Welcome back to corporate finance. Last time we introduced the new topic discounted cash flow analysis by discussing how corporations or people more generally should be making decisions. We discussed several different decision criteria focusing in particular on three, the NPV rule, the IRR rule, and the pay back period. We also discussed how in practice we should be taking a practical approach, and using the relevant information from all three rules. Today I want to talk about free cash flows, a critical element in implementing any of those decision rules. Let's get started. Hey everybody welcome back to corporate finance. Today we're going to start in on Lecture 2 of Discounted Cash Flow Analysis, but before doing so, let's do a brief recap of our last lecture. So we introduced the topic discounted cash flow analysis by discussing decision-making. And we talked about several different decision rules used in practice beginning with the NPV rule which is nothing more than the difference between the present value of costs and the present value of benefits. And while most academics, including me, will argue that this is the best rule that you should always use. I take a practical view, and recognize that other rules, such an internal rate of return, and payback period, contain relevant information for decision making. That if used wisely and in recognition of their limitations can lead to better decisions. And so that's sort of the over arching approach we're going to take to DCF is that there are several different decision rules. We'll rely on NPV but use what we can from other decision rules. Now, in this lecture I want to talk about, sort of the bedrock, one of the key components of any DCF and any sort of decision making and that's Free Cash Flow. Specifically, what is it? So let's get started. So, remember, there are two components to NPV. There are Free Cash Flows, and there's a discount rate, because NPV, if you recall from last time, is little more than just a discounted stream of cash flows. In this case, free cash flows. So recall NPV was formally defined as follows, and we recognize that this is really nothing new. Right? This is what we've been doing all along. What I'm going to focus here is on the numerator, the free cash flows. How do we get at these free cash flows in a corporate setting? Whether it's capital budgeting or valuation more broadly, how do we compute these FCFs? That's what this lecture's really about. So let's take a look. Free cash flow begins with revenue, or sales. We subtract off costs, and then we subtract off depreciation, actually depreciation and amortization, but mostly depreciation, by depreciation or amortization, both. Now you might wonder, well first, what is depreciation? Depreciation's just an accountant's way of recognizing the loss in value, the deterioration in value, of physical assets like plants and equipment. But it's sort of an accounting notion that doesn't represent a true cash flow. When a plant depreciates it's not as though money is leaving the company. You might wonder why we're even considering it. Well the reason we're considering it is because we're going to take this term In parenthesis that I've now bracketed and multiply it 1 times tc. Tc is the marginal tax rate. See even though depreciation doesn't represent any dollars flowing out of the company or away from a project. It's not a literal cost in terms of dollars. What it does is it does reduce our taxable income, it provides a tax shield. And so we have to take that into account when computing free cashables, because taxes are actual dollars leaving the company or the project. Now this quantity here goes by several names. They're all synonyms. Unlevered net income, net operating profit after taxes or NOPAT, or earnings before interest after taxes, EBIAT. Once we have this we're going to have to add back in depreciation and again that's just to net out the subtraction of depreciation here. It doesn't represent a true cash flow. What it does represent is a tax shield. So we add back in depreciation. Then we're going to subtract off. Let me get rid of that. Capital Expenditures, or any investments we have to make. And then finally, we're going to subtract off the Change in Net Working Capital. And that sometimes throws people for a little bit. What do you mean subtract off the Change in Net Working Capital? Well first, what is Net Working Capital? Well, Net Working Capital, NWC, is equal to, current, yeah that's supposed to be a u, current assets minus current liabilities. And current assets, that's loosely, cash plus accounts receivable plus inventory. And current liabilities, we're going to focus on accounts payable. Now some of you might say, what about short-term debt or long-term debt that's coming due? That's financing. Leave that aside. That's a separate issue. We'll talk about that in a little bit. Okay So, what goes into the free cash flow calculation is not net working capital. The change is important, because these are all what economists call stock variables, and we're trying to compute flows. So, we want to look at the change, the period over period change in net working capital, and subtract that from free cash flow. So what is free cash flow intuitively? Well, it's the residual cash flow that's left over after all of the project's requirements have been satisfied and the implications accounted for. It's the cash flow that can be distributed to the financial claimants of the company, debt and equity. That's another way to view it. It's not the same as accounting cash flow from the statement of cash