All right everyone, welcome back, we're going to do an example that highlights some more skills in Excel and shows us how to do a little bit more modeling in some complex situations. So here's the question on the screen. Please pause the video and read it if you have not done so already. This is a golfing example by design. I will call it the 19th hole. The 19th hole sells golf clubs through its golf outlet stories at the US and demand varies with price, seems pretty normal. You sell things for a higher price, people buy less of it, standard rules of economics. In the last year, the demand at each price level was recorded below. So below here is the table on the left which I've copied into Excel. Please make this table if you haven't done so already. Now, the company wants to estimate the relationship between demand and price, and then use the estimated relationship to answer the following questions. And you can see where the first one is going. We're going to assume the cost of producing a set of clubs is $250, assuming the price is a multiple of 10, what price should the company charge to maximize profit? So once again, this is going to be a profit model where we look at the revenue and the cost. So the first thing I want to do with this data to get a better handle of it is I'd like to graph the data. So let's highlight all the data, head over to the Insert tab, and we can look at some of the recommended charts, pick your favorite one. I think for this one a scatter plot is perfectly fine just to get a handle of what the shape of our data is. Yes, that's the thing, what the shape of our data is. And here we have as Excel tends to do, a title that doesn't make much sense. We might want to look at improving the title, so updated to price vs demand. And one other thing you might want to always consider is adding the chart element of both the X and the Y axis. This will help remind you what you're actually looking at. The X axis here is your price, this will be in dollars and the Y axis let's update the title to be the demand. Let's be mindful that demands is in hundreds, to get the actual demand we'd have to multiply all these numbers by 100. But to keep things sort of close together so we could view them on chart. So we have this nice sloping curve, we have this scatter plot, and we'd like some sort of function. We'd like some prediction to help us get what the demand will be at different prices. This way when I vary the price, remember as a manager, you control the price, not the demand, I can fill in the gaps. So a lot of people look at the scatter plot and they know how to do one thing and one thing only. Let's see if this is you. If I have a scatter plot, I head over to add chart element. I go to trendline and I hit Linear, and I add a linear trendline. This is sometimes called the line of best fit. This is called the line of - the least squares line or linear regression. And people are very happy with their linear regression. It's a nice thing to do, don't get me wrong. The line itself is more cosmetic. The thing we're actually going to use here is the equation. To add the equation go back to where you added the trendline, go to more trendline options and then you have to scroll down to the very bottom on the right and you have to check the box that says display the equation on the chart. And when you do that it puts a little box with the equation sort of an awkward unreadable spot. But if you move it to somewhere more readable, you can see the numbers in there. Now, unfortunately while this is great, there's a lot of math that went in to get this number and it happens at the click of a button, you can't reference these numbers inside the text box. There are other ways to get these numbers, but for the sake of our model, let's look at our linear model here. I'm going to just write the numbers over, this is the slope of a line friendly reminder that's mx plus B. Our intercept, which is our B is the number that's added here. And then the slope which is our M, you know why M is used for slope? It's a mystery for the ages, that's something I, let's move this over. I'm just going to copy them down. So I have 211.31, and then -0.3546. These numbers actually go on. These are rounded numbers. If you want to show more decimals or less, you can format the way the numbers look. I'm just going to grab the numbers that are here. Just realize these are rounded and we're not working with the exact numbers and that's okay. All right, great, so I have this linear model but one thing you might notice from the data is that the data starts to curve. It does seem to sort of bend around as the price increases. If you remember as easy it is to add a linear model, you might want to consider another type of model. Maybe linear isn't the absolute best one. And I've seen people model things on linear regressions because that's all they know how to do and that's what they argue for. So one thing I want you to consider is, "Is linear the best model?" I know it's an easy model and one you might be more familiar with, but is it linear data? Linear modeling is usually when data has consistent slope, slope is a rate of change, when it changes consistently. It seems to me that this price versus demand is not having a constant rate of change. So let's look at it another way to add another model here. Excel gives you lots of options for fitting a curve to a scatter plot. We can pick some fancier ones, I want to show you that even on the main menu, there are some that are not shown, you have these other ones here, like a logarithmic or polynomial. You can look at the graph also, it helps you with the picture as to which one you're going for. I want to go with power. Now this picture shows an increasing power function, ours would sort of be