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.