Practice Problem – IRR and NPV

Practice Question

Capital Budgeting
IRR
MCQ

Consider a project with an initial outflow at time 0 and positive cash flows in all subsequent years. As the discount rate is increased, the _____________.

A) IRR remains constant while the NPV increases.
B) IRR decreases while the NPV remains constant.
C) IRR increases while the NPV remains constant.
D) IRR remains constant while the NPV decreases.
E) IRR decreases while the NPV decreases.

Answer +
Correct Answer: E) IRR decreases while the NPV decreases.
Explanation +

To evaluate this multiple-choice question correctly, we need to understand the relationship between the discount rate, NPV, and IRR:

1. Definitions
  • NPV (Net Present Value): The sum of discounted cash flows. A higher discount rate lowers the present value of future cash flows, hence NPV decreases as the discount rate rises.
  • IRR (Internal Rate of Return): The discount rate that makes NPV equal to zero. It is an intrinsic characteristic of the project’s cash flows.
2. Key Relationships
  • The IRR is a fixed value once cash flows are known—it does not change if you test other discount rates.
  • However, when evaluating multiple projects or when plotting NPV profiles, a higher discount rate results in a lower NPV.
3. Clarifying the Confusion

Option E might seem misleading because IRR technically remains constant for a given project. But if we interpret "IRR decreases" as meaning "the attractiveness of the IRR diminishes" or "projects with lower IRR become less viable as the discount rate rises," the intent is clearer.

4. Correct Logic

In strict technical terms, the correct choice is:
D) IRR remains constant while the NPV decreases.

But if the exam assumes the options reflect broader project viability or if the IRR of new proposed projects declines as required returns increase, then E) may be accepted.

Final Verdict

Based on standard financial theory, the correct and most defensible choice is:
D) IRR remains constant while the NPV decreases.

Note: The answer in your key states "E", but the rigorously correct technical answer is "D". Confirm whether your course materials interpret this concept more flexibly.