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It can be hard to understand how stock analysts come up with "fair value" for companies, or

why their target price estimates vary so wildly. The answer often lies in how they use the

valuation method known as discounted cash flow (DCF). However, you don't have to rely on

the word of analysts. With some preparation and the right tools, you can value a company's

stock yourself using this method. This tutorial will show you how, taking you step-by-step

through a discounted cash flow analysis of a fictional company. 

In simple terms, discounted cash flow tries to work out the value of a company today, based

on projections of how much money it's going to make in the future. DCF analysis says that a

company is worth all of the cash that it could make available to investors in the future. It is

described as"discounted" cash flow because cash in the future is worth less than cash today.

(To learn more, see The Essentials Of Cash Flow and Taking Stock Of Discounted Cash

Flow.) 

For example, let's say someone asked you to choose between receiving $100 today and

receiving $100 in a year. Chances are you would take the money today, knowing that you

could invest that $100 now and have more than $100 in a year's time. If you turn that

thinking on its head, you are saying that the amount that you'd have in one year is worth

$100 dollars today - or the discounted value is $100. Make the same calculation for all the

cash you expect a company to produce in the future and you have a good measure of the

company's value. 

There are several tried and true approaches to discounted cash flow analysis, including

the dividend discount model (DDM) approach and the cash flow to firm approach. In this

tutorial, we will use thefree cash flow to equity approach commonly used by Wall Street

analysts to determine the "fair value" of companies. 

As an investor, you have a lot to gain from mastering DCF analysis. For starters, it can serve

as a reality check to the fair value prices found in brokers' reports. DCF analysis requires you

to think through the factors that affect a company, such as future sales growth and profit

margins. It also makes you consider the discount rate, which depends on a risk-free interest

rate, the company's costs of capital and the risk its stock faces. All of this will give you an

appreciation for what drives share value, and that means you can put a more realistic price

tag on the company's stock. 

To demonstrate how this valuation method works, this tutorial will take you step-by-step

through a DCF analysis of a fictional company called The Widget Company. Let's begin by

looking at how to determine the forecast period for your analysis and how to forecast

revenue growth. 

Next: DCF Analysis: The Forecast Period & Forecasting Revenue Growth » 

Table of Contents

1. DCF Analysis: Introduction2. DCF Analysis: The Forecast Period & Forecasting Revenue Growth3. DCF Analysis: Forecasting Free Cash Flows4. DCF Analysis: Calculating The Discount Rate5. DCF Analysis: Coming Up With A Fair Value6. DCF Analysis: Pros & Cons Of DCF7. DCF Analysis: Conclusion

DCF Analysis: The Forecast Period & Forecasting Revenue GrowthFiled Under » Cash Flow, Cash Flow Statement, Equity Valuation, Financial

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The Forecast Period 

The first order of business when doing discounted cash flow (DCF) analysis is to determine

how far out into the future we should project cash flows. 

For the purposes of our example, we'll assume that The Widget Company is growing faster

than thegross domestic product (GDP) expansion of the economy. During this "excessive

return" period, The Widget Company will be able to earn returns on new investments that

are greater than its cost of capital. So, our discounted cash flow needs to forecast the

amount of free cash flow that the company will produce for this period. 

The excess return period tells us how far into the future we should forecast the company's

cash flows. Alas, it's impossible to say exactly how long this period of excess returns will

last. The best we can do is make an educated guess based on the company's competitive

and market position. Sooner or later, all companies settle into maturity and slower growth.

(The common practice with DCF analysis is to make the excess return period the forecast

period. But it is important to note that this valuation method does not restrict your analysis

to only excess return periods - you could estimate the value of a company growing slower

than the economy using DCF analysis too.) 

The table below shows good guidelines to use when determining a company's excess return

period/forecast period: 

Company Competitive PositionExcess

Return/Forecast Period

Slow-growing company; operates in highly competitive, low margin industry

1 year

Solid company; operates with advantage such as strong marketing channels, recognizable brand name, or regulatory advantage 

5 years

Outstanding growth company; operates with very high barriers to entry, dominant market position or prospects

10 years

Figure 1

How far in the future should we forecast The Widget Company's cash flows? Let's assume

that the company is keeping itself busy meeting the demand for its widgets. Thanks to

strong marketing channels and upgraded, efficient factories, the company has a reasonable

competitive position. There is enough demand for widgets to maintain five years of strong

growth, but after that the market will be saturated as new competitors enter the market. So,

we will project cash flows for the next five years of business. 

Revenue Growth Rate 

We have decided that we want to estimate the free cash flow that The Widget Company will

produce over the next five years. To arrive at this figure, the standard procedure is to

forecast revenuegrowth over that time period. Then (as we will see in later chapters), by

breaking down after-tax operating profits, estimated capital expenditure and working

capital needs, we can estimate the cash flow the company will produce. 

Let's start with top line growth. Forecasting a company's revenues is arguably the most

important assumption one can make about its future cash flows. It can also be the most

difficult assumption to make. (For more on forecasting sales, see Great Expectations:

Forecasting Sales Growth.) 

We need to think carefully about what the industry and the company could look like as they

evolve in the future. When forecasting revenue growth, we need to consider a wide variety

of factors. These include whether the company's market is expanding or contracting, and

how its market share is performing. We also need to consider whether there are any new

products driving sales or whether pricing changes are imminent. But because that future can

never be certain, it is valuable to consider more than one possible outcome for the

company. 

First, the upbeat revenue growth scenario: The Widget Company has grown revenues at

20% for the past two years, and your careful market research suggests that demand for

widgets will not let up any time soon. Management - always optimistic - argues that the

company will keep growing at 20%.

That being said, there may be reasons to downplay revenue growth expectations. While the

company's revenue growth will stay strong in the first few years, it could slow to a lower rate

by Year 5 as a result of increasing international competition and industry commoditization.

We should err on the side of caution and conservatism and assume that The Widget

Company's top line growth rate profile will commence at 20% for the first two years, then

drop to 15% for the next two years and finally drop to 10% in Year 5. Posting $100 million of

revenue in its latest annual report, the company is projected to grow its revenues to $209.5

million at the end of five years (based on realistic, rather than optimistic, growth

expectations). 

Forecast Revenue Growth Profiles 

Current Year Year 1 Year 2 Year 3 Year 4

- $100 M 

20% $120 M

20% $144 M 

20% $172.8 M 

20%$207.4 M

- $100 M 

20% $120 M

20% $144 M 

15% $165.6 M

15%$190.4 M

Figure 2

Now that we've determined our forecast period and our revenue growth for that period, we

can move on to the next step in our analysis, where we will estimate the free cash flow

produced over the forecast period. 

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Now that we have determined revenue growth for our forecast period of five years, we want

to estimate the free cash flow produced over the forecast period. 

Free cash flow is the cash that flows through a company in the course of a quarter or a year

once all cash expenses have been taken out. Free cash flow represents the actual amount of

cash that a company has left from its operations that could be used to pursue opportunities

that enhance shareholder value - for example, developing new products, paying dividends to

investors or doing share buybacks. (To learn more, see Free Cash Flow: Free, But Not Always

Easy.) 

Calculating Free Cash Flow 

We work out free cash flow by looking at what's left over from revenues after deducting

operating costs, taxes, net investment and the working capital requirements (see Figure

1). Depreciation andamortization are not included since they are non-cash charges. (For

more information, seeUnderstanding The Income Statement.) 

 Figure 1 - How free cash flow is calculated

In the previous chapter, we forecasted The Widget Company's revenues over the next five

years. Here we show you how to project the other items in our calculation over that period. 

Future Operating Costs 

When doing business, a company incurs expenses - such as salaries, cost of goods

sold (CoGS),selling and general administrative expenses (SGA), and research and

development (R&D). These are the company's operating costs. If current operating costs are

not explicitly stated on a company's income statement, you can calculate them by

subtracting net operating profits - or earnings before interest and taxation (EBIT) - from total

revenues. 

A good place to start when forecasting operating costs is to look at the company's historic

operating cost margins. The operating margin is operating costs expressed as a proportion

of revenues. 

For three years running, The Widget Company has generated an average operating cost

margin of 70%. In other words, for every $1 of revenue, the company incurs $0.70 in

operating costs. Management says that its cost cutting program will push those margins

down to 60% of revenues over the next five years. 

