As you might expect, you can test of equality or non-equality using standard mathematical formulas:

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1 Logic Functions Despite the fact that the set of logic functions is one of the smallest function collections in Excel, it is definitely one of the most important. The reason for this is quite simple: it is this set of functions that allows us to make our spreadsheets react differently depending on certain outcomes. Without these functions we would only be able to report on historical data or build static scenarios. By leveraging logic functions we can turn our spreadsheets into powerful decision matrices and business intelligence tools. How Do Logic Functions Work? Before you can dive into logic functions, it is helpful to understand what they do and how they work, so let s take a look at the underlying logic behind a logic function. Scenario Testing The primary goal of logic functions in Excel is answering if a provided scenario is TRUE or FALSE. If you think back to your high school science class, you would have spent a lot of time on hypothesis testing. Essentially, that is what a basic logic function does. As an example, open up a blank spreadsheet and enter the following in cell A1: =B1=10 Excel will evaluate that and return the value FALSE. Why? Well, B1 starts with an = making it a formula. And the remaining portion is the portion of the formula that you want evaluated. Since B1 is empty it doesn t equal 10, and Excel therefore returns FALSE as a result. Now, type 10 into B1 and you ll see that A1 returns TRUE. As you might expect, you can test of equality or non-equality using standard mathematical formulas: Formula Hypothesis Being Tested =B1=10 Is B1 equal to 10? =B1>10 Is B1 greater than 10? =B1>=10 Is B1 greater than or equal to 10? =B1<10 Is B1 less than 10? =B1<=10 Is B1 less than or equal to 10? =B1<>10 Is B1 not equal to 10? You can also use cell references in place of the values as well, to drive scenarios that are far more complex. 1

2 Reacting to TRUE/FALSE Statements The secondary goal of logic functions is to be able to use these TRUE/FALSE results and react differently depending on which you have. By this means we can have Excel do one thing if the test is TRUE, and something completely different if the test is FALSE. Logic is used extensively throughout Excel. Some areas you ll find it used are: Formulas that you write to do things dependent on certain scenarios Conditional formats which format cells where certain (user defined) rules are met Inside certain function parameters (which you ll see by the end of this course) Three Commonly Used Logic Functions Now that you understand the basic purpose of logic in Excel and the underlying theory behind it, we ll look at some of the most commonly used functions in the logic arena. =AND() The AND() function is used in a formula to test multiple hypothesis that you supply. It will test each supplied hypothesis and, if every single provided hypothesis is met, this function will return TRUE. The syntax for this function is as follows: =AND(Logical1, [Logical2], ) The first parameter (Logical1) is a required logical test (like B1=10). The second parameter (Logical2) is surrounded by square brackets meaning that it is optional. The indicates that you can add more logical tests as well, should you need them. =OR() The OR() function is also used in a formula to test multiple hypothesis that you supply. Unlike AND(), however, OR() will test each supplied hypothesis and, if any one or more provided hypothesis is met, this function will return TRUE. The syntax for this function is as follows: =OR(Logical1, [Logical2], ) The first parameter (Logical1) is a required logical test (like B1=10). The second parameter (Logical2) is surrounded by square brackets meaning that it is optional. The indicates that you can add more logical tests as well, should you need them. =IF() The IF() function is by far the most powerful and commonly used of the logic function set. In this function, the author provides a hypothesis to be tested. In addition, the author also provides two more parameters for the function: what they would like to happen if the hypothesis is TRUE and what they would like to happen if the hypothesis is FALSE. 2

