CHAPTER 9: DISCOUNTED CASH FLOW (DCF) VALUATION
*
WITH FINANCIAL PLANNING MODELS
this version: July 27, 2003
Chapter contents
Overview.........................................................................................................................................1
9.1. What does “value of the firm” mean?.....................................................................................3
9.2. Using the DCF valuation—summary......................................................................................9
9.3. Projecting the FCFs and doing the DCF valuation with a financial planning model...........15
9.4. Advanced section: What’s the theory behind the model?....................................................20
Summary.......................................................................................................................................23
Exercises.......................................................................................................................................24
Overview
In Chapter 8 we learned how to use accounting concepts to build a financial planning
model of a company. In this chapter we use financial planning models to value a company. This
is something that almost every finance specialist has to do occasionally. The valuation technique
we employ—called discounted cash flow (DCF) valuation—is the valuation technique
universally favored by the finance profession. DCF valuations are often based on the financial
planning models discussed in Chapter 8. When these models are used to do a DCF valuation,
they are also used to do much of the sensitivity analysis which helps determine if the valuation is
reasonable.
Valuation is not intrinsically difficulty, but because there are several competing
definitions of what constitutes the “value of a firm,” people often get confused. To shed some
light on this issue, Section 9.1 discusses the different concepts of firm value. As you will see in
Section 9.1, finance specialists often identify the value of the firm with the present value of its
future cash flows. We will use the financial planning models of Chapter 8 to determine these
cash flows.
After discussing the concept of firm value in Section 9.1, we summarize the steps
involved in a DCF valuation in Section 9.2. We then go on to show you how to value a company
by building a full-blown DCF valuation model (Section 9.3).
Finance concepts used Present value Free cash flow Gordon model (Chapter 6) Terminal value Mid-year
valuation
Excel functions used - NPV
- Data tables
9.1. What does “value of the firm” mean?
The terms “value of a company” or “value of a firm” are often used interchangeably by
finance professionals. Even finance professionals, however, can use a confusing variety of
meanings for these terms. Here are a few of the meanings which are often intended: In finance the definition
most often used for “firm value” is the following: The value
of a firm is the market value of the firm’s equity plus the market value of the firm’s
financial debt. This section illustrates two methods of computing the firm value.
o The simplest method is to value the firm’s equity (its shares) using the firm’s
share price in the market, and to add to this the value of the firm’s debt.
o A second method, the DCF method, is based on discounted cash flows. In a
DCF valuation firm value equals the present value of the firm’s futures FCFs
plus the value of its currently available liquid assets. Often when individuals discuss the firm value, they really
mean the value of its
shares. It is better to use the term equity value for the value of a company’s shares
and to use the term firm value (or company value) to denote the market value of the
firm’s equity plus its debt. In our calculations we also show you how to compute the
value of a firm’s shares. Sometimes the term firm value is used to denote the accounting value of the firm.
Also known as the book value, this value is based on the firm’s balance sheets.
Because accounting statements are based on historical values, people in finance generally prefer not to use this
definition. At the end of this section we illustrate why
we do not like this valuation method.
Motherboard Shoes: What’s it worth?
To illustrate the different concepts of firm value, we’ll tell the story of Motherboard
Shoes. Motherboard is listed on the Chicago Stock Exchange, but the majority of the stock is
owned by the Motherboard family, which founded the company and still runs it. The current
date is 1 January 2005, and the Motherboards have received an offer for their shares from
Century Shoe International. They would like to know if the offer is a fair one.
Their investment advisor, John Mba has advised them that there are two plausible ways
to value the company (John just finished business school and liked it so much that he changed
his last name to reflect his new status). Each of the two methods has advantages and
disadvantages.
The share price valuation: Valuing a Motherboard by using current share price
The simplest way to value Motherboard is look at the value of its share. Motherboard
Shoes has one million shares, which were trading on 31 December 2004 at $50 per share. Thus
the market value of the firm’s equity is $50 million. In addition the company’s balance sheet
shows that it has short-term debt of $2.5 million and long-term debt of $7.5 million; John Mba
uses these balance sheet values (also called book values) of the debt as an approximation to the 1
debt’s market value.
The discounted cash flow (DCF) valuation: Valuing Motherboard by discounting its
future free cash flows
The advantage of the share-price valuation method illustrated above is that it is very
simple: The firm value equals the market value of the firm’s shares plus the book value of its
debt. Valuing the company at its current price of $50 per share is perfectly acceptable for
someone considering buying a few shares of the company, but it makes less sense if
Motherboard Shoes is selling a controlling block of shares. In this case the purchaser would
probably expect to pay more for the following reasons: If the purchaser tried to buy a big block of shares of
Motherboard shares on the open
market, he would probably have to offer more than the current market price per share.
