Which of the following is true when interest rates rise?

• A. The future value of a present cash flow remains unchanged.
• B. The present value of a future cash flow decreases.
• C. The present value of a future cash flow increases.
• D. The future value of a present cash flow decreases.

Answer: (B)

Verified step by step guidance

1. Understand the relationship between interest rates and present value: When interest rates rise, the discount rate used to calculate the present value of future cash flows increases. This results in a lower present value because future cash flows are discounted more heavily.
2. Understand the relationship between interest rates and future value: The future value of a present cash flow is determined by compounding the cash flow at the given interest rate. If interest rates rise, the future value of a present cash flow increases because the compounding effect is stronger.
3. Analyze the options provided: Evaluate each statement in the context of the relationships explained above. For example, 'The future value of a present cash flow remains unchanged' is incorrect because future value depends on the interest rate.
4. Focus on the correct statement: 'The present value of a future cash flow decreases' is correct because higher interest rates lead to a higher discount rate, reducing the present value of future cash flows.
5. Conclude the reasoning: The correct answer is based on the fundamental principles of time value of money, where interest rates directly impact the present and future values of cash flows.