Which statement about NPV and IRR is true?

Which statement about NPV and IRR is true?

• A. NPV ignores the time value of money; IRR accounts for it.
• B. NPV and IRR always give identical accept/reject decisions.
• C. IRR is always greater than WACC for any profitable project.
• D. NPV is the net present value of cash flows, and IRR is the discount rate that makes NPV zero.

Answer: (D)

The time value of money is central here: both NPV and IRR are built on discounting cash flows, but they use that discounting in different ways. NPV calculates the net value today by summing all future cash inflows and outflows discounted at a chosen rate, then subtracting the initial investment. IRR, on the other hand, is the specific discount rate that makes that net present value equal to zero. In other words, IRR is the rate at which the project breaks even in present-value terms. That definition is why the statement is the best choice. It precisely captures what IRR is and how it relates to NPV: IRR is the discount rate that forces NPV to zero, while NPV itself depends on the rate you choose to discount cash flows at. Because NPV and IRR are defined this way, you can see why the other claims don’t hold in all cases. NPV always accounts for the time value of money, so it’s false to say NPV ignores it. In some situations, especially with non-conventional cash flows, projects can produce multiple IRRs or ambiguous results, so the decision signals from NPV and IRR may differ. And while, for standard projects with conventional cash flows, IRR often exceeds the discount rate that represents the opportunity cost, it isn’t guaranteed in every scenario.

The time value of money is central here: both NPV and IRR are built on discounting cash flows, but they use that discounting in different ways. NPV calculates the net value today by summing all future cash inflows and outflows discounted at a chosen rate, then subtracting the initial investment. IRR, on the other hand, is the specific discount rate that makes that net present value equal to zero. In other words, IRR is the rate at which the project breaks even in present-value terms.

That definition is why the statement is the best choice. It precisely captures what IRR is and how it relates to NPV: IRR is the discount rate that forces NPV to zero, while NPV itself depends on the rate you choose to discount cash flows at. Because NPV and IRR are defined this way, you can see why the other claims don’t hold in all cases. NPV always accounts for the time value of money, so it’s false to say NPV ignores it. In some situations, especially with non-conventional cash flows, projects can produce multiple IRRs or ambiguous results, so the decision signals from NPV and IRR may differ. And while, for standard projects with conventional cash flows, IRR often exceeds the discount rate that represents the opportunity cost, it isn’t guaranteed in every scenario.