As he bought more and more shares, the price would go up; in addition, the
1
This is common practice. Most company debt is not traded on financial markets, and therefore there is no
easilyavailable market value for the debt. As a first approximation, most finance professionals use the book value of a
firm’s debt as a proxy for the debt’s market value.
announcement that someone was trying to take over Motherboard Shoes would—in
many cases—force the share price up. There are benefits to controlling a company that are not priced in the
market price per
share. The market price of a share reflects the value of a company’s future dividends
to a passive shareholder who has no control over the company. In general the value
of a controlling block of shares is larger than the market value, since the controlling
shareholder can actually decide what the company will do. He can also derive
considerable private benefits from running the company.
To deal with these problems, John Mba proposes to use the discounted cash flow (DCF)
valuation method to value the shares. DCF valuations are a standard finance methodology,
which defines the value of the firm as the present value of the firm’s future free cash flows
(FCF), discounted at the weighted average cost of capital (WACC), plus the firm’s initial cash
and marketable securities. Section 9.4 discusses the theory behind this method of valuation, but
for the moment we skip all the theory and simply present the formula:
2
Economists use the term private benefits to discuss all kinds of financial and non-financial benefits associated
with
firm ownership. The big car with a driver that the company gives its president is a private benefit of
ownership, and
so is the feeling of ownership—a psychological benefit, perhaps, but nonetheless valuable.
(Notice that the present value of the firm’s future FCFs is often called the firm’s
enterprise value.) After some work to estimate the future free cash flows, John comes up with
the following valuation:
There are a few things to explain about this valuation: John has projected 5 years of future FCFs and has also
projected a terminal value at the end of the 5 years. He explains that the finance methodology requires him to
estimate the allfutureFCFs present value of all the future free cash flows: PV . However,
discountedatWACC he thinks this is too much guesswork. Instead of estimating all future FCFs, he’s
estimated 5 years of FCFs and then estimated the terminal value, the value of
Motherboard at the end of year 5:
If the weighted average cost of capital is 20%, the enterprise value, the present value of
3
the FCFs and the terminal value, is $68,657,407.
Adding current balances of cash and marketable securities to the present value of the
FCFs and subtracting out the value of the firm’s debts gives an equity valuation of
$59,157,407 (cell B15). Since there are one million shares outstanding, this values each
share at $59.16 (cell B18).
The firm’s book value—a definition we’d rather not use
There’s another valuation method which John explains to the Motherboard family—the
accounting definition of firm value uses the balance sheet to arrive at the value of the firm. For
the case of Motherboard Shoes, the balance sheets at the end of 2004 look like:
The accounting definition of firm value relies on book values, the value of the firm’s debt
and equity as listed in the firm’s balance sheet. Recall from Chapter 7 that the accounting
definition, which is based on historical values, is a backward looking definition. The finance
definition of firm value is a forward looking definition (it discounts the future anticipated values
of the cash flows). John Mba thinks that the accounting definition gives an inappropriate valuation, and he’s
right.
In the case of Motherboard Shoes, the forward-looking DCF valuation
of the firm is $68,657,407 whereas the backward-looking accounting definition is $14,000,000.
9.2. Using the DCF valuation—summary
The DCF valuation of a firm is based on discounting the firm’s future expected free cash
flows (FCFs), using the weighted average cost of capital (WACC) as the discount rate. In this
section we summarize the steps for implementing this valuation, and in the next section we
illustrate a DCF valuation using a financial planning model we learned in Chapter 8.
Step 1: Estimate the weighted average cost of capital
The WACC is the discount rate for the future FCFs. We discussed the WACC in Chapter
5 In this chapter we will not go into the details of 6 and gave an example of how to estimate it.
estimating the WACC; calculating the WACC entails many assumptions and in many cases the
calculation itself becomes a topic of controversy among the parties involved in the valuation.
For this example, we assume that John Mba’s estimate of a 20% WACC is correct. In Section
4
Not to disparage accounting (very important) or accountants (most of whom would readily agree).
5
Later in the book, Chapter 15 gives another approach to estimating the WACC.
9.3 we will perform some sensitivity analysis (using an Excel Data Table) to show how changes
in the WACC affect the valuation.
