What is the present value (PV) of the following set of cash flows, discounted at an annual rate of 8\%? - Year 1: \$1,000- Year 2: \$1,500- Year 3: \$2,000\[PV = \frac{1,000}{(1+0.08)^1} + \frac{1,500}{(1+0.08)^2} + \frac{2,000}{(1+0.08)^3}\]Which of the following is closest to the correct present value?

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

Answer: (B)

Verified step by step guidance

1. Step 1: Understand the concept of Present Value (PV). PV is the current worth of future cash flows discounted at a specific rate. The formula for PV is \( PV = \frac{CF}{(1 + r)^n} \), where CF is the cash flow, r is the discount rate, and n is the year.
2. Step 2: Break down the problem into individual cash flows. For Year 1, the cash flow is \$1,000, for Year 2 it is \$1,500, and for Year 3 it is \$2,000. The discount rate is 8\% (or 0.08).
3. Step 3: Apply the PV formula to each cash flow. For Year 1, calculate \( PV_1 = \frac{1,000}{(1 + 0.08)^1} \). For Year 2, calculate \( PV_2 = \frac{1,500}{(1 + 0.08)^2} \). For Year 3, calculate \( PV_3 = \frac{2,000}{(1 + 0.08)^3} \).
4. Step 4: Add the present values of all cash flows together to find the total present value. \( PV_{total} = PV_1 + PV_2 + PV_3 \).
5. Step 5: Compare the calculated total present value to the given options (\$4,200, \$4,011, \$3,870, \$4,000) to determine which is closest to the correct answer.