decreasing, but it works exactly the same. I also have to, once I select power, once again click the box that says, display the equation on the chart, I close it, and there it is. It puts the equation a little bit in an awkward spot. We're starting to overlap, the trend lines are all the same color. It's a little difficult to see to be honest. So, I might want to consider if I was actually trying to show these graphs and - all I need is the numbers, but I'm just trying to show you. I might want to do three separate scatter plots if I really cared to show the difference. What I'm after here though of course, is the number on my power model, so a power function. Now, for those who forgot, what do the power functions look like? This is of the form, a number in front - a coefficient - so y equals a, and then the variable's in the base raised to a power. This is like y equals x squared, x squared is a type of power function. You could have 2x squared. So a would be 2 and b would also be 2 or 2x cubed. But the key point here is that the variable is in the base. And Excel will give you the numbers for both A and B. We have a constant A, and then we have our exponent which would be our B. Slide over the columns to make this a little more readable and I want to grab these from here. The exponent B, I know it's small but hopefully you can see it when you do it on yours. You get -0.908, that's fine. Again, that's a rounded number. That number probably goes on for more and more decimals. The problem is though, if I look at my constant A I have six E plus O6. Ok, friendly reminder what that is. E like handheld calculators is scientific notation and it's shorthand. So this is like 6 times 10 to the 6, so about six million or so. But let's, remember I said you can format these to do whatever you want. If you right click on this you can format the text. So when I right click I have an option for format trendline label, and it gives me the sidebar and it says okay this label, what is it? It picks "general," let's change it to a number and then you can always see it starting to change over here. You can pick how many decimals you want. You can do this for any trend line, for anything you want. We'll use - since this is a very large number, six million - I don't need the decimals - zero just to change it. And then when you're done, there's no like save button. It kind of happens automatically. Hit the X to close it out and now you can see that it's updated both my numbers and I probably didn't want both numbers to go to zero but already grabbed the b. So we're okay, notice it rounded it to minus two. But the key thing I want here is not 6 times 10 to the 6. I want to get out of scientific notation. I just want this coefficient A of 5871064. We're going to have to write these numbers and store them somewhere else on my spreadsheet so that I can reference them later. You can't reference these numbers inside of these little boxes that are there. All right, one more example just to make sure you get the hang of this and show you how many options you have. Obviously there's a lot more in Excel than what we're going to do, but let's look at an exponential function. Maybe this is an exponential growth. Once again, if you forgot what an exponential function looks like, it is similar to a power function but the biggest difference here is that - I have a number in front as I did before. These are functions of the form y= instead of the base being x, my base is actually the number e. e the number is 2.718 and change. So, it's e raised and then it's to the bx, the b now is the coefficient on x. So x the variable moves back upstairs. This is different than a power function where it was the base, it is now the exponential. e again is a number 2.718. So it looks like there's three letters in this formula but e is actually a constant. So I need to know my constant which is going to be my a and then my exponent will be my b. And let's actually add that curve to the chart, same as we did before. Go to chart design, go to add chart element, go to trend line, here, we can click the exponential function. Remember this just gives the picture, starting to get a little overlapping in my diagram. The picture is fine. It doesn't really help me that much though, for what I'm after, I certainly need to do more trendline options, click Exponential and then display the equation on the chart. That will give me the numbers that I need and then I can sort of decide if I'm happy with the number of decimals that are showing or not. I think for our purposes here it is perfectly fine. We're talking about, remember at the end of the day here, golf clubs, so I think rounding to a golf club to two decimals is perfectly fine. So let's see, our constant in front is 466.51 and then our coefficient b is -.005. I know it's small, but hopefully you can see that. Once you have these numbers, again, this all comes from the chart, this is just storage. These are not calculated by equations on the spreadsheet, they're just copied over. Once you have these things, you don't really need the scatter plot anymore. I'm going to leave it there, but we're really not going to use this. The point of this though, is a lot of people pick linear and they don't know why. They have nothing really good to say, this is what I've always done. So what I'd like to give you now is a tool where you can defend your model, you can say which one is best. There are a couple of ways to do this, but let's look at one called the mean absolute percent error and I'll write this all down. So first let's make a new table and we're going to do some prediction based on the different models. And what I want to do is I want to copy my data, I want to copy the price data. So I have it, I'm going to copy it down, we're going