i + j = 1
Similarity: Z = X
Cash Flow: n9 * 169130 + n9 * npr9 + n9h * 465530 + n9h * npr9h + n1 * pr1 + n1 * npr1 + n5 * pr5 + n5 * npr5 - r * I - np < n9 * 35 mio + n9h * 78 mio + n1 * 6.7 mio + n5 * 18 mio – L

Mainly Bernd Leitenberger’s numbers are applied here The propellant costs for the Falcon 9 Heavy are got by multiplying Leitenberger’s number for the first stage of the Falcon 9 by three.

Next let’s reconsider the salaries L. Stefan calculated salaries for 200 employees. I got 255 in average for 2006. Then the salaries in 2006 will have been $ 24,080,486.40 in total. These I insert into the equation system now plus the investment of $ 100 mio:

Falcon 9: 10 * X + g * 24080486.40 + 169130 + npr9 + p9 = 35 mio – (20958.4082353887 + 23151.7300274643)
Falcon 9 Heavy: 28 * X + h * 24080486.40 + 465530 + npr9h + p9h = 78 mio – (3 * 20958.4082353887 + 23151.7300274643)
Falcon 1: 1 * Z + 1 * Y + i * 24080486.40 + 16402,1 + npr1 + p1 = 6.7 mio – (5754,08494834638 + 306,884530578474)
Falcon 5: 6 * X + j * 24080486.40 + 91780 + npr5 + p5 = 18 mio - (26807.2663 + 11372.7797)
labor costs share: g + h + i + j = 1
Similarity: Z = X
Cash Flow: n9 * 169130 + n9 * npr9 + n9h * 465530 + n9h * npr9h + n1 * 16402,1 + n1 * npr1 + n5 * 91780 + n5 * npr5 - r * 100 mio - np < n9 * 35 mio + n9h * 78 mio + n1 * 6.7 mio + n5 * 18 mio – 24080486.40

At this point it becomes clear that g to j will have to take into account months and perhaps the number of launches.

And to set the remainders of the unkowns u9 etc. (npr9 etc.) requires to include your data, Klaus.

I’ll go on later.



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Post    Posted on: Tue Sep 04, 2007 11:11 am
To get the non-propellant-cost-portions of the former unknowns u9, u0h, u1 and u5 is very easy now because I said earlier that each of the u9… will not be higher than 20% of the launch price. The propellant-portions are known already and so the remainders can be got b<y subtracting the propellant-portions from the 20%:

Code:
Falcon 9:      20% of $ 35   mio = $  7    mio
Falcon 9 Heavy: 20% of $ 78   mio = $ 15.6  mio
Falcon 1:       20% of $  6.7 mio = $  1.34 mio
Falcon 5:       20% of $ 18   mio = $  3.6  mio


non-propellant-portions

Code:
Falcon 9:      $  7    mio - $ 169,130   = $  6,830,870
Falcon 9 Heavy: $ 15.6  mio - $ 465,530   = $ 15,134,470
Falcon 1:       $  1.34 mio – $  16,402.1 = $  1,323,597.9
Falcon 5:       $  3.6  mio - $  91,780   = $  3,508,220


Looking at the non-propellant costs of the Falcon 1 it turns out that the $1 mio for third party insurance, range costs etc. are covered and exceeded by that much. The excess-dollars cover variable costs beyond the propellant costs and will include a safety margin also. If there were $ 500,000 for third party insurance only then the safety margin and additional variable costs are assumed to be higher. The only risk regarding the results is that the investment into the engines and stages is set too low. But there is the way out by setting the non-propellant-costs to zero – then the upper boundary of the investment is got.

This can be considered to turn the results for the other rockets trustable. So the results can be inserted into the equation system.

What about g to j now?

Like already mentioned in the previous post they have to take into account the months. This can be done by looking into the launch manifest which lists the launches by quarter of the year. A quarter is three months and these months can be divided by the number of launches per rocket within that quarter. The labor costs of one year first have to be divided by four and then by the yet to be determined rocket-related factor. Next the result has to be divided by the number of launches per rocket.

The rocket-related factor has been set for two groups already. These are groups of employees the salaries of have to be distributed over the rockets equally. Since there are four rockets there is a quarter of the salaries of those employees per rocket each. This means that the structure of the employees regarding the tasks and work has to be applied:

Code:
launch operation team    25 employees    9.803922% of 255
R&D                      51 employees   20% of 255
admin., commerce         22 employees    8.7649402% of 255
manu., mounting         157 employees   61.5686275% of 255


The last row of the table includes the correction of an earlier and up to now unrecognized error.

