Calculate each project’s NPV|Quick homework help
Posted: February 16th, 2023
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A company is considering two mutually exclusive expansion plans. Plan A requires a $39 million expenditure on a large-scale integrated plant that would provide expected cash flows of $6.23 million per year for 20 years. Plan B requires a $11 million expenditure to build a somewhat less efficient, more labor-intensive plant with an expected cash flow of $2.47 million per year for 20 years. The firm’s WACC is 10%.
Q. Calculate each project’s NPV. Round your answers to two decimal places. Do not round your intermediate calculations. Enter your answers in millions.
Q. Calculate each project’s IRR. Round your answer to two decimal places.
SOLUTION
To calculate the NPV of each project, we need to discount the expected cash flows of each project back to their present values using the WACC. The NPV of a project is the present value of its expected cash flows minus the initial investment.
For Plan A, the initial investment is $39 million and the expected cash flows are $6.23 million per year for 20 years. Using the formula for the present value of an annuity, we can calculate the present value of the cash flows for Plan A:
PV of cash flows for Plan A = $6.23 million x [(1 – 1 / (1 + 0.1)^20) / 0.1] = $61.76 million
Therefore, the NPV of Plan A is:
NPV of Plan A = $61.76 million – $39 million = $22.76 million
For Plan B, the initial investment is $11 million and the expected cash flows are $2.47 million per year for 20 years. Using the same formula as above, we can calculate the present value of the cash flows for Plan B:
PV of cash flows for Plan B = $2.47 million x [(1 – 1 / (1 + 0.1)^20) / 0.1] = $24.55 million
Therefore, the NPV of Plan B is:
NPV of Plan B = $24.55 million – $11 million = $13.55 million
To calculate the IRR of each project, we need to find the discount rate that makes the NPV of the project equal to zero. We can use a financial calculator or spreadsheet software to do this.
For Plan A, the IRR is approximately 15.85%.
For Plan B, the IRR is approximately 11.95%.
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