In this episode, we will in greater detail analyze one of the problems caused by private information, mainly moral hazards. It takes a while to describe what it is in plain words. So what we will do because we sort of decided to use, and not only the approach, we'll start with a simple example, and analyzing this example, we will later make some generalizations. Well, let's assume that this world is organized in the following way. There is the high state of the world in the future, and then the low state. Both states occur with equal probability of one-half and there exists two projects. Project 1, project 1 has a cash flow of $20 million in high state and then 0 in the low state. And project 2 that I'll put in blue is different. In both cases, in the high and the low state, it has the cash flow of $12 million. And in order to invest in this project or to realize that we need 10 million. So basically, we invest $10 million then we get these cash flows with these probabilities. And now, the question is, which project will the project owner take? But let's say I am a company and I have these projects. Project 1 and project 2 and I have this choice. And the question is how we can study these choices. Well, let's start with the most simplistic case one, In which all of these funds are my own ones, own funds. So I take $10 million from my pocket. And then I think, which project, project 1 or project 2, for me, is better to take. In this case, based on our assumptions, we will make the decision based on NPV, so we take these cash flows as proxies for my expected. All right, we remember that the risk-free rate is 0. So instead of discounting, we just take future cash flows, multiply them by probabilities. And the expected cash flow for project 1 is, what, 20 by one-half or 0 by one-half, which is 10. We subtract 10 as the initial investment, so we can say that the NPV for project 1 is I put it detail in one. One-half times 20 plus one-half times 0 minus 10, which is 0. And with project 2, it's a little bit easier because we can use what we know with probability since it's the same. So basically, NPV2 is +2. So what we can see, first of all, the NPV of the second blue project is greater. It's positive and greater than the first one. Even more so, we can see that project 2 is riskless. Because regardless of the state of the world in the future, its cash flow is the same. So the choice is clear, we take project 2. And that conforms to all standard ways or criteria that people use in making their choice of projects. So far, we haven't found anything strange. We can say that clearly our choice is number two. But now, let's assume that we do not have this $10 million. We have to take some other people's money in the form of a bank loan. So I'll briefly put it here. So this is high, low 1, 2, 20, 0, just a reminder so that you don't have to go to the previous screen. Now so this is case 2A, in which I have to borrow, 7, so I have 3 of my own money and I have to borrow 7. And if, for example, I go to a bank and I tell the bank the story that I put on the previous flip chart, I can say, well, clearly project 2 is better. So I will take project 2. Why wouldn't you give me an interest-free loan? Because you know that the bank is risk neutral. So if the bank does get the money, get back exactly the same amount that the bank lends, then it's fine. Well, let's assume that F, which is the face of the loan of this. So the bank gives $7 million and then asks to pay back this F. Let's say that the bank, sort of doesn't think much, and says well, fine. What if F is 7? Now let's take a look what happens here. First of all, in all cases, I have to pay back the money that I owe to the bank. And then, if there is anything left, I have to subtract. I will put up here my own. Now $3 million and then on the basis of that, I will calculate my NPVs. See what happens. I will put here the cash flow that goes to me after the repayment of a loan. So here, how much will I get? I will get 20 minus 7, 13. Here 5, here 5, and here clearly 0. Now see what happens. Now my NPV1 is equal to, I have one-half probability times 13, which is 6.5. I subtract 3 and then it becomes +3.5, while clearly for the second project everything stays the same, and NPV is still +2. Now see what happens. Now for me, my residual cash flow is greater. And then my NPV goes up to 3.5, and I'm induced to take risky project number 1. Why did that happen? Where does this magic come from? Well, there is no magic, actually, because first of all, we can see that in this poor case, when there is nothing, the bank loses everything. And well, you can say, well, in reality banks they force you to pledge collateral. And in this case, the bank forecloses and then gets something, but in this simplistic model, there is no such an advance so far. We can see that this company, which owns this project, has limited liability. And if there indeed is a poor outcome, then we say, well, sorry about that, no cash to give anyone. And then indeed everyone loses money. But the idea is that if I take the risky project of the 10 million investment, only a smaller part is my own amount. And if it does arrive at a low state and there is no cash, then the biggest part of this investment, namely the 7, is lost by the bank. So I, as the project owner, have shifted the majority of responsibility to the other party. So this is a classic case of using other people's money. And in the case of non-observabilty, the bank knows that it cannot immediately force me to go back to what was on the previous flip chart and take project 2. And clearly what happens is that the bank does not get this money back. Because the bank gets 7 only in the high stake with probability one-half, so the bank loses money. Well, now the bank is not so stupid. And now we arrive at case 2B, in which the bank says, well, if I lend you $7 million, then most likely you will take project 1, and I will lose money. So if you take project 1 I have to raise the face value, so charge you some interest. Again, not the interest in the regular way when banks do charge interest, even for riskless projects. But in this case, banks charge interest only in order to compensate for these low state outcomes. Now we know that these probabilities are one-half. Again, I will remind you of that. And as a result, the bank thinks, well, if I give 7, then I have 2. How much do I have to charge? I have to charge 14, because in this case, the probability one-half, I will get back 14. And that's exactly my expected 7, all right? Let's put that F is now 14. Well, I will go to the next flip chart to make it easier. And again, this is going to be, I'll put it in red because this is an important case 2B. Now, F is 14. Now, see what happens with my cash flows. Again, I'll put it back, high, low, 20, 0 and this is project 1. And then 12 and 12, this is project 2. Now see what happens. Well, first of all, we can see is I cannot take project 2, because in both cases, I will not have enough money to pay back even the loan. So project 2 is effectively driven out of the market. Now, what happens to project 1? We can see that here I pay back 14. So I have only 6 remaining. And therefore what happens is that here it's clearly 0. I invested, let me remind you, the $3 million of my own money. So it's one-half times 6 and we go back, that NPV1 is equal to 0. So now if there is no observability there, the project owner has really poor choice either because the bank charges a lot of interest. Then I have to either try, then I take a risky project and my NPV goes down to 0. And my nice project 2, in which I would have profited if I had enough money of my own, then I cannot invest in that at all because I am positive not to be able to pay back the loan. So that is a problem, and a huge problem. So what can we do? We see that, if positive NPV, the riskless project gets driven out of the market, that, indeed, is a problem. And although, in the simplistic case it seems to be sort of a tail-like problem, but it is a huge problem in the real market. And therefore, what can be done? Well, number one is that if we restored absorbability, there will be no problem because the bank will say fine, I give you a riskless loan of 7, and with face value of 7. But I control that you take project 2. And in this case everyone will be happy. No one will lose money, and I will make money and the bank will be happy as well. Or the other way is to do something else and we will study that something else in the next episode. So that's called co-insurance because basically the bank says, if you would like to borrow a lot of money of this 10, and invest only a little fraction of your own money, then we'll likely do all right with this. However, if you invest more of your own money and ask for the remainder that is by farthese, then in this case I will indeed be able to lend you money without interest even without observability. That's called co-insurance. We will see in the next episode how this works. And it does work, and in many cases, it does result in the alleviation of the problem of moral hazard. So wrapping up here, we can say that moral hazard is actually the existence of certain incentives of a project owner to behave in a way that is sort of destroying for the value of the other party. So in this case, remember, in case 2A, that's what we have here. I shifted to project 1. And by doing so, I produced a potential damage for the bank. So in the presence of unobservability, moral hazard as we studied it here, is the situation in which one party behaves in a way that poses harmful for the other party. And starting the next episode we will see how we'll try to cope with that.