So 38.5688618% of the salaries are to be distributed equally. This means to multiply the salaries by that factor and next by 0.25. Then the first term of g to j is “0.385688618 * 0.25â€


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Post    Posted on: Wed Sep 05, 2007 4:30 pm
The salaries of the 157 employees to be distributed inequally over the rockets are best to be handled by a structure describing relations and a kind of hierarchy of the rockets and stages. When I started to consider this a few posts earlier I talked about a distinction between and by stages – one of the reasons was that the second stages all have only one engine which rules out engines as a criterion of distribution of salaries between the second stages.

Code:
rocket           weight     dia-   len   volume   payload in kg
                 in kg   mtr.      in m^3

                         2. stages

Falcon 1           395   1.70     8     42.73     670 (200 km)
Falcon 5          2300   3.70    14    158.34    4100 (200 km)
Falcon 9          2300   3.60    26    294.05    9300 (200 km)
Falcon 9 Heavy   2300   3.60    26    294.05   24750

                         1. stages

Falcon 1          1356   1.70    15     80.11
Falcon 5          7000   3.70    33    373.22
Falcon 9         16000   3.60    27    305.36
Falcon 9 Heavy   48000   3.60    54    305.36


The sums are

Code:
2. stages         7295   12.60    74    789.17   38820
1. stages        72356   12.60   129   1064.05
total            79661   25.20   203   1853.22   38820


At this point I recognize that the weight(s) of the payload(s) may have to be applied to the first stages indirectly perhaps – I will think about it after going on.

The following relations are got

Code:
2. stages   0,092   0,5   0,365   0,426   1
1. stages   0,908   0,5   0,635   0,574   0


From these relations it seems to be clear that on this level the payloads and the diameters do not be proper criterions.

Weight can be a criterion but there will be assistance by machines. Length is of meaning regarding construction checks and the like and labor may be playing a larger role – this also is valid regarding the volume perhaps. I didn’t calculate the surfaces yet but volume has to do with the shape which might have to be kept because of winds and the like – so I personally prefer to apply volume as the criterion on this level. On the other hand it might be possible that length takes into account indirect effects of the payload on the required amount of labor into the first stages better – but this effect should be considered on the next level I think.

Since I already said that this is an artificial or arbitrary way economically – which later should and will be removed – I do a break here.

Which improvements can you imagine, Would you prefer another of the principially possible criterions listed?



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Post    Posted on: Thu Sep 06, 2007 10:27 am
I thought over the distribution over the two groups again and recall that regarding the first stages I had in mind the work required to mount engines to a stage. This makes engines the best criterion for distribution of salaries over the first stages.

Regarding the second stages I had in mind work linked to weights of payloads and the like – so I simply will apply the maximum capacities regarding weight. Heavy payloads also might be larger which also may cause more work.

Indirect impacts of the different weights of or for the second stages on the first stages are taken into account by applying the different numbers of engines from my point of view – so no modifications are done.

The numbers of engines are

Code:
Falcon 1          1
Falcon 5          5
Falcon 9          9
Falcon 9 Heavy   27


42 engines in total. Then the factors on this level are

Code:
Falcon 1         0.0238
Falcon 5         0.1190
Falcon 9         0.2143
Falcon 9 Heavy   0.6429


The numbers are rounded.

The factors for the second stages on this level are prepared already in the previous post, where total of all payload weights was got. The factors resulting are

Code:
Falcon 1         0.0173
Falcon 5         0.1056
Falcon 9         0.2396
Falcon 9 Heavy   0.6375


The sums of these factors per rocket are

Code:
Falcon 1         0.0411
Falcon 5         0.2246
Falcon 9         0.4539
Falcon 9 Heavy   1.2804


Since these sum up to 2 a division by two is required – clearly the calculation means to calculate each rocket two times. It turns out that the numbers have to be shortened to get a sum of 1:

Code:
Falcon 1         0.02
Falcon 5         0.11
Falcon 9         0.22
Falcon 9 Heavy   0.65


I ‘ll go on later



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Post    Posted on: Fri Sep 07, 2007 11:54 am
Next the values got in the previous post are to be multiplied by 61.5686275% - the percentage of 157 employees of 255 employees. The remainder has been multiplied by another value already - 0.385688618 * 0.25 giving 0.096422155.

