学完本课程后，您将可以分析企业所做金融决策的主要类型。然后，您可以运用所学技能处理现实商务挑战，这也是沃顿商学院商务基础专项课程的组成部分。主要概念包括：净现值技术、资本预算原则、资产估值、金融市场运作和效率、公司财务决策以及衍生产品。

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From the course by University of Pennsylvania

企业金融概论（中文版）

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学完本课程后，您将可以分析企业所做金融决策的主要类型。然后，您可以运用所学技能处理现实商务挑战，这也是沃顿商学院商务基础专项课程的组成部分。主要概念包括：净现值技术、资本预算原则、资产估值、金融市场运作和效率、公司财务决策以及衍生产品。

From the lesson

第 3 周

本模块将通过资本预算案例继续讨论现金流量折现法。（您可能需要下载或查看教学中使用的Excel文件，“Tablet Case Spreadsheet.xlsx”，但是该文件对于理解课程内容来说并不是必须的。）本模块教学结束后，您将能根据定期现金流或者各种复利计算方式（例如每年、半季度或每月）对债券进行估值。通过计算这些问题，您将能理解真实世界中的各种金融决策，例如退休储蓄、房屋融资和再融资、车贷和其他金融相关问题。

- Michael R RobertsWilliam H. Lawrence Professor of Finance, the Wharton School, University of Pennsylvania

Finance

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 payback 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 cashflows,

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 two 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 as 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 overarching 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 or

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,

as 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.

Depreciation or amortization, both.

Now, you might wonder, well, first, what is depreciation?

Depreciation is just accountants' way of recognizing the loss in value,

deterioration in value of physical assets like plants and equipment.

But it's sort of an accounting notion.

It doesn't represent a true cash flow, right?

When a plant depreciates, it's not as though money is leaving the company.

So 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 parentheses that I've now bracketed, and multiply it times (1- t c).

Tc is the marginal tax rate, okay?

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 cash flows

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 the depreciation.

Then we're going to subtract off, 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, okay?

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.

Okay, all right.

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'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

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, look at this, this should be E,

there we go, is more precisely levered free cash flow.

Because free cash flow to equity is affected by the company's choice financial

structure, its leverage decision, how much debt it plans to take on.

So let me show you 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.

We're going to pull out the depreciation, the revenue comes in.

We're going to pull out the depreciation and costs.

We're going to pull out our taxes, okay.

That's going to give us our unlevered net income.

This is our NOPAT, or our EBIAT.

[COUGH] Then we're going to add back in the depreciation,

because it's a non-cash expense.

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 networking capital, the change

in networking 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 subtract out our after tax interest expense, and

I say after tax because remember, interest is tax deductible.

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 a 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.

So strategic decisions.

A useful way to think about strategic versus financial decisions is that

strategic decisions are going to affect the inputs to free cash flow and

free cash flow to equity.

But they're impacting here, right?

Strategic decisions are going to affect our market share and our revenue.

They're going to affect our costs, 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 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 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 unleveraged 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.

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?

And 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 or

trying to understand how we're going to forecast each of those components of

free cash flow out into the future.

Thanks so much.

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