 In the continuation of the investment decision criteria, we have few other quantitative techniques like net present value, internal rate of return and profitability index. Net present value is the excess of present value of cash inflows over the present value of cash outflows. If the difference is positive, this means we have more cash flows at their present value than the present value of cash outflows and in the presence of positive net present value, the project may be accepted and in case the net present value is negative, the project may be rejected. Then how to determine net present value of a project if the project has even amount of cash inflows? Let's take an example. In this example, assume we have an initial cash investment of Rs. 5000 and annual cash inflows of Rs. 3000 for a period of 5 years. Now we need to determine present value of this entity of Rs. 3000 and deduct the present value of this cash inflow from the present value of cash outflow which is Rs. 5000. We see that there is a positive figure of Rs. 3169. So this net present value is the positive present value. How to determine net present value of a project that has uneven cash inflows over the project whole life? In this case we need to determine present value of individual years cash inflows at first step. In the second step we accumulate all these present values of the cash inflows. The cumulative present value of these inflows is used to deduct the amount of present value of cash outflows. The resulting figure if positive will be termed as net present value or otherwise it is the negative present value. What is the rationale to choose net present value as a capital budgeting tool? The first point in this regard is that zero net present value means that projects cash flows are significant to in number one repay the invested capital and number two to provide the required rate of return this means that zero net present value means the project has generated enough amount of cash to pay back its investment and the project is able in terms of profitability to cover its cost of capital. In positive net present value signifies again that the project is generating more cash than it is needed to serve the debt and provide the required return to its capital providers. At the last the positive net net present value ensures value enhancement for the shareholders wealth. The other method is the internal rate of return. By internal rate of return we mean the discount rate at which net present value becomes equal to zero. This means at this discount rate the present value of cash inflows is equal to the present value of cash outflow. The benchmark criteria is that if the IRR on a project is greater than the cost of capital of this project or the IRR is greater than the required rate of return of the project the project may be accepted but if IRR on a project is lesser than the cost of capital of this project the project may be rejected. Why to use IRR for a given project? In fact IRR on a project is its expected rate of return. It is the return that the project is able to deliver to its owners. So it is the expected rate of return for that particular project. If IRR is greater than the cost of capital of the project then this means there would be certain surplus as a saving and this surplus saving will accrue to the shareholders as a value maximization tool but if the IRR on a project is lesser than its cost of capital this means that the wealth of the owners has been destroyed in the particular project and the cost is borne by the project owners. The break-even characteristics of IRR is such a nature that makes IRR very much sophisticated tool of capital budgeting. How to determine IRR of a project that has unequal cash flows? In this case we need to determine present value of cash flows through heat and trial. We need to have two types of NPVs the first NPV that is positive and the second NPV that is negative. We know that there should be a zero NPV. Now we have certain data our example as you can see on the screen. We have an NPV of 49 rupees at our discount rate of 10% and we have an other NPV that is negative 67. At 11% this means that as zero lies between negative 67 and positive 49 so our IRR would also lie between 10% and 11%. Now using these two discount rates and two net present values in an interpolation model we can determine the IRR and in this example the IRR is 10.42% so this is the rate that using 10.42% in particular is in this case the NPV would be equal to zero and what would be the process to determine IRR where the company has equal cash flows on a given project. In this example you can see on the screen we have annual cash outflow of 200,000 rupees and annual inflow of 68,416. In fact this is the present value of the cash inflows. If we divide present value of cash outflow which is 200,000 on annual inflows we come across a figure of 2.913%. As the project has 4 years useful life so in the table of present value interest factor annuity we come from horizontally a period of 4 towards the percentage rate. We see that at 2.9137 there is a rate of 14% so IRR on this type of project is 14% that we have determined using equal cash flows. Profitability Index Profitability index shows the relationship between cost and benefit of a proposed project. Profitability index is determined by dividing present value of cash inflows over the present value of cash outflows. This index tells that how much has been recovered against an investment of single unit of currency. For governmental and other non-profit organizations this profitability index is also known as benefit cost ratio. It is an important tool for guiding the financial analyst in the process of capital rationing. And decision rule is that if the profitability index is greater than 1 we can accept the project and if it is lesser than 1 we can reject the project. If profitability index is greater than 1 this means that there would be a positive NPV whereas if profitability index is lesser than 1 then this would yield a negative NPV.