Hi, my name is Grant Hobson. I work as a finance analyst, and today I'm going to talk you through some business maths, calculations and ratios. How to calculate internal rate of return or IRR? The internal rate of return is basically where the net present value of the cost and the net present value of the benefits to the investment equal zero and the IRR is commonly used to analyze investment decisions, and where we've got a positive favourable IRR, then it is deemed that the project should go ahead alternatively and if it's not favourable, then we wouldn't. We're going to run through a calculation now just to demonstrate how it works. So, the equation for the internal rate of return is as shown above. Basically, this is several variables within the calculation and you see there's a lower rate ad higher rate, so what we do for the calculation is we take one NPV rate and that outcome will generate a favourable return. We then want to take or generate a favourable or an average return and after that, we then take another NPV rate either increasing or decreasing, we get the opposite return, so we need one favourable and one adverse return. It will become clear as we work through the example and okay, so in this example, I'm saying that we're buying a machine for 160,000 pounds. It's given a 5-year life. The machine is going to save 40,000 pounds per year and as a residual value of 20,000 pounds. So, if we set up a table as below, as shown here, it will help you work through the calculation. You need to have an understanding of present value and discount factor and etc, or when you don't have that, it's worth getting an understanding before doing this calculation. As you see, I've already got discount facts included in here. So what I'm saying is that in year 0, so this is the point where we purchased the machine, the cash outflow, system of cash flow, here is 160,000 pounds. The present value for that cash flow is 160,000 pounds up for now. And then for the next 5 years, I've got a consistent saving of 40,000 pounds per year, so basically I put 40,000 pounds for years 1 to 5 and the present value of that next few years, our cash inflow, is 151,640. So this discount factor, this will play a, this is 40,000 pounds by 3.791. In the final year, I then get the residual income from the sale of this machine, it's then 20,000 pounds. That's just the one year income, so that in the table has a factor of 0.621, which gives us 12.40 so you'll see it's simply 20,000 multiplied by that factor. So I'm saying here that I've got a present value of these cash flows of 4,060 pounds. So at 10%, that's 4,060 and as I've said, as you can see below, so if we have a positive outcome, I then need to use a higher IRR. That's for our higher rate and the second that the calculation covers the IRR, it will be one or zero. Alternatively, if it was negative, we need to use a lower rate for stage 2. So having used 10% in calculating NPV in step 1, I'm now going to use 12% to try and hopefully get a negative outcome down here. So, I'll put in the same cash outflow in year 1, the same 40,000 pounds per year and the same residual value of 20,000. Now, you see that the present value or the discount factor have changed here and that's so because it's gone to a 12% rate, and you see that we've got a negative outcome of 4,460. So as we've now got a negative here and a positive here, I know that the internal rate of return will be a point between 10% and 12%, because that's the only place where the NPV will be zero. So no basically, what we need to do is take the elements from this data set and put them into the formula. So having decided that we need to find the rate between 10% and 12%, we now use the formula here above and insert the data in there. So the formula, so we take 10 which is the lower rate, we then add the NPV at that lower rate divided by the NPV at a lower rate and the NPV at a higher rate, so it's 4060 divided

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