I just wanted to confirm that the internal rate of return for John's
example is 15%, assuming that the constant capital has to be purchased the
period before production takes place.
There is an inherent ambiguity in talking about "the profit rate" period by
period on long-lived capital assets. After the asset has been discarded,
one can calculate an ex post internal rate of return, the discount rate
that equalizes the whole cash flow (including depreciation allowances) over
the life of the asset to its acquisition cost. This "profit rate" is a
single number for the whole project, and averages out its profitability and
costs over its lifetime, taking account of realized price changes. If price
changes of the output are correctly anticipated (which, of course, is not
necessarily true for real capitalist life) then the prospective rate of
return on the asset will be equal to this ex post rate of return. If, in
addition, resale capital markets are "perfect" and correctly forecast the
price of the output, (perhaps even more doubtful in capitalist reality)
then there will be a market price for the depreciating asset in each period
of its life which will represent its remaining economic value. This series
of market prices will establish a depreciation schedule. The emergence of
technically more advanced means of production will hasten the fall in the
economic value of existing assets, thus shifting some of the cash flow from
profit to depreciation. The various formulas used by accountants to
depreciate assets, such as straight-line, are obviously only approximations
to these ideal market measures.
But in my view the issue of depreciation accounting, though it leads to
some interesting mathematics (some of which I started to explore in my 1986
book, Money, Accumulation, and Crisis), is probably of secondary importance
in understanding both the long- and short-run dynamics of capitalist
production. A mistake in the formal depreciation accounting simply amounts
to a misallocation of cash flow between profit and depreciation, but from
the capitalist's point of view the important issue is the cash flow itself.
(This conclusion has to be modified to some degree in the light of
corporate income taxes that distinguish depreciation and profits.)