This is a reposting of an earlier article that gives an overview of the turnover formula and its applications.


academia turnover article PDF


  1. redbuccaneer says:

    Thank you that was great read! I am really interested in what your doing! I have question that is bothering me though. Can you please explain how would the turn-over formula be affected if the value contributed was different for each of the intermediary producer? Would it be possible to use it still? I know you go a bit on this in the article above but I am wondering if you could go into more detail?

  2. Below please find two articles on this website. I am no mathematician but fortunately a reader Aris is, and he put a lot of work into providing the maths needed for a deeper insight into the formula. The quick answer to your question is that a variation in the size of intermediate sales would change turnovers and not only that, it depends at what stage they occur. Thus, as Aris has shown, earlier variations have a bigger impact than during later stages. However, when dealing with aggregated sales we have to take them as an average. For example, if we aggregate final sales as we do, then we must aggregate intermediate sales as well. What I have done conforms to the method adopted by the statistical bureaus themselves. When they aggregate inventory turnover, which is similar, they take the aggregated total sales for the industry and divide it by the aggregated stock of inventories. Within that figure are tens of thousands of inventory turnovers that are either longer or shorter than the average. However what concerns us both, is the average for the industry.

    I hope this answers your question.

    Click to access turnover-equation-5-simulations-final.pdf

    Click to access turnover-equation-part-2-pdf.pdf

    • redbuccaneer says:

      Ah I see. Thats pretty great. I went through those articles. So the turnover formula works as long as no single producer does not have a large share in the value addition chain( and it not at the ends of the chain)? Does that happen often in real life though? Are there any producers that contribute a disproportionate share and are at the extremes of the chain?

      I have one more question, I was reading you review of Kilman’s book. I was wondering if it is possible to check the rate of profit using the turnover formula while using both historic and current costs and comparing them both?

      Thank you for the detailed answer!

  3. If we were looking at single producers turnovers, variations could provide alternative turnovers. But our concern is the macro picture. Even when analysts sell data on turnover for individual corporations, they do not concern themselves with this. Their formula is: cost of annual sales divided by current assets less current liabilities. So once again individual variations are ignored. I have tested the results obtained by the formula against the results obtained by these analysists and they match. I have tested the data against other empirical data such as days of inventory plus bills receivable less payable, or, days of inventory plus average period of payment and they all confirm the formula. My recent articles on China for example where this data is easily available confirms the accuracy of the formula against the whole of Chinese industry. At no time is the variation greater than 5%, usually around 2%.

    With regard to Kliman, you have to use replacement cost (really market value) for fixed capital when combining it with fluid or circulating capital because it too is priced at current market value. Otherwise you would be comparing apples to oranges. I am truly allergic to using historical cost in the denominator for the rate of profit. Kliman and Roberts end up with ridiculously high rates of profit. All this kind of inaccuracy is good for, is trends. If you are equally wrong in 1960 and 2010, then clearly the trend will be there. Currently the real rate of profit is about a third of the ones described by Kliman and Roberts which they posit around the 15% mark. At 15% there would be no crisis of investment even if this figure represented a fall from an even higher figure.

    • Having read my reply I realise I did not fully answer your question. No it will not affect aggregated or industry wide figures. These figures are in fact composed of different individual turnovers as well as variations in the size of and frequency of intermediate sales. What we need is a single aggregated figure where differences are smoothed out. So if we are looking at the car industry and we are seeking to reduce the cost of the gross output of this industry (a single figure) to working capital for the industry ( a single figure for the period), then we need a single turnover figure. This is why the formula works.

  4. redbuccaneer says:

    I see. That clears it!

    As regards to profits, I think one can add both historical and current prices. I mean capitalists do it all the time, they value their fixed capital at historic prices and their circulating capital at current ones. Thats the beauty of money.

    I think one needs both measures of profit. A rate profit with current prices is important to assess current and future investment prospects while a rate profit that takes into account historic prices is useful to assess investments that have already been “sunked in”.

    I dont agree with Kilman and Roberts measures of the ROP though since they dont have a good estimate for variable capital.

  5. In one sense you are right. Depreciation is taken on a historical cost basis, and thus current prices are connected through it to historical prices. Marx’s famous c+v+s where part of c is the consumption of fixed assets applies. However, it is important to understand market value in the round. Market value is not replacement cost. Replacement cost is higher, it is the price of replacing all the means of production. For example, a firm may have an insurance policy for fire which stipulates that damaged equipment will be replaced by new. If that firm experienced a major fire, the insurance company would end up paying more than the value of the equipment destroyed as it appears on the firm’s balance sheet. Thus when the statistical authorities describe current cost they are not referring to replacement cost but to the cost of fixed assets devalued by historically based depreciation. They are in fact describing market value. Market value is based on weighted change because it depends on the weight of depreciation offset by the weight of investment each year. Thus an industry with high rates of recent investment will have a lower weight of depreciation relative to investment, resulting in a reduction in the average age of the means of production in it. Conversely, an industry which began with high rates of investment which then tapered off will have a higher weight of depreciation and the average age of the means of production will be higher.

    Finally, historical rates of profit are a function of inflation. Here the real problem is the depreciation of money. Profit, which is measured in current monetary terms would be measured against capital which has been “de-priced” by a depreciating currency. That is why it will always yield a higher rate of profit. If, money was an invariable standard of price then there would be no difference between a rate of profit based on current prices and one based on historical prices. Of course where you are completely right is that current rates of profit are a better guide to the all important investment decisions made by investors, remembering that they will be using replacement costs rather than current costs.

    • redbuccaneer says:

      Ah. So, let’s say I have a car that initially costed 40,000 new in 2017, after 2 years because of depreciation(wear and tear = 1000, moral depreciation = 1000) now sells for 38,000 in 2019. Let’s assume the price right now for a new car of the same type is 39,000 (40,000- 1000). So in 2019:

      Market Value = 38,000
      Replacement cost = 39,000-

      Am I following you correctly? So when the BEA says current costs they mean 38,000? Ie they include both types of depreciation( moral and wear and tear)

      Also one more question, I was reading your pamphlet about the pricing system in the Soviet Union, and I came across this para:

      “Between 1946 and 1949 a serious effort was made to introduce financial planning. However, because it predictably disrupted the 4th Five Year Plan which in turn delayed the 5th Five Year Plan it was abandoned. Stalin thanked the architect of this financial effort, Kaznesensky, as he always did, by executing him in 1949.”

      That’s something I never heard about. Do you know where I could learn more about that?

  6. 38,000 is the correct answer. Gosh it is such a long time ago that I wrote the pamphlet. I think three computers ago. I will try and hunt down references for you on Kaznesensky.

  7. redbuccaneer says:


    Because google gives me nothing. Perhaps you meant Nikolai Voznesensky?

  8. Possibly. But then Stalin expunged whoever, from history. I came across Voznesensky as well when I googled the fourth and fifth 5 year plans.

  9. redbuccaneer says:

    But it can’t be Voznesensky though, since he wanted to introduce the profit motive like in the Kosygin Reforms.

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