One of the great things about electronic spreadsheets is that you can use them and improve them over time. You can compare forecasts to reality and make adjustments. You can add variables you didn't think about before. You can have other people work on the spreadsheet and extend it. It will grow, it'll get more complex, it'll get larger. Unfortunately, that introduces the possibility of error. In this lecture we'll look at some of the common errors that are frequently introduced into large electronic spreadsheets. To do that we need to start by understanding the difference between relative and absolute references in formulas. We'll then take a look at how to recognize errors in formulas. We'll look at identifying in particular, a kind of error called a circular reference. And we'll learn how to correct those circular references. And we'll finally use some general tools for auditing formulas, that touch a lot of different variables in your spreadsheet. To do that, let's return to the spreadsheet. One of the powerful ways to use spreadsheet models is to compare our plans to our actual experience, and then adjust our models to improve their utility in making future decisions. As we add to models, they can get larger and more complex, and with that complexity comes the chance of introducing error. Here you see a relatively simple cash flow model, based on a template provided by Excel. I've added a couple of changes to it, I included a minimum function for the range D11 to O11 as an output cell. The key use of a cash flow model is to anticipate cash shortages, so let's put that output cell up on top where we can see it. Last year we also had a high rate of returns, so I'm including that percent as an assumption we can easily adjust from one location. And I've referenced it, the 10% is a return rate. In the formula that calculates the returns and allowances for a given period. One common mistake can b introduced when copying formulas. By default when you copy a formula from one cell to the next it treats the cell references in your formulas as relative. Notice what happens when I copy the formula in January to the rest of the year. If you look at the new formula in E15 you'll see that the reference to the prior period has adjusted to indicate cell E14, and that's what we want. But the reference to the location of the sales growth rate has also adjusted, and we don't want that. To fix the problem, we can use dollar signs in the original formula. For the reference to the return rate, which should stay consistent across all periods. Now, when I copy the formula from January through the rest of the year, you'll see that when I look in February's cell reference, the relative value for the period in column E has copied forward correctly by adjusting, but the return rate is still fixed at cell F5. And that is the case for March and for the rest of the year. It's also easy to introduce an error referred to as a circular reference. For example, if I sum a range, as in this case a subtotal of cash paid out, it's often easy to make the mistake of including the cell in which I'm writing the formula in the range to be summed. So in this instance, if I by accident had included the cell that I'm actually writing the formula for within the range, Microsoft Excel will spot that and reference it as a circular reference. And you can then later come back and fix it. Here are a couple additional tools to help you find and fix errors. First by double-clicking to put focus on a formula, the cells and ranges included in the formula will be highlighted for your review. Finally, by holding down the control key and pressing the tilde key, that's the key to the left of the one key. You can display formulas instead of the calculated values, and you can print this view to perform a more detailed audit.