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You have two mutually exclusive projects. Both projects require initial investment of $20 million. Project 1 generated $4 million per year in perpetuity.Project 2 generated $3 million at the end of the first year and its revenue will grow 3% per year thereafter.The cash flows of both projects start at the end of the first year. <a> IRR<b> NPV, assume the cost of capital is 6%

Question

You have two mutually exclusive projects. Both projects require initial investment of 20million.Project1generated20 million. Project 1 generated 4 million per year in perpetuity.Project 2 generated $3 million at the end of the first year and its revenue will grow 3% per year thereafter.The cash flows of both projects start at the end of the first year. <a> IRR<b> NPV, assume the cost of capital is 6%

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Solution

To answer this question, we need to calculate the Internal Rate of Return (IRR) and Net Present Value (NPV) for both projects.

  1. Project 1:

    • IRR: The IRR is the discount rate that makes the NPV of a project zero. In this case, since the project generates 4millionperyearinperpetuity,theIRRistheannualreturnof4 million per year in perpetuity, the IRR is the annual return of 4 million divided by the initial investment of $20 million, which is 20%.
    • NPV: The NPV is the present value of cash inflows minus the present value of cash outflows. For a perpetuity, the NPV is the annual cash inflow divided by the discount rate. So, the NPV is 4million/64 million / 6% = 66.67 million. Since the initial investment is 20million,theNPVis20 million, the NPV is 66.67 million - 20million=20 million = 46.67 million.
  2. Project 2:

    • IRR: The IRR for this project is not as straightforward to calculate because the cash inflows are not constant. You would need to use a financial calculator or software to find the discount rate that makes the NPV zero.
    • NPV: To calculate the NPV, you need to discount each year's cash inflow back to the present. The first year's cash inflow is 3million,whichisdiscountedbackoneyearatarateof63 million, which is discounted back one year at a rate of 6%. Each subsequent year's cash inflow is the previous year's inflow increased by 3%, and this is discounted back at a rate of 6%. This is done in perpetuity. The sum of these discounted cash inflows is the total present value of the cash inflows. Subtracting the initial investment of 20 million gives the NPV. This calculation would also require a financial calculator or software.

In conclusion, without the exact IRR and NPV for Project 2, it's hard to make a direct comparison between the two projects. However, given the higher constant cash inflow and higher NPV for Project 1, it seems like Project 1 might be the better investment if all other factors are equal.

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