Final answer:
To calculate the cash flows for years 1-3 and the NPV, use the future value formula. Calculate the cash flows for each year by multiplying the principal by (1 + interest rate) to the power of the number of years. Then, calculate the NPV by discounting the cash flows to the present value using the same interest rate and subtracting the initial investment.
Step-by-step explanation:
To calculate the cash flows for years 1-3 and the NPV, we need to use the future value formula. The future value is calculated by multiplying the principal by (1 + interest rate) to the power of the number of years. In this case, the principal is $15 million.
Year 1 cash flow: $15 million × (1 + 0.15)¹ = $17.25 million
Year 2 cash flow: $15 million × (1 + 0.15)² = $19.84 million
Year 3 cash flow: $15 million × (1 + 0.15)³ = $22.76 million
To calculate the NPV, you need to discount these cash flows to the present value using the same interest rate. Then, sum up the present values:
- Year 1 present value: $17.25 million ÷ (1 + 0.15)¹ = $15 million
- Year 2 present value: $19.84 million ÷ (1 + 0.15)² = $15.56 million
- Year 3 present value: $22.76 million ÷ (1 + 0.15)³ = $15.62 million
Finally, calculate the NPV by subtracting the initial investment of $15 million from the present values:
NPV = -$15 million + $15 million + $15.56 million + $15.62 million = $31.18 million.