to make a new table about this big. And what I want to do is look at the predictions based on different models and we're going to do all three. We can certainly do more, we could do less. But let's do the three here that we have: linear, power, and exponential. And here's what I want to do. This is like the x value, the price in our formula becomes the x value, it is the input. So when the price is $450, what does the linear model predict as the demand? What does the power model predict as the demand? What does the exponential function predict as the demand? That means that I'm plugging them into the equation. I didn't write the linear one down but I might as well hopefully you know this though mx+b, I'm going to plug in all my numbers. So watch this, linear is m the slope times the price is x plus the b plus the intercept. So I'm plugging in the price. Remember I know the actual number from the table but I'm seeing what does my model predict? I'm looking for what are the values of the curve versus what are the actual dots on the scatter plot? And you hit enter then you get some numbers. So once more here's the formula good old mx+b. And once you have that, drag it down or double click it gives an error. So do as I say, not as I do. What did I forget to do here? I need to do absolute referencing on the B16. So we could do a little function, f4, that puts dollar signs on. That says when I drag you don't and then the slope B17 should also get locked in place. So really A21 is the only thing dragging. If you saw that before I did, good job. Now, let's do it again, that looks much better. Okay, so remember these are demands, these are actually golf clubs sold. The decimals don't make a lot of sense but just to sort of avoid rounding, I'll make one decimal to remind you that these should actually be decimals, we'll deal with them later. But one decimal is fine. I use the little rounding here, please don't truncate and causes some rounding errors which we don't really want. One more time, that's the linear model. Power model, I want the exact same thing. What does the power model predict? So I'm going to take my power model. Here's the formula, ax raised to the b. So my a from the graph is this large number near six million times x times my input which is price, raise it to the exponent that is b. Again, I need to lock in my values not going to make the same mistake twice. So, let's lock in D16 and D17 putting the dollar signs in front and enter when you're ready. I get some number. It's more decimals than we'll ever need. So let's shrink the decimals now before I drag it down. And the power model gives me it's prediction and these will be off from the actual data values and in a second we're going to measure how far off we actually are. So there's my power. Last function that we picked exponential function for no good reason. We want a then times e raised to the bx. So here's our constant a, let's lock it in now with our dollar signs and then times, now be careful e is a built in constant, if you want this constant in Excel, it's exp. This is the built in e 2.718 Euler's number if you want to use e. So and then we put in what we want, we want b times x. So be is this value, use your dollar signs to lock it down for dragging and then times x which is our price. This is the form of an exponential model. Notice they're all kind of close, kind of close. And so the question is which one is actually the best? A model, I don't care how good your spreadsheet looks or how much it actually works, it's only as good as sort of the assumptions behind it. So a lot of people just pick linear but there are many other options out there. How do you know which one is best? So these are our predictions based on the model. So maybe we'll merge this, show you we have these numbers. And now the question we're after is so what? What do I do with this? Well, let's compare this to the actual demand. So let's paste our demand values, right? Right next to it. There we go. Now these are actual numbers. And what I'd like to do is have some way to sort of capture how close the prediction was to the actual model. And we're going to do this a few ways to do this, but here's just one of them. We're going to use absolute percent error, okay? So what is absolute percent error? There's a formula for this where the absolute part says, we're going to use the absolute value. And then we're going to take the difference between what was actually predicted versus what was actually obtained, what the actual demand is. So we're going to take the absolute value. Let's start writing this out here. So absolute value, by the way, absolute value in Excel is abs. Some people make a mistake and they do like this vertical bar, that's not true. It's abs is the formula. So it's the absolute value of the linear prediction minus the actual demand. So this will be the absolute percent error for the linear model. Take the difference, take the absolute value. Notice that prevents you from getting a negative number in case the prediction is smaller than the actual demand. So absolute value keeps everything positive. We don't want any like accidental cancelations and then coming up with a lower error. And then because it's a percentage, you want to then divide this by the actual demand. Feels like a percent error if you've ever done one of those calculations. The absolute value is the only thing in there, making sure you don't get negative numbers. When you do that and you hit enter, you get back a big decimal, but we're usually after it as a percentage. So let's format this to a percent and what this is saying is the absolute percent error of the linear model. I should copy these models over, the linear model to the demand is about 15%. This prediction is about 15% off from the