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Sloan Inc. recently invested in a project with a 3-year life span. The net present value was $9,000 and annual cash inflows were $21,000 for year 1; $24,000 for year 2; and $27,000 for year 3.

The initial investment for the project, assuming a 15% required rate of return, was _____.

Net Present Value

User Hanabi
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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.

User Richard Gomes
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