Answer:
Step-by-step explanation:
To calculate the initial investment, we can use the formula for net present value (NPV) as follows:
NPV = present value of cash inflows - present value of initial investment
Given that NPV = $9,000 and the annual cash inflows for each of the three years, we can calculate the present value of cash inflows as follows:
PV of year 1 cash inflow = $21,000 / (1 + 0.15)^1 = $18,260.87
PV of year 2 cash inflow = $24,000 / (1 + 0.15)^2 = $18,137.32
PV of year 3 cash inflow = $27,000 / (1 + 0.15)^3 = $18,008.69
Therefore, the total present value of cash inflows is:
PV of cash inflows = $18,260.87 + $18,137.32 + $18,008.69 = $54,406.88
Now, we can rearrange the NPV formula to solve for the initial investment:
NPV + PV of initial investment = PV of cash inflows
Substituting the given values, we get:
$9,000 + PV of initial investment = $54,406.88
PV of initial investment = $54,406.88 - $9,000
PV of initial investment = $45,406.88
Finally, we can calculate the initial investment by finding the present value of $45,406.88 for 3 years at a 15% required rate of return:
Initial investment = $45,406.88 / (1 + 0.15)^3
Initial investment ≈ $29,508.88
Therefore, the initial investment for the project was approximately $29,508.88.