actual value. Once you have this, these are all draggable numbers, there's no dollar signs needed. I can just drag this down and it computes a percent error for each value. It's kind of trying to measure how far off as a percent error the curve is, or here, the line is, from the scatter plot. And what you do with all these numbers is remember each point contributes some error. Some values are closer than other ones. So linear predicted 51.7 and the actual value is 52. So there's a small contribution an error some are much further off like 34 versus 45. So you have all these numbers, what do we do? We take the average value of all these numbers and I get an average value, an average error, of 9.7%. So the average absolute percent error for the linear model is 9.7%. And what we're going to do here is we're going to do the same exact thing for all the models, and this is why this is a golf example. What's better, a large error or a small error? We want a small error, so we want to see what happens. All right, so let's do the exact same thing for the power function, let's practice our formula again. So we have abs, absolute value, of the predicted minus the actual, close up the parentheses, divided by the actual. Again we get a weird sort of decimal here. We don't want that, we can format that to a percentage. We can show one decimal to be fancy, we can drag it down and then we can take an average just dragging the formula over. So right away you can see the power model is actually a little better than the linear model, it has a smaller percent error. So the power function models this data - and we kind of saw that there was a curve built into the scatter plot, so perhaps it's not surprising as it may seem. Exponential, one more. Let's see if the exponential beats the power again like golf, low score is the winner. We do ABS, the absolute value of the exponential minus the demand divided by the demand. Close it up, convert it to a percentage. Show one decimal and drag it down and then we'll copy over the formula for the average. So we have two models here notice linear is actually the worst of all the models and the one that has the smallest the one that we're after here is going to be our power model. So this is sort of in defense of the model we pick here, again smallest value wins, like golf. So we're going to use the model with the smallest error. The power model does the best job of predicting the demand based on these prices. Fantastic, let's keep moving along. So now we have in defense of the power model, we're going to use the power model going forward. This is the thing we're actually going to use and we're going to - remember, we're still after this whole question. It's been a while but remind yourself the question - maximize the profit. What price when you're the manager, what price do we get to pick to maximize the profit? As a manager you pick the price, you unfortunately don't get to pick the demand, but you feel like you have a pretty good model. And so let's actually model the business. All right, so let's write down some of the information from before as a reminder of what we have, we have a unit cost of $250. This is per set of clubs, format this to be money, get rid of the penny. Now we have our sale price. This is like what are we going to sell it for? This is the play variable, this is the variable in play. What are we going to actually pick? The only rule per the question was that this had to be a multiple of 10. For no good reason let's pick a dummy number here. I don't like to leave these cells blank because I want to make sure my spreadsheet is working. If I'm, if I'm buying it for 250 let's sell it for $400, why not? And then once we have our sale here comes the calculations. Let's compute the demand. Demand now is coming from power model, demand is coming from the power model. This is extremely important. This is why we went to the trouble to figure out which model to use. What are we going to do here we're going to go back and remind ourselves the formula for the power function A times X raised to the B. So here's A, I'm not going to drag anything so I don't need dollar signs on it times my X, which is my input. So the sale price and then raised to the B. This is negative 1.908, and I hit enter. And so I'm predicting a demand, this is actually not dollars, this is numbers here. I'm predicting a demand of, let's say 63. Now be very careful here, as a reminder this demand and this is why it's all over the place here - is in hundreds. I might as well say what the actual demand is. So I don't have to worry about the units and take this number that I found and multiply it by 100. So let's start listing out the formulas here that I'm using. So one, I play with the sales price. That price, based on my model lets me determine the demand. That lets me fill in the gaps for the missing values. Then I compute my actual demand, these are sets of clubs. So let's kill the decimals, and we'll multiply this by 100. Mindful of our units. Let's go through and find our cost. In this example let's actually order what's demanded. So imagine the order comes in and then we place the order with the manufacturer. So we're only going to get, we're only going to buy what we have demand for. So the cost is going to be the 6000 number here and then it's going to cost me $250 per set of clubs. And so as a business owner is going to cost me 1.5 million based on this demand. Let's multiply the two numbers together the actual versus what's there. So we're going to fill every order as they come in and that's the only cost based on this model. This is the actual business cost. This is simple to show that this is really - defending the model is really the key to this problem. How does this company spend money? I have to order the