3 The syntax for this function is as follows: =IF(logical_test, [value_if_true], [value_if_false]) What this means, in English, is: Parameter Optional/ Required Details Default (if not provided) Logical_test Required The hypothesis you would like to test N/A Value_if_true Optional What you d like to happen if the test is TRUE TRUE Value_if_false Optional What you d like to happen if the test is FALSE FALSE So looking at our previous example, the following formula could be used to tell us something about the value in cell B1: =IF(B1=10,"B1 is equal to 10","B1 is not equal to 10!") The results of using this formula can be seen in Figure 1, shown below: Figure 1 Example 1 Rewarding Customer Loyalty Rather than ply on with more theory, let s take a look at a real-world example in which these formulas and functions might be used. Example Background In this example the Marketing department has approached us with an issue: they want to reward customer loyalty, but are having a hard time trying to build a program. They re looking for our help to evaluate some scenarios to see how they should construct the loyalty program. Specific things that the Marketing department want to accomplish: Reward number of visits. They feel repeat business is important and should lead to future purchases. Reward total dollars spent. Obviously this is the end game to reward! In addition they have decided that they have a budget of $12,500 that they can work with. So whatever program they look at needs to fit within that constraint. 3

4 They have helpfully provided us a list of customers, visits, and dollars spent by customer, which should be very helpful. So let s take a look and see what we can do. Open Example 1 Customer Mining.xlsx Example File Review Before we dive right in, let s take a look at what we are working with today. We have a listing of customer names in column A, customer visits in column B, as well as the total spend in column C. If we scroll down the sheet we see we have quite a bit of data here, 113 rows in fact. At the top of our sheet we see that someone has gone in and worked out what the lowest and highest customer spend are, as well as the lowest and highest number of customer visits. We also have a threshold given for what we are looking for: a $15,000 spend level and a minimum of 70 visits. If we click in cells F8:F10 we see that the formulas are already plumbed in for us. This will allow us to sum up the information that will go into the area under Revenues Where Criteria Meet Thresholds to come up with the total spend that meets the criteria of what we want. Cells F8:F10 contain a formula that will work out the total discount based on the total spend multiplied by 5%. This is great. A lot of the framework has been built for us to allow us to evaluate the proposed rebates once we ve plumbed in the logic portion. So now let s set about doing exactly that! Who Meets the Minimum Visit Threshold? The first thing we need to do is go through and determine whether or not the customer has met the minimum number of visits threshold. To do that we are going to select cell D14 and put in a simple logic formula to test if they have. To complete our goal, we need to determine if the number in cell B14 is greater than the threshold we have set in cell B5. The formula we want is: =B14>$B$5 The function will return TRUE, as shown in Figure 2, below: 4

5 Figure 2 Let s just check that out for a second. Adams has visited 73 times because this is greater than our 70- visit threshold the function returns TRUE. Great! That was our first logic formula, and it looks like it s working. Now, we have a lot of data here, so we want to be able to copy this formula down our sheet. Because we already created this with an absolute reference to cell B5 (the $ signs before the row and column mean it won t change as we copy it to other cells), we can just extend this formula down the table rows. To do so: Move your mouse to the bottom right corner of cell B14 until the cursor turns into a black + Double click the black + sign Figure 3 Because the column beside it has data to the end of the table, double clicking the Fill Handle (shown in Figure 3) will extend our formulas all the way to the end of the table, as shown in Figure 4: 5

6 Figure 4 To test it you can scan down the sheet, noting for example that cell D18 returns as FALSE with 58 records, and cell D19 returns as TRUE with 86 so our formula is working just fine. Who Meets the Customer Spend Levels? Now let s do a similar thing with the spend level. Here we will determine if a customer has spent more than the $15,000 threshold that has been set up in our spreadsheet. To set up the appropriate formula here: Select E14 Press = Click C14 Type > Click B4 Press the F4 key (to toggle from relative to absolute cell references) Press the Enter key It returns FALSE. This is correct as we can see that this Adams spend of $2, is not greater than our $15,000 threshold. 6

