For this section, we're going to be looking at ratios and percentages as with the other sections in this series. The goal here is to get you familiar with the techniques and the tools and to show you ways that these techniques and tools are going to used across the MBA curriculum, for whatever school you are going to be going to. The truth is that ratios and percentages come into play almost immediately as soon as you start any MBA program. People don't often say, "We're going to take a percentage," or "We are going take a ratio," what have you. What they do is they start talking about margins. So they say this is what the profit margin is or they might say, "Well, this company carries 20 percent EBITDA. Okay, those are the key words when we're talking about percentages, and it's a ratio of one number to another number. This is used in economics and finance when people are talking about elasticities. This is used in accounting quite a bit when you're deconstructing what's going on in spreadsheet, income statement or balance sheet or what have you. If you're doing some forensic accounting, doing a deep dive or cost accounting, we try to understand where's that costs coming from, what percentage are fixed, what percentage or variable. You need to be really comfortable with percentages. It's going to hit you almost immediately as soon as you start the program. So let's look at some of these things and get your good headstart you will. Okay. So the first thing about percentages here is that the idea is really straightforward, and the truth is that we've engaged in percentages, you've likely engaged in percentages on a regular basis. So a percentage of anything is really just some fraction of that thing related to the whole. So whatever it is that we're looking at, whatever this thing happens to be as a fraction of the whole thing. So if you say what percentage of my income am I spending on my housing? Okay, so if you've got a $2,000 rent here and you have an income of $10,000 monthly, then what happens is you've got a percentage of 0.20 or you might just say that's just 20 percent. Okay, she might say, "Okay, I'm spending 20 percent of my income on housing in this situation." Other times when we're looking at percentages, we're looking at, let's say a percentage change. In that case, what we have is something a little more like this. We say, "Oh, my boss just gave me a eight percent raise." So, "Oh, that's terrific. What just happened?" Well, that's a percentage change. So for percentage change, slightly different calculation, we draw this little Delta in here, percentage change. The Delta represents the change. That is the difference between a new value and the old value as a ratio of the old value. So if we're talking about an increase in your wages, what we would do is we'd say what is your new wage minus your old wage as a ratio of your old wage, right there. So what we have here is new minus old over old or new minus original over original. Sometimes I will say 2 minus 1 over 1. So if we're talking about a percentage change in quantity, new quantity, original quantity as a ratio of original quantity. You can calculate percentage changes little fancy, but with some algebraic manipulation. This ends up becoming this, W_n over W_o minus 1. That will also tell you your percentage change. Sometimes we might think about this as a return. So very simple return on investment. Again, these are the keywords that you should be listening for when it comes to looking at percentage changes. So somebody might be referring to and investment and saying, "Oh, what's the ROI on this? What's the return on investment?" What they're asking about is the percentage change. So what is your original value that you put into this investment and how much did you sell this thing for, so the very simple ROI would be new minus old as a ratio of old. You say, "Oh, I put 10,000 into this investments, we sold it for 12, and so the difference between 12 and 10 as a ratio of 10, so it's 2,000 as ratio of 10,000. So our investment, we have a 20 percent ROI, which is a very simple return. In other sections, we're going to be looking at, let's say, the change in stock prices and the return on a stock or the return on a portfolio. So in those cases, you will have this situation right here, you would say, "Okay, what is my portfolio value now?" Portfolio value now, minus the portfolio value when I purchased it, original, all over the portfolio value original. This is a very simple ROI, it doesn't take into account things like the opportunity cost or the time value of money. But still may give you a very good idea about what we have now, what we put into it, and what its return is. So this is a percentage change here. I will write that again one more time so that you see clearly. This would be a percentage change, we might also refer to this as a ROI or Return on Investment or a simple return. Let's do one more exercise to make sure that you're really comfortable with this. I think you are. Let's suppose that I bought an asset, I bought a painting for $12,000, and I sold it for $8,000. Can you actually sell an asset for less than you bought it for? Sure you can. So here we go. What was my percentage change on this investment? Let's look. So my new value is 8,000, we leave the zeros off this. My old value is 12,000 as a ratio of my old value, 12,000. So we have got negative 4 divided by 12 gives me negative 0.333 or negative 33.3 percent. Is it possible that your asset can have a negative 33 percent change, percentage change? Sure. I mean, I hope that doesn't happen, but sure it can. So when you're doing percentage changes, it's important to just follow a very simple formula and don't get caught up in the fact that you can or can't have a negative number because you can. I see this in my MBA students not too frequently, but every once in awhile where somebody will say, "Look, I don't like subtracting 12 from eight, that gives me a negative number. So I'd rather just say 12 minus 8 is ratio of 12." Well, that's very nice, but you're going to get something wrong. It's possible that you sell your portfolio for less than you purchased it for, and so you have a negative return. This happens, it happens frequently. So you have to be aware of it. Don't be caught off guard with the fact that you might have to subtract a smaller number from a larger number and you end up with a negative percentage change, because that's going to happen. So let's look at these two formulas one more time for just like my percentage. What I have is I've got my focus as a ratio of the entirety. So whatever I'm looking at here as a ratio of my whole. So it could be the question it comes up I worked for a manufacturing company and the company says I wonder what percentage our manufacturing costs, raw materials are as a ratio of our entire costs. So in this case, the numerator would be like your manufacturing expenses. So whatever you're manufacturing expenses are here as a ratio of your total expenses here. Let me show this to you on a spreadsheet as well. The other formula we have is looking at a percentage change, and so in this case, we might say what if we were looking at, I wonder how our manufacturing expenses were changing over time. In this case, what you'll want to do is you would look at manufacturing expenses from period two here, the new manufacturing expenses minus your old manufacturing expenses as a ratio of your old manufacturing expenses. What this would do is this would tell you how is your manufacturing expenses changing over time. One is a percentage, one of them is a percentage change. The second one I wanted to make sure that you are very comfortable with the fact that you might be subtracting a smaller number from a larger number and your percentage change might end up as negative. So don't get freaked out, plug-in the numbers as they should be plugged in. If it ends up being negative, then you just know that you might be moving in the wrong direction. So if your wages are changing in a negative direction, very sorry about that. That's probably why you're going to get an MBA, if your expenses are changing in the negative direction, that can be a really good thing. So don't get freaked out about the fact that it might be negative. Follow the rules that I have put down here and do the calculations. Let's do a couple of specific examples that are going to be relating quite nicely to your MBA programs.