clubs that I sell. How do I make money? Well sell them for a higher price, very simple business model. I am going to sell the ones that have been ordered at their price, and this is the green cell which we currently have at $400. So I'm making more than I'm spending and now I have my profit. Of course it's just my revenue minus the cost. I have all these values. Let's fill in the formula so you can see it. And hopefully this makes sense and we can play around with it. So here's where sort of the rookie comes in versus the experienced person. If you say wait a minute, I'm just buying these things at 250 that's fixed. Why don't I just sell these things for $1000. Let's raise the price like crazy, we'll make more money. So watch it right now. I have 400 and I'm making 955. It's a little under a million. Let's let's go nuts, sell for 1000. Somehow by raising the price by increasing the distance between my cost and sale price I've actually lowered my profit. What tends to happen in these kind of models is that the profit, the thing we're trying to maximize tends to form a downward facing parabola. So we could sit here and try to understand the model a little bit like what happens if I sell at 800? What happens if I sell at 700? Hopefully by now you're seeing where this is going. This has all the makings of a data table. So let's come over here on the side, and let's do a price as my input and then my profit as the number that I like the data table to find. As a reminder you need a ghost cell that we're not going to use but the table needs it and you're saying where is the profit in your model? So we're going to link back to B43 as our profit. And then this is just me I like to gray it out to sort of remind myself that this number is not really for me. The prices have to be a multiple of 10, I know that I'm buying it at 250. So I'm probably not going to sell it for anything less than 250. So let's start at like 260 and 270 and sort of work our way as far as we want we know that 1000 is too high. But heck let's go pretty large, maybe we'll go to like 900 or so. I don't know, 800? Let's go all the way to 600, why not? There's no right or wrong way to do this in the beginning. And once we kind of have a feel of what prices maximize the profit then we can narrow and change our values here. But right now I have a table in multiples of 10 from 260 to 600. Fantastic, I don't want to have to fill in every single value, the profit, that is what a one way table is for. So we highlight the table, by the way, notice I don't highlight the text of my header but I do include this sort of ghost cell. I head over to Data, I go to What If Analysis, I go to Data Table, and I remember this is the thing that the recording doesn't capture. So let me grab a screenshot of this box. Just to remind you this is saying for a one way table here, notice our inputs are column, we have a column of inputs. So it's asking you where in your model is your Column Input. It doesn't know that this is your price. So replace this with whatever header your column is. This is asking where in the model is your price, our sale price. So we're going to click the green cell in this second entry box. The Row Input, we're going to leave blank. We only fill that in when we have a header across the top. We have a two way table, something that we want to do. So we'll do that in a second. But here's the image we're going to do. Unfortunately, I don't know why the screen that I'm using recorder doesn't capture the box but once you do that again, I'm going to put right inside of cell input. I'm going to click the green cell for me it's B37 then I'm going to hit OK. And when I do that, watch what happens, the table gets filled in quite nicely. I have to format it and let it know that I wanted it be some numbers. Let's get rid of the decimals. And I have the different profits at all these different prices. And if you scan the table you can start to see it goes up and then you can start to see it actually goes down to make this even more visible to make this even more clear. Let's just show you that the numbers go up and they go down. I'll highlight my table and I will insert a scatter plot to show you the numbers go up and then they kind of start to decrease. It's not as obvious that they do. If we kept going on the table, this would be a little more exaggerated. Show you, let's see if I can do this here. If I put in 800 add these values in the chart. I'm just going to add a couple more values to show you what I'm after. So when I do add a few more values here at the high end, I'm just doing this to show you the point. It does go up and then it clearly goes down a little bit. So I added these numbers just show you there's some sweet spot somewhere around, I don't know 500, 550 where revenue is in fact maximized. In this course, I'll show you how to find this number exactly. Right now we're just kind of estimating it to get it pretty close based on these one and two way tables. The last thing I want to do here is sort of actually answer the question. Remin yourself the question. Assuming the unit cost of producing a set of clubs is $250 and the price must be a multiple of 10, what price should the company charge to maximize - there it is to maximize its profit? So here we can scan the list and see which value is the largest. One more just to sort of put the bow on top here, let's highlight all the values. Let's go to the home tab. Let's add conditional formatting, highlight cell rules and let's do, let's have it equal to the maximum value of my entire table. Red is usually negative so I'll change it to green and I'll hit OK, so you can do conditional formatting with cell values and this would be my maximum, it's automatically highlighting for me the largest value. It's just