However, as analysts and investors, we should be concerned that competing widget

factories might be built, thus squeezing The Widget Company's profitability. Therefore, as

we did when forecasting revenues, we will err on the side of conservatism and assume that

operating costs will show anincrease as a percentage of revenues as the company is forced

to lower its prices to stay competitive over time. Let's say operating costs will hold at 65% of

revenues over the first three projected years, but will increase to 70% in Year 4 and Year 5

(see Figure 2). 

Taxation 

Many companies do not actually pay the official corporate tax rate on their operating profits.

For instance, companies with high capital expenditures receive tax breaks. So, it makes

sense to calculate the tax rate by taking the average annual income tax paid over the past

few years divided by profits before income tax. This information is available on the

company's historic income statements. 

Let's assume that for each of the past three years, The Widget Company paid 30% income

tax. We will project that the company will continue to pay that 30% tax rate over the next

five years (see Figure 2). 

Net Investment 

To underpin growth, companies need to keep investing in capital items such as property,

plants and equipment. You can calculate net investment by taking capital expenditure,

disclosed in a company's statement of cash flows, and subtracting non-cash depreciation

charges, found on the income statement. 

Let's say The Widget Company spent $10 million last year on capital expenditures, with

depreciation of $3 million, giving net investment of $7 million, or 7% of total revenues (see

Figure 2). But in the two prior years, the company's net investment was much higher: 10%

of revenues. 

If competition does intensify in the widget industry, The Widget Company will almost

certainly have to boost capital investment to stay ahead. So, we will assume that net

investment will steadily return to its normal level of 10% of sales over the next five years, as

seen in Figure 2: 7.6% of sales in Year 1, 8.2% in Year 2, 8.8% in Year 3, 9.4% in Year 4 and

10% in Year 5. 

Figure 2 - Forecasting The Widget Company\'s operating costs, taxes, net investment and change in working capital over the five-year forecast period

Change in Working Capital 

Working capital refers to the cash a business requires for day-to-day operations, or, more

specifically, short-term financing to maintain current assets such as inventory. The faster a

business expands, the more cash it will need for working capital and investment. 

Working capital is calculated as current assets minus current liabilities. These items are

found on the company's balance sheet, published in its quarterly and annual financial

statements. At year end, The Widget Company's balance sheet showed current assets of

$25 million and current liabilities of $16 million, giving net working capital of $9 million. 

Net change in working capital is the difference in working capital levels from one year to the

next. When more cash is tied up in working capital than the previous year, the increase in

working capital is treated as a cost against free cash flow. 

Working capital typically increases as sales revenues grow, so a bigger investment of

inventory andreceivables will be needed to match The Widget Company's revenue growth.

In our forecast, we will assume that changes in working capital are proportional to revenue

growth. In other words, if revenues grow by 20% in the first year, working capital

requirements will grow by 20% in the first year, from $9 million to $10.8 million (see Figure

2). Meanwhile, we will keep a close watch for any signs of a changing trend. 

Figure 3 - Free cash flow forecast calculation for The Widget Company

As you can see in Figure 3, we've determined our estimated free cash flow for our forecast

period. Now we are one step closer to finding a value for the company. In the next section of

the tutorial, we will estimate the value at which we will discount the free cash flows. 

Next: DCF Analysis: Calculating The Discount Rate » 

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Having projected the company's free cash flow for the next five years, we want to figure out

what these cash flows are worth today. That means coming up with an appropriate discount

rate which we can use to calculate the net present value (NPV) of the cash flows. 

So, how do we figure out the company's discount rate? That's a crucial question, because a

difference of just one or two percentage points in the cost of capital can make a big

difference in a company's fair value. 

A wide variety of methods can be used to determine discount rates, but in most cases, these

calculations resemble art more than science. Still, it is better to be generally correct than

precisely incorrect, so it is worth your while to use a rigorous method to estimate the

discount rate. 

A good strategy is to apply the concepts of the weighted average cost of capital (WACC).

The WACC is essentially a blend of the cost of equity and the after-tax cost of debt. (For

more information, seeInvestors Need A Good WACC.) Therefore, we need to look at how cost

of equity and cost of debt are calculated. 

Cost of Equity 

Unlike debt, which the company must pay at a set rate of interest, equity does not have a

concrete price that the company must pay. But that doesn't mean that there is no cost of

equity. Equity shareholders expect to obtain a certain return on their equity investment in a

company. From the company's perspective, the equity holders' required rate of return is a

cost, because if the company does not deliver this expected return, shareholders will simply

sell their shares, causing the price to drop. 

Therefore, the cost of equity is basically what it costs the company to maintain a share price

that is satisfactory (at least in theory) to investors. The most commonly accepted method

for calculating cost of equity comes from the Nobel Memorial Prize-winning capital asset

pricing model (CAPM), where: Cost of Equity (Re) = Rf + Beta (Rm-Rf). 

Let's explain what the elements of this formula are: 

Rf - Risk-Free Rate - This is the amount obtained from investing in securities considered

free from credit risk, such as government bonds from developed countries. The interest rate

of U.S. Treasury bills or the long-term bond rate is frequently used as a proxy for the risk-

free rate. 

ß - Beta - This measures how much a company's share price moves against the market as a

whole. Abeta of one, for instance, indicates that the company moves in line with the market.

If the beta is in excess of one, the share is exaggerating the market's movements; less than

one means the share is more stable. Occasionally, a company may have a negative beta

(e.g. a gold mining company), which means the share price moves in the opposite direction

to the broader market. (To learn more, seeBeta: Know The Risk.) 

(Rm – Rf) = Equity Market Risk Premium - The equity market risk premium (EMRP)

represents the returns investors expect, over and above the risk-free rate, to compensate

them for taking extra risk by investing in the stock market. In other words, it is the

difference between the risk-free rate and the market rate. It is a highly contentious figure.

Many commentators argue that it has gone up due to the notion that holding shares has

become riskier. 

Barra and Ibbotson are valuable subscription services that offer up-to-date equity market

risk premium rates and betas for public companies. 

Once the cost of equity is calculated, adjustments can be made to take account of risk

factors specific to the company, which may increase or decrease the risk profile of the

company. Such factors include the size of the company, pending lawsuits, concentration of

customer base and dependence on key employees. Adjustments are entirely a matter of

investor judgment and they vary from company to company. 

Cost of Debt 

Compared to cost of equity, cost of debt is fairly straightforward to calculate. The rate

applied to determine the cost of debt (Rd) should be the current market rate the company is

paying on its debt. If the company is not paying market rates, an appropriate market rate

payable by the company should be estimated. 

As companies benefit from the tax deductions available on interest paid, the net cost of the

debt is actually the interest paid less the tax savings resulting from the tax-deductible

interest payment. Therefore, the after-tax cost of debt is Rd (1 - corporate tax rate). 

Finally, Capital Structure 

The WACC is the weighted average of the cost of equity and the cost of debt based on the

proportion of debt and equity in the company's capital structure. The proportion of debt is

represented by D/V, a ratio comparing the company's debt to the company's total value

(equity + debt). The proportion of equity is represented by E/V, a ratio comparing the

company's equity to the company's total value (equity + debt). The WACC is represented by

the following formula: WACC = Rex E/V + Rd x (1 - corporate tax rate) x D/V. 

A company's WACC is a function of the mix between debt and equity and the cost of that

debt and equity. On the one hand, in the past few years, falling interest rates have reduced

the WACC of companies. On the other hand, corporate disasters like those at Enron and

WorldCom have increased the perceived risk of equity investments. 

Be warned: the WACC formula seems easier to calculate than it really is. Rarely will two

people derive the same WACC, and even if two people do reach the same WACC, all the

other applied judgments and valuation methods will likely ensure that each has a different

opinion regarding the components that comprise the company's value. 

Widget Company WACC 

Returning to our example, let's suppose The Widget Company has a capital structure of 40%

debt and 60% equity, with a tax rate of 30%. The borrowing rate (Rd) on the company's debt

is 5%. The risk-free rate (Rf) is 5%, the beta is 1.3 and the risk premium (Rp) is 8%. The

WACC comes to 10.64%. So, rounded up to the nearest percentage, the discount rate for

The Widget Company would be 11% (see Figure 1). 

