## Wednesday, June 12, 2019

### IRR vs NPV

This post provides an example where the IRR cannot select the better project but the NPV does provide the answer.

Question One:  Project A involves an initial investment of \$1,000 and a return of \$1,000 in one year.   Project B involves an initial investment of \$1,000 and a return of \$1,000 in two years.   Show that both projects have an IRR of 0 percent and the IRR value cannot be used for project selection.

Assume the person has a cost of capital equal to 10 percent.   What are the NPVs of the two projects?  Confirm based on the NPV that project B is preferable to project A.

Answer to Question One:   The problem was solved with the XIRR and the XNPV functions in Excel.   The inputs to the XIRR function are the dates and the cash flow ranges.   The input to the XNPV function are the date range, the cash flow range and the assumption on the cost of capital, which in this case is 0.10.

The IRR and NPV for project A where \$1,000 is returned after one year is presented below.

 Project A Date Cash Flow 1/1/00 -1000 1/1/01 1000 XIRR 0% XNPV -\$91.15

The IRR and NPV for project B where \$1,000 is returned after two years is presented below.

 Project B Date 1/1/00 -1000 1/1/02 1000 XIRR 0% XNPV -\$173.77

Note that for both projects the IRR is 0.  In both cases, the investor ties up funds and gets 0 percent.  The difference is that that for project A the funds are tied up for one year while for project B the funds are tied up for two years.   Clearly project A is better to the investor than project B.

The NPV is larger (less negative) for project A than project B.   Losses are smaller for project A than project B.

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