Deriving the Internal Rate of Return from the Accountant's Rate of Return; A Simulation Testbench

This paper presents a realistic simulation testbench for evaluating the various methods for estimating the long-term profitability of business firms in terms of the internal rate of return (IRR) of their capital investments. The simulation model extends the earlier, rigid approaches by incorporating business cycles and capital investment shocks. Kay's IRR estimation method is used to demonstrate the usage of the improved simulation approach. When the growth rate and profitability are near each other, Kay's method yields accurate estimates as expected by theory. The more growth and profitability differ the less accurate will the estimates be. The magnitude (and even the direction) of the error depends on the depreciation method applied and the capital investments' contribution distribution. It is also seen that Kay's method is insensitive to full business cycles, but disrupted by excessive capital investment shocks.