flows but we can derive free cash flow from the statement of cash flows. Actually with just a few steps. Now I want to be precise here, the free cash flow, we've, we're going to compute here or as defined right here this is unlevered free cash flow. And I say unlevered to distinguish it from free cash flow to equity or free, or, or levered free cash flow which we'll discuss on the next slide. So, Free Cash flow to Equity, starts with Free Cash Flow, the definition of free cash flow, that's just this quantity right here, and then we've appended two terms. We're going to subtract off the after tax interest cost, and add back in any net borrowing. That is, borrowing above and beyond any repayment of debt. So another way to compactly write the free cash flow to equity is that it starts with unlevered free cash flow, the free cash flow available to debt and equity holders. And we subtract off the after tax interest expense and add in the net borrowing. So what is free cash flow to equity? It's the residual cash flow left over after all of the project's requirements have been satisfied, implications accounted for, and all debt financing has been satisfied. That's critical. We take care of the debt holders first because they're senior claimants. Free cash flow to equity is the cash flow that can be distributed to the shareholders, i.e., equity holders, of the project or the company. And free cash flow to equity this is, look at this, this should be E. There we go. Is more precisely levered free cash because free cash flow to equity is effected by the, the company's choice of financial structure. It's leverage decision, how much debt it plans to take on. So let me show you this, what we've just discussed schematically in terms of a hierarchy that's kind of getting us a little bit close to an income statement. Right remember free cash flow starts up at the top with revenue. Were going to pull out the depreciation, well let me, yeah the revenue comes in were going to pull out the depreciation and costs. We're going to pull out our taxes. That's going to give us our unlevered net income. This is our NOPAT or our EBIAT. Then we're going to add back in the depreciation because it's a non cash expanse and again that could be depreciation and amortization. We're going to subtract off our capital expenditures, our investment requirements, we're going to subtract off our investment in net working capital, the change in net working capital. And that's going to give us our unlevered free cash flows. These are the cash flows that can go to debt holders and equity holders. Then we're going to pull, subtract out our after tax interest expense. And I say after tax because remember, interest is tax deductible, right? It provides us a tax shield. And then we're going to add back in any net borrowing, so if the company borrows some debt in excess of what it repays, that's the cash in flow that's available for use by the equity holders. And what we're left with down here at the bottom is the levered free cash flow or the free cash flow to the equity holders. And so strategic decisions, a useful way to think about strategic versus financial decisions is strategic decisions are going to effect the inputs to free cash flow and free cash flow to equity. They're impacting here, right? Strategic decisions are going to affect our market share and our revenue. They're going to affect our cost, our investment decisions, right? Investment decisions, our operations, inventory, and the like. All of these strategic decisions are going to impact our unlevered free cash flow, and ultimately are our levered free cash flow. Financing decisions are down here. They're going to impact our leverage choice, the after-tax interest expense, the net borrowing. And, hence, that's why we refer to these cash flows here as unlevered. They're unaffected by leverage choices. Now, strictly speaking, that's not always true. In more advanced valuation courses you might see financing decisions feeding back on some of the inputs into unlevered free cashflow such as the ability of a firm to invest, or its revenue growth. But a useful bench mark and a common bench mark is just to recognize that financing decisions do not effect the unlevered free cash flow. And that's a great way, by the way, to check your computations in any sort of valuation or DCF exercise. At least one way is by recognizing that financial policy is not going to hit the unlevered free cash flows. All right. So let's summarize this now. You know, NPV is a decision rule that's going to quantify the value implications of decisions. That's what we learned last time. And there's two key components to it, right? There's free cash flows and discount rates. This lecture was all about, how do we put some meat behind that FCF term? How do we actually compute it? How do we derive it for a project, or a firm, or more broadly speaking? And what we saw is that there's a relatively simple formula for computing free cash flows and don't be misled by its simplicity. It applies broadly. We can always use this definition. The trick in practice is actually estimating the components and figuring out what hits unlevered free cash flow versus levered free cash flow. What's relevant for cash flow, what's not relevant for cash flow. The remainder of this topic is going to be geared towards answering those questions in the context of an actual example. So, coming up next we're going to start in on Forecast Drivers, and trying to understand how we're going to forecast each of those components of free cash flow out into the future. Thanks so much.