If the five-year discount factor is \(d\), which of the following expressions correctly represents the present value (PV) of \(1\) to be received in five years?

• A. \(PV = d\)
• B. \(PV = 1 + d\)
• C. \(PV = \frac{1}{d}\)
• D. \(PV = d^5\)

Answer: (A)

Verified step by step guidance

1. Understand the concept of present value (PV): The present value is the current worth of a future sum of money or stream of cash flows, given a specified rate of return or discount rate. It is calculated using a discount factor, which accounts for the time value of money.
2. Identify the given variables: In this problem, the discount factor for five years is represented as \(d\), and the future value to be received in five years is \(1\). The goal is to determine which expression correctly represents the present value of \(1\).
3. Recall the formula for present value: The general formula for present value is \(PV = FV \times d\), where \(FV\) is the future value and \(d\) is the discount factor. In this case, \(FV = 1\), so the formula simplifies to \(PV = d\).
4. Analyze the other options: The other expressions provided (\(PV = 1 + d\), \(PV = \frac{1}{d}\), and \(PV = d^5\)) do not align with the standard formula for present value. For example, \(PV = 1 + d\) adds the discount factor to the future value, which is incorrect. \(PV = \frac{1}{d}\) represents the reciprocal of the discount factor, which is not relevant here. \(PV = d^5\) raises the discount factor to the fifth power, which is also incorrect.
5. Conclude that the correct expression for the present value of \(1\) to be received in five years is \(PV = d\), as it directly applies the discount factor to the future value.