[ Music ] >> Alright, why don't we get these lesson objectives started, and first on the countdown here is why discount? So when we talk about discounting, we're basically saying cash flows tomorrow are worth less than today. Okay? So that probably isn't controversial, but the key question is, how much less are they worth? Okay? So two issues come into play. One is the time value of money, and when we're thinking of, you know, time value of money, just think of inflation, okay? So, you know, we're in environment 2015 where inflation's, you know, pretty close to 0 in a lot of countries, but historically, that's not, not the norm. And then second, the riskiness of the cash flows, and that's really what investment finance is all about, determining, you know, what assets, what stocks are more risky than others, okay? And we'll develop the notions of what do we mean by risk throughout the course, okay? So, wow, Le Penseur, sculpture by Rodin, what's he, what's he doing here? Well whenever you see this slide, it means that a question, and an in-lecture question is about to appear, and when you see the question, I want you to do what's said in the title here, like pause, think about the question, and then answer it, okay? And then once you've given it the old college try, come back and you can see my response to the question. So let's see the first question I have prepared here. So let's start out, you know, pretty straightforward. You have $200 dollars, you're going to invest this for two years and you're getting an interest rate at 10 percent per year, it's paid out at the end of the year. So $200 dollars savings, 10 percent interest paid out at the end of the year, you're holding it for two years, what's going to be your balance at the end? What's going to be the future value? [ Silence ] Okay, hopefully you've had time to get it done, why don't we go over to the tablet and let's talk about this problem a bit. $200 dollars, 10 percent interest rate, held for two years, what's going to be our balance at the end of, at the end of two years? So first let's just have, introduce some, you know, kind of terms here, FV equals future value, PV equals present value, and the general formula to convert present value to future value and future value to present value is shown here. So if you have, let's, you know, kind of highlight this. You have your present value here, you basically, you have your present value, you just, you know, gross that up by whatever the return is to get to your future value. So in our context, our interest rate was 10 percent, we are grossing that up by two years, okay? To get to our future value. Now, later in the course, in Module 4, we'll be talking about valuing firms, so in that case you're doing the opposite. You're making estimates about future values of cash flows, then you need to discount them back to get a value today, but the question we asked here was a first one, alright? So let's look at, you know, what, what answer do we get, what answer do we get for that? So the future value of the correct response is $242 dollars, and it's interesting how that $242 dollars is broken down. So, three parts of it. $200 of the $240 dollars is just simply the principle. Okay? The simple interest, the 10 percent of $200, $20 dollars per year for two years, is $40 dollars. So that's a simple interest part given here, 2 times 10 percent times 200, okay? Then finally, the compound interest part. So this is the interest on interest. So for the 10 percent earned in year one, we get interest rate, or a return of 10 percent on that, that's 2 dollars of the $242, $242 dollars. So you might wonder, like, hey, why do I have this question of, you know, kind of $200 dollars, two years, 10 percent, well this is actually a question I'm very familiar with. A good friend, a colleague of mine here at the University of Illinois, Jeff Brown, and I did this as a survey question, where we asked, you know, respondents from the state university retirement system in Illinois, we asked them precisely this question. Okay? And we made a rookie mistake in doing this survey here as we provided a textbox for people to provide their responses. So it turned out 55 percent of the, of the, of the folks got the $242 dollar answer correct, but a lot of people wrote in the textbox, I hate math, I'm doing a survey, why is this turning into a math exam? So it really kind of highlighted, to me, that, you know, as a finance professor, you may take it for granted that everyone's like, you know, kind of a, a math whiz, but that's kind of really not the case, just like, hey, I'm not an exercise whiz as you can kind of, you know, kind of clearly, clearly see. And, in fact, if you look at, you know, kind of polling data, 40 percent of adults hate math, okay? They, in fact, that was a, you know, kind of most-hated subject, twice as much as the next most unpopular subject. Obviously going into finance myself, you know, math is probably my favorite subject, but that's not the norm, okay? Now when you see headlines like this, that really, you know, kind of illustrates the point, we hate math, say 4 in 10 Americans, a majority, okay? Well, you know, technically a majority should probably be 6 out of 10, not 4 out of 