  This paper introduces a class of investment project's profitability metrics
that includes the net present value (NPV) criterion (which labels a project as
weakly profitable if its NPV is nonnegative), internal rate of return (IRR),
profitability index (PI), payback period (PP), and discounted payback period
(DPP) as special cases. We develop an axiomatic characterization of this class,
as well as of the mentioned conventional metrics within the class. The proposed
approach offers several key contributions. First, it provides a unified
interpretation of profitability metrics as indicators of a project's financial
stability across various economic scenarios. Second, it reveals that, except
for the NPV criterion, a profitability metric is inherently undefined for some
projects. In particular, this implies that any extension of IRR to the space of
all projects does not meet a set of reasonable conditions. A similar conclusion
is valid for the other mentioned conventional metrics. For each of these
metrics, we offer a characterization of the pairs of comparable projects and
identify the largest set of projects to which the metric can be unequivocally
extended. Third, our study identifies conditions under which the application of
one metric is superior to others, helping to guide decision-makers in selecting
the most appropriate metric for specific investment contexts.
