Hello, I'm Professor Brian Bushee and welcome back. In this video, we'll take a look at the one rule of grammar in the accounting language, the balance sheet equation. We'll see how the balance sheet equation makes all the financial statements fit together. We'll also use the balance sheet equation to solve some problems where we're missing one piece of information that we can fill in everything that we do know into the balance sheet equation and solve for what we need. Hope you enjoy the video. So if you've ever tried to learn a foreign language, you know that one of the most difficult things is learning all the rules of grammar, all the cases and declensions and the changes in verb endings, and all that stuff. Well, the good news about learning the language of accounting is that there's only one rule of grammar, the balance sheet equation or the accounting identity. This is that assets equal liabilities plus stockholders' equity at all points in time. Another way to say this, as we've talked about, is that the resources of the company equal to claims on those resources by the outsiders and by the owners. >> Can you give me an example of when this is used in the real-world? >> A good example to think about how we use the balance sheet equation in real life is when we buy something big like a house or a car. So let's say, we wanted to buy a $500,000 house, but we only $50,000 of cash. Well, we would need to go out and borrow $450,000 from the bank in a mortgage in order to buy the house. Then after we bought it, we'd have 500,000 in assets, the house which is equal to the 450,000 of liabilities, the mortgage plus 50,000 in equity, which is how much cash we put in, and which represents our claim on that house. The most important feature of the balance sheet equation is that it must always balance, and that's why we're going to talk about something called double-entry bookkeeping. If you increase something on one side of the equation, you have to increase or decrease something else to stay in balance. So there has to be at least two entries any time you tinker with the balance sheet equation. And as we'll see, the changes between two balance sheets are going to be summarized in the income statement, the statement of stockholders' equity, and the statement of cash flows. So, let me show you this graphically. So, let's say we have a balance sheet at the end of December 31, 2014. Assets equal liabilities plus stockholders' equity. We'll split the assets into cash, non-cash assets. And we'll split stockholders' equity into contributed capital and retained earnings which are concepts, we'll talk more about in later videos. Then we have a balance sheet at the end of the year. So we've got one at the beginning of 2015, at the end of 2015. The difference in the retained earnings is going to be explain in the income statement for the year ended December 31, 2015. And the difference in cash is going to be explain in the statement of cashflow for the year ended December 31, 2015. >> Here you go again with the difference between income and cash. Remind me, why are they different? >> Okay, let's go back to the house example. So let's say, on your first balance sheet at the beginning of the year, you have a $500,000 house which is your asset, $450,000 mortgage, which is your liability, and $50,000 of equity. Now let's say that during the year, the value of your house increases to $1 million. And I can't actually do this in practice but for the sake of the example, let's assume you could write up the value of the house from 500,000 to 1 million at the end of the year. So your balance sheet at the end of the year would have $1 million asset, the house, 450,000 of liabilities because the mortgage doesn't change. But your equity would go up from $50,000 to $550,000. Now, if we look at the statement that explains the changes in two balance sheet, none of these affects the cash flows statement because there's no cash impact of your house going upon value. In fact, your cash actually went down as you're paying in the mortgage. But your income statement would show a gain of $500,000 from the increase in your equity due to your ownership claim of the house. >> Housing prices going up? Can you give us a more contemporary example? >> Okay, so let's talk about what happened during the financial crisis of 2007, 2008, and 2009. There were banks out there that have assets called mortgage back securities. These are assets because their claims on collecting cash payments from people that took out subprime mortgages. So let's say, a bank had 10 billion of these mortgage back securities as assets. And let's say they had 9.5 billion of liabilities and half a billion of equity. Financial crises hits. These homeowners no longer make their mortgage payments, which means these assets drop in value. So now they have to be written down in value from 10 billion to, let's say, 1 billion. Now the liabilities don't change. In fact, that's why you need a government bailout because your liabilities don't change. But what does change is the equity. The equity drops by 9 billion as well. And so, it's another example where there's no cash flow impact of the change in these two balance sheets but we end up showing a $9 billion loss on our income statement due to the drop in our equity claims on those assets. Of course, we also have to mention the statement of stockholders' equity which to explains the changes in stockholders' equity between two balance sheets, which we will talk about more later in course. What I want to do next is show you how everything that we're going to talk about fits into this balance sheet equation. So we talked about how stockholders' equity is two components, contributed capital which is the money that we raise from shareholders and retained earnings which is what we create by