Hi, in this module, we continue to study analyzing business project. So far, we have learned how to find the project value by calculating its NPV. So we know that NPV analysis is a great tool which let's us know the value of the project we'll create. In this module, however, we will learn that the traditional NPV analysis can underestimate the value of the project because it ignores the value of options embedded in the project. More specifically, we would like to learn the following topics in this module. Types of options embedded in business projects, evaluation of projects using the decision tree approach, and evaluation of projects using an option pricing model named the Black-Scholes model. Before we get started, let's first quickly study the options basics. So what is an option? An option is a financial asset that gives you the right, but not the obligation, to buy or sell a given quantity of an asset on a prescribed date at the price agreed upon today. The definition of options suggest that to understand and describe an option, we need to know the following key components of an option contract. First, an option is not defined without identification of the underlying asset. So we first need to know the option gives us the right to buy or sell what? This what thing is called the underlying asset of the option contract. The second is the exercise price. We should make it clear that the option gives us the right to buy or sell the underlying asset at what price? The third component of the option contract is the expiration date. It lets us know the date on which we can exercise the option. In this course, we cover the European option only, which gives the holder the right to exercise her option only on the expiration date. Another popular type of the option is American options, which can be exercised on or before the expiration date. Perhaps you may have heard about stock options. A stock option is an option whose underlying asset is a company's stock. Financial assets, such as stocks or a stock market index, is probably the most popular underlying assets of options in the options market. We can also think of options, which has commodities such as crops or crude oil, as the underlying asset. But remember, in this module, we tried to identify options embedded in the real business projects. Or we could say that we are analyzing options whose underlying asset is a business project. And we call options, which is related to real business projects, a real option. Earlier, I said that an option gives the holder the right to buy or sell the underlying asset. But we actually have different names for those options which gives you the right to buy, and the ones which gives you the right to sell, respectively. A call option gives you the right to buy the underlying asset on the expiration date. If a business project gives you the right to purchase more projects in the future, the project, in fact, has an embedded call real option. On the other hand, a put option gives you the right to sell the underlying asset on the expiration date. If a business project gives you the right to abandon the project when it is not so profitable, it has a put real option in it. So now we can understand the following sentence without any problem. The CEO of Tirol was granted stock options of Tirol with the right to buy its stock at $30 in 2020. Now we can rewrite the sentence like this. The CEO was granted call options whose underlying assets are Tirol stocks, with the exercise price of $30 and the expiration date of Dec 31, 2020. Okay, then can we answer the question, does this call option have any value on the expiration date, December, 31, 2020, if the ending stock price is $33? Yes, the option has a positive value in that case because you have the right to buy stock at only $30 when the market price is $33. It gives you the profit of $3. Okay, now what if the ending stock price is $25? Does the option still have some value? No, not this time. The right to buy the stock at $30 doesn't give you any value when the market price is below the exercise price. Note, though, that it doesn't hurt the option holder either, because she has the right, but not the obligation, to purchase stocks on the expiration dates. For that reason, a call option typically has the following payoffs. The ending stock price on the expiration date is shown on the x axis, and corresponding option payoffs are shown on the y axis. The Tirol call option in the previous example does not have any value if the ending stock price is below $30. The option gives you profit when the stock price is above $30. For example, if the ending stock price is $40, The option payoff is $10, because you could purchase the stock at only $30. What if we had Tirol put option, which gives us the right to sell Tirol stock at $30 on December 31, 2020? Here we are talking about the right to sell, so we can easily imagine that the put option, you'll have a greater value when the ending stock price is lower. For example, we do not exercise the put option when the stock price is $35. We do not need the right to sell the stock at $30 when we can just sell the stock in the market at an even higher price.