The internal rate of return is a very useful decision rule in deciding whether or not to accept a project or a firm but in some cases, we don’t even have an IRR. It’s non-existent, There is no IRR for the cash flows of a given project and in those cases, we have to use the net present value.
You start a construction company and you raise or you get this first project where you get 5million dollars upfront is sort of a down payment and then you get the rest of the money for the project which is 17million at the end of year 5 so there’s going to be a five-year project now for the first 4 years of the project you’re gonna be incurring expenses as you build this building or whatever it is you’re constructing so there’s going to be 4million dollars a year in expenses and your cost of capital will be 10%.
I use the equals IRR function and however, you want to calculate it by hand you can do it we have another article about calculating IRR, and I got an error message in Excel because there is no internal rate of return for this project for this particular set of cash flows there is no IRR. So there’s nothing where the NPV would be zero there’s no rate of return. So basically we have to solve for NPV. We don’t even have an IRR to even compare against our cost of capital, so really IRR is meaningless here.
We’re just gonna discount all these cash flows and so forth so we’re gonna end up with a net present value of positive $2,876,201. So that means we are going to accept the project. So we used NPV because there is no IRR but just because we’re accepting this project and we had a positive NPV does not mean that if you have no IRR that you’re automatically gonna accept the project that it means that there’s a positive NPV it just as easily could have been that there was a negative NPV. So we could come up with a different set of cash that would end up with a negative NPV and still, no IRR so if there’s no IRR you don’t have any internal rate of return and it just doesn’t exist just forget about the internal rate of return altogether and go ahead and calculate the NPV and then here we’ve got a positive NPV so you accept the project. That’s your decision.