WACC for The Widget Company 

Cost of Debt Cost of Equity

0.40 [Rd x (1-.30)] + 0.40 [5.0 x 0.7)] + 0.40 [3.5] + 

0.60 [RF + b(RP)] 0.60 [5.0 + 1.3(8)] 0.60 [15.4] 

1.40 + WACC Rounded WACC 

9.24 10.64% 11% 

Figure 1

In the next section of the tutorial, we'll do the final calculations to generate a fair value for

the Widget Company. 

Next: DCF Analysis: Coming Up With A Fair Value » 

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Now that we have calculated the discount rate for the Widget Company, it's time to do the

final calculations to generate a fair value for the company's equity. 

Calculate the Terminal Value 

Having estimated the free cash flow produced over the forecast period, we need to come up

with a reasonable idea of the value of the company's cash flows after that period - when the

company has settled into middle-age and maturity. Remember, if we didn't include the value

of long-term future cash flows, we would have to assume that the company stopped

operating at the end of the five-year projection period. 

The trouble is that it gets more difficult to forecast cash flows over time. It's hard enough to

forecast cash flows over just five years, never mind over the entire future life of a company.

To make the task a little easier, we use a "terminal value" approach that involves making

some assumptions about long-term cash flow growth. 

Gordon Growth Model 

There are several ways to estimate a terminal value of cash flows, but one well-worn method

is to value the company as a perpetuity using the Gordon Growth Model. The model uses

this formula: 

Terminal Value = Final Projected Year Cash Flow X (1+Long-Term Cash Flow Growth Rate) (Discount Rate – Long-Term Cash Flow Growth Rate)

The formula simplifies the practical problem of projecting cash flows far into the future. But

keep in mind that the formula rests on the big assumption that the cash flow of the last

projected year will stabilize and continue at the same rate forever. This is an average of the

growth rates, not one expected to occur every year into perpetuity. Some growth will be

higher or lower, but the expectation is that future growth will average the long-term growth

assumption. 

Returning to the Widget Company, let's assume that the company's cash flows will grow in

perpetuity by 4% per year. At first glance, 4% growth rate may seem low. But seen another

way, 4% growth represents roughly double the 2% long-term rate of the U.S. economy into

eternity. 

In the section on "Forecasting Free Cash Flows", we forecast free cash flow of $21.3 million

for Year 5, the final or "terminal" year in our Widget Company projections. You will also

recall that we calculated The Widget Company's discount rate as 11% (see "Calculating The

Discount Rate"). We can now calculate the terminal value of the company using the Gordon

Growth Model: 

Widget Company Terminal Value = $21.3M X 1.04/ (11% - 4%) = $316.9M

Exit Multiple Model 

Another way to determine a terminal value of cash flows is to use a multiplier of some

income or cash flow measure, such as net income, net operating profit, EBITDA (earnings

before interest, taxes, depreciation, and amortization), operating cash flow or free cash flow.

The multiple is generally determined by looking at how comparable companies are valued

by the market. Was there a recent sale of stock of a similar company? What is the standard

industry valuation for a company at the same stage of maturity? 

In Year 5, the Widget Company is expected to produce free cash flow of $21.3M. Multiplying

this by a projected price-to-free cash flow of 15 gives us a terminal value of $319.9M. 

Widget Company Terminal Value = $21.3M X 15 = $319.9M

You will see that the terminal value can contribute a great deal to total value, so it is

important to use an exit multiple that can be justified. One way to make the multiple more

believable is to give estimates on the conservative side. Justifying a multiple of 15 with your

figures would certainly be easier to justify than one at 20 or 25. Because it can be tricky to

justify the multiple, this method isn't used as much as the Gordon Growth Model. 

Calculating Total Enterprise Value 

Now you have the following free cash flow projection for the Widget Company. 

Year 1 Year 2 Year 3 Year 4 Year 5Terminal Value (Gordon Growth

$18.5M$21.3

M$24.1M

$19.9M

$21.3M $316.9M

Figure 1

To arrive at a total company value, or enterprise value (EV), we simply have to take the

present value of the cash flows, divide them by the Widget Company's 11% discount rate

and, finally, add up the results. 

EV = ($18.5M/1.11) + ($21.3M/(1.11)2) + ($24.1M/(1.11)3) + ($19.9M/(1.11)4) + ($21.3M/(1.11)5) + ($316.9M/(1.11)5) EV = $265.3M

Therefore, the total enterprise value for The Widget Company is $265.3 million. 

Calculating the Fair Value of Equity 

But we are not finished yet - we cannot forget about debt. The Widget Company's $265.3M

enterprise value includes the company's debt. As equity investors, we are interested in the

value of the company's shares alone. To come up with a fair value of the company's equity,

we must deduct its net debt from the value. 

Let's say The Widget Company has $50M in net debt on its balance sheet. We subtract that

$50M from the company's $265.3M enterprise value to get the equity value. 

Fair Value of Widget Company Equity = Enterprise Value – Debt Fair Value of Widget Company = $265.3M - $50M =$215.3M

So, by our calculations, the Widget Company's equity has a fair value of $215.3 million.

That's it - the DCF valuation is complete. 

Having finished the DCF valuation, we can judge the merits of buying Widget Company

shares. If we divide the fair value by the number of Widget Company shares outstanding, we

get a fair value for the company's shares. If the shares are trading at a lower value than this,

they could represent a buying opportunity for investors. If they are trading higher than the

per share fair value, shareholders may want to consider selling Widget Company stock. 

You are familiar with the mechanics of DCF analysis and you have seen it applied to a

practical example; now it's time to consider the strengths and weaknesses of this valuation

tool. What makes DCF better than other valuation methods? What are its shortcomings? We

answer those questions in the following section of this tutorial. 

Next: DCF Analysis: Pros & Cons Of DCF » 

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Having worked our way through the mechanics of discounted cash flow analysis, it is worth

our while to examine the method's strengths and weaknesses. There is a lot to like about

the valuation tool, but there are also reasons to be cautious about it. 

Advantages 

Arguably the best reason to like DCF is that it produces the closest thing to an intrinsic stock

value. The alternatives to DCF are relative valuation measures, which use multiples to

compare stocks within a sector. While relative valuation metrics such as price-earnings (P/E),

EV/EBITDA and price-to-salesratios are fairly simple to calculate, they aren't very useful if an

entire sector or market is over or undervalued. A carefully designed DCF, by contrast, should

help investors steer clear of companies that look inexpensive against expensive peers. (To

learn more, see Relative Valuation: Don't Get Trapped.) 

Unlike standard valuation tools such as the P/E ratio, DCF relies on free cash flows. For the

most part, free cash flow is a trustworthy measure that cuts through much of the

arbitrariness and "guesstimates" involved in reported earnings. Regardless of whether a

cash outlay is counted as an expense or turned into an asset on the balance sheet, free cash

flow tracks the money left over for investors. 

Best of all, you can also apply the DCF model as a sanity check. Instead of trying to come up

with a fair value stock price, you can plug the company's current stock price into the DCF

model and, working backwards, calculate how quickly the company would have to grow its

cash flows to achieve the stock price. DCF analysis can help investors identify where the

company's value is coming from and whether or not its current share price is justified. 

Disadvantages 

Although DCF analysis certainly has its merits, it also has its share of shortcomings. For

starters, the DCF model is only as good as its input assumptions. Depending on what you

believe about how a company will operate and how the market will unfold, DCF valuations

can fluctuate wildly. If your inputs - free cash flow forecasts, discount rates and perpetuity

growth rates - are wide of the mark, the fair value generated for the company won't be

accurate, and it won't be useful when assessing stock prices. Following the "garbage in,

garbage out" principle, if the inputs into the model are "garbage", then the output will be

similar. 

DCF works best when there is a high degree of confidence about future cash flows. But

things can get tricky when a company's operations lack what analysts call "visibility" - that

is, when it's difficult to predict sales and cost trends with much certainty. While forecasting

cash flows a few years into the future is hard enough, pushing results into eternity (which is

a necessary input) is nearly impossible. The investor's ability to make good forward-looking

projections is critical - and that's why DCF is susceptible to error. 

