Consider a project where the initial cash flow is negative and where all subsequent cash flows are positive.
For this project, what must be true if the project's internal rate of return, or IRR, is less than the required rate of return?

a. Payback < 1
b. NPV < 0
c. PI < 0
d. Payback is undefined
e. NPV > 0

b. NPV < 0

Explanation:

The internal rate of return is the discount rate that equates the after tax cash flows from an investment to the amount invested.

The decision rule is invest if IRR > required rate of return and don't invest if IRR < required rate of return.

The net present value is the present value of after tax cash flows from an investment less the amount invested.

The decision rule is invest if NPV > 0 and don't invest otherwise.

The payback period measures how long it takes to recover the amount invested in a project from its cumulative cash flows.

There is no set acceptable pay back period. It is usually set at the discretion of firms.

The profitability index is the present value of a projects cash flows divided by the cost of investment.

The decision rule is invest if PI > 1 and don't if its otherwise.

For a project where the initial cash flow is negative and where all subsequent cash flows are positive, the NPV and IRR would agree.

From the question the IRR is less than the required rate of return which means the project shouldn't be embarked on. When the NPV is calculated, the same conclusion should be reached. So, the npv should be less than zero.

I hope my answer helps you

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