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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En provenance du cours de 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。

À partir de la leçon

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 talked about forecast drivers, or

the assumptions required to forecast free cash flows into the future.

Today, I want to apply the forecast drivers we

discussed last time in the context of our tablet case.

And apply them to the free cash flow formula to forecast free cash flows into

the future for the tablet project.

Let's get started.

Hey everyone, welcome back to corporate finance.

Today we are going to be talking about forecasting free cash flows.

But before doing so let's start with our recap of the last lecture.

Last time we laid out our forecast drivers and those were the assumptions

that are necessary to generate our free cash flow forecast.

In particular, they're the assumptions about each of the components

going in to our free cash flow formula.

Today I want to apply those forecast drivers to actually

forecast dollar cash flow.

Dollar free cash flows over the 5 year horizon for our tablet project.

So let's get started.

So here's our free cash flow formula, and

again the goal today is to translate the forecast drivers into dollar forecasts.

So as a brief reminder, here are our revenue forecast drivers.

We're going to start by forecasting the dollar revenues.

And we know that revenue equals market size, times market share, times price.

So for year 1,

our revenue forecast is just going to be the year 1 initial market size,

one million units, times our share, we're going to get 25% of that market.

And then we're going to multiply it by our per unit price of $200 for

a revenue forecast in year 1 at $50,000,000.

If we repeat that process for years 2 through 5,

we'll get our revenue forecasts for all 5 years, and there they are.

Now let's move on to costs.

And we'll start with COGS, Cost Of Goods Sold.

You can see that our forecast drivers here are expressed as a percentage and

in particular a percentage of sales.

So I'm going to repeat the sales forecast from the last slide here,

because we're going to need them to get a COGS forecast.

So if we look at year one, we can see that 80.66% of the sales

are assumed to be cost of goods sold.

So, we take our $50,000,000 revenue forecast,

multiply it times that 80.66%, and out pops an estimate, or

a projection of costs of goods sold in the first year of $40.33 million.

If we repeat that process through years 2 through 5, we're going to get a full blown

COGS forecast over the entire projection period.

Now let's move on to SG&A, still in the costs category.

Here we've assumed first year SG&A expense of $69.59 million.

Now it's in dollars all ready so there's not really anything to do.

It was just an assumption I made based on 1% of the 2008 company wide SG&A expense.

A number I essentially made up just for illustrative purposes.

But going forward in years 2 through 5,

we're going to assume that SG&A expense grows at 25% per annum.

So to get year 2 for example, we start with our $69.59

million expense in year 1 and we compound it up by 25%,

to get an estimate of $87 million for our second year SG&A expense.

And if we continue with that 25% annual growth,

we're going to get an actual SG&A series here.

Finally moving on to R&D, there's really not much to do here.

Because I've assumed dollar forecasts both for

the up front R&D necessary to get the project off the ground,

as well as the subsequent R&D required for any versioning.

So here are our R&D dollar forecasts.

I'm going to take a step back and put this together into a somewhat familiar format.

And we're going to start with the top line, sales forecasts, right here.

I'm going to subtract off my COGS to get at gross profit.

I'm then going to subtract off my SG&A expenses and

my R&D expenses to get estimates of EBITDA.

And EBITDA is a mouthful once you say it.

It's Earnings Before Interest Taxes Depreciation,

I'll abbreviate that, and Amortization.

Okay, now let's move on to capital expenditures.

So, our upfront investment is going to be $227 million.

Well, a little over $227 million, for the plants and the equipment.

Then we're going to invest in the first year of the project, 10% of that amount.

Followed by annual growth of 5%, 1%, 1% and 1%.

So to get our dollar forecast there's nothing to do for year zero,

that's just the $227 million.

For year 1 we're going to take 10% of that $227 million to get $22.77 million.

And then for year, let me clean that up a little bit, for

year 2 we're going to grow that at an assumed 5%.

So we compound up the 22.77 million at 5% to get an estimate,

or forecast of capital expenditures in year 2 of 23.9 million dollars.

And continuing that growth process for years 3,

4 and 5 at 1%, we're ultimately going to arrive

at our projected capital expenditures series.

There it is.

Now, we're going to assume we're going to straight line depreciate this

capital expenditures over 5 years.

What that means is one fifth of the capital stock is going to depreciate

each year.

So what I'm going to do to make things a little bit easier is I'm going to

create a row of accumulated capital expenditures, right?

So that's nothing more than the current plus all previous capital expenditures.

So this 250.5 is the 227 plus the 22.8.

The 274.4 is the 250.5 plus the 23.9 and on and on and on.

And the reason I'm doing that is to avoid keeping track of different vintages of

capital stock.

Since they all face the same depreciation schedule, at least by assumption.

And what I can do to compute the depreciation is simply divide last years

accumulated depreciation, sorry accumulated capital expenditures, by 5.

So, the 45.5 in year 1 comes from 227 divided by 5.