The results of the multiplication per rocket are

Code:
rocket          lev2   result
Falcon 1         0.02   0.012313726
Falcon 5         0.11   0.06772549
Falcon 9         0.22   0.135450981
Falcon 9 Heavy   0.65   0.400196079


Adding the other product results in value very slightly above 1 after summing up over all four rockets – so I shortened the numbers again and also rounded a way mathematically wrong. Please recall that the whole method of distributing the salaries is artificial and arbitrary nonetheless and so this mathematically wrong rounding is of no meaning – please recall also that I will remove the requirement of this way later.

Then the values for g to j are got as

Code:
rocket          res.    factor
Falcon 1         0.109      i
Falcon 5         0.164      j
Falcon 9         0.231      g
Falcon 9 Heavy   0.496      h


Inserting these values into the equations the system looks

Falcon 9: 10 * X + 0.231 * 24080486.40 + 169130 + 6830870 + p9 = 35 mio - (20958.4082353887 + 23151.7300274643)
Falcon 9 Heavy: 28 * X + 0.496 * 24080486.40 + 465530 + 15134470 + p9h = 78 mio - (3 * 20958.4082353887 + 23151.7300274643)
Falcon 1: 1 * Z + 1 * Y + 0.109 * 24080486.40 + 16402.1 + 1323597.9 + p1 = 6.7 mio - (5754,08494834638 + 306,884530578474)
Falcon 5: 6 * X + 0.164 * 24080486.40 + 91780 + 3508220 + p5 = 18 mio - (26807.2663 + 11372.7797)
labor costs share: 0.231 + 0.496 + 0.109 + 0.164 = 1
Similarity: Z = X
Cash Flow: n9 * 169130 + n9 * 6830870 + n9h * 465530 + n9h * 15134470 + n1 * 16402,1 + n1 * 1323597.9 + n5 * 91780 + n5 * 3508220 - r * 100 mio - np < n9 * 35 mio + n9h * 78 mio + n1 * 6.7 mio + n5 * 18 mio - 24080486.40

In principle it’s looking as if calculations and modifications can or even should be started now by applying the data Klaus posted – but what has been done in between improved the overview.

Because of that improved overview I recognized that the Cash Flow-equation is of nearly no purpose in this system which appears to tend to turn it to be of less use. The reason is that I inserted $ 100 mio for the variable I. This is correct but the equation doesn’t contain no unknown more the value for is intended to be found via this system of equations.

So this must be altered. I will insert I again – being aware that I is composed by the – yet unknown partially - investments into the engines, the aluminium and the manufacturing of the reusable rockets. This will add an 8. equation – but one of the former ones is completely solved and will be removed for this reason.

Another point is that up to now no such system applied at this board required the involvement of time – but here this must be done. The number of employees applied here is related to a time where no or nearly no work on the Falcon 9s has been done. And the value of I doesn’t include the additional investment Musk said to be required to develop the Falcon 9s.

So the labor costs need to be multiplied by a factor involving the temporal structure of costs and investment.

Both the additional equation altering the equation system and the fundamental altering of the system by involving time I will do later.



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Post    Posted on: Sun Sep 09, 2007 2:54 pm
One problem obvious now is that in 2006 the investment done was $ 100 mio only but the Falcon 9s are incorporated into the equation system while Musk has said that he WILL have to invest additional $ 100 mio for the Falcon 9, So The Cash Flow-equation is contradictional at present – it includes the Falcon 9s on the left side but NOT on the right side of the equation-sign.

This has to be improved somehow – which will be done via the number of launches which was zero for the Falcon 9s in 2006.

The investment has to be broken down into the engines of the different Falcons and the salaries of the manufacturing employees. The work of those employees to produce the stages is part of the investment and can be incorporated by the factors calculated in past posts

But this is insufficient since the Falcon 9s have their own price-equations in the system which can, should and must be kept. But there the labor costs of 2006 are applied while no Falcon 9 has been produced in 2006. So the labor costs of the Falcon 9s have to be adjusted somehow nonetheless.

This can be done easyly by looking for the first launch of the Falcon 9s and adjusting the labor costs by the growth-factor I got in an earlier post. The averag salaries for the next and each future year can be calculated and applied.

