The question asks if there is any use in calculating IRR if a project wasn't funded by getting a loan. The short answer is yes, this metric can be helpful regardless of the source of funding for the project.
IRR (Internal Rate of Return) is roughly defined as the discount rate which makes the present value of the project’s cash inflows equal to the present value of the project’s outflows. A simplistic conceptualization looks at a single outflow (investment) followed by a series of inflows (returns); see the attached Investopedia reference for the series-notated formula used.
IRR calculates the effective rate of return on a set of cashflows, and as such is independent of the cost of capital. It can be used to compare the relative attractiveness of several projects. It can also be compared to the cost of capital, to determine if the project constitutes a good use of that capital. It is here where the role of debt financing versus equity financing enters the decision process, as the balance between the two will be important in determining the firm’s cost of capital. The Harvard Business Review article referenced below is a nice, simple discussion of some of the nuances to be addressed in actually using IRR in a business setting.