there to call it out. So the answer to part A, we would sell - this is again the manager's choice here. We would sell at a price of $530 for a profit of 1.042213. Now this is oddly specific and again you can imagine some rounding errors here, but about $1 million. This would maximize our profit. Again, this answer is only as good as the model behind it. And we did a little bit of analysis in the beginning to really say why this is the right model to use. All right, let's look at the second question. The second question says, how does the optimal price depend on the unit cost of producing a set of clubs? So remember all of this is based on our unit cost of 250. So let's say you get an email or a letter from the manufacturing and saying that they're increasing their cost as a manager, you want to be prepared for this. So now all of a sudden, this number is in play as well. And so as the cost changes, what is the best price that we should sell the clubs for? When two numbers are in play you're not going to do a one way table anymore. Let's do - where can we fit this? Down at the bottom here. Let's do a two way table and we're going to play around with both the price values multiples of 10. Why don't I grab this large table again? Let's grab all these values - where should I put it? Maybe I'll just put it right below it. I'll grab all the values here. Remember how a two way table works? Let's do price on the left and then we can do our unit cost on the right. Our current cost is at $250. Again, no I don't know what the increments are going to be. It wasn't given, so let's just guesstimate. We'll say we'll go up by 50 so 250. 300 then we'll go up to like 550. Again, you can expand or change these numbers as you want. In any one way or two way table you pick the header values. So here's the unit cost. So the first prior one was only for 250. In that sort of blank cell right above and to the left of your headers this is your ghost cell. This is what we want to fill in. So here we're going to fill in the profit This is a number that Excel needs but we don't so I like to gray it out. We can then merge to make this a little more readable of our headers so we'll merge the unit cost across the top and we will merge down on the left, our price. I then highlight all the numbers, do not include the text headers, and then I go to data and then what if analysis and data table. The same box as before pops up. I know it's not showing on the screen, you have your row inputs. So this is like row across the top where this where is this row of inputs going? This is your cost. So in that cell is asking where in your model is your unit cost? So for me it's B36 and then the column input cell, this is your price and that for me would be B37. So you hit both of those, you hit enter and all the numbers get filled in automatically. This is very nice. Now let's format this to be actual dollar signs. If you get those hashtags that just means the column's too small. Just widen the column. And what I'd like to do is sort of do this conditional formatting one at a time. Notice, So maybe leave all these numbers here. It's a big table. But what would I do here? If I highlight the entire first row, I can put on conditional formatting and use my highlighting cell rules and make it equal to the max, and I'll highlight the exact same row again. Red is usually bad. Green is good so I'll change the color to green. And just to show you that it's working as well for the two way table. When the cost is 250. My profit is maximized at $530. But now you have even more information. If the unit price goes up to 300, let's add conditional formatting to the second column, then this would be let's do equals max and let's highlight the rows one more time. Close the parentheses and then fill it with Green Tech and as a manager now we're done. Now unfortunately you can't drag the conditional formatting over. So if you wanted to do this conditional formatting, you have to do it for each one. It's a little annoying. If someone knows a shortcut, please let me know. But this says the price now to be maximize our profit will be less. That makes sense because our unit cost is going up. We would maximize that. But our price that we want to sell it at is now not $530 but 600. And this table you can go through and read it off for different values and you can play with different scenarios as you go through. So excellent use here of a one way table and a two way table. Last but not least the question that sort of takes a step back and says, is the model an accurate accurate representation of reality? Again, a little bit open ended question. But I'd like to ask are these numbers reasonable to get, would you know different demand at different prices? Probably yes. If you had large stores across and we're changing prices up in some more expensive cities, you can charge more for things. So that data is probably reasonable. And then going through this, we did linear, power, and exponential. Is there a better model that's out there? Do you know a better way to do this? Could you get a more accurate description? A more accurate representation of this relationship between price and demand? Something to think about. Could you make this better? I like what we have so far. I think it looks nice. I think it's working, we can defend this our choices along the way and we certainly have price points for different values of unit costs. So a very functional model. If there's anything now, I might just clean this up, use multiple tabs and make this a little more reasonable. It's getting a little long and sort of unwieldy. But other than purely cosmetic and readability, it is working nicely. And we have solved the problem of the 19th hole. All right, great job on this example. We'll see you next time.
