QuestionApril 14, 2026

A 5-year project with an initial investment of 1,000 annual cash inflows of 250 , and a cost of capital of 15 percent would be expected to have an NPV of square

A 5-year project with an initial investment of 1,000 annual cash inflows of 250 , and a cost of capital of 15 percent would be expected to have an NPV of square
A 5-year project with an initial investment of 1,000 annual cash inflows of 250 , and a cost of capital of 15 percent would be expected to have an NPV of square

Solution
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Answer

The NPV is approximately ( \(-\161.96\) ), indicating the project would reduce value and is not financially attractive. Explanation 1. Understanding NPV formula Net Present Value is calculated as the sum of the present values of future cash inflows minus the initial investment. The formula is: \[ \text{NPV} = \sum_{t=1}^{n} \frac{\text{CF}_t}{(1 + r)^t} - \text{Initial Investment} \] Here: - \( \text{CF}_t = 250\) (annual cash inflow) - ( r = 0.15\) ) (cost of capital) - ( n = 5\) ) years - Initial investment = ( ( \(1000\) ) ) **Summary:** Apply standard NPV formula. 2. Applying Present Value of Annuity formula for inflows Since annual inflows are constant, we use the Present Value of Annuity formula: \[ \text{PV} = \text{CF} \times \left[ 1 - (1 + r)^{-n} \right] / r \] Substitute values: \[ \text{PV} = 250 \times \frac{1 - (1.15)^{-5}}{0.15} \] First, compute \((1.15)^{-5}\): \[ (1.15)^5 = 2.011357 \quad \Rightarrow \quad (1.15)^{-5} = \frac{1}{2.011357} \approx 0.497176 \] Now: \[ 1 - 0.497176 = 0.502824 \] Divide by ( ( \(0.15\) ) ): \[ \frac{0.502824}{0.15} \approx 3.35216 \] Multiply by ( ( \(250\) ) ): \[ \text{PV} \approx 838.04 \] **Summary:** Present value of inflows ≈ \838.04 3. Computing NPV Subtract the initial investment from the total PV of inflows: \[ \text{NPV} = 838.04 - 1000 = -161.96 \] **Summary:** NPV is negative ≈ -\161.96

Explanation

1. Understanding NPV formula <br /> Net Present Value is calculated as the sum of the present values of future cash inflows minus the initial investment. The formula is: <br />\[<br />\text{NPV} = \sum_{t=1}^{n} \frac{\text{CF}_t}{(1 + r)^t} - \text{Initial Investment}<br />\] <br />Here: <br />- \( \text{CF}_t = 250\) (annual cash inflow) <br />- ( r = 0.15\) ) (cost of capital) <br />- ( n = 5\) ) years <br />- Initial investment = ( \(1000\) ) <br /><br />**Summary:** Apply standard NPV formula. <br /><br />2. Applying Present Value of Annuity formula for inflows <br /> Since annual inflows are constant, we use the Present Value of Annuity formula: <br />\[<br />\text{PV} = \text{CF} \times \left[ 1 - (1 + r)^{-n} \right] / r<br />\] <br /><br />Substitute values: <br />\[<br />\text{PV} = 250 \times \frac{1 - (1.15)^{-5}}{0.15}<br />\] <br /><br />First, compute \((1.15)^{-5}\): <br />\[<br />(1.15)^5 = 2.011357 \quad \Rightarrow \quad (1.15)^{-5} = \frac{1}{2.011357} \approx 0.497176<br />\] <br /><br />Now: <br />\[<br />1 - 0.497176 = 0.502824<br />\] <br /><br />Divide by ( \(0.15\) ): <br />\[<br />\frac{0.502824}{0.15} \approx 3.35216<br />\] <br /><br />Multiply by ( \(250\) ): <br />\[<br />\text{PV} \approx 838.04<br />\] <br /><br />**Summary:** Present value of inflows ≈ \$838.04 <br /><br />3. Computing NPV <br /> Subtract the initial investment from the total PV of inflows: <br />\[<br />\text{NPV} = 838.04 - 1000 = -161.96<br />\] <br /><br />**Summary:** NPV is negative ≈ -\$161.96
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