Internal Rate of Return and Net Present Value

The net present value (NPV) and internal rate of return (IRR) methods of analysis are closely related and sometimes used together when making corporate finance decisions in capital budgeting.

Let’s look at an example:

Last Tuesday, Abby’s Corner lost some of their financial data when their backup servers crashed. The company’s CEO recalled that the internal rate of return (IRR) of Project Tidy is 14.6%, but she can’t recall how much Abby’s Corner originally invested in the project. Moreover, the crashed erased the figure for the project’s net present value (NPV). However, she did find the details of the annual net cash flows expected to be generated. She also noted how Project Tidy had the same level of risk as the companies average project and the WACC for Abby’s Corner is currently at 9%

YearCash Flow
Year 1$1.6M
Year 2$3M
Year 3$3M
Year 4$3M

Calculate Initial Investment

So in this situation what can you do? Well if you recall that the IRR of a project represents the return it would generate when NPV is zero and that the project has the average risk, we can use the IRR to find the initial investment by discounting the project’s cash inflows and summing them together:

Or solve with a financial calculator:

InputKeystrokeOutput
0CF 0
1,600,000 CF 1
3,000,000CF 2
3,000,000 CF 3
3,000,000 CF 4
14.5I/YR
NPV7,413,064

Calculate NPV

Now that we have found the projects initial investment we can now solve for the projects NPV by discounting the expected future cash flows at the projects cost of capital (WACC) of 9%:

InputKeystrokeOutput
-7,413,064CF 0
1,600,000 CF 1
3,000,000CF 2
3,000,000 CF 3
3,000,000 CF 4
9I/YR
NPV1,021,692
Excel Formula 
= NPV(9%,1600000,3000000,3000000,3000000) - 7413064 

Summary

In summary, we have been able to calculate both the NPV and the initial investment into the project using the IRR. Remember that if a projects cash inflows decrease, the IRR will also decrease because the project has become less profitable.