Hi, in this lecture, we are going to learn another popular capital budgeting technique, the payback period. First of all, the definition of the payback period is as follows. It's the length of time, which is usually measured in years it takes to recover the initial cost of an investment from its expected cash flows. If you have invest in a project, one of your biggest concerns will be about how soon will be able to get paid back. The payback period is the right tool to answer that question. The payback period could be a very sensible decision, especially when you have liquidity constrain. As a start up, your company would face lots of promising investment opportunities, but you might not have enough resources to finance the project. In that case, you might want to make sure to undertake a project with a short payback period. So, how do we calculate the payback period of a business product? Unfortunately, there is no easy way of calculating it. We do not have a formula to rely on and the calculation of the payback period is sometimes time-consuming even if we use Excel. You'd remember the example project with which we did an exercise on calculating NPV in the previous lecture. Using the same example, we'll learn how to calculate the payback period in Excel manually. In this project, the initial outlay was $1,000. That means for this project, the payback period question becomes how long will it take for the project to recover the initial cost of $1,000? Do we get paid back in year one? No, we had the cash inflow of only 120 in year 1. How about in year two? Do we get paid back by year two? No, by that time, we would have the total cash inflow of only $400. Why 400? Because we had 120 in year 1 and then additional 280 in year 2. Now, you realize that what matters each year is the cumulative cash inflow by that year. So, why don't we calculate the year by year cumulative cash inflows starting from year one in row six? Since we want to get the sum of multiple cash flows, we'll use the sum function here. For example, if you want to calculate the cumulative cash flow in year three, you get the sum of the numbers in cells from D5 to F5. Similarly, if you want to calculate the cumulative cash flow in year four, you get the sum of the numbers in sales from D5 to G5. In fact, we can fill out all cells in row six quite easily if we enter the following formula in cell B6 and copy it to the rest of the cells in the same row. Note that I have frozen the beginning cell, D5 using the absolute reference. Since I did not freeze the ending cell as I copy to the right, the ending cell in some function will change while the beginning cell will be always fixed at cell D5 which is what we need for the cumulative cash flow calculation. So, just copy the formula in cell D6 to the right and we get year by year cumulative cash flows. Now we can see that we do not get paid back by year three, but we do get paid back by year four. Here, we can just roughly say that the payback period of the project is somewhere between three years and four years. However, sometimes we might need to calculate the exact payment period of the project. The first step in that calculation is to find out how much cash inflow we need exactly in year four, if the payment period is between three years and four years. We have collected $760 by the end of year three and our goal is still to collect $1,000, then we can measure the difference between the absolute value of the initial investment and the cumulative cash inflow by the end of the previous year. If we get a cash flow of just $240 more in year four, we finally achieve our goal. And from those 2 highlighted numbers, we learn that it would not take a full year for us to collect 240 in year 4 when the cash inflow in that year is 600, then how long will it take to recover 240 in year 4? Well, to answer this, we need to make an assumption which is a reasonable one. In my opinion, that the annual cash flow of $600 will be evenly distributed throughout the year, then we could argue that it'll take 240 divided by 600 year in year 4 to collect $240. That is 0.4 year in year 4. Now we have calculated the exact payment period of this project which is the sum of 3 and 0.4, which we just calculated for year 4. Please don't forget the first three years it took to recover $760. The payback period of this project is 3.4 years. Depending on the situation, sometimes it'll be better to know the exact the number instead of just having a range, such as between three years and four years. And now, it is time to learn how to make a decision using the payback period rule. The rule for the payback is that we accept the project, if the payback period is shorter than some preset limit. It means that different companies will use different cutoff periods for the payback rule. If you, who are the top management of the company believe that your company cannot accept the project with a payback period longer than five years, for example, the cutoff period becomes five years. Let's assume that your company has set the cutoff of 3.5 years for the project in the previous example. Do we accept the project? Yes, because the payback period of the project, 3.4 years is shorter than the company's cutoff of 3.5 years. Please note that we had to know the exact payback period in this case to make a decision using the payback period rule. Based on the three questions for good capital budgeting techniques, let's see whether the payback period is a good capital budgeting decision rule. First, does the rule consider the time value of money? The answer is no. If you remember, we did not discount future cash inflows while calculating the payback period in the previous example. Second, does the rule adjust for risk? The answer is no, because we haven't used the discount rate at all which reflects the risk of the project. Finally, does the rule let us know whether the project creates value for the firm? It's no again. The payback period lets us know the length of time it takes to payback, but doesn't tell us about the value of the project. Despite those weaknesses, the payback period rule is still one of the most popular capital budgeting techniques in practice. Here are some advantages of the payback period rule. First, it's easier to calculate the payback period. Of course, it took longer for us to calculate the payback period in Excel today than to calculate NPV, but the point here is that when we calculate the payback period, we do not have the estimate the appropriate discount rate for the project. Estimating the discount rate is a very tricky and sophisticated process in practice, but we do not need to deal with it if we use the payback period rule. Second, as managing at the beginning, the payback period rule appreciates liquidity. Perhaps this is why the rule is more popular among small firms, which usually suffer from financial constraints than among large firms. In the next lecture, we'll learn the last capital budgeting technique in this course, the internal rate of return.