Step 2: Project a reasonable number of FCFs
A financial planning model’s predictions of future FCFs are based on the assumption that
the parameters of the model will not change by too much. Most financial analysts define
6
“reasonable” to mean number of periods over which this basic assumption is not too silly.
Everyone recognizes that a firm’s environment is dynamic and that the model parameters will
change over time, a fact that is usually addressed by doing sensitivity analysis (see section 9.4).
John has assumed that he can reasonably project the next 5 years of cash flows.
Step 3: Project the long-term FCF growth rate and the terminal value
Valuation using the DCF method in principle requires us to project an infinite number of
future FCFs, but in a standard financial planning model we project only a limited number of
FCFs. A solution to this problem is to define the firm’s terminal value as the firm value at the
end of year 5. The definition John uses is contained in Figure 1.
6
The author defines “not too silly” as something he can explain to his mother with a straight face (and that she
won’t laugh at him).
As you can see, there are 3 parts to this valuation equation:
Line 1 is the present value of the first 5 years of free cash flows. John has projected these
cash flows one-by-one, using a financial planning model (details to come in Section 9.3).
Instead of projecting the present value of each of the cash flows in years 6, 7, 8, …,
infinity, John has chosen to summarize them in the present value of the terminal value.
Terminal value is what we project the firm to be worth at the end
of projection horizon. In Section 9.4 we explain how this expression for the terminal value is derived. For now
we assume that John’s prediction of Motherboard’s terminal value is correct. Line 3 gives the value of the cash
and marketable securities. The terminal value formula requires us to estimate the long-term FCF growth rate.
In the financial planning model for the Motherboard Shoes FCFs, this long-term growth rate is different
from the sales growth rate projected for the company’s next five years. As you will see in Section 9.3, John
projects a relatively high growth rate of sales of 10% for Motherboard over the 5 year horizon of the planning
model. John’s criterion for choosing the long-term FCF growth rate of the company is that a company’s cash
flows cannot grow forever at a rate greater than the economy in which it operates. He estimates that the longterm growth of the U.S. economy is 5 percent, and that this rate is also the long-term rate for Motherboard
Shoes. Using his model, John Mba estimates that Motherboard’s year-5 FCF is $13,029,110.
Using the WACC of 20 percent and the long-term FCF growth rate of 5 percent, the company’s
terminal value is $91,203,773:
Step 4: Determine the value of the firm
At this point all the elements of the firm valuation formula are in place:
-WACC: the discount rate for the FCFs and the terminal value
- Five years of FCFs projected from the financial planning model
- The terminal value of the firm
-The firm’s initial (year 0) balances of cash and marketable securities
We can now value the firm:
The value of the firm is $69,157,407 (cell B9). In cells B15 and B18 we’ve added two
more steps:
Step 5: Value the firm’s equity by subtracting the value of the firm’s debt today
from the firm value
The firm value is the value of the firm’s debt + equity. We are often interested in valuing
only the firm’s equity—our estimate of the market value of the firm’s shares.
Stock market analysts often use the estimate of a firm’s equity value to arrive at a pershare valuation of the firm. They then compare this estimated per-share value to the current
market price to come up with a buy or sell recommendation for the stock. Since Motherboard
Shoes has 1,000,000 shares outstanding, the estimated market value per share is
This share valuation is higher than the current market value per share of $50. If the DCF
valuation analysis were being used to make recommendations about the stock, we would expect
the analyst would make a “buy” recommendation for the Motherboard Shoes. In this case the
analysis is used by John Mba to recommend that Motherboard be taken over for more than its
current price per share.
Step 6: Adding mid-year valuation
In Chapter 4 (page000) we discussed mid-year valuation of cash flows. The idea was
that when cash flows occur over the course of the year and not at the end of the year, we should
0.5
take the standard present value formula and multiply it by
1 WACC . For Motherboard
Shoes, mid-year valuation makes sense, since the company’s sales occur throughout the year and
not just at year-end. In the spreadsheet below you can see how mid-year valuation affects the
value of the firm and projected share valuation: Cell B8 shows that the present value of future
cash flows and terminal value firm value increases from $69 million to $75 million. In cell B18
you can see that the projected share value increases to $65.71.
Step 7: Don’t trust anything! Do a sensitivity analysis
Valuations are based on a formidable number of assumptions! When we do sensitivity
analysis, we evaluate the effect of changing values of the main variables on the value of the firm.
Our “weapon of choice” for sensitivity analysis is the
Data Table feature of Excel (see Chapter
30). We leave our demonstrations of sensitivity analysis for the next section.
