Hi, we learned that the traditional NPV analysis has a problem, because it ignores the adjustment that a firm can make after a project is accepted which we recall the real options. We also know that the traditional NPV analysis will underestimate the true value of the project, because it misses the value of the real options. In this module, we'll attempt to identify three major types of real options in business projects and see that the true value of a project is actually greater than what the NPV on the list suggests. The first type of real option is the option to expand. And next, we'll study the option to abandon. Finally, we'll examine the option to delay. In examining real options in business projects, we'll follow the decision tree approach in this module. Using a decision tree, we can graphically show the alternatives available to us in each time period. In the decision tree approach, the modified NPV which is adjusted for the value of real options is the weighted average of all possible NPVs in different scenarios where probabilities of different states are used as weights. The value of real options arises, because we can learn by observing what happens in the next time period and adapting our behavior based on our observation. To understand the option to expand, let's consider the following project. This project requires the initial investment of $10 million today and expected cash flow from year one to year six are $2 million per year. The discount rate is given at 20%. Let's first calculate the NPV of this project without considering the real option of the project. Calculating NPV in excel is not something new to us at all. We've been there done that. Just remember that the initial cash flow in year zero should not be included in the NPV function. This project has a negative NPV and the traditional NPV analysis will reject this project, but what if there was some uncertainty about future annual cash flows from year one to year six? What if there is actually 50% chance that annual cash flow will be $5 million per year and another 50% chance that the annual cash flow will be negative $1 million? Perhaps the original annual cash flow estimate of 2 million was just reflecting the expectation regarding the uncertainty and it's the average of 5 and negative 1 is 2. We can also assume that we can observe the outcome in year 1 by checking whether the cash flow in year one is 5 million or negative 1 million. And more importantly, if scenario one turns out to be correct, we'd like to exercise the option to expand embedded in this project and it is expected that we could double the annual cash flows starting from year two. We'll recalculate the NPV of this project in Excel now by considering the option to expand. Now, we have to consider the two different scenarios case one and case two both of which have the probability of 50% or 0.5. If we consider the option to expand that we can exercise in year 1, we would need to rewrite cash flows in case one in row 11. To calculate NPV, we first consider the initial investment of 10 million in C10 which doesn't change. But as we know that case one and two have probabilities of 50% of occurring, we need to use the weighted average of future cash flows by using the probabilities as weights. As a result of considerations of options expand in a good state, we now got a positive NPV for this project which will change our capital budgeting decision. So, what is the value of the option to expand in this project? The value of the real option would be the difference between NPV with consideration of the option and NPV without consideration of the option. So for this project, the value of option to expand seems to be huge which is about $6 million. Next, let's study the option to abandon. Managers not only have option to expand, but also options to abandon the existing projects. We'll use the same project, but now assume that the company does not have the option to expand in a good state. Instead, it could benefit from the option to abandon if the death state occurs. The assumptions are the same. We could observe the outcome in year one. Now if scenario two turns out to be correct, we'd like to abandon this project. If we know that annual cash flows will be negative in remaining years, there's no reason for us to continue operation of this project, then case two has just a single negative cash flow in year one and no more cash flows in remaining years. In Excel, future cash flows of case number 2 should be rewritten as in row 13. NPV is calculated using the same way. We can expect that the NPV should be greater than the one we have above, because we've quit early by exercising the option to abandon if the bad state occurs. Well, the option to abandon in this example did not make the NPV positive, but at least made it less negative. The option to abandon had the value of $1.25 million, which is the difference between two NPVs shown on the screen. The option to delay also gives the business project additional value. Sometimes, you'll find that having a negative NPV today does not necessarily mean that the project is a bad one. We can exercise the option to delay and just wait until the project becomes profitable. Perhaps oil and mining industry provides the best examples of the option to delay. Even if you own a gold mine, mining gold could be a negative NPV project today if the gold price is too low. However, that does not mean that your gold mine is worthless. Your gold mine has the option to delay, which will make you wait until producing gold becomes profitable again.
