Internal Rate of Return (IRR) method
　　Often an entity would want to establish its internal rate of a project for various reasons e.g., for decision-making purposes. By IRR we mean a rate that will be used to discount future cash inflows to make the total of the present values equal the cost of the project. The attempt being made under IRR is to find a rate that will equate the NPV of a project to be zero. The IRR therefore is the maximum rate of discount that will be used to finance a project without making a loss from it. Again in a mutually exclusive situation, the project that has the highest IRR is the one to recommend. The reason being that the IRR is showing the highest rate that can be used to finance a project without incurring a loss from it. Students often suggest to the author that the IRR should be called the break-even rate. His reply to them is often, if this makes you understand IRR you should use that term for it.
　　In order to find the IRR manually, this is done by the trial and error approach. By this we mean using a discount rate which gives a positive NPV and another rate which gives a negative NPV. Then apply the formula:
　　IRR = A + a x (B -A)
　　a + b
　　Where:
　　A = The lower discount rate which gives the positive NPV
　　B = The higher discount rate which gives the negative NPV
　　a = The value of the positive NPV
　　b = The value of the negative NPV
　　Please note that a and b should be added together as the negative sign in b is ignored.
　　Now let us demonstrate these various methods using a case from a fictitious company we shall call AICO Plc.
　　Case
　　Senior management of AICO Plc have identified that there is a strategic need for a replacement machine to be acquired in one of their production departments. They have to make a choice between two models ofthe machine ? model 1 is called Super and model 2 is called Deluxe. They are unsure as to which of the two models they should buy. They have given you the following profiles of the two models. They want you to use the four investment appraisal techniques discussed above. You are required to recommend which of the two models is better under each appraisal technique and to explain briefly why you have recommended one in place of the others under each technique. You are told that funds are only available for only one model.
　　The cost of capital is 12% and AICO depreciates all its fixed assets on the straight-line basis. By cost of capital is meant what it costs to raise the required finance for the project.