To calculate the Net Present Value (NPV) of the investment, we need to discount each of the expected cash flows back to the present value using the desired rate of return (11.00% in this case). The formula for NPV is:
\[ \text{NPV} = \sum \frac{C_t}{(1 + r)^t} \]
where:
- \( C_t \) = cash flow at time \( t \)
- \( r \) = discount rate (11.00% or 0.11)
- \( t \) = year
Given the cash flows:
- Year 0: -$87,617.00
- Year 1: -$24,594.00
- Year 2: $25,455.00
- Year 3: -$54,237.00
- Year 4: $38,635.00
We can calculate the NPV as follows:
-
Year 0 Cash Flow: \[ NPV_0 = -87,617.00 \]
-
Year 1 Cash Flow: \[ NPV_1 = \frac{-24,594.00}{(1 + 0.11)^1} = \frac{-24,594.00}{1.11} ≈ -22,157.66 \]
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Year 2 Cash Flow: \[ NPV_2 = \frac{25,455.00}{(1 + 0.11)^2} = \frac{25,455.00}{1.2321} ≈ 20,677.38 \]
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Year 3 Cash Flow: \[ NPV_3 = \frac{-54,237.00}{(1 + 0.11)^3} = \frac{-54,237.00}{1.3676} ≈ -39,650.94 \]
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Year 4 Cash Flow: \[ NPV_4 = \frac{38,635.00}{(1 + 0.11)^4} = \frac{38,635.00}{1.5181} ≈ 25,456.35 \]
Now we sum up all the NPVs:
\[ \text{Total NPV} = NPV_0 + NPV_1 + NPV_2 + NPV_3 + NPV_4 \]
Calculating the total:
\[ \text{Total NPV} = -87,617.00 - 22,157.66 + 20,677.38 - 39,650.94 + 25,456.35 \]
Calculating step-by-step:
\[ = -87,617.00 - 22,157.66 = -109,774.66 \] \[ = -109,774.66 + 20,677.38 = -89,097.28 \] \[ = -89,097.28 - 39,650.94 = -128,748.22 \] \[ = -128,748.22 + 25,456.35 = -103,291.87 \]
Thus, the NPV of this investment opportunity is approximately -103,291.87.
Conclusion: The NPV of the investment is -103,291.87, indicating that the investment would not meet the expected 11% return and may not be a viable opportunity under these cash flows.
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