Calculating The Rate Of Turnover and Annual Rate of Profit

In their very poor response to my recent article in the WW, Bruce Wallace and Steve Dobbs write,

“The ‘turnover time’ argument was well known to Marx and is a bit more complicated than Bough thinks. Constant capital may be fixed or circulating. Fixed constant capital (such as plant and machinery) may be turned over once every 10 years (not, as Bough dreams, 10 times a year). Circulating constant capital (such as raw materials) may be turned over every six weeks. Marx saw this as a complication in presenting the law of value and in working out a general rate of profit (without which you cannot begin to discuss the law of the tendential fall in the rate of profit). He dealt with this mainly in Capital, volume 2 (subtitled The process of circulation of capital). This difficulty makes the calculation of the annual rate of profit, which Bough thinks is a crucial problematic concept, a little tricky.” 

No one doubts Marx was well aware of the argument over the rate of turnover, given that he developed it! Fortunately, both he and I understand it rather better than Wallace and Dobbs do it appears. Contrary to their claims, there is nothing complicated, problematic or tricky about it, and not only does Marx spend ten chapters out of twenty-one in Capital II, describing the basis of the rate of turnover, and the annual rate of surplus value, (which Wallace and Dobbs describe as "a phoney novelty") but Engels takes that further in Capital III, Chapter 4, and shows how it results in an annual rate of profit (they also wrongly claim that Chapter 16 where the annual rate of surplus value is developed, was written by Engels! It wasn't. Its in manuscript 2 of Marx’s material edited by Engels. Its Chapter 4 of Capital III on the effect on the rate of profit that was written entirely by Engels. God preserve us from experts!). The first problem for Wallace and Dobbs is that they do not even seem to have grasped, despite all the chapters Marx spent on it, that the rate of turnover is a rate of turnover of circulating capital, and so their wittering on about the rate of turnover of the fixed capital is totally irrelevant. Engels gives several examples, in Chapter 4, to demonstrate how the matter of the fact, set out by Marx, that the fixed capital must always be present, is easily dealt with.

The concept of the annual rate of surplus value, and annual rate of profit is straightforward. It is essentially the same concept as that used in relation to the AER (Annual Equivalent Rate) that banks have to display as opposed to the nominal rate of interest. Suppose I borrow £1,000, and the rate of interest is shown as 10% per month (which is the kind of thing the Pay Day Lenders do). The interest for the month is £100, which I pay at the end of the month. But, I roll the loan over every month for the year on the same basis. At the end of the year, the total interest I have paid is £1200, which against the £1000 I borrowed, means the annual rate of interest was not 10%, but 120%.

Now turn it round the other way. I have £1,000 which I want to lend out at 10% for the month, and which I do. At the end of the month I get back my £1,000 plus £100 in interest. Now, I lend this same £1,000 out again for another month etc. At the end of the year I will have received £1200 in interest. The total value of loans I will have made is £12,000, and so the £1200 of interest on this total amount laid-out is 10%. But, in reality, the situation is no different than the first. Although, the total amount of loans I have made is £12,000, it is still the same £1,000 that has simply been advanced 12 times during the year. The actual amount of “capital” I advanced was only £1,000, it just kept coming back to me to be laid out again. So, in reality, my actual annual rate of profit is again, not 10%, but 120%.

The situation is exactly the same when it comes to the annual rate of surplus value, and annual rate of profit. If I advance £1,000 in wages and materials, made up £100 wages and £900 materials, for example, for a month, and at the end of the month I get back £1100 from the commodities I sell. That means I've made £100 surplus value. For the month, I have made 100% rate of surplus value on the £100 of labour-power advanced, and I have made 10% profit, on the total amount, £1,000, of capital I have advanced.

But, just as with the AER interest on the money I borrow or save, the capital I advanced £1,000, has now returned to me, and I can lay it out again to buy materials and labour-power for another month. At the end of the year I have advanced this £1,000 of capital 12 times, so the total laid out capital for the year is £12,000. If you looked at my account books it would show, I'd spent £1200 on wages, and £10,800 on materials. My profits would appear as £1200, and so measured against this laid out capital, my cost of production, my rate of profit appears to be 10%. But, in actual fact, just as with the AER, I have only ever had £1,000 of capital, its just kept coming back to me to be laid out for wages and materials, over and over again. So my annual rate of profit is not 10%, but 120%!

