Laurman Inc. is considering the following project: an initial investment of \$50,000 in securities expected to yield annual returns of \$6,000 for 10 years. If the required rate of return is 8%, what is the net present value (NPV) of the project?

• A. \$1,200
• B. $-8,721
• C. $-2,815
• D. $-5,620

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the concept of Net Present Value (NPV). NPV is a method used to evaluate the profitability of an investment by calculating the difference between the present value of cash inflows and the initial investment. The formula for NPV is: NPV = ∑(Cash Flow_t / (1 + r)^t) - Initial Investment, where 't' is the time period, 'r' is the discount rate, and 'Cash Flow_t' is the cash inflow at time 't'.
2. Step 2: Identify the given values from the problem. The initial investment is \$50,000, the annual cash inflow is \$6,000, the duration is 10 years, and the required rate of return (discount rate) is 8%.
3. Step 3: Calculate the present value of the annual cash inflows using the formula for the present value of an annuity. The formula is: PV = Cash Flow × [(1 - (1 + r)^-n) / r], where 'Cash Flow' is the annual inflow, 'r' is the discount rate, and 'n' is the number of years. Substitute the values: Cash Flow = \$6,000, r = 0.08, and n = 10.
4. Step 4: Subtract the initial investment from the present value of the cash inflows to determine the NPV. Use the formula: NPV = PV - Initial Investment, where 'PV' is the present value calculated in Step 3 and 'Initial Investment' is \$50,000.
5. Step 5: Interpret the result. If the NPV is positive, the project is expected to generate more value than its cost and is considered a good investment. If the NPV is negative, the project is expected to generate less value than its cost and may not be a good investment.