Valuations are particularly sensitive to assumptions about the perpetuity growth rates and

discount rates. Our Widget Company model assumed a cash flow perpetuity growth rate of

4%. Cut that growth to 3%, and the Widget Company's fair value falls from $215.3 million to

$190.2 million; lift the growth to 5% and the value climbs to $248.7 million. Likewise, raising

the 11% discount rate by 1% pushes the valuation down to $182.7 million, while a 1% drop

boosts the Widget Company's value to $258.9 million. 

DCF analysis is a moving target that demands constant vigilance and modification. A DCF

model is never built in stone. If the Widget Company delivers disappointing quarterly results,

if its major customer files for bankruptcy, or if interest rates take a dramatic turn, you will

need to adjust your inputs and assumptions. If any time expectations change, the fair value

will change. 

That's not the only problem. The model is not suited to short-term investing. DCF focuses on

long-term value. Just because your DCF model produces a fair value of $215.3 million that

does not mean that the company will trade for that any time soon. A well-crafted DCF may

help you avoid buying into a bubble, but it may also make you miss short-term share price

run-ups that can be profitable. Moreover, focusing too much on the DCF may cause you to

overlook unusual opportunities. For example, Microsoft seemed very expensive back in

1995, but its ability to dominate the software market made it an industry powerhouse and

an investor's dream soon after. 

DCF is a rigorous valuation approach that can focus your mind on the right issues, help you

see the risk and help you separate winning stocks from losers. But bear in mind that while

the DCF technique we've sketched out can help reduce uncertainty, it won't make it

disappear. 

What's clear is that investors should be conservative about their inputs and should not resist

changing them when needed. Aggressive assumptions can lead to inflated values and cause

you to pay too much for a stock. The best way forward is to examine valuation from a

variety of perspectives. If the company looks inexpensive from all of them, chances are

better that you have found a bargain. 

Next: DCF Analysis: Conclusion » 

DCF Analysis: ConclusionFiled Under » Cash Flow, Cash Flow Statement, Equity Valuation,Financial

Statements Fundamental Analysis, Fundamental Analysis, Cash Flow, Cash Flow

Statement,Equity Valuation, Financial Statements

Investopedia: Are you looking for more information on currency trading? Try our Forex Walkthrough, it goes from beginner to advanced.

By Ben McClure 

Contact Ben 

As you have seen, DCF analysis tries to work out the value of a company today, based on

projections of how much money it will generate in the future. The basic idea is that the value

of any company is the sum of the cash flows that it produces in the future, discounted to the

present at an appropriate rate. 

In this tutorial, we have shown you the basic technique used to generate fair values for the

stocks that you follow. But keep in mind that this is just one approach to doing DCF analysis;

every analyst has his or her own theories on how it should be done. 

Although manually working your way through all the numbers in DCF analysis can be a time-

consuming and tricky process at times, it's not impossible. Yes, using a DCF model probably

entails a lot more work than relying on traditional valuation measures such as the P/E ratio,

but we hope this step-by-step guide has shown you that it is worth the effort. 

DCF analysis treats a company as a business rather than just a ticker symbol and a stock

price, and it requires you to think through all the factors that will affect the company's

performance. What DCF analysis really gives you is an appreciation for what drives stock

values. 

Here are some external resources that you may want to check out: 

Damodaran Online - Aswarth Damodaran, professor of finance at New York University's Stern

School of Business, has created an excellent website devoted to valuation techniques. He

offers numerous DCF models set up in Excel spreadsheets, and he gives details on the

intricacies of the models. 

Valuing Intel: A Strange Tale Of Analysts And Announcements - Bradford Cornell, professor

at UCLA's Anderson Graduate School of Management, has produced an excellent DCF

analysis that assesses market and stock analysts' reactions to an Intel Corp. earnings

announcement. 

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Discounted Cash Flow

Discounted Cash Flow – Not just a discount? | Photo: CGIpromotions

The purpose of the Discounted Cash Flow (DCF) valuation is to find the sum of the

future cash flow of the business and discount it back to a present value. I use the F Wall

Street method of valuing a business along with some tweaks here and there to suit my

tastes in the free and best valuation spreadsheets you can find on this site.

The advantage of this method is that it requires the investor to think about the stock as

a business and analyze its cash flow rather than earnings.

The first and foremost reason a business exists is to make money where money = cash,

not earnings. Since cash is what a business needs in order to maintain and grow its

operations, it’s only right to consider the possibility of its future cash growth rather than

earnings growth.

The disadvantage is that DCF is not suitable for start ups, growth companies or capital

intensive companies where the cash flow cannot be accurately determined. The error of

prediction and assumptions must also be dealt with in the DCF, which we cover with

margin of safety.

I’ll go through the many assumptions to consider with a DCF and how to effectively use

it with the stock valuation calculator

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Discounted cash flowFrom Wikipedia, the free encyclopedia

This article needs additional citations for verification. Please help improve this article byadding citations to reliable sources. Unsourced material may be challenged and removed.(January 2010)

Spreadsheet uses Free cash flows to estimate stock's Fair Value and measure the sensibility of WACC and Perpetual

growth

In finance, discounted cash flow (DCF) analysis is a method of valuing a project, company, or asset using the

concepts of the time value of money. All future cash flows are estimated and discounted to give their present

values (PVs)—the sum of all future cash flows, both incoming and outgoing, is the net present value (NPV),

which is taken as the value or price of the cash flows in question. Present value may also be expressed as a

number of years' purchase of the future undiscounted annual cash flows expected to arise.

Using DCF analysis to compute the NPV takes as input cash flows and a discount rate and gives as output a

price; the opposite process—taking cash flows and a price and inferring a discount rate—is called the yield.

Discounted cash flow analysis is widely used in investment finance, real estate development, corporate

financial management and patent valuation.

Contents

  [hide] 

1   Discount rate

2   History

3   Mathematics

o 3.1   Discounted cash flows

o 3.2   Continuous cash flows

4   Example DCF

5   Methods of appraisal of a company or project

6   Shortcomings

7   See also

8   References

9   External links

10   Further reading

Discount rate[edit]

Main article: Discounting

The most widely used method of discounting is exponential discounting, which values future cash flows as

"how much money would have to be invested currently, at a given rate of return, to yield the cash flow in

future." Other methods of discounting, such ashyperbolic discounting, are studied in academia and said to

reflect intuitive decision-making, but are not generally used in industry.

The discount rate used is generally the appropriate weighted average cost of capital (WACC), that reflects the

risk of the cashflows. The discount rate reflects two things:

1. Time value of money (risk-free rate) – according to the theory of time preference, investors would

rather have cash immediately than having to wait and must therefore be compensated by paying for

the delay

2. Risk premium  – reflects the extra return investors demand because they want to be compensated for

the risk that the cash flow might not materialize after all

History[edit]

Discounted cash flow calculations have been used in some form since money was first lent at interest in

ancient times. As a method of asset valuation it has often been opposed to accounting book value, which is

based on the amount paid for the asset. Following the stock market crash of 1929, discounted cash flow

analysis gained popularity as a valuation method for stocks. Irving Fisher in his 1930 book The Theory of

Interest and John Burr Williams's 1938 text The Theory of Investment Value first formally expressed the DCF

method in modern economic terms.

Mathematics[edit]

Discounted cash flows[edit]

The discounted cash flow formula is derived from the future value formula for calculating the time value of

money and compounding returns.

Thus the discounted present value (for one cash flow in one future period) is expressed as:

where

DPV is the discounted present value of the future cash flow (FV), or FV adjusted for the

delay in receipt;

FV is the nominal value of a cash flow amount in a future period;

i is the interest rate, which reflects the cost of tying up capital and may also allow for the risk

that the payment may not be received in full;

d is the discount rate, which is i/(1+i), i.e., the interest rate expressed as a deduction at the

beginning of the year instead of an addition at the end of the year;

n is the time in years before the future cash flow occurs.

Where multiple cash flows in multiple time periods are discounted, it is necessary to sum them as

follows:

for each future cash flow (FV) at any time period (t) in years from the present time, summed

over all time periods. The sum can then be used as a net present value figure. If the amount

to be paid at time 0 (now) for all the future cash flows is known, then that amount can be

substituted for DPV and the equation can be solved for i, that is the internal rate of return.

All the above assumes that the interest rate remains constant throughout the whole period.

Continuous cash flows[edit]

For continuous cash flows, the summation in the above formula is replaced by an integration:

where FV(t) is now the rate of cash flow, and λ = log(1+i).

