A project has the following cash flows:\[\begin{align*}\text{Year 0:} & \ -\$10,000 \\\text{Year 1:} & \ +\$3,000 \\\text{Year 2:} & \ +\$4,000 \\\text{Year 3:} & \ +\$5,000 \end{align*}\]What is the payback period for this project?

• A. 1.8 years
• B. 2.2 years
• C. 3.0 years
• D. 2.5 years

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the concept of the payback period. The payback period is the time it takes for the cumulative cash flows from a project to equal the initial investment. It is calculated by summing the cash flows year by year until the initial investment is recovered.
2. Step 2: Start by identifying the initial investment, which is the cash flow at Year 0. In this case, the initial investment is -\$10,000.
3. Step 3: Add the cash flows from subsequent years to the initial investment cumulatively. For Year 1, the cash flow is \$3,000. Subtract this from the initial investment: -\$10,000 + \$3,000 = -\$7,000. The project has not yet recovered the initial investment.
4. Step 4: For Year 2, the cash flow is \$4,000. Add this to the cumulative cash flow from Year 1: -\$7,000 + \$4,000 = -\$3,000. The project still has not recovered the initial investment.
5. Step 5: For Year 3, the cash flow is \$5,000. Add this to the cumulative cash flow from Year 2: -\$3,000 + \$5,000 = \$2,000. The project recovers the initial investment during Year 3. To calculate the exact payback period, divide the remaining amount to be recovered (\$3,000 at the end of Year 2) by the cash flow in Year 3 (\$5,000), and add this fraction to the number of years already passed (2 years).