Regarding NPV (Net Present Value) profiles for capital projects, identify the correct statements about the relationship between discount rate and NPV and the interpretation of the profile.

Introduction / Context:
An NPV profile depicts how a project's NPV changes as the discount rate varies. It is a practical tool for visualizing sensitivity to the cost of capital, identifying the internal rate of return (where NPV = 0), and comparing mutually exclusive alternatives over a range of discount rates.

Given Data / Assumptions:

• NPV is computed as present value of inflows minus present value of outflows.
• Discount rate ranges from 0 upward.
• Cash flow timing is fixed for the scenario.

Concept / Approach:

If the discount rate is 0, present value equals nominal amounts, so NPV equals total inflows minus total outflows. As the discount rate rises, future inflows are discounted more heavily, reducing present value; hence NPV declines, producing a downward-sloping curve to the right. The profile is typically curvilinear due to exponential discounting.

Step-by-Step Solution:

Verification / Alternative check:

The IRR corresponds to the discount rate where the profile crosses the x-axis; multiple sign changes can produce multiple IRRs, consistent with observed curve shapes.

Why Other Options Are Wrong:

• Any single statement omits other accurate properties; 'None' contradicts finance fundamentals.

Common Pitfalls:

• Comparing projects at one discount rate without checking sensitivity across plausible capital costs.
• Ignoring timing differences that strongly affect curvature.

Final Answer:

All of these