Welcome back at this webcast. I'm Han Smit. I'm a professor of Corporate Finance at Erasmus School of Economics. In this webcast, we're going to show you how to value a production facility with multiple options using options valuation. This can be the case if the facility is part of an acquisition. The production facility in this example has embedded expansion and contraction options. Such options are generally present in mining and minerals, manufacturing, and many other industries. These options may be particularly valuable when demand uncertainty is high. For instance, in the case of new product introductions in uncertain markets. Think about, for example, when Tesla introduced the Model 3. These products became much more successful than initially expected, so management would have valuable flexibility to expand production. Let us consider a practical case of an expansion option, in which a company has acquired a production facility that is larger than required for current production levels. The facility can therefore accommodate future expansion. The consideration by management to include or acquire the option to expand in the production facility is important when management needs to make capacity decisions in response to changing market conditions. This is especially valuable when it allows management to respond quicker than its competitors. For example, when it buys vacant land or builds in excess plant capacity from the outset. Similarly, the flexibility to decrease or contract production may also be important when management has to select between technologies or plants with a different construction-to-maintenance mix. For instance, management may find it preferable to build a plant with lower initial construction costs, but with higher maintenance expenditures in order to profit more from the flexibility to contract operations. The value of the option to contract comes from the ability to cut down on maintenance costs if market conditions turn out to be less favorable than originally anticipated. These options will be typically be exercised only if future market developments turn out different than expected and can make otherwise unprofitable base-case investments worth undertaking. Let us consider the valuation of a hypothetical car manufacturing facility with embedded options. In this valuation of a production facility we have an option to expand and an option to contract production capacity. The figure again depicts the analogy with a portfolio of options. On the horizontal axis we have the underlying value or present value of cash inflows. The cash flows are however uncertain. On the vertical axis, we see the value of the facility including the embedded options, known as the expanded value. We will show that this facility is similar to a portfolio of a stock combined with a fraction of a call and a put option. First, consider the value of the production facility without any of the options. The payoff is similar to the payoff of a share. This is the 45-degree line, like this. This give the static value strategy of running the production facility. Second, we can consider the expansion option. Suppose that in our example, management has the option to invest an additional outlay and increase advertising expenditures one year after the initial investment, which would increase the scale of the car manufacturing and value of the facility by half. So, let's say we have an expansion factor e of 50 percent. Then, in year one, management has the flexibility either to maintain the scale of operations at base scale at no extra cost, or expand the scale of the project by 50 percent by paying the additional investments, with an additional value of e times V, minus the investments or zero, whichever is the highest. In fact, it's similar to a fraction of 50 percent of a call option with a maturity of one year and an exercise price equal to the required additional investment over one year for the expansion. Third, we introduce the contraction option. Again, suppose that one year after the initial investment, there is an alternative of maintaining the current scale of operations, or contract the scale of operations by 50 percent. So c is 50 percent. Then, by contracting, we can recover an amount of R. This may be the case, for instance, if part of the investment in the base scale can be recovered by selling the assets or business units in secondary markets. The option to contract is similar to a fraction of 50 percent of a standard put option, which equals the maximum of the net present value of contraction, or zero, whichever is the highest. If we would calculate the payoff at maturity, it would look similar like this. If events turn out worse than expected, we exercise the option to contract, over here in the figure. When we combine the expansion option and the contraction option, we actually have a portfolio of a share and fractions of two options. Combining the put and the call option with the value of the production facilities, we get the following payoff at year one: it's either the maximum of zero, doing nothing, expand, this is this value, or contract, that's this value. Clearly, if conditions are as expected, management would maintain the base capacity. However, if next year the market conditions are better than expected, management may find it valuable to exercise the option to expand. If, however, the market conditions next year turn out to be unfavorable, management may find it favorable to exercise its option to contract the scale of its operations and recover part of the investment. Obviously, we're not only interested in the value one year ahead. The relevant question is: what is the current value of this facility with its embedded portfolio of options? The current value of this facility using the expanded present value calculation, equals the static value of the facility, plus the value of the portfolio of options. The static value of this production facility equals the present value of expected cash inflows. The multiple embedded options represent additional flexibility value, which can be estimated using option valuation formulas taking the risk-neutral expectation. The current value actually is then represented by this curve. So, to summarize: the expanded present value of the production facility is the static value, plus the value of a portfolio of options. Such a valuation can be particularly useful when presented with an acquisition decision regarding a new facility, when managers need to decide to invest in such a facility, or for risk management purposes to analyze the sensitivity of the company to changes in demand. The option to expand is similar to a fraction of a standard call option, while the contraction option can be viewed as a fraction of a put option. Now, you understand the structure of the facility with multiple options, you can actually make an assignment. I hope it works out for you. See you in the next webcast.