But then g to j must be adjusted also since it would be wrong to assume that those employees the salaries of have been considered as costs of the Falcon 9s would have NOT been working in 2006.

This seems to mean nothing else than a recalculation of g to j. i and j can be distributed over Falcon 1 and Falcon 5 using g and h. Next the employees and salaries for the Falcon 1 and Falcon 5 will be kept but the factors for the Falcon 9s will be recalculated applying the employees in 2007, 2008, 2009 or so.

Because of the alternative launch manifests Klaus posted there are several alternative values for g to j in parallel.

This has an impact on the Cash Flow-equation as well because the factors distributing the salaries of the manufacturing employees have an effect on the structure of the investment of $ 100 mio also.

At this point another clarification seems to be of help also – there are two alternative values for the rate of depreciation r: One without the loss of the Falcon 1 and another one that includes that loss.



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Post    Posted on: Mon Sep 10, 2007 3:33 pm
Let's have a look onto the equation system as it looks before insertion of any numbers:

Code:
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: n9 * pr9 + n9 * npr9 + n9h * pr9h + n9h * npr9h + n1 * pr1 + n1 * npr1 + n5 * pr5 + n5 * npr5 - r * I - np < n9 * F9 + n9h * F9H + n1 * F1 + n5 * F5 – L


The L in the equations Falcon 1, each other Falcon listed in the launch manifest-versions Klaus posted and Cash Flow is going to be replaced by L2006 as the labor costs of 2006.

The L in the remaining equations will be replaced by L2007 if the year of the first launch (for example) is 2007, L2008 if it is 2008 and so on.

Next based on L2006. L2007 etc. g to j can be calculated newly to get the values fitting into the structure of time. Applying the manufacturing components only leads to factors or values to be applied in the already mentioned equation for the investment I.



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Post    Posted on: Tue Sep 11, 2007 10:24 am
Obviously there are two different alternatives when looking into the launch manifest-versions Klaus posted - only Falcon 1 launches in 2006 or Falcon 1 as well as Falcon 5 launches in 2006.

This menas two alternative values for i including two alternative years regarding the validity of j. g and h both are NOT valid in 2006.

The case that only Falon 1 launches in 2006 means that i is 1 while the alternative means the requirment of calculations.

At this point it will be proper to apply fractions of the year also without incorporating them into g to j.



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Post    Posted on: Thu Sep 13, 2007 10:28 am
Like can be seen in Klaus post there wer the follwoing scenarios for 2006 if delays are incorporated:

Code:
           num launches
rocket    Q1   Q2   Q4

Falcon 1   1    1    1
Falcon 5   0    0    1

OR

Falcon 1   1    0    2

OR

Falcon 1    2         1


Obviously two launches of the Falcon 1 per qurtaer of year are possible.

So additionally to the factors g to j the number of employees should be multiplied by 0.25 and then be divided by 2 regarding the Falcon 1.

So there is an additional factor for launch capacity.



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Post    Posted on: Thu Sep 13, 2007 1:39 pm
Not sure, but have you seen that SpaceX has bumped all their launches to next year? (not that it matters for calculation, but maybe it affects your delaynumbers)


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Post    Posted on: Thu Sep 13, 2007 3:25 pm
Hello, Stefan,

yes I know that - I simply look at it as if we still were in 2006 and the valid launch manifest is one before the first Falcon 1-launch or one before August 2006.

I do so because Elon Musk said in August 2006 that SpaceX is Cash Flow-positive which I cannot but suppose to involve all launches planned in 2006 - they wouldn't do or announce launches they haven't been paid for already.

The other reason is that dealys don't effect a price already paid.

What the delays have an effect on is what launches will have to be considered to include labor costs properly. Launches delayed into 2006 have to be considered for sure. Launches planned for 2006 should be considered also even if dekayed into 2007 in between. Launches planned for 2007 before delays already have to be kept out of consideration. The launches are of menaing for labor costs only here.

...



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Post    Posted on: Fri Sep 14, 2007 1:22 pm
According to what I said in my previous post there is a factor not required originally – fraction of the year:

f <= 1

This factor must be applied to the labor costs L. Of course it would be more correct to apply the factor calculated much earlier for getting the average monthly growth of the number of employees and really this factor will be applied later – but under another aspect. Here the problem is that only the number of launches per a fraction of the year larger than one month is available – f is 0.25 here.

