 There are certain other factors that a financial analyst needs to consider during the process of capital budgeting. These factors include NPV profile, ranking conflicts between NPV and IRR and multiple or no IRR. So far as the NPV profile is concerned, it is a graph that shows relationship between multiple NPVs against the corresponding discount rates. In NPV profile, we see that the relationship between NPV and the discount rate is a downward sloping and the curve is convex from the origin. Dear students, we can see an NPV profile on the screen. This NPV profile shows that NPV against the discount rate is showing a downward trend or we can see that it is a convex from the below. This line has three distinctive features at 0% discount rate. We see that NPV is the maximum that is $34,000 whereas at a point where the discount rate is 19.52%, NPV is equal to 0 and hence 19.52% is the discount rate. Till this discount rate, the NPV is positive but decreasing and at the discount rate above than this IRR, the NPV is start becoming negative. So far as ranking conflicts between NPV and IRR is concerned, we see that for a single and conventional project, there exists no conflict between IRR and NPV as both the criteria is in agreement with each other. But when we talk about mutually exclusive projects, then these two criterion may not be in agreement and this disagreement may be due to two different factors like differing cash flow patterns of the mutually exclusive projects and the project skills. Now there is a golden rule that in such cases NPV rules the IRR. On the screen, dear friends, you can see a graph that is showing ranking conflicts due to differing projects cash flows. We have two projects, project A and B. We have an initial cash outflow which is equal followed by a series of cash inflows having different patterns. NPV of project A is 53.59 where is project B has NPV of 73.21 and project A has IRR of 21.86% and project B has an IRR of 18.92%. Now if we see these two projects independently, then both of the projects can be accepted as project A has higher IRR but project B has higher NPV. Now if we see the NPV profile of these two projects, we see that in the left panel we see dotted line that shows project B's NPV profile and a thick dark line that shows NPV profile of project A. There is a point at which these two lines cross each other. Now the point where NPV's of different projects cross each other, this point is called as a crossover rate. This crossover rate is 15.09% where both the projects have equal NPV of 27.98%. If we go deeply into this graph, we see that from 0% to the crossover rate, project B has higher NPV over project A but beyond this crossover rate, project A has higher NPV than the project B. Now on the screen, we see cash flows of two different projects having different skills. Project A has initial outflow of $100, project B has initial outflow of $400. So we can say that project A is smaller than project B. These projects have future cash inflows. Now project A has an NPV of $58.49 whereas project B has NPV of $138.88. Project A has IRR of 34.9% whereas project B has IRR of 25.21%. If we see these two projects as independent one, we can choose both of these two projects as project A has higher IRR over project B and project B has higher NPV of project A. When we see these NPV profiles of these two projects at the left below panel, we see that project B's NPV profile is shown through thick dotted line whereas project A has an NPV profile depicted through thick flat line. The point where these two projects have their NPVs crossed each other, the point is termed as crossover rate. This crossover rate is 21.86%. At this rate, both of the projects have equal NPV. Now before these discount rates, project B has higher NPV over project A and beyond these discount rates, project A has higher NPV than project B. NPV assumes reinvestment of the future cash flows at the discount rate and not at the IRR. In fact, IRR is always unknown. IRR assumes no investment of future cash flows at the same rate throughout the life of the project. If the future cash flows can be reinvested at the IRR, then there is no need to use required rate of return as the discount rate. In this case, we see that NPV criteria uses the most realistic discount rate which is the opportunity cost of capital. Another benefit to using NPV as the project DCN criteria is that the NPV shows the gain earned by a project in terms of currency units and not in terms of percentage relative to the invested capital. The IRR gives a rate that might not last for the whole life of the project. Therefore we see that NPV is theoretically a sound DCN criteria. There appears another problem with reference to the IRR and that is we might have multiple IRRs or we have no IRR. On the screen, we see that we have a multiple IRR problem in which we have a project that has two different signs, one at the time of zero. The project has negative cash outflow as an initial cash outflow. Then at time two, the project has another cash outflow that is showing negative sign. In this case, we might have multiple IRRs. We see the NPV profile, we see that we have an IRR at first that is 100% and then we have another IRR that is 200%. If we observe this NPV profile, we see that from 0% to 100%, the NPV is negative. At 100%, it is 0 from 102 to 100% between the two IRRs, the NPV is positive. And from the second IRR onward, the NPV is showing a negative value. What is the solution of multiple IRR problems? We have a solution to this problem and the solution is the modified IRR. Modified IRR is the rate that equates the present value of terminal value of the all cash flows of a project to the present value of cash outflows of the project. In other words, we can say that we compute a present value of all terminal values of the project and we equalize this value with the initial cash outflow. Now how we compute the present value of terminal values of the project cash inflows? We use a VEC that is weighted average cost of capital or cost of financing. We use this VEC to discount the future cash flows of the project. And then we use another rate and that is the modified IRR rate. We use this rate to equate the discounted terminal value with the equality of the initial cash outflow. In this way, the modified IRR avoids the problem of multiple IRR. We see that an example where $100 is the initial outflow then we have future cash inflows of $10, $60 and $80. Now we grow, we discount in fact the future cash flows at 10% which is the VEC and in this way we have a terminal value of $158.1. We have now and cash inflow cash outflow of $100 and when we equalize these two values using a certain discount rate, this discount rate is termed as modified IRR. We may have situation where we may find no IRR for the project on the screen. Here students we see that we have a cash outflow of $100 then we have cash inflow of $250 at time 2 but $300 as a negative cash inflow or outflow for the period 1. If we see the NPV profile of this project, we see that we have a 0% to 400% and we have nowhere a 0 NPV during this discount range. In other words we find there is no IRR for this project but if an NPV profile has no IRR is there a problem or this NPV is of no use. We note an NPV profile with no IRR means that there is no discount rate that can transform this NPV into a 0 NPV. So this another mean that project has all positive cash inflows for the days to come. In this case there exist no IRR for this project.