The final phase that we talk about with respect to calculating the cash flows associated with a project is, what I'll refer to as, the terminal phase. And the terminal phase is going to include a bunch of different things. So in the very last year, what's going to happen? In the very last year, you're going to get the final cash flow from just operating the project. But then, if the project is actually ending, there will usually be some salvage value associated with the end of that product. Maybe the salvage value is just that you have a machine that you're now going to sell in the secondary market. And so, there's some salvage value associated with that machine. You're going to sell it for a certain amount. And, that cash flow is going to come in when you sell that project. When you sell that machine, there will probably be either a gain or a loss associated with the sale of that, and you'll have to take that tax consequence into consideration as well. That salvage value could also be negative, however. Let's suppose that that machine had to be disposed of in some environmentally friendly way. That you actually couldn't just sell it for scrap or the secondary market. But you actually had to pay somebody to dismantle that machine and dispose of it properly. So in that case, there actually could be a negative salvage value associated with the end of the project. And then the third component that will normally happen when a project comes to an end is whatever working capital you've built up in receivables and inventory, those are usually going to be released, right. So that, you had receivables that were built up and customers owed you money, you would anticipate, as you no longer sell that product, that you would still collect that money from costumers. So any working capital investments that you have made in inventory, receivables that have payables, that's actually going to be released at the end of the project, and you want to take that cash flow into consideration as well. Those are the things that you take into consideration when you think that a project has a finite life. And most projects have a finite life. You buy a machine, it's only going to last for a certain number of years. You're going to produce a product, it's only going to be a viable product for a certain number of years. But occasionally, you will have projects where you actually think they're going to last for a very long time. And what do you do in that case? Well here's where our friend, the cashflow perpetuity model, comes into play. So if you believe that you have a project that will be infinitely lived, or as we talked about before, last 50 to 60 years, one of the ways to try to capture all the value and the cash flows is to use that perpetuity model. And if you remember what that was you would take the cash flow for year end plus one. You would divide by the discount rate minus the growth rate. And that would give you the present value of a set of cash flows as of time n starting with n plus one and going through infinity. But remember the assumptions to use this that we talked about before the DR has to be constant, that the growth rate, the percentage growth rate has to be constant. It has to be that the discount rate r is strictly greater than g and that that cash flow in year end plus one is positive. So how would you actually use this? Suppose that you forecasted the cash flows for a new product for ten years. And during that time, the growth in the product sales went up. But after say, year seven they started to come back down. And let's suppose by the end of year ten you now anticipate that the growth rate associated with the product is going to be close to the inflation rate or three percent. So what would you do to capture the value in the cashflows from year 11 on out that you anticipated those cashflows are going to grow with 3%? So you would take that year 11 cash flow and you would apply the perpetuity model with it. So you would divide that by whatever your discount rate is minus your growth rate and in this case we're assuming it's 3%, and that's going to give you the present value of the cash flows from year eleven through infinity as of year ten. That's the key thing. It's as of year 10, so now what do you do? You take that value as of year 10 and you have to discount it back to time zero by taking it and dividing it by one plus the discount rate raised to the tenth power and that discounts that value back to time zero. And then you would add that value to the present value of the cash flows that you had for the first ten years, and then that would give you the total value of that project. So again, here's where the cash flow perpetuity model comes into play. So let's remember. So what are we going to do? We're going to calculate the Net Present Value by taking the initial investment and subtracting it. And if that initial investment occurs over multiple years you're discounting those cash flows. So you had an initial investment in time zero. That's not discounted. But if you have more investment at time one, that's discounted. Back one year, if you had more investment in time two, that's discounted. Right? So you're going to calculate what your initial investment is, including discounting investments over time. You're going to then add the discounted value of the cash flows during the operating phase. And you're going to add the discounted value of the terminal phase. And as we saw before, if the net present value is positive, you're going to accept that project. And if the net present value is negative, you'll reject the project.