10, so this just, you know, kind of proves, proves the point of Americans not liking math and some of them, at least who are writing the headlines, not being very good, very good at it. Okay? But this is actually something that can come back to haunt you, like not being good with nutrition and exercise can come back to haunt you later on in health. Not being good at math can help you through, can hurt you with your financial decisions. Because what's one of the most important factors in finance? It's the power of compound interest. So let's go through a little example here to highlight how important compound interest is in terms of, you know, accumulation of wealth. So let's say you have $1,000 dollars to invest, so let's make this kind of like a practical problem here, like you want to set aside an extra $1,000 bucks. And you're going to do this for one year, two years, five, ten, twenty, thirty years, and again, let's keep this 10 percent rate of return per year. So over these various horizons, let's consider what will your final wealth be, how much of that wealth is original principle? Obviously it's $1,000 dollars. How much of that wealth is the simple interest? And how much of that wealth is the interest on interest? The compounding interest effect? Okay? So let's look at the composition of wealth here across these various time horizons and the breakdown of compound interest, and as you go here from left to, left to right, you can really see how this compounding effect takes hold. You may have heard the saying, you want your money to work for you, well that's exactly what's happening when you look at the 30-year investment horizon. So if you're only putting the money aside for two years, this 10 percent return, your dollar grows to a dollar twenty-one, of that dollar twenty-one, only one cent is compound interest, or I'm sorry, this is in thousands of dollars, so of the $1,210 dollars, you know, only, you know, $10 dollars of that is compound, is compound interest. How about if we go out to 30 years? Okay? Well there, $17,450 dollars is your accumulation, of that $17,000, over $13,000 of that is the interest on interest. So this is getting your money to work for you, this can work for a positive or a negative. This can work for a positive if you're saving for retirement and you start at age 35, look what happens when you're 65, this works as a negative if you're borrowing money, you have a credit card balance and you just pay the minimum, this compound interest here is basically, you know, kind of the interests that you're paying to, paying to the credit company. Ah, Le Penseur again. So you know what this means. Time for a question. Okay, and in fact, this time, I actually have a series of two questions back to back. So they're related. So let's start with the first one here. Question one, $50,000 dollars. So imagine you have some settlement where you're going to be paid $50,000 dollars three years from now, and you're up late at night and you see this commercial about a firm that will pay you money today for future settlements, and you want to know, are they giving you a good deal or not? Okay? Suppose interest rate is 2 percent, okay, so 2 percent interest rate, what does that mean the present value of that $50,000 dollars three years is, three years from now is, when interest rates are 2 percent? That's the first of the series of two questions. Okay, great! You got question one done, now let's kind of finish up the second question, what if interest rates change? They go up? Instead of them being at 2 percent, now they're at 5 percent. Okay? So what's the new present value of this $50,000 dollars that's paid out three years from now when interest rates are 5 percent? [Pause] Alright, so we have $50,000 dollars three years from now. And then interest rate, or, you know, later on we'll call this the discount rate, 2 percent, so 2 percent to the third, because we're getting this payment three years from now, $47,116 dollars. Okay? So, you know, the interest rates are very low, so money in the future is, you know, kind of worth pretty similar to what money, money today is, you know, or, in the, at least in this, this question. So now let's go to answer two here. So this kind of puts a new wrinkle on it. What if interest rates go up? Like at least in 2015, it's a low inflationary environment, there's a concern, will the Federal Reserve raise interest rates, what's going to happen to the value of this future income if interest rates go up 3 percentage points, from 2, 2 to 5? So let's, you know, solve, solve that here. Basically in this case, if the interest rate goes up, the value is going to go down. Okay, and then just, you know, kind of solving through here, $50,000 divided by 1.05, this money is coming three years from now and we get the interest payments at the end of the year, that's $43,192. So, you know, about $4,000 dollars less...than when interest rates were 2 percent. So, obviously, you could make a natural analogy to the value of stocks if the future cash flows are worth less, the value, you know, if the future cash flows are worth less, the stock price is less. So as interest rates are going up, future cash flows are less valuable, current values are going down.
