The simulation will be carried out for different growth situations, depreciation theories, and cash flow schedules. As expected, it will be seen that Kay's method is applicable only when the unapplicable annuity theory of depreciation is used. The revenues each year can formally be linked to the expenditure by a contribution distribution as shown below.
N represents the life-span of the capital investment project.
It is easy to see that the internal rate of return r is then defined by the equation The process generating the financial data is created by repeating the capital investment expenditure yearly increased by a growth rate of k. Three different depreciation methods will be considered and applied, i.e. the annuity method of depreciation, the discounted revenue depreciation method, and the straight-line method. Consider the annuity method of depreciation first. The presentation of the simulation model in the case of annuity depreciation is now complete. In this case the book value vt at the end of year t is defined by It is also shown in Appendix III that the accountant's yearly rate of profit at then equals the internal rate of return r.