[MUSIC] In very simple environments where single-point forecasts are good enough, Level 1, discounted cash-flow analysis is the standard tool to guide capacity investment decisions. For discrete futures, Level 2, decision trees are the appropriate analytical tool. Decision trees can capture one or multiple decisions and one or multiple chance nodes. For strategic capacity sizing, we are considering one decision and one chance node for quantity X. This is also called scenario analysis. We will next outline the steps to build a decision tree, or scenario analysis required to make a capacity decision in the face of uncertainty. The canonical model to evaluate capacity decision under uncertainty is represented by the decision tree. We must decide on the capacity size K, before observing the unknown factor X, say demand, that affects the value V. Say, price times the minimum between the demand and the capacity. The size can represent the number of newspapers that a newsboy is buying in the early morning before knowing how many will be demanded and sold. This model is therefore called the Newsvendor Model. When X assumes a discrete set of values or scenarios, Xi each with probability pi and an associated contingent value Vi of k, the expected value of the capacity is its weighted average. Let us apply the canonical news vendor model to a simplified capacity sizing problem. And while doing so, we also illustrate a typical five steps for scenario analysis. Step one, determine the factors of uncertainty of the model. Assume you must decide the capacity K of your operating system. But you are facing uncertain demand for your product. The factor of uncertainty X then is the size of the demand. In other words, X equals d. Step two, determine the scenarios. Your market research team is forecasting an expected demand for 100 units. However, a swing of 25 units is likely. The consensus is that a forecast with three demand scenarios, low, expected, high, is a good enough representation of the future. Step three, assign probabilities. Your consensus forecast assigns the following probabilities to the three scenarios. X equals 75 with probability 25%, X equal 100 with probability 50%, and X equal 125 with probability of 25%. Step 4, estimate cash flow for each scenario. Assume your operating profit per unit sold is 10. Of course, you cannot sell more units than are demanded or than you have capacity to produce. Assume also that you wanted high capacity utilization in each scenario so that you set k equal to 75. The cash flow in each scenario equals units sold times unit margin. V1 equals $750, V2 equals $750, and V3 equals $750. Step five, compute the expected NPV. The expected value of operating profits is $750. Assuming that one unit of capacity costs $5, the capital expenditure, CapEx, on assets is 5 times 75 equals $375. The expected NPV thus is $375. The question is whether 75 is the optimal capacity size. [MUSIC]