NPV method, the Payback Method, and the IRR method Discussion Question

The finance department of a large corporation has evaluated a possible capital project using the NPV method, the Payback Method, and the IRR method.  The analysts are puzzled, since the NPV indicated rejection, but the IRR and Payback methods both indicated acceptance. Explain why this conflicting situation might occur and what conclusions the analyst should accept, indicating the shortcomings and the advantages of each method.  Assuming the data is correct, which method will most likely provide the most accurate decisions and why?