DF (r/1+r)-1

Example DCF[edit]

To show how discounted cash flow analysis is performed, consider the following

simplified example.

John Doe buys a house for $100,000. Three years later, he expects to be able to

sell this house for $150,000.

Simple subtraction suggests that the value of his profit on such a transaction would be

$150,000 − $100,000 = $50,000, or 50%. If that $50,000 is amortized over the three

years, his implied annual return (known as the internal rate of return) would be about

14.5%. Looking at those figures, he might be justified in thinking that the purchase

looked like a good idea.

1.1453 x 100000 = 150000 approximately.

However, since three years have passed between the purchase and the sale, any cash

flow from the sale must be discounted accordingly. At the time John Doe buys the

house, the 3-year US Treasury Note rate is 5% per annum. Treasury Notes are

generally considered to be inherently less risky than real estate, since the value of the

Note is guaranteed by the US Government and there is aliquid market for the purchase

and sale of T-Notes. If he hadn't put his money into buying the house, he could have

invested it in the relatively safe T-Notes instead. This 5% per annum can therefore be

regarded as the risk-free interest rate for the relevant period (3 years).

Using the DPV formula above (FV=$150,000, i=0.05, n=3), that means that the value of

$150,000 received in three years actually has apresent value of $129,576 (rounded off).

In other words we would need to invest $129,576 in a T-Bond now to get $150,000 in 3

years almost risk free. This is a quantitative way of showing that money in the future is

not as valuable as money in the present ($150,000 in 3 years isn't worth the same as

$150,000 now; it is worth $129,576 now).

Subtracting the purchase price of the house ($100,000) from the present value results in

the net present value of the whole transaction, which would be $29,576 or a little more

than 29% of the purchase price.

Another way of looking at the deal as the excess return achieved (over the risk-free rate)

is (114.5 - 105)/(100 + 5) or approximately 9.0% (still very respectable).

But what about risk?

We assume that the $150,000 is John's best estimate of the sale price that he will be

able to achieve in 3 years time (after deducting all expenses, of course). There is of

course a lot of uncertainty about house prices, and the outcome may end up higher or

lower than this estimate.

(The house John is buying is in a "good neighborhood," but market values have been

rising quite a lot lately and the real estate market analysts in the media are talking about

a slow-down and higher interest rates. There is a probability that John might not be able

to get the full $150,000 he is expecting in three years due to a slowing of price

appreciation, or that loss of liquidity in the real estate market might make it very hard for

him to sell at all.)

Under normal circumstances, people entering into such transactions are risk-averse,

that is to say that they are prepared to accept a lower expected return for the sake of

avoiding risk. See Capital asset pricing model for a further discussion of this. For the

sake of the example (and this is a gross simplification), let's assume that he values this

particular risk at 5% per annum (we could perform a more precise probabilistic analysis

of the risk, but that is beyond the scope of this article). Therefore, allowing for this risk,

his expected return is now 9.0% per annum (the arithmetic is the same as above).

And the excess return over the risk-free rate is now (109 - 105)/(100 + 5) which comes

to approximately 3.8% per annum.

That return rate may seem low, but it is still positive after all of our discounting,

suggesting that the investment decision is probably a good one: it produces enough

profit to compensate for tying up capital and incurring risk with a little extra left over.

When investors and managers perform DCF analysis, the important thing is that the net

present value of the decision after discounting all future cash flows at least be positive

(more than zero). If it is negative, that means that the investment decision would

actually lose money even if it appears to generate a nominal profit. For instance, if the

expected sale price of John Doe's house in the example above was not $150,000 in

three years, but $130,000 in three years or $150,000 in five years, then on the above

assumptions buying the house would actually cause John to lose money in present-

value terms (about $3,000 in the first case, and about $8,000 in the second). Similarly, if

the house was located in an undesirable neighborhood and the Federal Reserve

Bank was about to raise interest rates by five percentage points, then the risk factor

would be a lot higher than 5%: it might not be possible for him to predict a profit in

discounted terms even if he thinks he could sell the house for $200,000 in three years.

In this example, only one future cash flow was considered. For a decision which

generates multiple cash flows in multiple time periods, all the cash flows must be

discounted and then summed into a single net present value.

Methods of appraisal of a company or project[edit]

This is necessarily a simple treatment of a complex subject: more detail is beyond the

scope of this article.

For these valuation purposes, a number of different DCF methods are distinguished

today, some of which are outlined below. The details are likely to vary depending on

the capital structure of the company. However the assumptions used in the appraisal

(especially the equity discount rate and the projection of the cash flows to be achieved)

are likely to be at least as important as the precise model used.

Both the income stream selected and the associated cost of capital model determine the

valuation result obtained with each method. This is one reason these valuation methods

are formally referred to as the Discounted Future Economic Income methods.

Equity-Approach

Flows to equity  approach (FTE)

Discount the cash flows available to the holders of equity capital, after allowing for cost

of servicing debt capital

Advantages: Makes explicit allowance for the cost of debt capital

Disadvantages: Requires judgement on choice of discount rate

Entity-Approach:

Adjusted present value  approach (APV)

Discount the cash flows before allowing for the debt capital (but allowing for the tax relief

obtained on the debt capital)

Advantages: Simpler to apply if a specific project is being valued which does not have

earmarked debt capital finance

Disadvantages: Requires judgement on choice of discount rate; no explicit allowance for

cost of debt capital, which may be much higher than a "risk-free" rate

Weighted average cost of capital  approach (WACC)

Derive a weighted cost of the capital obtained from the various sources and use that

discount rate to discount the cash flows from the project

Advantages: Overcomes the requirement for debt capital finance to be earmarked to

particular projects

Disadvantages: Care must be exercised in the selection of the appropriate income

stream. The net cash flow to total invested capital is the generally accepted choice.

Total cash flow  approach (TCF)[clarification needed]

This distinction illustrates that the Discounted Cash Flow method can be used to

determine the value of various business ownership interests. These can include equity

or debt holders.

Alternatively, the method can be used to value the company based on the value of total

invested capital. In each case, the differences lie in the choice of the income stream and

discount rate. For example, the net cash flow to total invested capital and WACC are

appropriate when valuing a company based on the market value of all invested capital.[1]

Shortcomings[edit]

Commercial banks have widely used discounted cash flow as a method of valuing

commercial real estate construction projects. This practice has two substantial

shortcomings. 1) The discount rate assumption relies on the market for competing

investments at the time of the analysis, which would likely change, perhaps dramatically,

over time, and 2) straight line assumptions about income increasing over ten years are

generally based upon historic increases in market rent but never factors in the cyclical

nature of many real estate markets. Most loans are made during boom real estate

markets and these markets usually last fewer than ten years. Using DCF to analyze

commercial real estate during any but the early years of a boom market will lead to

overvaluation of the asset[citation needed].

Discounted cash flow models are powerful, but they do have shortcomings. DCF is

merely a mechanical valuation tool, which makes it subject to the principle "garbage in,

garbage out". Small changes in inputs can result in large changes in the value of a

company. Instead of trying to project the cash flows to infinity, terminal value techniques

are often used. A simple annuity is used to estimate the terminal value past 10 years, for

example. This is done because it is harder to come to a realistic estimate of the cash

flows as time goes on involves calculating the period of time likely to recoup the initial

outlay.[2]

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How to Calculate Discounted Cash FlowBY Jonas Elmerraji|10/18/07 - 02:58 PM EDT

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NEW YORK (TheStreet) -- Discounted cash flows are used by pros in the finance world all the time

to figure out what an investment is actually worth. And while calculating discounted cash flows can

be an involved process, it can also be a lucrative one as well. Here's a look at DCF valuation and

how you can use it on your personal investments and finances.

What Are Discounted Cash Flows?Think of discounted cash flows this way: they're a way of taking a payoff from an investment in the

future, and putting it in terms of today's money. Discounted cash flows take into account the time

value of money -- the fact that one dollar 10 years from now is worth less than $1 today.

If I loan that dollar to someone, I'm costing myself all the interest or gains that I would earn if I saved

or invested it. I'm also pitting 10 years of inflation against my dollar's buying power. What that means

is that when all is said and done, my dollar's only worth around 51 cents (I'll get to how I calculated

that in a bit), which means that I'm losing about half of my money.

