Which of the following changes would decrease the present value of a future payment?

• A. Decreasing the time until payment is received
• B. Increasing the discount rate
• C. Receiving the payment immediately
• D. Decreasing the discount rate

Answer: (B)

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 stream of cash flows, given a specified rate of return (discount rate). The formula for present value is PV = \( \frac{FV}{(1 + r)^t} \), where FV is the future value, r is the discount rate, and t is the time until payment.
2. Analyze the impact of increasing the discount rate: When the discount rate (r) increases, the denominator \( (1 + r)^t \) becomes larger, which decreases the present value. This is because the future payment is discounted more heavily.
3. Evaluate the effect of decreasing the time until payment: If the time (t) until payment decreases, the exponent \( t \) in \( (1 + r)^t \) becomes smaller, which increases the present value. Therefore, decreasing the time until payment would not decrease the present value.
4. Consider receiving the payment immediately: If the payment is received immediately, \( t = 0 \), and \( (1 + r)^t \) equals 1. This results in the present value being equal to the future value, which is the maximum possible present value. Thus, receiving the payment immediately would increase the present value.
5. Analyze the effect of decreasing the discount rate: If the discount rate (r) decreases, the denominator \( (1 + r)^t \) becomes smaller, which increases the present value. Therefore, decreasing the discount rate would not decrease the present value.