Mathematical analysis of average rates of return and investment decisions: The missing link

This paper expands Teichroew, Robichek and Montalbano's (TRM) (1965a,b) rate-of-return model into a complete and general model of economic profitability for investment decision-making. Specifically, TRM's assumptions are relaxed and a project rate of return is derived, expressing the project's overall economic protability; direct relations among rates, costs of capital and net present value are supplied. The various value drivers are identified and isolated, and the NPV is decomposed into financing NPV and investment NPV. The approach allows for any pattern of financing rates, investment rates, and costs of capital. Relations with old literature and new literature on rates of return are shown: the link between them is obtained by making use of the mean operator (i.e., affine combinations of rates) and via the one-to-one correspondence between rates and invested capitals.