Discounted cash flows take these factors into account to calculate what a reasonable valuation is

today for a company's success years down the road.

Why Use Discounted Cash Flows?DCFs are omnipresent in the finance world -- they're used by everybody, from analysts to portfolio

managers -- even Warren Buffett is known to make decisions based on discounted cash flow

calculations. But why?

Discounted cash flows give investors a better picture of a company's value today because they

account for what it might be worth tomorrow. You probably wouldn't buy a car without knowing what

it's worth, so why would a stock be any different? Having a more relatable dollar value in front of you

can help you make better-informed investment decisions.

Discounting can actually be used for more than just cash flows. Historically, cash flows   have been

discounted because they represent cold hard tangible assets. They're also devoid of income

statement items like depreciation expenses that affect a company's income without affecting the

amount of money the company has.

How Do You Discount Cash Flows?Word to the wise: discounting cash flows involves math -- and a fair amount at that. One of the most

basic formulas for discounted cash flows is a present value calculation:

The discount rate mentioned in the formula is the opportunity cost (time value of money) -- in the

case of my dollar loan, it's the inflation and lost interest that made my dollar worth so much less 10

years after I lent it. In the case of stocks, the discount rate is typically the cost of the company's

capital.

It gets a little trickier for multiple periods. But never fear, for those of us who aren't

"mathemagicians," there are a plethora of online calculators (some of which you'll find in the

homework section of this article) that allow you to drop in your numbers in order to calculate the

present value of your cash flows.

How to Avoid Common DCF MistakesDiscounting cash flows can be tricky. Remember, you're using estimates here for future numbers, so

"bad" or unreasonable estimates can mean worthless numbers. According to Jim Troyer, a Principal

at The Vanguard Group, these future projections are one of the biggest snags for investors new to

DCF. "There are two main things people do," Troyer says, "make assumptions at random, and

project the past into the future." Troyer describes these mistakes as "blind trend projection" and

"inconsistent assumptions."

Troyer warns investors: "Most firms can't grow faster than the economy forever. When you use

discounted cash flows, it's important not to project too strong of growth rate too far out. A very small

change in something like the discount rate can have a huge affect on present value."

It's also important to remember that numbers aren't static -- they change over time. Don't put too

much stock in DCF valuations that might be out of date. A perfectly valid valuation made three years

ago might not be at all in line with a company's present day value.

DCF valuations represent long-term projections, so don't fall into the trap of thinking that just

because a company is supposedly overvalued it isn't a good short-term investment. Discounting

cash flows mainly deals with assessing a company's fundamentals and doesn't take into account the

technical issues that might send a "bad" stock's price soaring in the short run.

DCF Methods VaryThe methods used for discounting cash flows can vary depending on the type of investment you're

trying to value. Here are a few popular uses for DCF.

Bonds. One of the central elements of bond valuation is the use of discounted cash flows. With the

bonds, though, the numbers are a lot more concrete. Troyer says, "The bond market is essentially a

giant DCF engine. It's the same way with stocks, but the numbers aren't as scientific." Why? With a

bond, variables like number of periods, future cash flow, and discount rate (coupon in the case of a

bond), are all given and don't change.

Despite the fact that the discounting of bond cash flows are generally factored into the bond's

pricing, if you're into bonds, then understanding DCF is a must.

Stocks. Stocks are an area where DCF is a popular tool. The stock market is also a place where

poorly thought-out DCFs can lose big money.

Stocks have added elements of confusion when it comes to DCF since they don't have the static

numbers that bonds do. Because of this, calculating discounted cash flows for equities adds an extra

element of risk that's actually taken into account in more complex DCF equations.

Real estate. Real estate is another area where DCF calculations are popular. If you're a "flipper"

(someone who buys properties to quickly fix up and sell for a profit), then you're doing yourself a

major disservice if DCF doesn't come into your decision-making process.

DCF Recap: My $1 Loan ExampleLet's go back to my $1 loan. How did I determine that 10 years from now I'd only have 51 cents?

Because my friend will be repaying me with $1 in 10 years, the future cash flow to me is just $1.

To determine the discount rate (or rate of return, using a future value calculator), I had to consider

two things: inflation and the interest I'd be missing out on. With U.S. inflation currently around 2.5%

(according to the C.I.A. World Factbook), and my savings account paying out 4.5%, I'm missing out

on 7% annually. That's my discount rate. We'll compound annually for simplicity's sake, which would

mean 10 periods. So, taking the equation I showed you earlier, my equation will look something like

this:

Granted, this is a very simple example. If you want to learn more complex DCF computations, make

sure to check out the homework at the end of this article.

DCF valuation can be a fantastic tool to determine what an investment is worth in today's money.

But that doesn't mean that it's without its pitfalls -- bad assumptions and projections can break the

benefits of calculating DCF. When used correctly, discounted cash flows can really add a lot to your

investment decision process.

DCF HomeworkSo do you want to get Buffett-like analysis skills? Here are two activities that can help you hone your

ability to discount cash flows.

1. Explore Professor Damodaran's Web site. If you want to learn more advanced concepts and

formulas about discounted cash flows, visit the Web site of Professor Aswath Damodaran at the

NYU Stern School of Business. His site on valuation, corporate finance and investment offers lecture

notes, tutorials, sample problems and worksheets that can help enhance your valuation abilities.

2. Practice with online calculators. Go to an online DCF calculator and practice making your own

projections for real stocks with historical data. How do your estimates hold up? Here are a few online

calculators of varying complexity:

Present Value and Future Value (University of Illinois at Chicago)

Various Financial Calculation Tips for Microsoft Excel (Eastern Illinois University)

Jonas Elmerraji is the founder and publisher of Growfolio.com, an online business magazine for

young investors.

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Retail Investor .org

Valuing Stocks using Discounted Cash Flows

The Basic Issue

Before even thinking about valuing stocks using discounted

cash flows, first see how this method fits into the possible

investing strategies discussed on the Big Picture

Strategy page. This methodology for valuing projects is very

powerful. It has three basic inputs; the cash flow dollars, the

timing of those cash flows and the rate of return demanded.

But there are more than a few problems when trying to use it

for valuing stocks.

The model presumes receipt of, and benefit from, all the cash

flows by the investor himself. That will be true of the stock's

purchase and sale price and its dividends. But what about

companies which pay no (or small) dividends? Then the

eventual sale price becomes the dominant factor in the

stock's valuation. When the current value is derived from the

future resale price, any assumptions about the valuation at

the later date self-justify the current value. If the current value

depends on discounted cash flows, then that future sale price

will also depend on discounted cash flows. So any analysis

would have to go far into the future, until the discount rate

makes those cash flows immaterial. That analysis is never

done, with any valuation methods using cash flows.

The model has no inputs for dilutions of ownership

percentages. It is never calculated on a 'per-share' basis.

When shares are issued and bought-back, or when options

are used for compensation, the stock owner's percentage

ownership of the whole changes.

The model has no inputs for non-cash barter transactions,

e.g. DRIPs, or shares-for-buyouts.

As this methodology has gained popularity, so too

management has finessed analysts by hiding the company's

problems in these ignored transactions.

There remains the huge problem of defining exactly "what"

cash flow. For a directly owned project, all cash generated is

under the control of owners and available to them (the

total changes in cash = the first column of the diagram

below). But shareholders have no control over a company's

cash - either the total change in cash or possibly some

subset, of a subset, of a subset, of that total (working your

way to the right of the diagram). What definition of 'cash'

should be considered 'as if' under the control of

shareholders?

Discounted Dividends

An old valuation model using discounted cash flows is

the Discounted Dividend model (the Gordon Growth formula).

The formula is derived mathematically by summing the present

value (discounted value) of each future year's dividend. But is

it really a discounted cash flow model? No. It misses the point.

The idea behind calculating the Net Present Value of cash

flows requires an active estimate of each future cash flow - its

size and timing. In contrast, the discounted dividend models

simply assumes the cash flows to be equal (adjusted for

growth) forever. At best, an allowance is made for one change

(possibly two) in the future. What is being accomplished by the

calculation is not 'discounting cash flows'. The model

effectively 'capitalizes' the yield. There is a qualitative

difference between the two systems.

E.g. you find a perpetual preferred share's value by

'capitalizing' its income - by dividing the dividend $$ by your

required return. E.g. you capitalize real estate's profits by

dividing the operating cash flow by your required Cap Rate.

