Hi, welcome to the last lecture of this course. In this lecture, we'll evaluate a business project, as if the project is an option itself, by applying the Black-Scholes option pricing model. Theoretically, we can price any options using the Black-Scholes model regardless of their underlying assets. That means, even real options embedded in business projects, can be priced using the model, if we know the five inputs of the real option. We'll use an example of the lease of a silver mine to demonstrate how the option pricing approach is used when evaluating business projects. In this project, you lease an undeveloped silver mine for two years. If you develop the mine in year 0, or right now, with the cost of $1.3 million, you will be able to mine 8 million pounds of silver in year 1. The current price of silver is $0.95 per pound, but it is expected that the silver price next year will be $1.00 per pound. If you decide to mine silver in year 1, the extraction cost will be $0.85 per pound. The standard deviation of the change in silver price is known to be 25% per year. Finally, the appropriate discount rate for this project is 10% and the risk-free rate is 5%. So, how would you determine the value of this lease contract? There is no lease fee in this project, but the owner of the mine just wants us to take the risk associated with development of the mine. What is the biggest risk that concerns you regarding this project? The risk comes from the uncertainty about the silver price next year. We expect the price will be $1.00 per pound next year, but it is just an expectation. What if the price suddenly drops? What if the price goes down even below $0.85 per pound, which is the extraction cost per pound? But one good thing to know is that, we have the option to abandon in this project. That is we will not mine silver in year 1, if the silver price goes below $0.85 per pound. But before we apply the option pricing approach, we'll first attempt to calculate the value of the project using the traditional NPV analysis. In the NPV calculation, we first consider the initial development cost of $1.3 million. For year one, we calculate the cash flow, by multiplying 8 million pounds of silver, by the difference between expected price per pound and extraction cost per pound. The fair estimate of the next year's silver price is $1.00 and the cost is 0.85 per pound. Using the discount rate of 10%, we'll discount the second cash flow, which occurs one year from now. The expected NPV is negative, and the traditional NPV analysis will reject the project. Now let's see what the Black-Scholes model would say, about this project. To use the model, we'll need to find values of the five inputs. But first of all, do you see that in this project, which has the option to abandon? To use the model, you'll need to find the values of the five inputs. But first of all, do you see that this project with the option to abandon, is a call option itself? Yes, this project is indeed a call option, because you'll exercise the option or you'll mine silver in year 1, If the ending silver price is above $0.85. If the ending silver price is below $0.85, 1 year from now, you do not mine silver, or in other words you do not exercise your option. So, the five inputs of this call option are, S will be the current silver price $0.95 x 8 million pounds which is $7.6 million. The exercise price K is $0.85 x 8 million pounds which is $6.8 million. We just learned that the extraction cost here serves as the exercise price in this project. The standard deviation is 25% and the risk-free rate is 4%. The time to the expiration date is 1 year, as the year 1 silver price will go third 1 year from now. And that is when we need to make a decision on whether we should mine silver. Now, let's go to the Excel spreadsheet, to apply the Black-Scholes Model for this problem. We can use the same template we made to price a call option on stocks, in the previous lecture. The template you've created in the previous lecture, will automatically calculate the call option price, as soon as you change values of the inputs for this project. The Black-Scholes model says that, the silver mine project which is a beat real call option, has the value of $1.36 million. That is the project value as a call option is $1.36 million. Remember that the development cost, which we had to pay immediately, was $1.30 million. The development cost can be interpreted as, the price you need to pay to purchase this project, or this call option. Since the value of the option is greater than what we need to pay to purchase the option, we conclude that, this lease project has a slightly positive value of about $60,000. So, we should accept the project. Remember that, the traditional NPV analysis mistakenly rejected the project, because it ignored the option to abandon embedded in this project
