# Investment Basics - Course 403 - Introduction to Discounted Cash Flow

By: Steve Bauer | Wed, Feb 2, 2011

This is the twenty-third Course in a series of 38 called "Investment Basics" - created by Professor Steven Bauer, a retired university professor and still active asset manager and consultant / mentor.

## Introduction

In the previous Course, we toured the many different valuation ratios, which compare a stock's market price with financial measures such as the underlying company's earnings, book value, and dividends. These ratios provide a quick and dirty way to determine how a stock is valued, but usually require a lot of context to be useful.

It's easy to understand why a faster growing company may deserve a higher P/E or P/S ratio than a slower growing one, but how do we go about estimating what the absolute value of any company should be?

Enter discounted cash flow (DCF).

Valuation methods based on discounted cash-flow models determine stock prices in a different and more robust way. DCF models estimate what the entire company is worth. Comparing this estimate, or "intrinsic value," with the stock's current market price allows for much more of an apples-to-apples comparison. For example, if you estimate a stock is worth \$75 based on a DCF model, and it is currently trading at \$50, you know it's undervalued.

Estimating a stock's fair value, or intrinsic value, is no easy task. In fact, it is quite complex, involving all kinds of variables that are themselves tough to estimate. Even so, I do use discounted cash-flow models to value most all the stocks I may have interest in. Despite their complexity, valuations based on DCF models are much more flexible than any individual ratio, and they allow an investor to incorporate assumptions about such factors as a company's growth prospects, whether its profit margins are likely to expand or contract, and how risky the company is in general.

## Estimating Future Cash Flow

The main idea behind a DCF model is relatively simple: A stock's worth is equal to the present value of all its estimated future cash flows. Putting this idea into practice is where the difficulty lies.

The first step to valuing any stock with a DCF model is estimating the future cash flows the underlying company is going to generate. Many variables go into estimating those cash flows, but among the most important are the company's future sales growth and profit margins. Projecting such variables doesn't involve simply extrapolating present trends into the future. In fact, doing so can often lead you to believe a stock is worth a lot more (or less) than it really is.

When predicting a company's revenue growth, it's important to consider a variety of factors, including industry trends, economic data, and a company's competitive advantages. A company with strong competitive advantages (remember the - wide economic moat?) may grow faster than its competitors if it is stealing market share. Paying attention to a firm's customers is also important. For example, if GM (GM) or Ford (F) says it will produce fewer cars over the next couple of years, it would be wise to check your revenue growth assumptions for auto parts suppliers.

Determining a company's future operating profits entails similar detective work. Looking into a company's costs is an obvious first step. Chemical companies heavily reliant on oil and natural gas, for example, could see profit margins contract if these materials go up in price and they cannot pass these cost increases on to customers.

On the other hand, some companies benefit from operating leverage. Operating leverage means that as a company grows larger, it is able to spread its fixed costs across a broader base of production. As a result, the company's operating profits should grow at a faster rate than revenue. Think back to eBay (EBAY). It can add thousands of customers with only very modest investments to its existing computer systems. Likewise, a software company sees most of its costs in development. Adding an additional customer doesn't change this key cost.

One question that must be asked of any discounted cash-flow model is exactly what kind of cash flows are you going to be discounting? In the old days, investors used something similar to a dividend discount model, which essentially sums up all the future dividend payments a company is expected to make and expresses them in terms of today's dollars. However, discounting dividends is of little help for valuing companies that pay no dividends, which includes many firms today. Rather, most DCF models nowadays use some form of cash flow, or reported earnings with non-cash charges excluded. The DCF model that we will talk about in this and the following lesson discounts free cash flow, which is defined as operating cash flow minus capital expenditures.

Free cash flow represents the cash a company has left over after spending the money necessary to keep the company growing at its current rate. It's important to estimate how much the company reinvests in itself each year via capital expenditures. Reinvestment can take the form of a company purchasing machinery to start up a new production line, or retail companies opening new stores to expand their reach.

Prof's. Guidance: There are actually two types of DCF models: "free cash flow to equity" and "cash flow to the firm." The first involves counting just the cash flow available to stockholders and is a bit easier to understand. The second involves counting the cash flow available to both debt and equity holders and has several additional steps. I will talk about just the first method here, though both methods should give you roughly the same result for any given company.

## Discounting and Discount Rates

Once we project the cash flows we expect a company to generate in the future, we have to discount those future cash flows back to the present to account for the time value of money. After all, a dollar today is worth more than a dollar 10 years from now, because the dollar today can be invested to earn a return over the next 10 years.