7 Once again, double click the fill handle (just like we did for our last column) to copy this formula all the way down our table so that it looks as shown in Figure 5: Figure 5 Let s do another quick scan, just to make sure this formula is working as we d expect. While most of the rows are showing FALSE, indicating that those customers spend levels are under the $15,000 threshold, F22 is showing TRUE. Looking at C22 we can see that it is definitely exceeding the spending level we re looking for, so the TRUE result displaying in F22 is absolutely correct. Gross Spends from Customers Who Meet the Visit Threshold So now we have worked out whether someone actually meets those thresholds. That doesn t help Marketing understand the effect on their planned loyalty program though. In the spreadsheet that Marketing provided, they already set up cells F8:F10 to summarize the total customer revenues for each scenario that they wish to evaluate. We need to calculate the total sales dollar value of those customers to feed them in to that matrix. So let s start by calculating the total dollars spent by customers who had more than 70 visits. This is where we start to put IF functions to work. What we want to get Excel to do here is put the total spend in cell F14 if D14 is TRUE. If D14 is FALSE, we want Excel to put in 0. If you recall from earlier, the syntax for the IF function is as follows: =IF(logical_test, [value_if_true], [value_if_false]) So logically speaking, we should be able to sub those portions into the formula as follows: =IF(D14=TRUE,C14,0) 7

8 Let s try that. Select F14 and start typing it in As you start typing TRUE you ll notice that the Intellisense pops up, indicating that there is a TRUE() function. This function doesn t take any arguments, and its only purpose is to evaluate to TRUE. But the rub is that you can t ignore those brackets and just put in TRUE, or Excel will return an error. So the modified formula you need to enter is: =IF(D14=TRUE(),C14,0) Upon committing this formula, you ll see that it returns $2, Cool! To see how this works, replace all the ranges in the function with the values in their cells, remembering that TRUE() returns TRUE (without the parenthesis): =IF(TRUE=TRUE, ,0) Excel then evaluates the test in the middle: =IF(TRUE, ,0) Since we ve asked to return if the test evaluates to TRUE, that is what we get back. Now here s a trick. We don t actually need to enter the =TRUE() portion of that function at all this will work equally well: Why is that? =IF(D14,C14,0) Again, let s step through and evaluate this the way Excel would. It starts with D14 and coverts that to the value in the cell. So the formula gets evaluated to: =IF(TRUE, ,0) Excel has all the pieces it needs to make its decision already! Whichever variant you ve used, copy it down the table using the fill handle trick and notice which customers total sales are pulled over. Figure 6 8

9 Gross Spends from Customers Who Meet the Spend Threshold So what about the spend level? Let s give that one a try. Our criteria for this formula are: IF Spend Level (E14) is TRUE THEN C14 OTHERWISE 0 So subbing that into the IF function syntax, we get: =IF(E14=TRUE,C14,0) And because we already have a column with the TRUE/FALSE values, we can shorten this to: =IF(E14,C14,0) Enter that into cell G14 and copy it down the table so that you get the results shown in Figure 7: Figure 7 Status Check Let s take a second to figure out what we know. The matrix in F7:I10 was already plumbed with the formulas to sum up the values in the columns that we just populated. So now we can start seeing the effects of what we ve been doing: 9

10 Figure 8 As we check now, we can see that we have more than $200,000 of sales where customers have met the minimum visit threshold of 70 visits during the period. If we multiply that by 5% we have $10,000 worth of discounts that we would be giving out. That is good as it is less than the $12,500 that Marketing wants to work with. We can also see that we have more than $57,000 of sales where the customers met the minimum spending level of $15,000. And if we gave them a 5% discount, it would work out to about $2,800. Let s add those two together to see what would happen if we offered both programs. Highlight the two totals and then take a look at the Quick Info section at the bottom of your screen, as shown in Figure 9, below: 10

11 Figure 9 This is by far the quickest way to figure out that our total is $12,936, a value that is more than Marketing s $12,500 budget. Gross Spend from Customers Who Meet Either Threshold What s interesting about the $12,936 total generated by implementing both rewards levels is that it would actually be giving a 10% discount to some customers if they met both the spend level and the visits criteria. Maybe we should look at it and say what would happen if we gave them a 5% discount if they met either of the two criteria, instead of both This will take a little more work as we need to look at a new formula. This time we need to add a new criteria that says if it meets this OR that. Specifically, in the case of cell H14, we want our IF() function to work as follows: IF D14 OR E14 are TRUE 11

