We now proceed. In the previous episode we saw that the introduction of monitoring allows us not only to finance a good project with the use of a fixed income contract namely lending. But also to make this lending quite efficient, we saved the amount of money that you received in a low state even if we cannot recover the whole amount of loan but still rebuild is become a part of that reduces the face. Now all that is great but what if now, this $6 million that we have to use for financing, cannot be raised from just one investor? Remember, that the key advancement the key idea was monitoring. So we said that $20,000, that is the cost of monitoring, is a small amount compared to this 6 million. That allowed us with this minor cost to save a significant expected cash flow of $1 million. But what if now we have small investors, let's say we have 60,000 investors, each investing $100 in the same project. Well, you can see that the big problem is that these small guys can not afford monitoring at the cost of $20,000, because it's much higher, way higher than this. And clearly the face value that they would have to charge, if the old monitor is huge. Now you can say, they do not have to monitor each of them but then we face the famous free rider problem. If just one monitors them, all others don't have to and as a result no one does. Well, clearly we seen the source of demand for an intermediary. Someone who comes accumulates these small amounts $100 in a pool of 6 million and then there's someone does monitoring at the cost of $20,000 and then brings back the whole setup that we had in the previous episode. So this someone should have a contract of a debt contract of liquidation with these small investors, because In order to prevent collusion, they have to somehow say, well you know, we have to be sure that you will pay our money back. And this is the old way to have the debt counter liquidation. But then this intermediary does monitor the borrower and by doing so that opens up some opportunity to probably make money. Now the key story here is that the intermediary will call this intermediary a bank from now on can raise more than $6 million. It can raise more money and can finance more than one borrower. And if profiles of states of these borrowers are not perfectly correlated, then this bank enjoys diversification. So we can see that now we can see that there is a bank and the bank enjoys diversification. Again, this is not exactly the same diversification that we will study in the next course of this specialization when we talk about portfolios and securities. This is just a way to reduce the probability of a poor outcome in which we lose money. And then this bank does delegated monitoring. Saving the situation when the bank monitors on behalf of all investors. Now I claim that under this set up, the bank can make money. In order to prove that or to demonstrate that if you will, what I will do on the next page of this flip chart, I will assume that now we have two projects with the same cash flow profiles, and the same probable of high and low states but those are independent. And then the bank with the cumulative money from 120,000 investors, each investing $100, and they will see that the setup, the bank will be able to make money. Well, let's see what picture we have here. Now we have two projects and they are independent. In the sense that I used before. So their outcomes occur independently one from the other. And now we have instead of just one dimension, we have two dimensions in the following picture. We have a matrix. So this is 0.80, and this is 0.20, and this is also 0.80, and this is 0.20. So this is a breakdown. So instead of just one line with 0.80 and 0.20, now we have a matrix 2 by 2 that has 4 areas. So this area, this is the case of high, high. That occurs with probability of 0.64 because it is 0.80 times 0.80. The fact that we multiply probabilities stems from the idea that projects are independent. Now this is, what? This is low high, right? Because it is low from the first part product of high and this occurs with probability with 0.16. This is high low, also probability of 0.16. And this is low, low the probability of 0.04. So probabilities here are the areas of these. If these are two squares, and these are two boxes, like this, if you will. Now let's see what happens to where the cash flows that arrive from both projects. In a high, high state we have how much? We have 15 plus 15, so we have 30. Here we have 15 from the high state plus 5. Again, we engage in monitoring, so this 5 is actually recognized, so this is 20. Clearly we have here also 15 plus 5, which is 20 and only in this small box we have output in red 5 plus 5 which is just $10 million. So these are the cash flows that are here. So what happens is now we see the pool of cash that arrives from these projects. What we have to do to proceed, we first have to realize what kind of contracts are realized between first, the bank and the borrowers. And second, the bank and investors. From now on, we will call these investors depositors, because they will deposit money with the bank. And we already said a few words, that the debt construct of liquidation is the only option for the contract between the depositors and the bank, because the depositors cannot monitor the bank. However, the contract between the bank and the borrowers will be the contract we have monitoring. So having seen all of that, we both see that from this set up. The bank can enjoy the situation in which not only is it feasible for the bank to finance both projects, but also the bank will be able to make a positive amount of money as a result.