E.g. you find a stock's value by capitalizing its earnings -

dividing earnings by your required earnings yield (using P/E

metrics).

The Gordon equation finds the security's value necessary to

make the sum of the dividend yield plus growth equal the

investor's required rate of return. The equation can be derived

without any discounting at all. It 'capitalizes' the dividends.

Capitalizing Cash Flow or Price-to-Cashflow

There is another valuation system that may be labeled as

'discounted cash flows', but it is really only a 'capitalizing'

model. Instead of capitalizing dividends or earnings, it

capitalizes some defined measure of 'cash flow'. Cash flow is

divided by some appropriate required return (equivalent to the

earning yield, so let's call it 'cash yield') to determine a

security's value.

This is what has happened when you hear the 'experts'

saying "It is trading at just 4 times cash flow." This multiple of

Price to CashFlow (P/C) is equivalent to the P/E multiple. But

there are many problems.

No matter what measure of cash flow you use, the flow

varies widely year by year. Yet when you capitalize a

particular year's cash flow you are presuming it is 'normal'

and will continue forever (with presumed growth).

No matter what ACTUAL cash flow you measure, it will

always need adjustments before it can be considered

'normal'. A lot of those adjustments effectively recreate

accrual accounting.

Poor cash flow (however measured) in one year may well be

because great things are happening. Expansion opportunities

require investment. But capitalizing cash flow would value the

company lower, not higher.

Price/Cash quotes, (eg) 4 times cash, or 8 times cash, are

meaningless numbers. Is 8 good or bad. 4 seems much

cheaper but is it so cheap as to raise red flags? Why are Oil

and Gas companies considered appropriately valued at 5

time cash flow, while Industrials are valued at 15 times cash

flow?

Most of us are familiar with P/E multiples. We know

the historical averages and extremes. We know what

values are appropriate for different industries or

growth rates. But none of that is true for P/C. Should

we consider the P/C in comparison to the P/E, or in

comparison between stocks? Is 'half-the-PE'

appropriate? What are we supposed to DO with the

number?

How do you evaluate the company with a high P/C only

because it has chosen to (eg) lease equipment instead of

buying it?

The cash flow $$ used must be defined somehow that makes

sense. You are familiar with valuations based on earnings

and dividends. But the cash flow definitions most always

used are FAR larger than earnings or dividends. Arguments

can be made for and against the inclusion of most all the sets

and sub-set of cash shown in the diagram above. Free Cash

Flow (FCF) sounds as if it is the metric to use, but how

exactly is it defined? You cannot see it in the diagram above.

Its failings are discussed on the Cash Truths That

Aren't page.

Discounted Cash Flow

The true discounted cash flow model is necessarily made of

two parts. For the first period of years the company's cash

payments and receipts are modeled year by year, line item by

line item. The yearly net cash is discounted back to the

present. After that a steady sustainable rate of growth is

presumed for the long run. The stock's presumed value at that

time, using simple P/E metrics usually, is also discounted back

to the present.

One model is presented by Aswath Damodaran on

this spreadsheet. His book detailing the method is published

online from this directory.

For each year of the foreseeable future the expected net

cash increase/decrease is calculated. It reflects the left

column in the diagram above.

o Net Income (Warning! other models start from other

points and will therefore have other adjusting

entries.)

o less increases to working capital

o plus new financing received net of debt principal

repaid

o less purchases of fixed assets for growth and

replacement

o plus (to reverse out) depreciation and amortization

Each year's change in cash is discounted back to the

present.

The value of the stock at the end of the foreseeable phase is

derived using the more basic P/E or Discounted Dividend

models. This is also discounted to the present. So the model

still has the problem of deriving a valuation for the company

at the end of the period where discounted cash flows are

measured. It really only delays the problem of valuation. A

huge amount of work is involved in modeling the first period,

but that level of exactitude is destroyed by the

generalizations involve in the valuation at the end of that

period.

Damodaran's CashFlow (unlike most all other's) is predicted to

be less than the accountants' earnings (Net Income) because

he includes the costs of growth investments. --

Increases to Working Capital are necessary for growth,

even if the growth is due only to inflation. It is most common

to see the current quarter/year's change in current assets

used as if it is a 'normalized' value. In fact there are large

swings from quarter to quarter, year to year, even though

over the longer term the funding level is stable for a given

level of sales.

Don't include in your analysis of working capital: cash,

the current portion of long-term-debt and bank debt. It

is cash you are trying to measure and the debt is

handled separately.

Net Financing Received equals the net excess of new debt

proceeds over any repayments. Companies most often keep

their debt-to-equity ratios stable, so growth is financed by a

combination of retained earnings and net new debt. Too

often investors subtract the required debt repayments from

CFFO in their calculation of FCF, ignoring new debt. This

ignores the reality that company's debt balance is rarely

reduced. It is replaced. With operating growth, debt will

probably grow too.

Remember to add the higher interest payments that

result from additional debt in the year-by-year cash

flow modeled.

Damodaran reduces his CashFlow by the cost of long-life

assets (showing in the left column of the diagram above

asLong-Term Investments). Notice how his estimates are

LARGER than the depreciation booked. You will almost

never see an analyst making that assumption.

Companies also grow by paying for Goodwill and

Intangible assets. You could argue that these

expenses should be included in the cost of new fixed

assets. But in reality most often these are paid for by

issuing additional share capital of the company. There

is no cash flow. Since the model does not reflect any

changes to the percentage ownership of a share, it

seem appropriate to ignore both these sides of the

transaction.

Depreciation and amortization are correctly added back to

Net Income in everyone's calculation of cash flows. Their

economic reality is replaced by the asset's cash costs.

Conclusion

While discounted cash flow analysis is an excellent

methodology for evaluating projects over which you have

complete control, for valuing common stock it is full of

problems. What measure of cash flow do you use: Earnings,

Dividends, CFFO or Free Cash Flow?

Retail investors must appreciate that correctly derived Free

Cash Flow involves a lot of time and industry knowledge,

which they probably do not have. Maybe using the traditional

valuation metrics are not a bad idea.

Price / Earnings

Price to Book

Price to Sales

Dividend Yield

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

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You are here: Home / Investing / How to Value Stocks using DCF…and the Dangers of Doing So

How to Value Stocks using DCF…and the Dangers of Doing So

POSTED ON SEPTEMBER 10, 2012 // 66 COMMENTS

Warren Buffett wrote in his 1992 letter to shareholders of Berkshire Hathaway…

In the Theory of Investment Value, written over 50 years ago, John Burr Williams set forth the equation for value, which we condense here: The value of any stock, bond or business today is determined by the cash inflows and outflows – discounted at an appropriate interest rate – that can be expected to occur during the remaining life of the asset.

What Buffett defines here is essentially what we know as the discounted cash flow or DCF, a key method to calculate intrinsic value of companies.

The interesting thing to note here is that no one knows whether Buffett has ever used DCF himself!

Even Buffett’s business partner and alter ego Charlie Munger has occasionally said that he has never seen Buffett doing any DCF calculations.

In fact, this is what Buffett wrote in his 2002 letter…

Despite our policy of candor, we will discuss our activities in marketable securities only to the extent legally required. Good investments are rare, valuable and subject to competitive appropriation just as good product or business acquisition ideas are. Therefore we normally will not talk about our investment ideas.

Anyways, despite his secretiveness, Buffett has been vocal about the importance of DCF several times in the past.

But if you were to believe a majority of security analysts out there, they will tell you to simply avoid DCF. The reason they give is that DCF is dependent on 5-10 years of future cash flows, predicting which is highly uncertain.

So they use relative valuation multiples like price to earnings, price to book value, or EV/EBITDA (which are also based on predictions!).

But you must recognize the simple fact that multiples are not valuation. In fact, multiples are simply shorthand for the intrinsic valuation process, which must generally be based on the DCF method.

You must never confuse the two – multiple based valuation and intrinsic valuation.

Of course, doing a P/E based valuation of stock can save you a lot of time and hard work (and that’s why most analysts use this). But it will be merely a case of garbage in-garbage out.

In fact, the simplicity of such ratios is a sign of inaccuracy, not accuracy. As Keynes said, “It is better to be vaguely right than precisely wrong.”