Year 250.1 comes from the 250.5 divided by 5.

And again, all we're doing is, what's really going on is,

this capitol stock is depreciating by another 5, another 20%.

And then this depreciate's by 20%, so we add those two to get the 50.1.

And we continue that on, and on, and we’re left with, we get our depreciation series.

Now here's a question.

What happens to all of this physical capital at the end of the project?

At the end of the 5 years?

It certainly doesn't evaporate?

Right? It doesn't disappear.

We can sell it, or we can redeploy it for another purpose.

So we need to recognize that.

Otherwise, we're going to under estimate cash flows.

So, what I'm going to do is I'm going to take that,

all of that capital expenditure, that Accumulated Capital Expenditure and

I'm going to subtract from it the Accumulated Depreciation.

That is, I'm just going to sum up all of the depreciation.

To get this 274.8.

The difference between the Accum CapEx and

the Accum Depreciation is the Book Value of the assets for $72.8 million.

Now I'm going to assume that I can't sell that on a dollar for dollar basis,

rather I'm going to have to sell it at a discount.

$0.50 on the dollar and so the liquidation value, the money I can actually get for

it, which is different from the book value is assumed to be $36.4 million.

But remember we have to deal with taxes and so

what we're really interested in are the after tax proceeds from selling this.

So we're going to get $36.4 million.

But we're going to experience a book loss because the value for

which we can sell the assets, by assumption I might add,

this isn't always the case, is less than the book value of the assets.

I multiply that times the tax rate.

So we get a little bit of a tax shield here from our loss.

And the result, our after tax proceeds that are actually greater

than the liquidation value, we're going to get $45.6 million.

And so, the end result is that we have our projected capital expenditures,

here, but once I factor in the after-tax proceeds from the sale of these assets.

We're actually going to have a negative capital expenditures in that last year,

that fifth year.

Which is going to reflect an inflow of money.

So now let's turn to net working capital, more precisely the change in net working

capital but we'll start with net working capital.

Which is, you remember is Cash + Inventory + Accounts Receivable- Accounts Payable.

And here where all of our assumptions or our forecast drivers for

the components of the net working capital.

Let's start with the top, the cash requirements.

We're going to require 50% of SG&A in cash and 100% of our

R&D expenditures, so we're going to need our SG&A forecasts and

our R&D forecast to back out the cash requirements.

Notably for year one we're going to need 50% of our

SG&A expendidtures or $34.8 million held in cash.

But we're also going to need 100% of our R&D expenditures,

100% of the $25 million, or $25 million,

we're also going to need to hold that in cash.

So our cash requirements are the sum of these two, and are given by this row.

And again we're just going to repeat that, sorry, year by year for two, three,

and four.

Turning to inventory, our forecast drivers lay out the inventory days but

the inventory days are based on cogs so

I'm also going to need my cogs series which I put here for convenience.

So to compute the first year inventory requirements,

I'm going to take my days in inventory 7.58.

I'm going to multiply that by my COGS expenses.

And I'm going to divide that by 365 to get

an estimate of first year COGS at $837,000.

If I keep doing that, year after year, we’ll get our inventory requirements.

Turning to accounts receivable, we’ve got days receivable assumptions,

those are based on sales, so here’s are my sales, forecasted sales.

When I apply the days receivable to the sales, say for year one for example.

I've got 38.49 days receivable times the $50,000,000

divided by 365 days gets me a forecasted or projected accounts receivable

of $5.2 million, a little over $5.2 million at the end of year one.

We continue that process for years two through five.

There's our accounts receivable projections.

Finally, we turn to accounts payable.

I've got days payable assumptions of 61.54 days.

This is based on COGS, so here's my COGS series for convenience.

I apply my days payable forecast to our forecasted COG series, and

out pops the accounts payable forecast.

Repeating that process again years two through five.

We get our accounts payable.

There's a typo.

Accounts.

We get our projected accounts payable series.

And we can put this all together, our cash inventory, accounts receivable and

accounts payable forecast to compute net working capital for each year.

Remember it's going to be cash plus inventory,

plus accounts receivable minus accounts payable.

That gets us our net working capital, but here's a question.

What happens to all this working capital here at the end of the project?

Specifically, what happens to all the cash that's sitting there, or

the inventory or the accounts receivable,

the customers from whom we're waiting to receive payment.

Or the accounts payable, the suppliers who are awaiting our payment?

What happens to all that net working capital?

Well, like physical assets, it doesn't just disappear, in fact most of

it is going to be recovered, not all of it and I'll explain why in just a second.

In particular, we're going to be able to recover the cash,

we're going to be able to recover some money from the inventory.

But by assumption, back in our forecast drivers,

we’re assuming we’re only getting 25 cents on the dollar, for this inventory.

That is probably obsolete, and either not worth much in terms of scrap, or

on some secondary market.

We’re going to have to pay, well excuse me, well we’re going to have to pay all of

our accounts receivable, but we’re also going to have to collect, sorry.

