Accounting Rate of Profit and Internal Rate of Return 1

In a recent paper on the knotty problem of the relationship between the accounting rate of profit and the internal rate of return, John Kay has elegantly derived some simple equations describing that relationship. ² He has shown that, over the entire life of an investment (from zero outlay to zero return), a suitably weighted average of the accounting rates of profit is equal to the internal rate of return from the investment. ³ As a special case of this result, the accounting rate of profit when constant over the entire life of the investment must equal the internal rate of return. He has also shown that, for a firm in steady-state growth, the accounting rate of profit will coincide with the internal rate of return if the firm is growing at its natural rate (i.e. if all profits are continuously reinvested), or if the accountant’s valuation of its assets coincides with that of the economist. Where neither of these conditions prevails, the internal rate of return of a steadily growing firm may be expressed as a linear function of the accounting rate of profit, the slope of the line being given by the ratio of the book value of the net assets to the value which an economist would place upon them. ⁴