Hi. Welcome back to Finance for Non-Finance Professionals. This is the fourth lecture of week one. In the first three lectures, we talked about interest rates, compounding growing cash over time at those interest rates. In the third lecture, we talked about discounting, bringing those future values back into the present through discounting. What we're going to do now is use those first three lectures for our first real valuation tool, which is using discounted cash flows as the basis for all financial valuation that we do. When we think about discounted cash flows, or DCF like we call it in finance, it's a method of valuing an investment. We can put a value on almost anything using this method, using these kind of cash flows. We're going to think about what all the future cash coming in on an investment is and then we're going to think about using the present value technology that we talked about in lecture three to bring everything back into the present. Once we bring everything back into the present, that's going to give us a basis for forming prices and that price, that DCF, that valuation is going to form the basis of how we put values on things. Why do we investors buy different kinds of assets? If you think about all the things that you could do with your money today, you can buy real estate or stocks or bonds or any of the things that you could do with your money today. Why are you putting money into that investment? Why are you being patient with your money, like we talked about in the first lecture? You're being patient because you want to earn some rate of return on that money and use that money later. You're being patient. You're using real estate, stocks or bonds or any investment as a vehicle for getting the wealth that you have today into the future, and earning some rate of return for being patient. When you think about why you're doing that, when you think about what is it that you want to earn, what you want to have at the end of the day is cash. When you decide later on that you're going to retire, or you buy a retirement home, or you go on a cruise, whatever it is that you're going to do, what you're going to need to pay for, or all the things that you want to buy later is cash. So what we want to do is make a plan or a forecast of how much cash you're going to have coming in on an investment over time in the future. And then what we're going to do is discount those cash flows. How much cash is coming in? When does the cash come in? And with the answers to those two questions, we can put a value on anything, real estate, stocks, bonds, anything that you can think of. The most exotic derivative that you could think of, we can put a value on it by mapping out, forecasting the cash flows, discounting them back into the present, and then just adding up all those present values, discounted cash flows. Let's think about a really simple example of a bond, a contract between an issuer and a bondholder. The buyer of the bond is basically lending money to the issuer. He's saying, the bond issuer says hey, I need a bunch of money right now, I'll pay you back later when the bond comes due. The person that's buying the bond says okay, here, take my money for a little while, I'll be patient until you pay me back later. Basic idea of a bond. The issuer's going to pay an interest rate on a loan, and then when the loan comes due, they're going to pay back the principal at maturity. Let's think of a simple example. I've got a bond for $3,000, it's going to make annual payments of $250 for five years, and let's say the discount or interest rate is 7%. What's that bond worth? If we sold those bonds today, how much would we pay for them? We can actually answer that question now. What are the cash flows? When are they coming in? What are they worth today? Add them all up, that's the value of the bond. We can see that graphically, interestingly. I'll put a timeline out here with all of the cash on the bond. What we see here are five payments of $250 coming in, the first payment, second, third, fourth payment and then the fifth payment plus the repayment of principal $3,000. Those are all the payments and the timeline tells me when they're coming in. What do I need to do now? I just need to discount them, discount each of the cash flows back into the present. Take that first $250, discount it back today, the present, that gives me to $233.60. Take the second cash flow, smash down two periods, that gets me to $218.4. The third cash flow, the fourth cash flow, the fifth cash flow, discounting one over one plus R to the t each time as t goes 1 2 3 4 and 5. When are the cash coming in? That's the timeline. Discount each of them individually, bring them all back into the present and now you can see that all the numbers are lined up in the 0 column. Those are all present values. All I need to do now is sum up those present values, that gets me a total of $3,164. That's what the bond's worth. The bond's worth $3,164. That's the sum of the discounted cash flows. Now basic concept forms the conceptual framework for almost all the valuation we do in finance. It's that simple. You want to figure out how much cash is coming in the future, discount it into the present and add it up. The sum of the discounted cash flows forms the basis for all valuations in finance. That's how much the bond will be worth if we sold it today. Why would anyone pay more or less? If we know what the cash flows are, somebody would have to be using a different discount rate or have be more or less patient than you, but at that this can't rate the bond is worth $3,164. We could think stock evaluation the same way. If I had to share of General Electric that was trading on the New York Stock Exchange, what's the cash to shareholders? Maybe it's the stream of dividends. When are the dividends coming in? Stock analysts would forecast when and where those dividends are coming in and we would form a valuation for General Electric shares based on discounted cash flows. We could think about using that discounted cash flow framework for doing almost anything. In fact, that's would stock analyst on Wall Street do, is they come up with forecasts for how much money is coming on various stocks and then use DCF to form the basis for their stock recommendations. We could apply that principle to real estate, mergers and acquisitions, derivatives. We could do it for just about anything that's got a cash flow on it, that's coming in the different times, we can use DCF, discounted cash flow to form the basis for all financial valuation.