A project has the following cash flows:\[\begin{align*}\text{Year 0:} & \ -\$10,000 \\\text{Year 1:} & \ +\$4,000 \\\text{Year 2:} & \ +\$4,000 \\\text{Year 3:} & \ +\$4,000 \end{align*}\]What is the internal rate of return (IRR) for this project (rounded to the nearest whole percent)?

• A. 23%
• B. 28%
• C. 12%
• D. 18%

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the concept of Internal Rate of Return (IRR). IRR is the discount rate at which the net present value (NPV) of all cash flows equals zero. It represents the project's break-even rate of return.
2. Step 2: Write the NPV formula for the cash flows provided. The formula is: \( NPV = \sum_{t=0}^{n} \frac{C_t}{(1 + r)^t} \), where \( C_t \) is the cash flow at time \( t \), \( r \) is the discount rate (IRR), and \( n \) is the number of periods.
3. Step 3: Substitute the given cash flows into the NPV formula: \( NPV = \frac{-10000}{(1 + r)^0} + \frac{4000}{(1 + r)^1} + \frac{4000}{(1 + r)^2} + \frac{4000}{(1 + r)^3} \). Simplify the equation to find \( r \) such that \( NPV = 0 \).
4. Step 4: Use trial-and-error or financial calculator/software to solve for \( r \). Start with the given answer choices (23%, 28%, 12%, 18%) and calculate the NPV for each rate. The correct IRR will make \( NPV \) closest to zero.
5. Step 5: Once the correct \( r \) is identified, verify that it satisfies the condition \( NPV = 0 \) using the substituted cash flows. This confirms the IRR for the project.