# Free Cash Flows

Today I want to talk about free cash flows, a critical element in implementing any of those decision rules.

Remember, there are two components to NPV. There are Free Cash Flows, and there is 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 have been doing all along. What I am 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 is capital budgeting or valuation more broadly, how do we compute these FCFs?

That is 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** is 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 is not as though money is leaving the company.

You might wonder why we are even considering it. Well, the reason we are 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 does not 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. Therefore, we have to consider those when computing free cashable, because taxes are actual dollars leaving the company or the project.

Now this quantity here goes by several names. They are all synonyms. Unlevered net income, net operating profit after taxes or NOPAT, or earnings before interest after taxes, EBIAT.

Once we have this we are going to have to add back in depreciation and again that has just to net out the subtraction of depreciation here. It does not represent a true cash flow. What it does represent is a **tax shield**. So we add back in depreciation.

Then we are 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 has supposed to be current assets minus current liabilities. And current assets, that’s loose, 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 is coming due? That is financing. Leave that aside. That is a separate issue. We will 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 that economists call stock variables, and we are trying to compute flows. So, we want to look at the change, the period over the period change in net working capital, and subtract that from free cash flow.

So what is free cash flow intuitively? Well, the residual cash flow is left over after all of the project’s requirements have been satisfied and the implications accounted for.

The cash flow can be distributed to the financial claimants of the company, debt, and equity. That is another way to view it. It is 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’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 are 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 is critical. We take care of the debt holders first because they are 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 affected by the company’s choice of financial structure. It is leverage decision, how much debt it plans to take on.

So let me show you this, what we have just discussed schematically in terms of a hierarchy that is kind of getting us a little bit close to an income statement. Right, remember free cash flow starts up at the top with revenue. We are going to pull out the depreciation, well let me, yeah the revenue comes in were going to pull out the depreciation and costs.

We are going to pull out our taxes.

That is going to give us our unlevered net income. This is our NOPAT or our EBIAT. Then we are going to add back in the depreciation because it is a non-cash expense and again that could be depreciation and **amortization**. We are going to subtract off our capital expenditures, our investment requirements, we are 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 cash flows can go to debt holders and equity holders.

Then we are 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 inflow 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 affect the inputs to free cash flow and free cash flow to equity. They are influencing here, right? Strategic decisions are going to affect our market share and our revenue. They are 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 influence our unlevered free cash flow and ultimately are our levered free cash flow. Financing decisions are down here. They are going to influence 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 are unaffected by leverage choices. Now, strictly speaking, that is not always true. In more advanced valuation courses, you might see financing decisions feeding back on some of the inputs into unlevered free cash flow such as the ability of a firm to invest, or its revenue growth. But a useful benchmark and a common benchmark is just to recognize that financing decisions do not affect 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 is going to quantify the value implications of decisions. That is what we learned last time. And there are two key components to it, right? There are 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 is relevant for cash flow, what is not relevant for cash flow?