Hi, everybody. Welcome to Startup Valuation class. There are two kinds of methods to find the value of your startup. The discounted cash flow method and multiple method. For the moment we are going to assume that you know the earnings of your startup. You're going to learn how to find the earnings of your startup later in this class. In this class, you are going to learn the discounted cash flow method, it is also called DCF in short. In order to understand the DCF method, you need to learn the concept of time value of money. Let me give you a simple example to understand the concept of time value of money. Suppose we invest $100 in a project that pays you $110 one year later. What is your return on investment? It is 10%. You can write the equation as $100 x (1 + 10%) = $110. In this equation, $100 is the present value of $110. 10% is the interest rate. And $110 is the future value of $100. You can rewrite the equation using these names, instead of the numbers. Present value x (1 + interest rate) = future value. Future value is FV in short. Present value is PV in short. Interest rate is just called rate in short. Then we can rewrite the equation as PV x (1+rate) = FV. Let's practice how to get future value using the following examples. Suppose you locate a one year investment opportunity that pays 15% per year. If you invest $400 today, how much will you have at the end of the one year? In order to use the FV formula you just learned, first you need to identify what PV is. PV is the amount of investment, so it is $400. Next, identify what rate is. Rate is the interest rate, so it is 15%. Now you can set up an equation that is FV = $400 x (1+15%) = $460. Therefore, you would have $460 at the end of the one year. Let's learn how to use Excel to find FV for the above equation. Why don't you download an Excel file called time value of money Excel template provided in this course. When you open the file, it should look like the one in this slide. In Excel template, there are five variables you can find, and each are highlighted. In order to start the question just mentioned in this class, we are going to use template for future value. Calculation of future value requires information about number of period, interest rate, present value, and period payment. First, we know that present value is $400. So type in 400 in the cell for PV as it is shown in this slide. Next, type in 15% for the rate as it is shown in the slide. Next, type in 1 for the NPER as it is shown in the slide. We will put 0 in for the PMT until we learn what PMT is later. The highlighted cell for FV shows -$460. It is same as we found using the mathematical formula except the sign. You may be wondering why FV is negative. It is because Excel assumes that a positive PV means that you're borrowing money. Therefore at the end of the period you have to pay back FV. If you want to receive positive FV, you must input a negative value for PV. Next, suppose you locate a 2 year investment that pays 15% per year. If you invest $400, how much will you have at the end of the 2 years? As you found in the previous question, the value of the investment a year later is $460. Now you need to invest $460 for 1 more year at 15% to find out how much you will have at the end of the two years. The equation would be FV = 460 x (1 + 15%) = $529. Therefore, you will have $529 at the end of the 2 years. In the previous solution $460 is the same as $400 x (1+15%). Therefore, we can also find FV at end of the 2 years by substituting $460 with $400 x (1+15%). That is FV = [$400 x ( 1 + 15%)] x (1 + 15%) = $400 x (1 + 15%) raised to the power of 2. As you can see in this example, we can make an equation to get FV at the end of n years as PV times 1 + rate raised to the power of n. Why don't you start Excel template and solve the question with Excel? As we did before, type in 400 for PV. Type in 15% for rate. Type in 2 for NPER since investment period is 2 years. Again PMT is 0. Then you see the future value is -529, which is the value of the investment in 2 years as $529. Now, let's apply what you just learned to solve the following question. Assume you deposited that $500 today in an account that pays 5% interest. How much will you have in two years? Let's solve this problem with the Excel template Type in 500 for PV. Type in 5% for rate. Type in 2 for NPER. Type in 0 for PMT. Then you see that FV is 551.25. That is what you have in 2 years is $551.25. Let's apply FV concept to find future dividend of Samsung corporation. Let's assume that Samsung's current dividend amount is $2 per share, which is expected to grow by 10% per year. What will be the amount of dividend of Samsung after three years? Let's solve this problem with the Excel template. Type in 2 for PV, since the current dividend amount is $2. Type in 10% for rate since the growth rate of dividend is 10%. Type in 3 for NPER since we are looking for a dividend in 3 years. Type in 0 for PMT. And you see that FV is 2.66. That is the expected dividend amount of Samsung is $2.66. I hope now you understand the concept of time value of money and how to calculate the future value.