 During the capital budgeting process, an analyst may face certain issues with reference to project evaluation. These issues may come from mutually exclusive projects or they may come from the unequality of project lives or these issues may occur due to the problem of capital rationing. For mutually exclusive projects, these are the projects as we have earlier seen that compete with each other. These projects may form a group and in the group there would be one project that the analyst needs to choose and to choose a project competing with other projects, the basic and fundamental decision criteria is the NPV that is the project with the higher NPV would be selected. Now let's discuss an example of mutually exclusive projects who have unequal lives. We have two projects, project S and project L. Project S has a life of two years and after two years there is a replacement and project L has a life of three years and then after three years there is the project replacement. The NPV of project S is $28.93 and project L has an NPV of $35.66. Both the projects have required rate of return 10% that is used as a discount factor. What is replacement chain analysis? In replacement chain analysis we in fact analyze the project chain replacement since the inception of the project. This means that during the life of the project if there is a project replacement then the project is analyzed from its inception and not at the point where the replacement takes place. Then what is the solution? The solution is that there is an equivalent way we need to equalize the lives of the project to analyze the competing projects. Here we have two approaches to do this replacement chain analysis. One approach is least common multiples of lives and the other approach is termed as equivalent annual annuity. A benefit of these two different approaches is that these two work differently but result the same value. Dear friends on the screen you see the application of first approach that is the least common multiple of lives. In this approach in fact we extend the time horizon of our analysis so that the lives of both the competing projects divides exactly into the selected time horizon. Now we see that our first project that is a project S has a life of two years after two years there is a replacement and we have project L who has a life of three years now its replacement is due after three years. If we see the approach that is least common multiple we have factors of two and three when we take the L sum of these two values we arrive at a figure of six. This means that we need to extend our analysis to period of six years. This means we have three replacements for project S and two replacements of project L. This means that when we discount our cash flows for both project S and project L we come to a different NPV for each of the projects. For project S the NPV is 72.59 dollars and for project L the NPV is 62.45 dollars. Both have a discount rate of 10 percent. Now at given time period of six years and a given discount rate of 10 percent clearly the project S can be selected as it has higher NPV over project L. In second approach that is the equivalent annual annuity or EAA. We determine the present value of annuity who has a collective value equal to the value of net present value of a given project. It works in two ways at first we compute the NPV of the given project and then we determine the present value of this NPV and this present value of the NPV is termed as the equivalent annual annuity. Now coming to the example where S project has an NPV of 28.93 dollars if we determine present value of annuity of this amount the EAA is 16.67 dollars and for project L we have the NPV of 35.66 dollars. Now determining the present value annuity of this amount we come to the figure of 14.34 dollars. Now we have analyzed the annuity value of the both projects NPVs. Now if we see the value to determine project selection we can see that the project S has higher EAA and the decision criteria is that the project with higher EAA will be selected. Another issue that we can face is the capital rationing. Capital rationing is a situation where the financial analyst is constrained with the financial budget. This means that he has many project options but limited budget to choose. In fact the capital rationing has a problem of misallocation of the project because in open economy capital markets allow funds allocation using the best rate of return that maximizes the wealth of the investor. But capital rationing cannot do this wealth maximization to the efficient funds allocation. The reason is that the capital rationing is occurred due to the funds constraints. There are two types of rationing soft rationing and hard rationing. Soft rationing is a situation where the financial analyst can go beyond the fund and he can spend funds beyond the limit means he can go for the overspending subject to a valid and appropriate justification against the decision. And so far as the hard rationing is concerned here there is no choice for the financial analyst to go beyond the budget constraints. In hard rationing the selection criteria is the profitability index. Now we have an example where we have three classes of projects ranged from project one to project 12 and we have four projects in each class. We have to choose four projects in each class and the project has a point limitation of thousand dollars. If we see the first class that is project one from project four we see that we can spend on project one and project two only because these two projects has positive NPVs and total NPV is two hundred and ninety dollars. Also these projects have higher profitability indices over the projects of three and four along with these two these projects have also higher IRR. Now out of one thousand dollars we can spend only eight hundred dollars on the first two projects. Now what about the rest two hundred dollars these two hundred dollars can be used as distribution to the shareholders as cash dividend or they may be used as share repurchase being a cash distribution among the shareholders. For the second class of projects that is from project five to project eight we have first three projects where we can spend our full amount of thousand dollars. These three projects have a cumulative NPV of four hundred and forty dollars. So the selection criteria is the NPV because these projects are ensuring a positive value creation for the shareholders also supported by our decision profitability indexes of these all three projects is greater than one. Now come to the third class of our projects who range from project nine to project twelve We have a project nine with three hundred dollars as the NPV and project twelve as hundred dollars as NPV also we have project ten as two hundred and seventy dollars. But to select the project two along with the project three we needs a total investment of twelve hundred dollars. But we know that we have a project limitation funds limitation of one thousand dollars and we cannot go for fractional projects. So we have to skip the project ten and project eleven project eleven we skip because we have a good option of project twelve. So in this class we go for project nine and project twelve with a cumulative positive NPV of four hundred dollars also these two projects have a profitability indexes of greater than one and good IRRs.