After applying f the number of launches n – already incorporated into the equation system in the Cash Flow-equation - must be applied as a factor which is a divisor really.

Then the term got is

f * 1/n * L2006

at present.

This term has to be applied to the launch costs - these will be the salaries for the launch operations team only.

This means that those salaries will be broken off the labor costs and that the remainder has to be considered to be part of the investment into the rockets! This part will go into the new investment-equation and thus into the Cash Flow-equation. R&D as well as manufacturing of rockets and engines are investments because they lead to a product that can be applied again and again – the rocket(s).

The monthly growth of the number of employees will be applied to properly take into account the time of the planned first launch of a rocket – the yearly average number of employees will be kept as part of the Cash Flow-equation.

At present n can be set to 2 for the Falcon 1 because two Falcon 1-launches seem to be possible per f = 0.25 according to the data Klaus has saved and posted. This means f * 1/n = 0.25 * 1/2 = 0.25 * 0.5 = 0.125. For the Falcon 5 n must be set to 1 because there seems to be no information that more than one Falcon 5-launch per f = 0.25 is possible – f * 1/n = 0.25 * 1/1 = 0.25.

What’s left is the recalculation of I and j. Of course all this has to be done for the Falcon 9s also. But it all can be done only after L has been replaced by L2006, L2007, L2008 entirely and have been broken down to those quarters of those years where launches were planned and incorporated into the equation system.



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Post    Posted on: Thu Sep 20, 2007 4:16 pm
I decided to first modify the equation system using the term talked about in the previous post:

Falcon 9: 10 * X + f * 1/n9 * g * LXXXX + pr9 + npr9 + p9 = F9 – (a + b)
Falcon 9 Heavy: 28 * X + f * 1/n9h * h * L YYYY + pr9h + npr9h + p9h = F9H – (3 * a + b)
Falcon 1: 1 * Z + 1 * Y + f * 1/n1 * i * L2006 + pr1 + npr1 + p1 = F1 – (e + f)
Falcon 5: 6 * X + f * 1/n5 * j * L2006 + pr5 + npr5 + p5 = F5 - (c + d)
labor costs share: g + h + i + j = 1
Similarity: Z = X
Cash Flow: n9 * pr9 + n9 * npr9 + n9h * pr9h + n9h * npr9h + n1 * pr1 + n1 * npr1 + n5 * pr5 + n5 * npr5 - r * I - np < n9 * F9 + n9h * F9H + n1 * F1 + n5 * F5 – L

Where

n1 = 2 and
n5 = 1

are known already.

In difference to before achieving improved overview the salaries of the launch team are distributed over one or two rockets only now. To decide that precisely a look into the data Klaus posted is required. Afew posts ago I posted a table of the number of launches per quarter of the year and per rocket launches were planned for in 2006. The first version of the launch manifest Klaus posted obviously indicated that the Falcon 1 and the Falcon 5 can be launched in one and the same quarter of the year. This means that the salaries for the launch team seem to have to be distributed equally over the two rockets.

Regarding the circumstance that in other quarters of the year no Falcon 5 is launched then seems to mean that some people of the launch team are unemployed. They simply will have other tasks then. That they get salaries is taken into account by the Cash Flow-equation where the salaries are going into in total. This is another example showing that the equation system involves something that is economically not possible.

Another question is that later there will be three and four rockets – as if the distribution of the launch team is cahnging and there would have to be i2006, i2007, i2008 and so on. This is NOT the case – the number of employees is growing and because of this I tend to consider the launch team to be growing. This also will be solved later by removing economical impossibilities.

So the the portion of the factor for the salaries of the launch team has to be 0.5 obviously – instead of the former 0.25. According to earlier posts this will be valid also for the R&D-team and the administration team.

What about the manucturing team? The team of 2006 has NOT to be distributed over four rockets but over two only. Regarding this team the numbers have to recalculated really.

Code:
rocket           weight     dia-   len   volume   payload in kg
                 in kg   mtr.      in m^3

                         2. stages

Falcon 1           395   1.70     8     42.73     670 (200 km)
Falcon 5          2300   3.70    14    158.34    4100 (200 km)

                         1. stages

Falcon 1          1356   1.70    15     80.11
Falcon 5          7000   3.70    33    373.22

sums

2. stages         2695    5.40    22    201.07    4770
1. stages         8356    5.40    48    453.33
total            11051   10.80    70    654.40    4770

relations to the sums

2. stages   0,244   0,5   0,314   0,307   1
1. stages   0.756   0.5   0.686   0.693   0


Like done earlier the volume-relations – 0.307 and 0.693 – will be applied for the distribution over the two groups of stages.