9.3. Projecting the FCFs and doing the DCF valuation with a financial
planning model
So far we’ve shown how John Mba performs his valuation, but we haven’t shown the
financial planning model which produces the free cash flows.
The model looks a lot like those discussed in Chapter 8.
Here it is, with the mid-year valuation discussed in the previous section:
Several features of the model used by John Mba to value Motherboard Shoes are:
Net fixed assets are assumed constant. John assumes that—as long as depreciation is
invested back into fixed assets—Motherboard Shoes will need no more fixed assets.
Another way of thinking about this assumption is that the major expenses incurred for
fixed assets are equal to the depreciation expenses. As you can see in row 30 of the model this does not mean
that fixed assets at cost are constant. It does mean, however,
that in the FCF calculations lines 45 (depreciation) and 48 (capital expenses) cancel out. John assumes that in
each of the next five years, Motherboard Shoes will repay $1
million of its $10 million debt. Cash is the plug.
Given the full-blown financial planning model, there are obviously many sensitivity
analyses we can perform. Below we show two data tables. The first table analyzes the effect of
the sales growth assumption (cell B2 of the model) on the share valuation. John Mba has
estimated sales growth of 10% annually for the next 5 years. As you can see, the effect of this
assumption is quite dramatic. The greater the sales growth (cell B2), the greater the valuation of
Motherboard’s shares:
Excel Note: Data tables
This may be the appropriate place to review Data Tables, which are covered in
Chapter000. What may be confusing in the previous data table is the “65.71” in cell B74.
This is a reference to the share price calculation in the initial model The data table asks
Excel to redo this calculation for the sales growths in cells A75:A84.
A second sensitivity analysis performed by John Mba is the effect of the weighted
average cost of capital and the long-term growth rate (cells B55 and B56) on the per-share
valuation. Notice that these two parameters affect the valuation in two ways:
To examine the effect of these two parameters, John builds a two-dimensional data table:
The results produced by this sensitivity analysis are not surprising:
Going across rows shows that as the WACC increases, the value per share decreases.
Since a larger WACC means that the present value of a future cash flow is less, this is to
be expected.
Going down columns shows that the larger the long-term growth rate expected from
Motherboard Shoes, the more the shares are worth. Again, this is not a surprise, since
larger long-term growth rates mean higher FCFs after the year-5 model horizon. As
noted in the box below, our terminal value model only works when the long-term growth
rate is less than the WACC. When this assumption is not true (meaning: the long-term
WACC), we’ve had Excel write “nmf” (“no meaningful figure”).
The growth >technique for doing this is explained below.
9.4. Advanced section: What’s the theory behind the model?
In this section we explain some theoretical points about the valuation model illustrated in
the previous section. Not all of this is easy, and you may (understandably) want to skip this 1
section.
Why is the firm’s value related to the PV of the future FCFs?
Our basic valuation formula is:
The enterprise value of the firm is defined to be the value of the firm’s operations. In
financial theory, the enterprise value is the present value of the firm’s future anticipated cash
flows. In this section we explain these concepts.
The valuation process
One way of viewing valuation is through the use of the accounting paradigm, but using
market values. We rewrite the balance sheet by moving the current liabilities from the
liabilities/equity side to the asset side of the balance sheet:
1
Why would an author put a section like this in this book? Our experience is that ultimately almost all finance
professionals are called upon to do valuations. At some point in every valuation, someone is going to question
your
techniques and theory. That’s the time to come back to this section.
Note that this means that we can write the enterprise balance sheet in a slightly different
form:
We can use the FCF projections and a cost of capital to determine the enterprise value of
the firm. Suppose we have determined that the firm’s weighted average cost of capital (WACC)
Then the enterprise value of the firm is the discounted value of the firm’s projected
is 20%.2
FCFs plus its terminal value:
In this formula, the Year-5 Terminal Value is a proxy for the present value of all FCFs from year
6 onwards.3
Terminal value
In determining the terminal value we use a version of the Gordon model described in
Chapter 6. We have assumed that—after the year 5 projection horizon—the cash flows will
grow at a rate of growth equal to the sales growth of 10%. This gives the terminal value as:
2
In Chapter 6 we introduced the topic of the WACC and showed you how to calculate this using the Gordon
dividend model. In Chapter 14 we show an alternative calculation of the WACC which uses the security market
line. In this chapter we simply assume a value for the WACC.
3
We don’t actually project these cash flows. We determine the terminal value based on year-5 FCF.
