Mendez Company has identified an investment project with the following cash flows: Year 0: \(-\$10,000\), Year 1: \$4,000, Year 2: \$4,000, Year 3: \$4,000. If the required rate of return is 10\%, what is the net present value (NPV) of the project?

• A. \$1,241
• B. \$2,000
• C. $-1,241
• D. \$0

Answer: (A)

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 present value of all cash inflows and outflows using a discount rate (in this case, 10%). The formula for NPV is: \( NPV = \sum \frac{C_t}{(1 + r)^t} \), where \(C_t\) is the cash flow at time \(t\), \(r\) is the discount rate, and \(t\) is the year.
2. Step 2: Identify the cash flows and the discount rate. The cash flows are: Year 0: \(-\$10,000\), Year 1: \$4,000\, Year 2: \$4,000\, Year 3: \$4,000\, and the discount rate is \(10\%\) or \(0.10\).
3. Step 3: Apply the NPV formula to each cash flow. For Year 0, the cash flow is \(-\$10,000\), and since it occurs at \(t = 0\), it is not discounted. For Year 1, Year 2, and Year 3, discount each cash flow using the formula \( \frac{C_t}{(1 + r)^t} \). For example, the discounted cash flow for Year 1 is \( \frac{4,000}{(1 + 0.10)^1} \).
4. Step 4: Sum the discounted cash flows. Add the discounted values for Year 0, Year 1, Year 2, and Year 3 to calculate the total NPV. The formula becomes: \( NPV = -10,000 + \frac{4,000}{(1 + 0.10)^1} + \frac{4,000}{(1 + 0.10)^2} + \frac{4,000}{(1 + 0.10)^3} \).
5. Step 5: Compare the calculated NPV to the given answer choices. Once the NPV is calculated, match it to the closest value among \(\$1,241\), \(\$2,000\), \(-\$1,241\), and \(\$0\).