Question

can you briefly explain the following concepts; mutually exclusive project, independent project, multiple internal rates of return, and cross-over rate.

Answer 1

Mutually exclusive project : They are a set of projects from which at most one will be accepted. For example, a set of projects which are to accomplish the same task. Thus, when choosing between "Mutually Exclusive Projects" more than one project may satisfy the Capital Budgeting criterion. However, only one, i.e., the best project can be accepted. In this case cash flows of one project are affected by selection of another meaning that one project will be totally forgone if another is selected. Eg: Decision of buying a Mini Bus will affect the decision of buying a Tempo car both for one single location.

Independent Project: This is the exact mirror image of mutually exclusive projects wherein the cash flow stream of one project doesnt seem to be affected by rejection/acceptance of some other project. For Eg: the decision of buying a Bus by fedex will not affect the decision to invest in renovating the new buidling.

Multiple IRRs : The multiple internal rates of return problem occur when at least one future cash inflow of a project is followed by cash outflow. In other words, there is at least one negative value after a positive one, or the signs of cash flows change more than once. In this case, we say that the project has non-normal cash flows. In contrast, normal cash flows have one or more consecutive cash outflows followed by cash inflows. If a project has a non-normal cash flow, it can have more the one IRR. Eg:

Year	CF A
0	(1,000)
1	1,000
2	1,100
3	1,300
4	1,000
5	(3,700)

Above project will have 2 IRR like 5.07 and 82.4%

Cross-over rate: Crossover Rate is the rate of return (alternatively called weighted average cost of capital) at which the Net Present Values (NPV) of two projects are equal. It represents the rate of return at which the net present value profile of one project intersects the net present value profile of another project.

In capital budgeting analysis exercises, crossover rate is used to show when one investment project becomes superior to another as a result of a change in the rate of return (cost of capital).