[SOUND] [MUSIC] The next real option we're gonna talk about is the option to wait. The option to wait comes from the idea that companies in some cases will have the option, the benefit of waiting for more information before you commit cash to a project. So it might make sense in some cases, rather than investing in a positive NPV project today, waiting a bit longer, getting more information to make sure that the project truly is positive NPV, or whether there is a better alternative. So we will illustrate this option with a specific example of a gold mine, which is a classic example of an option to wait. And we're gonna get numbers and all that, okay? These are the numbers that we're going to use. So you own the rights, so there is a monopoly, which is something I'm gonna talk about later. You own the rights to operate a gold mine for three years, okay? And there is a certain cost to open the mine, and if you open the mine, you can extract a number of ounces of gold. Here we have 1,000 ounces, okay? And let's assume, this is something I'm gonna talk about at the end, let's assume that this investment is irreversible to begin with, okay? So once the mine is open you have to keep it open until the end of the three years, okay? Let's say that the current gold price is 500 an ounce, and each year there is a chance that the gold price is going to go up or down. This is where the value to wait is going to come from. In some cases it may make some sense for us to wait and to get more information on what the price of gold is, okay? There is an extraction cost of 460. No fixed cost of opening the mine, so all costs are variable. So other assumptions about discount rates, okay? We are going to assume for simplicity that cash flows happen at the beginning of the year. So the moment you open the mine, you can already extract the gold and sell it. This is not realistic, but we really don't have to deal with this issue here, it's simpler to do the problem this way, okay? So for example, if you open the mine today, you're going to get the 1,000 ounces immediately, and then sell it in the market, okay? So you get your profit immediately, okay? The question we're gonna try to answer is should you open the mine today or should you wait one year to get more information on the price of gold? And again the way we're going to do this is by building a decision tree. Like as we did with the R and D, we're going to go here and think about a decision tree. In this case the decision tree is going to be based on the price of gold. Okay, so gold starts today at $500 an ounce, and we have an expectation that the price could move up or down with an equal probability, okay? And we are thinking of I know we're thinking of a two year horizon for this problem right? The mine keeps open for 3 years but remember our assumption that we extract the gold today. So 2 years ahead, the price of the gold 2 years ahead is going to determine the profit that you're making in year 3. Okay, so that's why we have it like that. So, the price could go up to 600 or it could go down to 400. And naturally, the profitability of the mine is going to depend on the price of gold, okay. This is what's going to make this problem interesting, okay. Before we do the calculations, it's very important to understand, that we understand the problem. Okay, what is the trade-off, right? As with other net present value problems, it is essential for us to understand the nature of the problem. Before we get into calculations, and start throwing out numbers, let's try to understand what's going on. So here is what happens, right? So if you open now, okay? Gold price is currently 500, so you're gonna be profitable, okay? Remember that the cost of extraction is 460. If the gold price goes down, right? And you have decided to open the mine now, you're gonna make a loss, okay? On the other hand, right, if you wait, if you don't open the mine today you are essentially giving up the current profit. So, you say, okay, I'm gonna wait. I know that by doing that I am giving up on the current profit. The benefit here is the main benefit. The main benefit is that if you decide to wait, you can avoid this state of the world where the gold price is low and the mine becomes unprofitable. So you're essentially opening the mine only if you know that the mine is gonna be profitable, okay? So that is the tradeoff that we have to think about, and try to put numbers on, okay? In terms of calculations, this is what we're gonna do to try to solve this problem, okay? What I want us to do, is to build a profit tree from the tree with the gold prices. So today, if we open the mine, we're gonna make a profit. The profit's gonna turn out to be 40. I will show you the calculations in a second. And then, of course, the profit's gonna go up or down depending on where we are, right? If the gold price goes down, then there's gonna be a loss next year. If you're gonna be making an annual loss of a 10,000, okay? And then I also here, right, you're gonna be making a loss of 60,000 if you decide to open the mine today and keep it open, right? Then you're gonna be making a large loss in year 3 by operating your mine. And remember, the investment is irreversible, so you cannot close the mine. We'll talk about that later. Just to give a couple examples here where we got those numbers. I know that's always a question that I get when I teach this, okay? So right, if you open the mine today, the profit is 40,000 cuz you extract 1,000 ounces and you make a profit of $40 per ounce, okay. If the gold price goes down to 450, then you're making a loss of 10,000 cuz your margin goes down to minus 10, okay. So very simple calculation really, okay? So what is the NPV of opening today, right? if you go back to the profit 3 and look at the numbers this is what's gonna happen, okay. If you open today you pay the opening cost which is -70 and then you get the profit of 40. Okay, and then we have to take the probability