This is the way, Marx and Engels say, that the capitalists hide the real extent to which workers are exploited, and the real extent of the rate of profit being made. For example, suppose, the capital above is a car maker, like Mercedes, and the figures are in tens of millions of pounds. So, its total sales for the year would be 1100 x 12 = £132 billion. Out of this its costs would be £120 billion, and its profit would be £12 billion. If it produces 10 million cars, the price per car is £13,200, and the profit on each car is £1,200. The cost price of each car is £12,000, and so the profit margin is 10%. Again, its because they present the profit margin as the same thing as the rate of profit, that enables the capitalists to pretend that their actual rate of profit is much less than it really is.

And, as Marx and Engels set out, the consequence of this is that the higher the rate of turnover of capital, the higher the annual rate of profit compared with the nominal rate of profit, or the profit margin. But, this is important for capital also, because say the rate of turnover of this example, was 120 times rather than twelve times, as a result of much higher productivity. Then it might be the case that the annual rate of profit was still 120%, but then the nominal rate of profit or profit margin would be only 1%, not 10%. In that case, they would only make £120 profit on each car. Its obvious that although the annual rate of profit, and total amount of profit hasn't changed here, this much smaller profit margin means that any slight change in the market could make the sale of each car unprofitable!

Now what about this supposedly “complicated”, “problematic” and “tricky” issue of the fixed capital? Let's take the example of a builder. The builder has a variety of fixed capital from excavators, down to the individual hammers used by the joiners. Each of these bits of equipment not only have different values, but they have different lifespans. The reason this issue is tricky for those who use an historic pricing method for calculating the rate of profit as opposed to the reproduction cost method used by Marx, is that the former is really a rate of profit based on invested money-capital, whereas Marx makes clear that his rate of profit is based on the current value of the advanced productive-capital, i.e. the physical productive-capital, not some amount of money-capital invested at some point in the past.

If you use the historic cost model, Marx's analysis of the rate of turnover of capital poses you with problems, because it requires an actual current valuation of the actual fixed capital advanced to production, not some previous advance of money-capital, which may or may not relate to the actual capital currently being used in production. For Marx, however, the solution was simple, take the actual physical fixed capital being used for production, and assess its value in monetary terms. As this fixed capital always has to be present for production to take place, it must always be counted in its entirety as part of the advanced capital.

Suppose, the value of all these diggers, hammers etc. is then £1 million, and they lose as an average 10% of this value each year in wear and tear, which is passed on into the value of the houses they build.

The builder builds uniform houses, and always builds 20 houses at a time, which he knows he can sell on average 1 week after they are completed. Each house requires £80,000 of materials for its construction, and £20,000 has to be spent on wages per house. The builder makes £20,000 of surplus value on each house. It takes 4 weeks to build each development of 20 houses. So, the capital turns over every five weeks, in other words, as seen above, at the end of five weeks, the 20 houses are sold, and the materials and labour used in their construction, along with the wear and tear of the fixed capital used in their construction, has been returned to the builder, so that he can once more advance it to buy materials and labour-power to construct the next 20 houses.

The total cost per house is then:

£80,000 Materials,

£20,000 Labour

£20,000 Surplus Value

The total amount of wear and tear on fixed capital for the year is £100,000, but this covers 10 turnovers of capital. In one turnover period, therefore, the wear and tear is £10,000, and as there are 20 houses built in a turnover period, the wear and tear of fixed capital comes to £500 per house.

The total price of a house is then £120,500. The profit on the house is £20,000, so the profit margin per house is 200/1205 x 100 = 16.6%. If we calculated the rate of profit for the year on this basis, there would be 200 houses built. The total laid out for materials would be £80,000 x 200 = £16 million; the total paid out for wages would be £4 million, the total for wear and tear of fixed capital would be £100,000, and the total profits would be £4 million.

So, the total amount of capital laid-out for the year including wear and tear would be £20,100,00. The firm's total revenue would be £24,100, 000 and its total profit would be £4 million, giving again a rate of profit of 16.6%.

However, as Marx says, the actual rate of profit, the annual rate of profit must be based on the actual capital advanced, not the capital laid out. We saw the effect of that above, which is that here the circulating capital (materials plus labour) is turned over 10 times a year, so the actual circulating capital advanced is only that required for one turnover period – 5 weeks.

