Which of the following would increase the present value of a single future cash flow, assuming all other factors remain constant?

• A. Decreasing the discount rate
• B. Increasing the discount rate
• C. Increasing the number of periods until payment
• D. Decreasing the amount of the future cash flow

Answer: (A)

Verified step by step guidance

1. Understand the concept of present value: Present value (PV) is the current worth of a future sum of money or cash flow, discounted at a specific rate. It is calculated using the formula: PV = \( \frac{FV}{(1 + r)^n} \), where FV is the future value, r is the discount rate, and n is the number of periods.
2. Analyze the impact of the discount rate: A lower discount rate (r) reduces the denominator \((1 + r)^n\), which increases the present value. Conversely, a higher discount rate increases the denominator, decreasing the present value.
3. Evaluate the effect of the number of periods (n): Increasing the number of periods until payment (n) raises the power of \((1 + r)\), making the denominator larger and reducing the present value. Decreasing the number of periods would have the opposite effect.
4. Consider the amount of the future cash flow (FV): A decrease in the future cash flow directly reduces the numerator (FV), which lowers the present value. Increasing the future cash flow would increase the present value.
5. Conclude the correct factor: Decreasing the discount rate increases the present value because it reduces the rate at which the future cash flow is discounted, making the current value of the cash flow higher.