Let's look at an example of an inflation index in practice. The index example we're showing has five years with some cashflow numbers. They might be revenue, they might be costs. We're assuming a 5% rate of inflation. The initial cashflow shown in the top row exclude inflation. The next row down shows the inflation index. This is 1 plus the rate 5% to the power of 1 in the first column to the power of 2 in the second column to the power of three in the third column. So it's simply brackets 1 plus that inflation rate of 5%. Fix that to the power of the period number, which is in the very top row. Then we just multiply the cash flow by the inflation index. So period one cash flows 100, I need to add 5% on top of that as inflation. I just multiply it by the index of 1.05 to give me 105 as my inflation adjusted cash flow.
Looking at this example of using a flag, in this case, we have the cash flows in the top line, 100 flat every year, and we have an inflation index. Again, it's going at 5% increase per year. So that's just 1 plus 5% to the power of however many years have gone by. But what we want to show is that inflation doesn't start in the initial couple of years of the model. That might be because we have a fixed price contract for this cost or a fixed revenue base. In that case, we don't want to add any inflation. Inflation only kicks in in the third year. The one that's dated the 31st of December, 2023.
By that stage, three years worth of inflation has accumulated compounding. It comes up to 15.7%. That's what we see in the index number in the circle. 1.157625. The inflation flag is just a simple formula, like a normal flag. It says if the date is bigger than or equal to the time that inflation commences 31 December, 2023, give me a 1, otherwise give me a 0. So the first two columns, the date is not bigger than or equal to the end of 2023. So it shows me a 1, and the next three columns are a 1. How do we then calculate the inflation adjusted flow? Be careful. Don't just take the initial cash flow times by the index times by the flag, because that would then give you zero in the first two years. What we want is if the flag is a 0, just give me the cash flow number in the top row. Otherwise give me the cashflow number times by the inflation index. In this case, what we're showing is that in the third year, 2023, the price of whatever this item is that we are modeling has increased substantially. It goes from 100 dollars to 116. It's a catch up of three years worth of inflation.
