What is the present value (PV) of the following set of cash flows, discounted at an annual rate of 8\%? \[\begin{align*}\text{Year 1:} & \quad \$1,000 \\\text{Year 2:} & \quad \$1,500 \\\text{Year 3:} & \quad \$2,000 \end{align*}\]Choose the closest answer.

• A. \$4,011
• B. \$4,000
• C. \$3,870
• D. \$4,200

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the concept of Present Value (PV). 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 PV of a single cash flow is: \( PV = \frac{FV}{(1 + r)^n} \), where \( FV \) is the future value, \( r \) is the discount rate, and \( n \) is the number of periods.
2. Step 2: Break down the problem into individual cash flows for each year. For Year 1, the cash flow is \( \$1,000 \), for Year 2, the cash flow is \( \$1,500 \), and for Year 3, the cash flow is \( \$2,000 \). Each cash flow will be discounted separately using the formula for PV.
3. Step 3: Apply the PV formula to each cash flow. For Year 1, calculate \( PV_1 = \frac{1000}{(1 + 0.08)^1} \). For Year 2, calculate \( PV_2 = \frac{1500}{(1 + 0.08)^2} \). For Year 3, calculate \( PV_3 = \frac{2000}{(1 + 0.08)^3} \).
4. Step 4: Sum up the present values of all individual cash flows to find the total present value. The formula is \( PV_{total} = PV_1 + PV_2 + PV_3 \).
5. Step 5: Compare the calculated total present value to the given answer choices (\$4,011, \$4,000, \$3,870, \$4,200) and select the closest value.