into account right? A year from now, you could either be making a large profit of 90, or you could be making a loss of -10. So this calculation is taking the probabilities into account in the same way that we included the probability of the drug being successful, when we did the R and D calculation. So there is a 50% chance of 90, 50% chance of 10 and then we discount using the 5% discount rate. And here we have the year 2, there is a 25% chance of a very high profit, that's what you want, right? But then there is also 25% chance of a negative profit of -60, okay? So, we discounted by 2 periods, right, because you're two years ahead. And if you do all of these calculations, you're gonna get an NPV of 44,367, okay? Make sure you understand this calculation. This is the standard NPV calculation, but it has these probabilities, right? So for example, you can ask yourself, do I really understand this probability? Right, so why is the probability of the 140K profit equal to 25%, right? The reason, of course, is because to get to 140, you need two up moves, right? You need the gold price to go up next year and then to go up again two years from now. Each move has a 50% chance, okay? So make sure you understand this calculation. And here's a question for you. It's very useful that you try to build a decision tree yourself rather than just looking at mine. Now I want you to think about the waiting option, okay? Let us think about what happens if we decide to wait. What does the profit tree look like in that case? Here's the answer, okay? Remember, if you don't open today, right, you're essentially giving up today's profit, okay. So you're gonna get 0 instead of 40, right? The benefit is that, remember, this state of the world here in the bottom was a loss state. The gold price went down. The company was losing money, okay. If you decide to wait until tomorrow, then you are essentially avoiding this loss. And going forward to period 2, to the third year of extraction, again you are getting 0, okay? Here this state was very bad cuz the gold price is too low. But, you can avoid that by waiting a year. You only open the mine if the mine is profitable. So, essentially you are guaranteeing that the mine is gonna be profitable by waiting a year, okay. That's how the profit tree should like and I hope you are able to get these numbers correctly. If not, try to think about what you've done wrong, okay cuz that's an important skill to be able to view this profit tree yourself, okay. Given these three, computing the NPV should be easy, right? We can even think about it here. So you're gonna open the mine tomorrow, right? So you're gonna pay the 70K here, and get a profit of 90, okay? And then you get these additional profits 2 years from now. If the gold price goes down you'll essentially get 0, okay? So this is what the NPV of waiting looks like. There is a 50% chance of opening the mine, okay? That happens one year from now and you get a profit of 20, okay? Cuz it's 90- 70, and then we take into account the probabilities that you're going to end up in the high gold price state, right? 25% chance of being 140, 25% chance of the profit being 40. You discount that 2 years and you get an NPV. The NPV in this case is 50,340, okay. So let's think about the decision, right. So we computed the NPV of opening now is 44,367, right. So the way I like to explain this is if you force the manager to make a decision today, if you tell the manager rule. You either open today or never, then yes, you should do it cuz the NPV is positive, right? But if you wait an extra year, then the NPV is even higher, okay? The NPV of waiting is 50,340, okay? So the right decision here is to wait. Opening the mine is a great investment, it's not bad. But waiting would be even better, okay? Nobody likes waiting, but in this case it turns out to be the optimal decision for this company, all right? Before we end, let's talk about a couple of ideas that are very important. The first one is that the value of the option to wait is going to depend on the amount of uncertainty that you have in the economy. In this case it's going to depend on the uncertainty on the price of gold, okay? So suppose if volatility is high, suppose we are in a case where gold prices are extremely volatile, right? What happens is that, fluctuations in the price of gold are going to cause very large profit gains and very large losses, okay. So in this case if you decide to wait and open the mine only tomorrow, you are essentially avoiding a very large loss, right? By waiting you can avoid the state of the world that the gold price is very low, and you're gonna be stuck with a very unprofitable mine, okay? So waiting eliminates this large loss, 0 looks great, right? If you're gonna lose money, 0 looks great, okay? The other issue that we're gonna talk about is that competition also matters. Remember from the very beginning we assumed that you have an exclusive right to open this mine. So you have a monopoly. In most cases companies do not have a monopoly. They may not have the ability to wait because competitors may decide to start similar projects. Let's think of this here in our decision tree. In many cases, companies are gonna be in a situation where if they decide to wait, they lose the profit today. But they may also lose profits tomorrow if the competitor decides to start a similar project. Then you're going to lose profits and the profit is gonna be low. The profit might have been higher if you had started today because that might deter the competitor from starting a similar project. So this is how we would think about the effect of the competition on the option to wait. So every time you're trying to value an option to wait, you have to consider whether the company really has the ability to wait and whether that would not be bad from a competitive stand point, right. Waiting in some cases may give an opportunity for competitors to come in and take your profits away.