DCF: Problems and solutionsIf you were to go through the DCF calculation excel, there are three key variables you need to calculate the DCF value of a company:

1. Estimates of growth in future free cash flows (FCF): Growth in FCF over say

the next 10 years, using last 3 years average FCF as the starting point. (Click

here to see the calculation of FCF from a company’s cash flow statement)

2. Terminal growth rate: Rate of growth in FCF after the 10th year and till infinity.

3. Discount rate: Rate at which the future cash flows must be discounted to bring

them to present value.

Now there are three key issues that arise with these variables:

1. What growth rate to assume for future FCF estimates?

2. What discount rate to assume?

3. What terminal growth rate to assume?Let me help you with how do I answer these questions for calculating DCF valuations myself.

1. How do I predict future FCF?As an analyst, I always found it difficult to predict growth rate in volumes, sales and profits. But I still tried to do that – after all, I was paid to predict the future!

However, as I’ve realised over the years, trying to find a perfect answer to the question “What growth rate to assume?” is like trying to find a “perfect couple”. None exist! 

Given this limitation of trying to predict the future, I’ve changed my way of analysis to value stocks based on the present data rather than what will happen in the future.

That’s why I now don’t try be accurate with my FCF growth estimates. I just try to be reasonable and use common sense.

For most stocks, I generally perform a 10-year 2-stage DCF analysis. What this means is that I assume a particular growth rate for the first five years of my FCF calculations (as you can see in my DCF excel), and then another number for the next five years.

I rarely go above 15% annual growth rate for the first five years, and 8% for the next five.

The best practice is to keep growth rates as low as possible.

If the company looks undervalued with just 5% annual growth in FCF over the next 10 years, you have more upside than downside.

The higher you set the growth rate, the higher you set up the downside potential.

To repeat, while assuming FCF growth rate for the future, just be reasonable and use common sense.

A caveat – don’t take cues from the past as the past performance is rarely repeated in the future.

2. How much discount rate do I assume?In simple words, discount rate is the rate at which you must discount the future cash flows (as estimated using above growth assumptions) to the present value.

Why present value? Because we are trying to compare the company’s intrinsic value with its stock price “now”….in the present.

Just to help with an example, what price would you pay for an investment today if company ABC’s future cash flow is worth Rs 1,000 after 1 year?

If the discount rate is 5%, you must pay Rs 952 now (1000/1.05).

If the discount rate is 10%, you must pay Rs 909 now (1000/1.1).

If the discount rate is 15%, you must pay Rs 870 now (1000/1.15).In other words, the higher the discount rate you assume, the lower you must pay for the stock as of now.

Finance textbooks and experts would tell you to use Capital Asset Pricing Model (CAPM) to calculate discount rate. I used CAPM myself to arrive at discount rates in the past.

However, if you are worried what CAPM is, don’t be because you can avoid knowing about it and still live happily ever after….like I am living. 

Look at discount rate as the “annual rate of return” you want to earn from the stock.

In other words, if you are looking to invest in a business that has comparatively higher (business) risk than other businesses (like in case of most mid and small cap stocks), you may want to earn a 15% annual return from it.

For valuing such businesses, take 15% as the discount rate.

In case of relatively safer businesses (think Infosys, HUL, Colgate), earning around 10-12% annual return over the long term is a good expectation (because these businesses will also provide some stability to your portfolio during bad times).

For valuing such businesses, take 10-12% as the discount rate.

Better still, assume a constant discount rate for all companies. I am gradually turning to this model – of taking a constant 15% discount rate for all kind of businesses (safe or risky).

“But this way, how would you adjust for the risk in each business?” you may ask.

Simple – adjust the risk in FCF growth estimates. That is where the real risk lies, right?

3. How much terminal growth rate do I assume?As I mentioned above, I do a 10-year FCF calculation for arriving at a stock’s DCF valuation.

But the companies I’m valuing won’t cease to exist after 10 year. Some will survive for 10 more years, some for 20 years, and very few for 50 years.

That is where the concept of “terminal value” (or the value after 10th year and till eternity) comes into picture.

The terminal value I generally assume lies between 0% and 2%. Assuming higher terminal value (>3-4%) is like assuming the company to grow bigger than the world economy in the infinity, which isn’t possible.

So the idea is to keep it as low as possible. Best to keep it at 0%.

Voila, I got a perfect intrinsic value!No sir! Even after being reasonable and using common sense in assuming FCF growth rate, terminal growth rate and discount rate, there is 0% guarantee that you will arrive at a “perfect” intrinsic value using DCF (or for that matter, using any intrinsic value method).

Believe me, however reasonable, realistic, rational (whatever you may want to call it) you get in calculating intrinsic values, you are bound to go wrong.

This is for the simple reason that you are still trying to predict the future…which is unpredictable.

Now what to do?

Hey, you forgot “margin of safety”?Valuation is an imprecise art (yes, however smart you may think you are!). Also, the future is inherently unpredictable.

Thus, it’s important to bring in the most-important investing concept of “margin of safety” into the picture.

This is what Graham wrote about margin of safety in The Intelligent Investor…

Confronted with the challenge to distill the secret of sound investment into three words, we venture the motto, MARGIN OF SAFETY.

Margin of safety is simply the discount factor that you use with your intrinsic value calculation. So if you arrive at an intrinsic value of Rs 100 for a stock that trades at Rs 80, you might think that you have found a bargain.

But what if your intrinsic value calculation is wrong? Yes, it will be wrong, at least 100% of the times!

Thus, you will do yourself a world of good by buying the stock only at say 50% discount to your intrinsic value calculation, or around Rs 50.

Image Source: Stockbullets.com

Now when you bring your intrinsic value assumption down to Rs 50 – by giving a 50%

discount to the original calculated value of Rs 100, don’t think that you are trying to be

ultra-conservative.What you are doing is providing yourself protection against:

1. Bad luck

2. Bad timing, and

3. Bad judgment.As simple as that!

Margin of safety was, and will always be, the bedrock of value investing.

You can’t ignore this at any cost…or it will turn out to be a costly affair!

So, never ignore the power of DCF…The DCF model can provide a useful valuation estimate if you follows these simple principles:

Invest in companies with business certainty – financial stability, business

predictability.

Invest in companies with sustainable competitive advantage.

Do the hard work of analyzing past financial statements (over at least a 10-year

period).

Use conservative assumptions of FCF growth of around 10-15%, terminal growth

rate of 0-2%, and discount rate of 10-15%.

Use margin of safety to protect against bad luck, bad timing, and bad judgment.

Be honest by not modifying your original assumptions just because you “like’ the

stock but DCF is saying otherwise.That’s about it!

Or is it?

Let’s do “Reverse DCF”Most of you must have not heard of the concept of “reverse DCF”.

Don’t worry, it’s not that complex a subject that the name might suggest! You do a “reverse DCF” by reversing just one assumption in your original DCF calculation – the FCF growth rates.

The aim of reverse DCF is to get the intrinsic value to match the stock’s current price – to find out what’s the FCF growth estimates the stock market is pricing in the stock.

Let’s understand this with an example. Colgate’s current stock price is around Rs 1,230. However, assuming FCF growth rates of 10% (for 1-5 years) and 8% (for 6-10 years), we arrive at an intrinsic value of Rs 398.

Now, we need to tweak the FCF growth rates in such a way, that this Rs 398 rises to around the current stock price of Rs 1,230.

Just try that on your own – calculations will show that when you raise the FCF growth rate to 26% for both the 5-year periods, the stock’s intrinsic value will rise to Rs 1,233…or almost near the current price.

What this indicates is that the stock market is currently pricing Colgate at a level that is justified only when the company can grow its next 10-years’ FCF at an average annual rate of 26%!

Now you need to answer whether such a long-term growth rate is realistic and achievable. Or whether the market has irrational expectations from Colgate’s business.

Just for your information, Colgate has grown its FCF at an average annual rate of 16% over the past 8 years. So a 26% growth rate over the next 10 years really looks on the higher side.

But as an investor, you must take a call on that!

That’s all I have to discuss on the subject of DCF as of now. I would like to leave you with the link to a very good resource – The Dangers of DCF – written by James Montier in 2008.

Finally, an important quote from a noted statistics professor, George E P Box – “All models are wrong; some are useful.”

So learn about DCF, use it, but expect to be wrong!

All the best!

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