[MUSIC] Let us start from exactly where we ended at module two. Okay? So, this is the problem that you're working with in the final assignment of module two. It's a problem that describes the situation that many real world companies may face. The specific situation here is that the company has to decide whether to speed up the collection of accounts receivable or not. Okay? So you have the data on annual sales currently the company receives 80% immediately. Okay? And 20% after one year and the firm has the choice to move to 90% immediate collections. So you get 90% of the cash immediately. Right? But then the cost is that, if the firm does that, sales are going to go down by 2%. Okay? So that was the nature of the problem. And in the final assignment of module two you worked with these numbers to derive these cash flows, the cash flows for both collection systems. So those are the values of cash flows that are coming in the firm in both cases. Okay? So, in the existing system you get 800 today. Right? It's 80% of sales and then you get the full amount next year and the year after, which is 1 billion. Okay? If you move to the new system you're gonna get 882 today but the cost is that sales are going to go down. Right? So your sales go down to 980. Right? If you need to recap this calculation please go to the final assignment of module two. You can find a video where I explain that. You can look up your work as well. Okay? But this is the situation. Right? And you can see it in the numbers the trade off that the firm faces. Right? If you move in to a quicker collection you're gonna get cash earlier. Right? The amount of cash that you get today increases. Okay? But your sales goes down. Right? This is the fundamental trade off that we talked about when we were talking about working capital investments like receivables and inventory. Right? Increasing receivables, is likely to increase sales because customers like, they will appreciate having time to pay for the goods, but it costs the company terms of time to receive cash. So it ties up cash, cash takes longer to come in. Okay, so now we have these numbers. Our job is going to be to develop tools that are going to allow the company to really make a decision on whether they should change the collection system or not. Okay. To do that, we have to introduce this very important idea which is the idea of incremental cash flow. Okay. The way that I like to think about incremental cash flow is extremely simple. Okay. It really is the idea of new minus old. Any time a company has to make a decision on an investment the relevant cash flows that we're going to consider are new minus old. So whatever the new system is minus the old system. The new product minus the old product if there is one. Okay? So these ideas you're going to see as we progress, it's a very, very general idea. So remember this concept, new minus old. Okay? Let's apply it here to our receivables example. Right? So you have the old system that cash flows in the existing system, that's the old. Okay? And then you have the cash flows in the new systems, that's the new. Right? So the idea of incremental is just to do new minus old. Right? It's pretty simple here. Right? So the incremental cash flows are going to be $82 million today. Right? It's 882 minus 800. And then starting tomorrow, next year, and the year after. Right? You're going to lose $20 million. Right? So look at these numbers, think about them for a while. Right? It seems, just by looking at these numbers, it seems the new system looks quite attractive. Right? You're getting $82 million, and you're just losing 20 million. Right? So, it seems good. The problem, as we're going to see next, is that something is missing. Okay? Remember what we've been talking about. We talked about this idea in module one for example. Every time a company makes a decision, you have to think about all the consequences. It's not just today. It's not just current profit. It's not just current cash flows, you have to think about every consequence, every cash flow. Right? To value a form for example, to find the stock price, you have to think about all the future cash flows. So really, what is missing here is the future. Okay? Future cash flows, what is going to happen in the future. Right? And if you think about this problem, if you look at your assignment solution, it's very easy to see that what will happen is that the same situation is going to repeat itself. Every year the same situation is going to happen over and over again in the existing system. Right? What happens is you sell a 1000 or a billion here. Right? Collect $800 million immediately and then you collect the receivables from last period. Which are equal to 200 million, so you're total collection is 1 billion every year. With the new system you sell 980, collect 882 immediately and then you collect the receivables from last period. Okay, which are equal to 98, so you're going to get $980 million every year. And this is going to go on. Right? The way we're going to write this down is as a timeline. Okay? I like to think of this sequence of cash flows as a timeline. And let me go over here to show you something important. Okay? Notice that here we have three dots. Okay, these three dots here at the end. Okay? What these three dots are going to mean in this timeline is that these cash flows are going to go on into the future. Okay? So these go on and on. Okay? This is what these three dots mean, and then these three dots are going to show up in other problems as well. Okay? When we write the timeline, we may not write today, next year, year after. A simpler way of writing this is with numbers. You can represent today by writing a zero, next year you write a one, year after you write two, year after you write three, and then it goes on. Okay? The advantage of doing this with numbers is that, you can work with timelines even if the lumps of the period here is not a year, you can still work with timelines. Right? So example if this is a month, if cash flows happens every month you can still represent cash flows using a timeline. Okay? Except that in that case the length of the period is going to be one month. If you recall model two when we worked on our inventory management problem, we already had a timeline in that case the timeline was represented in quarters. Right? Because the problems there is that the company had to have the inventory in place a quarter before the goods were sold. Okay? So this is the idea of a timeline. Every time we work with these corporate decision problems we're gonna try to calculate incremental cash flows and then express, and then write them down in a timeline. Okay? So here's the timeline that we just talked about. Okay? Zero, one, two, three, and then the little, the three dots. Okay? And now we have the numbers, we have all the numbers here. Right? You can see, you can express the trade off we're thinking about in numbers. So to speed up the collection payment, the collection of receivables, you're gonna get $82 million today, and then you're gonna lose $20 millions every year starting next year. Okay? So what should the company do? Just by looking at these numbers now it's not obvious. Right? Now it's not obvious because this $20 million is going to go on and on. So is that good or bad for the company? Right? Is that gonna be better? Is it better to receive the $82 million today and then lose $20 million every year, or is it better not to do anything and keep the old collection system? To answer this question, we're going to have to develop the concept of Net Present Value. The reason I love this example is that it really shows you why we need to define, to think about net present value to answer questions about corporate decisions. Okay? We are missing this concept. That's where we are going next. We are going to develop the concept of net present value and then we are going to use the concept of net present value to answer this question. Should the company do it or not?