Within the group of 1. stages the number of engines will be applied again:

Code:

Falcon 1          1
Falcon 5          5

6 engines in total

Falcon 1         0.1666
Falcon 5         0.8334


Within the group of 2. stages the payload-weight was applied:

Code:
Falcon 1         0.1405
Falcon 5         0.8595


The the new sums of per rocket are

Code:
Falcon 1         0.3071
Falcon 5         1.6929

division by 2

Falcon 1         0.1535
Falcon 5         0.8465


Like done originally 0.615686275 has to be multiplied by these two:

Code:
Falcon 1   0.0945078432125
Falcon 5   0.521178432634


To these 0.385688618 * 0.5 = 0.192844309 have to be added.:

Code:
Falcon 1   0.2873521522125
Falcon 5   0.714022741634


Again this is slightly more than 1 – so let’s shorten it to:

Code:
Falcon 1   0.29   i
Falcon 5   0.71   j


These now could be inserted into the equation system. But first I should be considered now and before any insertions the Falcon 9s need to be reconsidered because of the time structure.

The investment into the Falcon 1 are the engines Z and Y plus the manufacturing-psrt of the saleries which is 0.0945078432125 * L2006 which has been made 0.1 * L2006 in between. The investment into the Falcon 9 then is 6 * X plus 0.52 * L2006. Then

I = 1 * Z + 1 * Y + 0.1 * L2006 + 6 * X + 0.52 * L2006 + R is valid where R is that portion of I that did NOT go into the rockets but in buildings etc..

I don’t insert this into the system because no other numbers are inserted above but replace the factors by i1 and j1 and add three other equations i1 + i2 = i and j1 + j2 = j with i2 = j2. Then there are eleven equations now – but three of them are auxiliary only because the values are known already:

Falcon 9: 10 * X + f * 1/n9 * g * LXXXX + pr9 + npr9 + p9 = F9 – (a + b)
Falcon 9 Heavy: 28 * X + f * 1/n9h * h * L YYYY + pr9h + npr9h + p9h = F9H – (3 * a + b)
Falcon 1: 1 * Z + 1 * Y + f * 1/n1 * i * L2006 + pr1 + npr1 + p1 = F1 – (e + f)
Falcon 5: 6 * X + f * 1/n5 * j * L2006 + pr5 + npr5 + p5 = F5 - (c + d)
labor costs share: g + h + i + j = 1
Similarity: Z = X
Cash Flow: n9 * pr9 + n9 * npr9 + n9h * pr9h + n9h * npr9h + n1 * pr1 + n1 * npr1 + n5 * pr5 + n5 * npr5 - r * I - np < n9 * F9 + n9h * F9H + n1 * F1 + n5 * F5 – L
Investment: I = 1 * Z + 1 * Y + i1 * L2006 + 6 * X + j1 * L2006 + R
Auxiliary1: i1 + i2 = i
Auxiliary2: j1 + j2 = j
Auxiliary3: i2 = j2

The auxiliary equations easyly could be inserted into labor costs share.



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


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Post    Posted on: Fri Sep 21, 2007 4:33 pm
To insert the correct years for XXXX and YYYY and the correct values for g, h, n9, n9h, n1 and n5 the launch manifest-version Klaus posted must be considered entirely now.

First of all the shifts have to be incorporated into them. The first version starts in Q4 2004 for Falcon 1 – this date was shift to Q1 2006 which are 5 qurters. The second version is up to date regarding 2006. The third version needs a shift by 1 quarter. This results in

Code:
           2006                2007                     2008
rocket     Q1   Q2   Q3   Q4   Q1   Q2   Q3   Q4   Q1   Q2   Q3   Q4

           version 1

Falcon 1   1         1         1
Falcon 5                         1              1

           version 2

Falcon 1   1              2              1             1    1    1
Falcon5
Falcon 9                                           1    1         1

           version 3

Falcon 1   2         1                                       1    1
Falcon 5
Falcon 9                                 1                     1


I left away one Falcon 1-launch of the third version which would be shifted to Q1 2009.

