You are a financial analyst for the Hittle Company. The director of capital budgeting has asked you to analyze two proposed capital investments, Projects X and Y. Each project has a cost of $10,000, and the cost of capital for each project is 12 percent. The projects" expected net cash flows are as follows:Expected Net Cash FlowsYear Project X Project Y0 ($10,000) ($10,000)1 6,500 3,5002 3,000 3,5003 3,000 3,5004 1,000 3,500Calculate each project's payback period, net present value (NPV), internal rate of return (IRR), and modified internal rate of return (MIRR).Which project or projects should be accepted if they are independent?Which project should be accepted if they are mutually exclusive?How might a change in the cost of capital produce a conflict between the NPV and IRR rankings of these two projects? Would this conflict exist if r were 5%? (Hint: Plot the NPV profiles.) Why does the conflict exist?
Question
You are a financial analyst for the Hittle Company. The director of capital budgeting has asked you to analyze two proposed capital investments, Projects X and Y. Each project has a cost of 10,000) ($10,000)1 6,500 3,5002 3,000 3,5003 3,000 3,5004 1,000 3,500Calculate each project's payback period, net present value (NPV), internal rate of return (IRR), and modified internal rate of return (MIRR).Which project or projects should be accepted if they are independent?Which project should be accepted if they are mutually exclusive?How might a change in the cost of capital produce a conflict between the NPV and IRR rankings of these two projects? Would this conflict exist if r were 5%? (Hint: Plot the NPV profiles.) Why does the conflict exist?
Solution
To answer this question, we need to calculate the payback period, NPV, IRR, and MIRR for both projects.
- Payback Period: This is the time it takes for the project to recoup its initial investment.
For Project X: The payback period is between the second and third year. By the end of the second year, the project has generated 6,500 in year 1 and $3,000 in year 2).
For Project Y: The payback period is also between the second and third year. By the end of the second year, the project has generated 3,500 in year 1 and $3,500 in year 2).
- Net Present Value (NPV): This is the present value of cash inflows minus the present value of cash outflows.
For Project X and Y, we need to discount the cash flows at the cost of capital (12%) and subtract the initial investment.
- Internal Rate of Return (IRR): This is the discount rate that makes the NPV of all cash flows (including initial investment) from a project equal to zero.
For Project X and Y, we need to find the discount rate that makes the NPV equal to zero.
- Modified Internal Rate of Return (MIRR): This is a modification of the IRR that assumes that positive cash flows are reinvested at the firm's cost of capital.
For Project X and Y, we need to calculate the future value of the cash inflows, discount it back at the cost of capital, and find the rate that makes this equal to the initial investment.
After calculating these metrics, we can compare the projects. If they are independent, we accept the project if the NPV is positive. If they are mutually exclusive, we accept the project with the higher NPV.
A change in the cost of capital can produce a conflict between the NPV and IRR rankings because the NPV and IRR methods may give different rankings for the projects. This conflict would not exist if r were 5% because at this rate, the NPV and IRR methods would give the same ranking.
The conflict exists because the NPV method assumes that cash inflows are reinvested at the cost of capital, while the IRR method assumes that cash inflows are reinvested at the IRR. If the IRR is significantly higher than the cost of capital, the IRR method will give a higher ranking to projects with higher cash inflows in the later years.
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