We're continuing our course, Decision Making and Scenarios. I'm Professor Rick Lambert of the Wharton School and we're going to be continuing Module 4, New Product Ventures. In this lecture we're going to be talking about expanding beyond the time horizon. So we've already done the spreadsheet, forecasted out the future cash flows, done the NPV calculations. We've done a lot in terms of formulating and evaluating alternative scenarios. We want to add one more to that, and that is, what's going on at the end of the project? So in our example, we had assumed that we're going to terminate the product venture at the end of period 8. So this resulted in a series of one-time cash flows. Sell off the property, plant and equipment, sell the remaining inventory, we did it at a reduced price, collect on the remaining receivables, pay off the remaining payables, other disposal costs. Now, this last one is an easy one to overlook or to underestimate, so make sure you pay attention to that one. These are all one time costs. They all occur in period 8, so it's relatively easy to calculate their impact on the overall NPV of the project. But what if we continue beyond the forecast horizon? Either by continuing the project itself or rolling it over into a new project. You could think about a firm as rolling over many projects that are going on indefinitely. So we can actually use the same techniques that we've talked about to value a firm as a whole, not just a project. We can think of a firm again as a set of projects. Some are operating simultaneously but new ones arise to take place of the old ones as they get phased out. Now we can't really apply the exact same techniques that we did because a firm has an indefinite life and we can't forecast out all the way to infinity. So what we usually do to try to address this is a two part approach to forecasting and valuation. We make it individual yearly forecasts for a finite horizon, 3 to 7 years, so that's what we've done in our example so far. And then we make a more ad hoc or simplified assumption about what's going to happen beyond that time. This is often called the terminal value. So what happens beyond the forecast horizon? Usually we assume that the firm goes into steady state beyond the forecast horizon. So what's steady state? Some possible interpretations for that. One is that the cash flows are constant beyond the forecast horizon. Say, equal to whatever the cash flow from period 7 was. So if we have a constant cash flow that extends out forever, that's called a perpetuity. An alternative assumption is, the cash flows grow at a constant rate beyond the forecast horizon. This is called a constant growth perpetuity. These are often good approximations, as to what's going to happen, but really their main virtue is that the math is easy. So what is the math on a constant growth perpetuity? Suppose you have a cash flow that starts out at C, grows at g% per year and we're going to discount that all back at r percent. Well the present value of that whole big stream, an infinitely long stream, is simply, the cash flow that it's going to start at, divided by the discount rate minus the growth rate. Now for this calculation to make any sense, the growth rate has to be less than the discount rate. So if we're going to grow forever at the same rate, you can't grow at too high a rate, otherwise you'd take over the universe, okay? So the growth rate has to be less than the discount rate for this to make sense. Now in our case, the constant growth perpetuity doesn't start until year 8. So when we're going to do present values, we've gotta discount this back a little bit more relative to that formula. So some different assumptions about what goes on beyond the year 7 operating phase. In our first line, this is what we had implicitly built in to the spreadsheet, we're going to have a one time cash flow in period 8 of $9,800. The present value of that is 6,148 that got added to the present value of what happens in the first 7 years which was 20,476, but what if we keep going beyond that. What if we have other projects that will extend the cash flow stream at the same rate that they were in period 7? If we have a perpetuity, even if it doesn't grow, the present value of that cash flow stream is $381,299, way bigger than what we had got if we just terminate. The overall present value of cash flows, including the first 7 periods, then is over 400,000. If the cash flows grow even at just 2% beyond what they started in period 7, the present value jumps up to 583 for the beyond horizon portion and over 600 for the firm as a whole. So you can see that most of the value in a firm comes from the cash flows way into the future. The short term cash flows don't make that big a difference to the overall firm valuation. And this is what present values tell us about valuation. So this brings us to the end of our course. In the course, we've tried to develop a framework for evaluating business decisions and strategies. We've stressed the importance of thinking about business strategies in terms of the financial consequences that these strategies will have. To do this requires thinking about the business activities that will occur, the resources that will be employed and the obligations that will be incurred. We stress the value of accounting systems for keeping track of all these things in a systematic way. How balance sheets, income statements, and cash flow statements are all linked together. Balance sheets list the resources and obligations associated with the business strategy. Income statements calculate the profits associated with the business activities and events that occur during that period. Cash flow statements calculate the inflows and outflows of cash that derive from those business activities and events. Ultimately, it's the future cash flow that the strategy or the project is going to generate, that's what's relevant but the balance sheet and the income statement are going to be useful in predicting what that cash flow is going to be. In fact, we showed how you could express the future cash flow statements in terms of the future income statements and the balance sheets. Once we have the stream of future cash flows, how do you compare different streams of future cash flows? We show that the net present value criteria is the most economically sensible way to do that. Done properly, it reflects the opportunity cost capital and the riskiness of the strategy. Net present value calculations allow you to look at an investment that's going to generate an uncertain return in the future, and allow you to answer well, how big does that return need to be for the investment to be worthwhile? How does the answer depend on how far into the future it takes till we get that return? And how does it depend on how risky or how uncertain that future return is going to be? We talked about the value of spreadsheets in making assumptions clear cut, making calculations easy, and importantly, re-calculations easy. Also in allowing easier exploration of risks and alternative scenarios. After you've initiated the project, these same forecasts that we had developed can now be used to help monitor the progress of the project. This allows us to spot if things are going off course and help us decide what to do about it. What you learn on one project can be very helpful in structuring your thinking about the next project. Business success involves an ongoing iterative process of valuation, evaluation and learning. Our course has developed important tools to help you do this better. So on behalf of Professor Holthowen and myself, I want to thank you for joining us in our course, Decision Making and Scenarios. We hope you've learned a lot, and we wish you much success in applying these ideas in trying to identify and improve new projects and exciting new ventures.