I am sorry – I obviously was in error regarding the Falcon 5 – it was shifted from 2006 to 2007 according to this and the results from yesterday have to be doubted again. But it will be reconsidered below. Another error in an earlier version of this table was intended that time to avoid a useless column.

But the Falcon 5 still will have to be a part of the investment equation because Elon Musk has said that the Falcon 9 requires a second $ 100 mio. May be that the Falcon 9-investment has been shifted to Falcon 9 when Falcon 5 was cancelled.

This seems to be the point where I should think about labour costs and investments again. The R&D into the Merlin and the Kestrel of the Falcon 1 have been done not only in 2006 but in years before 2006 also. But I don’t incorporate the labour costs of those years here although they have been investment. This makes me think a bit. Looking at it I become aware that I am looking for the investments into engines here mainly. The engines were ready in Q1 2006 and thus already produced. This means that the labour costs have gone into them already and to include them explicitly again would mean to include them twice or more – which would be wrong.

What about the other Falcons then? In principle the same is valid – but in 2006 the Falcon 9 wouldn’t have been there – and so I keep the equation system as it is. The engines of the Falcon 5 would have been produced in 2006 to be able to launch the Falcon 5 in Q1 2007.

I add labour costs for manufacturing of the Falcon 1 in Q1 2006 – and will do the same for the Falcon 5 in Q1 2007. As far as this causes a remainder of an error in 2006 that error will be not that large – and also is an effect of something economically impossible. The launch team distribution still seems to be correct to a sufficient degree because in Q1 2007 both rockets would have one launch within Q1. Of course the size of the launch team should be suspected to have grown then but it will be not that much I think and I can imagine to check how large the effect of the error will be.

The first Falcon 9 would be launched in Q2 2008 according to both versions involving the Falcon 9. I will take the salaries of Q1 2008 and Q2 2008 as investment into the Falcon 5 and the Falcon 9. The remainder of the year with the originally planned first launch of the Falcon 9 I will consider to be for the manufacturing of the Falcon 9 while the remainder of the year of the first Falcon 9-launch I will consider to be the time to manufacture the two additional first Falcon 9-stages as boosters for the Falcon 9 Heavy.

A launch of a Falcon 9 Heavy seems not be listed in the three versions of the launch manifest. But since the other Falcon 9-launches involve a first stage each and the two such first stages are the boosters of the Falcon 9 Heavy this rocket can be artificially included.

So the way of getting g and h has been designed rawly.

LXXXX is L2008 now and LYYYY is L2008 also while an additional L2007 is required for the Falcon 5.

Falcon 9: 10 * X + f * 1/n9 * g * L2008 + pr9 + npr9 + p9 = F9 – (a + b)
Falcon 9 Heavy: 28 * X + f * 1/n9h * h * L 2008 + pr9h + npr9h + p9h = F9H – (3 * a + b)
Falcon 1: 1 * Z + 1 * Y + f * 1/n1 * i * L2007 + pr1 + npr1 + p1 = F1 – (e + f)
Falcon 5: 6 * X + f * 1/n5 * j * L2006 + pr5 + npr5 + p5 = F5 - (c + d)
labor costs share: g + h + i + j = 1
Similarity: Z = X
Cash Flow: n9 * pr9 + n9 * npr9 + n9h * pr9h + n9h * npr9h + n1 * pr1 + n1 * npr1 + n5 * pr5 + n5 * npr5 - r * I - np < n9 * F9 + n9h * F9H + n1 * F1 + n5 * F5 – L
Investment: I = 1 * Z + 1 * Y + i1 * L2006 + 6 * X + j1 * L2007 + R
Auxiliary1: i1 + i2 = i
Auxiliary2: j1 + j2 = j
Auxiliary3: i2 = j2

May be that the auxiliary equations and the investment equation have to be corrected.



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


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Post    Posted on: Sun Sep 23, 2007 12:23 pm
Because of the previous post let’s calculate the labour costs for 2007 and 2008 now.

The monthly growth of the number of employees was got as 8.46. Then there the follwoing numbers of employees

Code:
year   beginning   end   average

2007   299         382   341
2008   391         474   433


At least one of the numbers has been rounded up.