We’re going to have to, let's get rid of that, we're going to have to pay

our accounts payable and we're going to have to collect our accounts receivable.

The upshot of this is we're going to recover $51.375

million in net working capital at the end of the project.

So our change in net working capital,

remember we're interested in the year on year change is given by this row.

Let's just briefly discuss it.

Get rid of that guy.

So, the first change is 59.1 minus zero which is 59.1.

The second change is the 49.7 minus the 59.1 gets me minus 9.4.

And on and on and on.

And in the last year we would have 25.6 minus the 28.2,

but then we'd have to add back in the 51.3,

to get networking capital of 48.6, which reflects recovering

all of that working capital at the end of the fifth year.

Now, there is a bit of an assumption, well, there's a lot of assumptions, but

one of the assumptions here is that we were covering all of the working capital

right at the end of period five.

In reality, you're probably going to collect that within or during year six.

So, I could have extended this to a sixth year, but

it's not going to make too big of a difference.

The discounting effect is going to be small.

So I just wrap it all up in this fifth year here.

We have all the pieces now.

Right?

And what I want to do first is organize them into a useful and

familiar format, what I'll call a quasi-income statement.

And it's a quasi-income statement because it's missing an important item and

it's applying taxes slightly differently.

I'll explain that when I get there.

So we start top line with sales, subtract off cogs that gets us gross profit.

We're going to subtract off SG & A, subtract off R & D,

that gets us our EBITDA.

And sorry ignore these numbers here.

What they are, they are references to rows in the spreadsheet,

they're just a useful way to keep track of things.

We're going to pull off our depreciation, that's going to get us our EBIT.

We're going to apply our tax rate to our EBIT to get our tax expense,

which we subtract from EBIT to get our NOPAT.

Now I call this a quasi income statement, because what's missing here is interest.

No interest.

That's financing.

We're after unlevered cash flows so that's not relevant here.

It's also quasi because the taxes are applied to EBIT as

opposed to pre-tax income which comes after interest.

All right.

So this is our NOPAT series.

Let's carry that NOPAT forward up to here.

Add back in depreciation, subtract off capital expenditures and

subtract off the change in net working capital to get what were really after or

ultimately after which is free cash flows.

These are the free cash flows to the project.

Now some other things to keep in mind when you're going after free cash flows.

First of all are Opportunity Costs, alternative uses of resources.

Right? They're not free.

Second, Project Externalities.

And this is a biggie In our context you can imagine that

the tablet might cannibalize or take away sales from other product lines,

maybe desktops, for example.

You also want to be cognizant of spillovers.

You could imagine that in the process of developing and

selling this product, this tablet.

We might learn something about our production process that applies to

other product lines or

it might lead us to the development of an entirely new product line.

We need to recognize these Externalities that are associated with this project.

Sunk Costs, ignore those.

What do I mean by Sunk Cost?

Imagine we commissioned a marketing study back in 2006,

2 years before we were valuing this project or deciding on this project.

The costs associated with that marketing project as of 2008 are completely

irrelevant.

They're sunk.

They're irrelevant for decision making.

All that matters are the costs going forward and benefits.

Other non-cash items such as amortization, we have to take that into account.

Particularly because that generates a tax shield, but

also other non-cash items like stock based compensation, stock grants,

restricted stock awards, options, employee stock options and the like.

Salvage values.

We touched on this in this lecture, right?

Assets don't just disappear and neither do liabilities.

So we have to take into account any salvage values or

liquidation values associated with our assets.

Execution risk.

Look, this is a risky project, but the way we're going to capture execution risk,

that is risk unique to this project, is not through the discount rate.

And I'll come back to talk about that later on in the class when we get

to estimating the discount rate.

This is specific to the project, so it's got to affect the free cash flows, and

the way it's going to affect that Is we're going to look at expected free cash flows.

That's the way to think about the numerator in the NPV calculation.

And we can also capture this through sensitivity analysis by looking at

different scenarios, different forecasts for free cash flows.

That's going to come up in a little bit when we talk about sensitivity analysis.

And one last point is I've assumed an annual frequency here but

there's nothing special about that.

We could have done this on a quarterly frequency.

We could have done it on a monthly frequency, semi-annual, take your pick.

What determines the cash flow frequency is really the situation,

it's project dependent.

And it's sector dependent, so

don't think there's anything special about annual frequency.

We know how to deal with non-annual frequency cash flows and

discounting them, so it's not a problem at all.

All right, let's summarize this.

What we did in this lecture is we actually forecasted the dollar values of

the free cash flows, and the way we did it is we built it up

from our forecast drivers of the components within free cash flows.

This is one of the two basic inputs into a DCF, the other being the discount rate.

And the question now is what do we do with these free cash flows?

Well that's the topic of our next lecture where we take a look at decision criteria.

So thanks for listening and I look forward to seeing you in the next lecture.

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