Before we put interest into the income statement, it's worth understanding the circularity issue. And I'm gonna first approach this by doing it on an algebraic basis. So let's imagine we have a revolver facility and we have a beginning balance of 0. We had no revolver in the prior year. And then what I'm going to do is I'm gonna do an issuance of the revolver and we'll kind of assume that this happens partway through the year or halfway through the year. And then we'll also gonna add any interest and then we'll get the ending balance. And the reason I'm adding the interest is you have got to add interest because if you've run out of money, you need to borrow in this case 100, but you also need to borrow the interest on that as well. So it's important to include that. But I'm gonna do this algebraically. So if I just do the sum of the ending about there, it's a hundred, I'm gonna put in an interest rate now. And the interest rate, I'm gonna make it very simple. I'm gonna make it 10%. So I'm gonna calculate my interest expense as an initial calculation by taking the sum of the beginning balance and the issuance. And I'll multiply it by the interest rate. But because the issuance is only generated partway through the year, and in the model, we'll replicate this by using an average. I'm just going to divide it by 2. So in our model, what we would see is interest expense of 5. The problem is that you have to borrow that 5 million as well. So what you then have to do is you have to calculate interest on interest. And the interest on interest calculation is going to be the 5 million extra that we need to borrow times the interest rate, but divide by 2 because remember, you're only going to need to raise the 100 million halfway through the year if you build up that requirement gradually every day. So actually we need to borrow an additional 0.3 million. But of course, if you need to borrow the additional 0.3 million, you need to borrow some extra money and therefore you will be charged interest on that. So the interest on interest again will be the 0.3 times the 10% divided by 2.

And you can see we start to get a pretty small number. So what I'm going to do is I'm just going to expand the decimal places a little bit here just so we can see the detail because I want to continue the interest on interest. And if I'm clever, what I can do is I can take the prior amount times the interest rate and I'll just absolutely reference the interest rate. So we can do another interest on interest. And you can see the difference gets smaller and smaller. In fact, that 5 million starting interest expense, then we add another 250,000, then another 12,500 of interest, and then we've got $625 of interest. Then we've got $31 of interest. Then we've got 1.50 dollars of interest, then we've got less than a cent of interest. And again, you can go on and on and on, but at some point even the bank gets bored. So at that point we'll say, okay, what is the overall borrow requirement? And I can do that just by taking the sum of the beginning balance and all the interest on interest. So we estimate that we're going to have to borrow in total about 105.263157894453100

Now that process of iterating through the calculation is exactly what Excel is going to do. In our model rather than do this using an algebraic method that I've just illustrated, instead what we will do is we'll take the interest rate times the average of the beginning and ending balance. And when I hit enter, I get the error message error error. We created a circular reference and Excel can't complete the result. So the first thing that happens is you get a 0 in Excel and you get the arrows on the spreadsheet. This means that we've got a circular reference. Now in this case, I do want this circular reference, but I need Excel to iterate through. So I'll do alt FT and I'm going to go to the formulas assumption and I'm going to just check the enable iterative calculation. And you can see it's either going to iterate until a maximum 100 times or until the change in the number is no greater than 0.001 with the next iteration. It's obviously going to reach the maximum change first. Because if you just look at our algebraic method, it's gonna do one iteration in row 12, two iterations in row 13, and then in row 14 it's the third iteration. And that change is slightly larger than 0.001. So it will do a fourth iteration in row 15 and then stop. So if I now hit enter and I just increase the decimal slightly, you can see it has actually gone down to row 14. If I recalculate, you'll see that the accuracy gets to row 15. If I recalculate again, you can see it goes to row 16. And I'll just keep on doing this until I get the same result as below. I'm not using the F9 key because otherwise it turns the recording off. But you can see that what happens now, the ending amount using Excel's iterative function gets the same result as our algebraic method. And that's what's going on in the model. And let's apply this to the model.