The positive NPV of $4,437 indicates that the project is financially viable with a cost of capital of 10%.
NPV with 10% Cost of Capital
Given:
Initial Investment: $10,000
Cash Flows:
Year 1: $2,000
Year 2: $3,000
Year 3: $4,000
Year 4: $5,000
Year 5: $6,000
Cost of Capital: 10%
Formula:
NPV = ∑ Cash Flow / (1 + r)^t - Initial Investment
where:
r is the cost of capital
t is the year
Calculations:
Year Cash Flow Discount Factor Present Value
1 $2,000 0.909 $1,818
2 $3,000 0.826 $2,478
3 $4,000 0.751 $3,004
4 $5,000 0.683 $3,415
5 $6,000 0.621 $3,726
Total Present Value: $14,437
NPV:
NPV = $14,437 - $10,000 = $4,437
Interpretation:
The positive NPV of $4,437 indicates that the project is financially viable with a cost of capital of 10%. This means that the expected discounted value of the future cash flows is greater than the initial investment. In simpler terms, the project is expected to generate enough return to compensate for the initial investment and the cost of capital.
Complete question:
Initial Investment given the cash flows, initial investment, and varying costs of capital, calculate the NPV using this formula for each cost of capital from 11.0% to 15.0% in 0.5% increments. Once calculated, fill in the NPV values in the table under the respective cost of capital rates.
Suppose you have an initial investment of $10,000 and the following cash flows for each year:
Year 1: $2,000
Year 2: $3,000
Year 3: $4,000
Year 4: $5,000
Year 5: $6,000
You want to calculate the NPV using a cost of capital of 10%.