operating the business. Retained earnings is going to equal whatever retained earnings were at the beginning of the period, plus any net income earned during the period minus any dividends paid out to shareholders. That's why it's called retained earnings because it's the earnings or net income less any dividends paid out. And then net income, as we talked about in a prior video, is revenues minus expenses. So if we put all of this into the balance sheet equation, we get one big, complete balance sheet equation, which is assets equal liabilities plus contributed capital, plus your prior retained earnings, plus revenues minus expenses, minus dividends that you pay during the period. >> Zut alors. Are you going to make us do some mathematics with this? >> Why, yes, I am going to ask you to do some math. Now, I'm going to give you some problems, give you a chance to try to answer the problems, and then we'll talk through the answers. After I read the problem, you'll see a little pause icon on the screen. If you want to try to answer the problem before I give you the answer, pause the video at this point. Try to come up with the answer and then resume the video. But if you want to just roll through and hear the answer right away, then it's okay to keep the video going. This is the beginning of the procedure that we follow anytime that I give you some questions that I want you to try to answer during the video lecture. Okay, here is the first one, assets = 100, liabilities = 50, what is stockholders' equity? We can solve this one with the balance sheet equation. We know that assets are 100, liabilities are 50. The only thing that's missing is stockholders' equity, which has to be 50. So that we have 100 on the left hand side and 100 on the right hand side. Next, liabilities increased by 100 and stockholders' equity is unchanged. What is the change in assets? Again, we can use the balance sheet equation to answer this, but now we're looking at changes in the numbers. So stockholders' equity is unchanged, liabilities go up by 100. The only way for the equation to stay in balance is for assets to also go up by 100. Next, all non-cash assets are 70, total liabilities are 60, total stockholders' equity is 30. What is cash? We can use the balance sheet equation for this one if we separate assets into cash and non-cash assets. So we have liabilities of 60 and stockholders' equity of 30, that's 90 on the right hand side. Non cash assets are 70. The only thing missing is cash which has to equal 20 so that we have 90 on each side. Next, cash decreases by 10 and all non-cash assets increase by 15. What is the change in liabilities? We can use the same equation but we have to be a little bit careful. We have cash going down by 10, non-cash assets going up by 15. We're looking for liabilities, but we don't know what happened with stockholders' equity. And because we don't know what happened in stockholders' equity, we actually don't have enough information to solve this. Now if we knew that stockholders' equity had not changed, then liabilities would have had to go up by 5 so that we have an increase in 5 on both sides of the equation. But without knowing what happened to stockholders' equity, we technically don't have enough information to answer this one. >> Come on. A trick question, really? >> Sorry about the trick question, but I promise that it won't be the last. Next, we have retained earnings increasing by 100, dividends are 50. What is net income? Earlier in the video, we look at the equation for retained earnings, where retained earnings is equal to prior retained earnings, but they were at the beginning of the year, plus net income during the period minus dividends. So we know that the change in net income, their change in retained earnings. Retained earnings minus prior retained earnings is 100. We know that dividends is 50. So the only thing missing is net income, which has to be 150 for this to balance. Next, we have revenue increasing by 100, all other categories are unchanged except assets. What is the change in assets? We have to use the complete balance sheet equation to solve this one, so that we break stockholders' equity into contributed capital, prior retained earnings, revenues, expenses, and dividends. So we know that revenues are going up by 100. Everything else is unchanged but assets, which means that assets also have to go up by 100 so that both sides of the equation increase by 100. Finally, expenses increase by 60 and all of the categories are unchanged except cash. What's the change in cash? Well again, use the complete balance sheet equation but now, we'll split assets, and the cash, and non-cash assets. So we know that expenses went up by 60, everything else is unchanged except for cash. Now notice on the right hand side of the equation, expenses going up by 60 means the right hand side goes down by 60, which means that cash also has to go down by 60 for us to stay in balance. >> I think I can do this. Can we do more math problems? >> Finally, some positive feedback. The purpose of this exercise was to preview the type of problem that you're going to be doing a lot in this course. There's going to be a certain piece of information that you need that you're not given. But, you can take all of the other information that you're given and a set of equations, which will usually be in the form of T accounts or journal entries. Fill in everything you know, and then solve for that one piece of information that you need, but you can't find in the finance statements. Wow, has it been 12 minutes already? Time sure flies when you're doing the balance sheet equation. So I'm going to go ahead and wrap up this video, and we'll come back next time and talk in more detail about assets, liabilities, and shareholders' equity. I'll see you then. >> See you next video.