38. What is the relationship between the discount rate and net present value (NPV)?
Answer: C
Higher discount rates lead to lower net present values (NPV).
As the discount rate increases, the present value of future cash flows decreases, which in turn lowers the net present value (NPV) of a project.
A) Increasing the discount rate increases net present value (NPV) up to a break-even point.
This option is incorrect because an increase in the discount rate does not increase NPV; rather, it decreases the present value of future cash flows, leading to a lower NPV. There is no concept of a break-even point in this context as it pertains to the relationship being tested.
B) Higher discount rates lead to higher net present values (NPV).
This statement is incorrect. In reality, higher discount rates reduce the present value of expected future cash flows, which means that net present value (NPV) will decrease, not increase. Therefore, this option does not reflect the fundamental relationship between discount rates and NPV.
C) Higher discount rates lead to lower net present values (NPV).
This option is correct. As the discount rate rises, the present value of future cash flows diminishes, resulting in a lower NPV. This relationship is critical in financial analysis, where understanding the impact of discount rates on NPV is essential for investment decisions.
D) The discount rate and net present value (NPV) are directly proportional for most projects.
This statement is incorrect. The relationship between discount rates and net present value (NPV) is inversely proportional: as the discount rate increases, NPV decreases. This fundamental principle is essential for evaluating the viability of projects in financial modeling.
Conclusion
In conclusion, option C accurately captures the inverse relationship between discount rates and net present value (NPV), confirming that higher discount rates lead to lower NPVs. The other options fail to represent this relationship correctly, as they suggest a direct or positive correlation, which contradicts established financial principles. Understanding this relationship is crucial for effective project evaluation and investment decision-making.