[MUSIC] The final real option that we're going to talk about is the option to abandon an unprofitable project, okay? Sometimes closing a project, abandoning a project is the right thing to do, okay? Of course all projects have to be constantly reevaluated, right? You know, once you decide to invest in a drug, for example, to invest in R&D, to buy a machine, to open a division, any cooperative decision has to be constantly reevaluated. In fact, one of the topics we're going to talk about in module four is how to evaluate ongoing projects and divisions, that's one of our topics. For now, let's talk about the value of this option to abandon. So the idea is that you can exercise this option, you can use this option by shutting down a project That has become negative NPV. The other way that companies can exercise this option of course is by selling projects. Perhaps the project is not as valuable to you as it is to a competitor so it may be worthwhile to abandon this project, move on, sell it to someone else. Try to make some cash, and go do something else. So shutting down projects in many cases is the right thing to do, okay? Let's talk about this option in the context of our example, the gold mine right? We assumed in the beginning that the gold mine was irreversible, so you could not close the mine once it's opened. That is likely to be a little bit not realistic assumption, unless the government forces you to keep the mine, right? You probably have a license from the government. The government might force you to extract gold anyway. But if that's not the case, the company is very likely to be able to close the mine by paying a closing cost. We call that a decommissioning cost. Those are synonyms. You could think about the decommissioning cost as the closing cost. So let's say in our example there is a closing cost of $5,000. So that's not a huge cost. How would that change your analysis? Now, we have to consider the option of opening today and then closing tomorrow if the gold price goes down. Remember the main benefit of waiting was that we could wait until tomorrow and avoid opening the mine if the gold price we went down. Now, we have a third option which is to open today. Make the profit, pocket the money, but then close tomorrow if the gold price goes down. So I've made the profit tree for you in this case. Now, what we have, we have the profit here at the beginning, and this is the important change, if the gold price goes down, and the mine becomes unprofitable, you can close it by paying $5K. Okay, you pay $5,000 and you close the mine, and then of course, the mine remains closed until the end, you just make a zero profit. If the gold price goes up, of course, you're going to keep the mine open and make the profit, right? It's not worth closing the mine in that case. So that is the three that correspond to this third option, and notice that the $5K here is precisely the decommissioning. So now the question for you, previously in the previous question you worked out the decision tree. Now I've done the decision tree for you. Try to use the decision tree to compute the NPV. Okay, so let's check your answer. Right, let's see if you've done the right calculation, all right. So what we have, we have the NPV right, is gonna be 2 minus 70 because you open at times zero. Plus the date zero profit right, so let's mark the numbers when we take that into account right. And then here, next year we have a 50% chance of a profit of 90. We have to discount that by 5%. And then there is a 50% chance of a loss. The loss now is only $5K, times the -5, okay? Again, we're going to discount that one period okay. There is nothing here, if you close the mine there is zero. So the only numbers we need to consider are the numbers there, so it's 25 times 140, right? Divided by 1 plus 5% to the second, okay? Plus 25% times 40. Okay, so we're taking this number into account. Okay? So here's the entire calculation done for you. Remember, here we have to discount by two periods as well, right? Because we are two periods ahead. So that's how the NPV would look like, okay? If you do this calculation, you should have obtain an NPV of 51, 292. So that's the NPV of opening now and closing tomorrow if the gold price goes down. So now we have three NPVs if you open now and keep it open is 44. If you don't open now and wait it's 50, 340. If you open now and close tomorrow it's 51,292. So now the optimal decision is to open today and exercise the option to abandon. So in this case, the option to abandon, to close the mine becomes valuable, right? It actually makes it more likely you're going to start the mine today. Okay, an important observation here is the notion of irreversibility, right. We can capture the notion of irreversibility which is the commissioning cost. If the cost of closing the mine was very high then it would obviously not make sense to open today and close tomorrow. In the first example that we gave we assume that this cost was infinite so you could never close the mine. And then we worked with a cost of 5.5k, okay? So of course the cost would be at any specific value right, the notion that is important to realize is that this cost is what's gonna capture reversibility for us. Investments that have high shut down costs are going to be reversible and those are going to be the investments for which the option to wait is the most valuable. Because if an investment is irreversible, it really makes sense to wait. Until you are sure that this investment is going to be positive NPV. If the investment is not irreversible, then you might as well start today and close it tomorrow if things turn out to be bad. Okay? So let's give a few examples of irreversible investments. For example, building a factory maybe and irreversible investment, right? Once you have put all the equipment into, in place, it may be very difficult to close the factory. There are lots of fixed costs. So, you may end up having to operate the factory even if your sales turn out to be worse than expected, for example, okay? Or testing a drug on thousands of patients which is the example we just talked about for RND. Once you've done that testing, its gone, right? You can't go back and recover that money. That's completely irreversible, right? So companies, drug companies, have to really evaluate, think about whether it makes sense to continue doing research or not, because those are definitely reversible investments.