12 THEN C14 OTHERWISE 0 So how do we do this? Let s see if we can leverage the OR() function that was discussed earlier. The theory behind the OR() function was that it would return TRUE if any of the conditions were met. We could therefore nest an OR() function into the logical test of the IF() function, as it also returns a TRUE/FALSE value. As a reminder, the syntax for the OR() function is as follows: =OR(Logical1, [Logical2], ) So let s see how this would look for us. We could put in the cells we want to test: =OR(D14=TRUE, E14=TRUE) And we know that we don t really need the =TRUE part, so =OR(D14, E14) To nest this into our previous IF() function, we would drop the leading = (our IF function already has an = sign to start the formula), and we d end up with: =IF(OR(D14, E14),C14,0) So drop that into cell H14 and copy it down the table. The results will look as shown in Figure 10. You can see from the fact that the total value is displayed in rows 14, 19, 22, and so on, that this function is correctly pulling back results where visits exceed the 70-visit threshold, or where the customer spend level is in excess of $15,000. Figure 10 Casting our eyes back up to the matrix table, we can also see that we have just over $243,000 in sales from customers who have visited more than 70 times or have spent more than $15,000. At a 5% reward level, that gives us $12,100, which is in line with our budget from the Marketing department. This is definitely interesting but let s look at it just one more way 12

13 Gross Spend from Customers Who Meet Both Thresholds We looked at our numbers when one of these criteria was true so what happens if we look at it to see if both are true? In other words: IF D14 AND E14 are TRUE THEN C14 OTHERWISE 0 This is very close to the previous formula, with only one difference. In the past example we wanted to get records if any criteria were true (OR), where this time we need all records to be true. Fortunately, we have the AND() function to work with, which is almost identical to OR(). In fact, the only difference is around the way it returns the TRUE/FALSE values. Let s take our previous formula and substitute AND for OR and see what happens. Enter the following in I14 and copy it down the table: =IF(AND(D14, E14),C14,0) At first glance, it looks like column I returns 0 in all cells, but if you scroll down the table you ll see that isn t the case. There is one customer (James in row 53) who meets both criteria. Now let s look back at our matrix and see what we can learn, and if we can come up with a near-perfect solution for marketing to work within our budget. Generating the Ultimate Reward Program The rewards matrix currently shows all the customer spending levels and discounts calculated at a 5% level, as shown in Figure 11: Figure 11 But now we can play with these results a little bit. We already know that rewarding based on both visits and spend level at 5% would create a program that costs $12,936 to implement; a fact that can be proven by summarizing either F10:G10 or F10:I10. Being that this is over the $12,500 budget, that won t be acceptable. So what if we decided to reward customers with either criteria the 5%, but changed it to an extra 2% for those that qualified for both. Let s do that, change the 5% in cell I9 to 2%. 13

14 Figure 12 Well that changes things a bit. Now our total for either and both is just under $12,500. This means we have met the Marketing department s requirements and we can reward the loyal customers that visit frequently, more than 70 times or the ones with large purchases, over $15,000. As an extra incentive we can also reward those customers that do both with a further rebate! This step-by-step tutorial was taken from the accompanying e-book included in the video course Formulas and Functions: Logic and Lookups. Begin your journey to spreadsheet mastery with PD Net s Excel Certificate Program Do you want to delve into Excel and learn how to unlock its power? PD Net offers the Microsoft Excel Certificate Program, it is a practical and flexible online education program consisting of 10 in-depth courses, covering core Excel knowledge relevant in business and finance. This comprehensive program will provide all the required information and tools to become an Intermediate Excel User. Learn more 14