Like for 2006 the salaries for 2007 and 2008 are going to be calculated using the average:

L2007 = $ 32,201,748.48
L2008 = $ 40,889,610.24

Next g and h should be looked for – in principle the value of j would have to be replaced but like already said I don’t think the error to have that large an effect. Ass n be seen by the launch manifests Klaus posted the time between the first planned Falcon 1-launch and the first planned Falcon 9-launch is longer by two to four quarters of a year longer than in the case of the first planned launch of a Falcon 5 – and in so far it may counteract the small error to handle the Falcon 9s and the Falcon 5 a bit differently.

Since there are no Falcon 9 Heavy launches in the launch manifests it might look as if g and h would have to be 1 at first glance. At this point it starts to be of meaning that the two addiotional first stages for the Falcon 9 Heavy will be produced after the first launch of the Falcon 9 – which is assumed here.

So it is again like with Falcon 1and Falcon 5 – the time until the first launch of a Falcon 9 in 2008 can be counted as manufacturing for the Falcon 9 and the time after the launch is the manufacturing time for the two additional first stages.

But one aspect is different to the other rockets here – no second stage is being produced if I understand correct. So the data are as follows:

Code:

rocket           weight    dia-   len   volume   payload in kg
                 in kg     mtr.         in m^3

2. stages

Falcon 9          2300   3.60   26   294.05   9300 (200 km)

1. stages

Falcon 9         16000   3.60   27   305.36
Falcon 9 Heavy   32000   3.60   54   305.36


The weight of the Falcon 9 Heavy has been reduced here because only two stages need to be produce since the first one already exists – may be that this assumption is considered to be an error or mistake but I have my doubts if someone like Elon Musk will produce three additional first stages if he alreday has one. He may have developed ways to simply add the additional two stages to the alreday existing and by the first launch of a Falcon 9 Non-Heavy tested one. This also removes an error or mistake in the first version of the table above where the weight of three first stages was listed but the sum of the heights of only two.

The sums then are:

Code:
2. stages         2300   3.60   26   294.05   9300 (200 km)
1. stages        48000   7.20   81   710.72
total            50300  10.80  107  1004.77   9300


So the valid relations are:

Code:
2. stages        0.046   0,3   0,243   0,293   1
1. stages        0.954   0.7   0.757   0,707   0


According to this all the criterion engines will have to be modified a bit also. The total number of engines to be considered – first stage – is 9 of the Falcon 9 and 18 of the Falcon 9 Heavy. Then the total is 27 and the factor for the Falcon 9 is 0.333 while the factor for the Falcon 9 Heavy is 0.667.

In difference to earlier the factor for the second satges seems to be got already because there is only one second stage now. Then the factors at present are

Code:
Falcon 9         1.333
Falcon 9 Heavy   0.667


Again these factors must be divided by 2:

Code:
Falcon 9         0.667
Falcon 9 Heavy   0.333


These are the factors for manufacturing. The manufacturing team has to be multiplied by them. The total of the other teams together still has be distributed equally. But the number of rockets is three now – not four because there is no launch of a Falcon 9 Heavy to be found in the launch manifest.

Before going on in the next post there are two small errors to be corrected in the equation system – L2006 and L2007 need to cahnge places and the Falcon 5-engines must be removed from the investment-equation:

Falcon 9: 10 * X + f * 1/n9 * g * L2008 + pr9 + npr9 + p9 = F9 – (a + b)
Falcon 9 Heavy: 28 * X + f * 1/n9h * h * L 2008 + pr9h + npr9h + p9h = F9H – (3 * a + b)
Falcon 1: 1 * Z + 1 * Y + f * 1/n1 * i * L2006 + pr1 + npr1 + p1 = F1 – (e + f)
Falcon 5: 6 * X + f * 1/n5 * j * L2007 + pr5 + npr5 + p5 = F5 - (c + d)
labor costs share: g + h + i + j = 1
Similarity: Z = X
Cash Flow: n9 * pr9 + n9 * npr9 + n9h * pr9h + n9h * npr9h + n1 * pr1 + n1 * npr1 + n5 * pr5 + n5 * npr5 - r * I - np < n9 * F9 + n9h * F9H + n1 * F1 + n5 * F5 – L
Investment: I = 1 * Z + 1 * Y + i1 * L2006 + j1 * L2006 + R
Auxiliary1: i1 + i2 = i
Auxiliary2: j1 + j2 = j
Auxiliary3: i2 = j2




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