The last equality is derived in a manner similar to the dividend valuation of shares (the Gordon
model) discussed in Chapter 6.
Summary
The valuation of a business (“how much is it worth”) is one of the most important
activities of a financial analyst. In this chapter we have described how to do a discounted cash
flow (DCF) valuation using the financial planning models of Chapter 8. To do a DCF valuation
you have to understand almost all facets of the business:
How the business works—this affects the financial parameters used in the financial
planning model. The composition of the firm’s current assets and current liabilities
(meaning: its net working capital needed to do its business) and the amount of fixed
assets (buildings and equipment and land) needed to do this business—all of these factors
affect a firm’s valuation.
How to compute the cost of capital. The weighted average cost of capital (WACC) is the
discount rate used to value the future FCFs of the firm. In this chapter we have not
discussed its computation (Chapters 6 and 15 give different aspects of the WACC computation).
How to use Excel to do the relevant computations.
6.1. What does the firm’s WACC mean?
The weighted average cost of capital (WACC) is the average return that the company
has to pay to its equity and debt investors. Another way of putting this is that the WACC is the
2
average return shareholders and debtholders expect to receive from the company. The
definition of the WACC is:
Here’s a simple example to show what we mean: United Transport Inc. has 3 million
shares outstanding; the current market price per share is $10. The company has also borrowed
. United
$10 million from its banks at a rate of 8%; this is the company’s cost of debt r
D = 40%.Transport has a tax rate of TC
The company thinks its shareholders want an annual return on their investment of 20%; this 20% return is the
company’s cost of equity r .To compute United Transport’s WACC we use the formula:
2
In finance the expected return, the required return, the cost of capital (be it cost of equity or cost of debt), the
required rate of return are all synonyms. They all represent the market-adjusted rate that investors get (or
demand)
on various investments or securities.
3
We use the symbol T to indicate the corporate tax rate.
The United Transport WACC computation shows you that the WACC depends on five
critical variables. r , the cost of equity. r is the return required by the firm’s shareholders. Of the five
parameters in the WACC calculation, r is the most difficult to calculate. A model for calculating r
is given in Section 6.2.
4
How did United Transport come to the conclusion that its shareholders want a 20% return? This is the
question in
the computation of the WACC, and we will spend a lot of this chapter discussing the answer. So be patient!
 E, the market value of a firm’s equity. We will usually take E to equal the number of
shares of the firm times the market price per share.
 r , the cost of debt. r is the cost of borrowing for the firm. In most cases we will take
D D
r
to be the firm’s marginal interest rate—the interest rate at which the firm could borrow
D
additional funds from its banks or by selling bonds. A detailed example of the
calculation of r
for an actual firm is given in Section 6.4.
D
 D, the market value of the firm’s debt. In most cases we will take D to be the total value
of the firm’s financial obligations. An actual example of a calculation for D is given
below in Section 6.4.
 T , the firm’s tax rate. Most often we calculate T by computing the average tax rate of
CC
the firm; see Section 6.4 for an example.
6.2. The Gordon dividend model: discounting anticipated dividends to derive
the firm’s cost of equity r
In this section we present a formula for computing the firm’s cost of equity r . We will
call the formula the Gordon dividend model, in honor of Myron Gordon who first set out the
5
model in 1959.
This section has two subsections:
In the first subsection we derive a model for calculating the value of a firm’s shares based
on their future anticipated dividends.
5
The model is sometimes simply called the Gordon model; others call it the dividend discount model.
Summing up
In this chapter we have calculated the firm’s weighted-average cost of capital (WACC).
The WACC is the risk-adjusted discount rate for the firm’s free cash flows. It is often used to
value projects whose riskiness is similar to the riskiness of the firm’s existing activities, and it is
also used to derive the value of the firm. Both of these uses have been illustrated in this chapter.
The WACC is defined as:
In the table below we summarize how we derived each of the elements of this formula:
A final warning
Cost of capital calculations are critical for valuations and controversial. They involve a
mixture of theory and judgment. Almost every number in the WACC calculation above can be
determined in several ways. In many cases professionals do extensive sensitivity analysis on the
WACC and the FCF growth to establish a price range—the range of valuations which appears to
be reasonable, given the variation in plausible assumptions. The most important modification you might want to
make to the WACC calculation above involves the cost of equity r.An important competing model to the
Gordon model is the capital asset pricing model (CAPM). In Chapter 14 we will show you how to use this
model to calculate the cost of equity.