That means £1.6 million for materials, plus £400,000 for wages. The wear and tear, however, do not form part of the advanced circulating capital. This is not capital actually advanced, because its the total value of the fixed capital that is advanced. That has to be the case, because as Marx says, the production could not have occurred without all of the fixed capital being present. Rather the value of the fixed capital advanced is then the whole £1 million. We can then calculate the annual rate of profit on the same basis as was done above. That is to take the profit for the year, and measure it against this advanced capital value.

That is £4 million profit and £1 million fixed capital, £1.6 million materials, £400,000 for wages = £3 million. The annual rate of profit is then 4/3 = 133.33%, which contrasts rather sharply with the profit margin of 10%!

The effect then can be seen of a rise in productivity. Suppose, the 20 houses are built in 2 weeks instead of 4. In that case, the turnover period is three weeks instead of five. But, although the same amount of materials will be required to build these houses, the amount paid out in wages will now be 60%, of the previous figure, because only 3 weeks of wages are paid out for the turnover period.

The advanced capital is then £1 million for fixed capital, £1.6 million for materials, £240,000 wages. With the same rate of surplus value of 100%, that means that only £240,000 of surplus value is produced in this turnover period, but by the same token instead of the capital turning over 50/5 = 10 times, it now turns over 50/3 = 16.66 times. The annual profit is then £240,000 x 16.66 = £3,998,400. So, the annual rate of profit becomes 137.88%.

So, it seems the “complicated”, “problematic” and “tricky” issue is not a problem for a “bungling amateur” who understands Marx, to resolve, even if it is for two “experts” who do not. 

Just to emphasise that point, and so there is no thought that I have just made up this methodology, let me give one of the examples used by Engels in Chapter 4 to prove that I have used exactly the same method as he and Marx.

“Take capital I, consisting of 10,000 fixed capital whose annual depreciation is 10% = 1,000, of 500 circulating constant and 500 variable capital. Let the variable capital turn over ten times per year at a 100% rate of surplus-value. For the sake of simplicity we assume in all the following examples that the circulating constant capital is turned over in the same time as the variable, which is generally the case in practice. Then the product of one such period of turnover will be:

100c (depreciation) + 500c + 500v + 500s = 1,600

and the product of one entire year, with ten such turnovers, will be 

1,000c (depreciation) + 5,000c + 5,000v + 5,000s = 16,000, 

C = 11,000, s = 5,000, p' = 5,000/11,000 = 45 5/11 %.”

Note that there is no problem here for Engels in dealing with the fixed capital, which is determined to have an average turnover period of ten years – hence its annual wear and tear of 10%. Note too, that the turnover period is determined only by the turnover time of the variable capital, because as Engels correctly states, the turnover time of the materials is determined by the labour that processes it.

The product of one year is £16,000, and the cost of this production is £11,000 (1,000 wear and tear, 5,000 materials, 5,000 labour). The annual rate of profit here amounts to the same figure, only because the advanced capital total is also £11,000, but comprises £10,000 fixed capital, £500 material and £500 labour. But, Engels goes on,

“But should capital I have only 5 instead of 10 turnovers of its variable part per year, the result would be different. The product of one turnover would then be: 

200c (depreciation) + 500c + 500v + 500s = 1,700. 

And the annual product: 

1,000c (depreciation) + 2,500c + 2,500v + 2,500s = 8,500, 

C = 11,000, s = 2,500; p' = 2,500/11,000 = 22 8/11%. 

The quantity of surplus-value appropriated in one year is therefore equal to the quantity of surplus-value appropriated in one turnover of the variable capital multiplied by the number of such turnovers per year. Suppose we call the surplus-value, or profit, appropriated in one year S, the surplus-value appropriated in one period of turnover s, the number of turnovers of the variable capital in one year n, then S = sn, and the annual rate of surplus-value S' = s'n, as already demonstrated in Book II, Chapter XVI, I.”

Note that here, the laid-out capital for the year is £6,000, (1,000 wear and tear, 2,500 materials, £2500 labour) whereas the advanced capital is still £11,000, that is £10,000 fixed capital, 500 materials, 500 labour.