Suppose it is possible to invest our money at a 5% annual rate of return. In that case, \$1 today will become \$1.05 one year from now. Two years from now, it will become \$1.1025 (\$1.05 x \$1.05). Three years from now, it will become \$1.053, or \$1.1576, and so on.

To find the present value of \$1 of future cash flow, divide that future cash flow by the appropriate multiplier from the above example. A cash flow of \$1 one year in the future is worth \$0.9524 (\$1/\$1.05) in the present. If we invest that \$0.9524 at 5%, in one year we'll have exactly \$1. A \$1 cash flow two years in the future is worth \$1/\$1.052, or \$0.9070, in the present. The further into the future we go, the less a given cash flow is worth right now. Generalizing this concept, the following formula is quite important:

Present Value of Cash Flow in Year N =
CF at Year N / (1 + R)^N
CF = Cash Flow
R = Required Return (Discount Rate)
N = Number of Years in the Future

Let's go through a few more examples. Suppose we have a \$1,000 cash flow three years in the future with a 7% rate of return. The present value of that cash flow is:

\$1,000 / (1 + .07)^3 = \$816.30

The same cash flow five years in the future would be worth:

\$1,000 / (1 + .07)^5 = \$712.99

And finally, a \$1,000 cash flow five years from now, but this time with a 10% discount rate, would be worth:

\$1,000 / (1 + .10)^5 = \$620.92

As you can see from these examples, the further out a cash flow is, the less it is worth in today's dollars. Also, the higher the rate of return used to discount the future cash flow, the lower the present value.

## Cost of Capital

The rate we use to discount a company's future cash flows back to the present is known as the company's required return, or cost of capital.

A company's cost of capital is exactly as its name implies. When a company raises capital from its lenders and owners, both types of investors require a return on their investment. Lenders expect to be paid interest on their loans, while owners expect a return, too.

A stable, predictable company will have a low cost of capital, while a risky company with unpredictable cash flows will have a higher cost of capital. That means, all else equal, that the riskier company's future cash flows are worth less in present value terms, which is why stocks of stable companies often look more expensive on the surface. The cost of capital used in a DCF model can have a significant impact on the fair value, so it's important to pay attention to this estimated figure.

The rate you would use to discount cash flows if using the "cash flow to the firm" method is actually a company's weighted average cost of capital, or WACC. A company's WACC accounts for both the firm's cost of equity and its cost of debt, weighted according to the proportions of equity and debt in the company's capital structure. Here's the basic formula for WACC:

(Weight of Debt)(Cost of Debt) + (Weight of Equity)(Cost of Equity)

For example, if the market value of a company's equity is \$600 million and it has \$400 million of debt on its balance sheet, then 60% of its capital is equity and 40% is debt. If the company's cost of equity is 10% and its cost of debt is 7%, then its WACC is:

(60% x 10%) + (40% x 7%) = 8.8%

Prof's. Guidance: If using the "cash flow to the firm" DCF method, the WACC would be your discount rate. However, this method does not discount free cash flow. Rather, it discounts operating earnings before interest but after taxes. Arriving at this figure involves complicated adjustments for interest and taxes. To keep it simple, we will just use the "free cash flow to equity" method in our example in the next Course.

## Two Types of Capital, Two Costs

Where do the cost of equity and debt come from? The cost of debt is relatively straightforward: It's the interest rate a company must pay to borrow money, based on the current yield on any of the bonds the company has issued. Just as a person with an excellent credit rating can borrow from banks at lower rates than someone who has missed payments in the past, financially strong and stable companies can borrow at lower rates than riskier firms.

The cost of equity is a little more complicated and is often a topic of debate in both academia and the business world. Modern finance theory says that a given company's cost of equity is determined by measuring the risk-free rate investors can achieve (typically the yield on Treasuries) and an equity premium, with this premium determined by the company's stock volatility. The calculation under this theory is called the capital asset pricing model (CAPM), but in our opinion it doesn't always work well in practice. After all, a stock's volatility (which is subject to Mr. Market's temperamental ways) really doesn't tell you much about the fundamental factors that pose a risk to future cash flows.

When I take the time to value companies, I try to come up with a cost of equity for each company based on a variety of risk factors: how cyclical its business is, how big it is, how much cash flow it generates, the strength of its balance sheet, and its economic moat. One might say that we use a "fundamental risk premium."

I start by assuming that the average risk-free rate over time will be 5.0%, and that the average risk premium will be 5.5%. In other words, for the perfectly average company with the perfectly average risk profile, we assume the cost of equity is 10.5% (based on the 5.0% risk-free rate plus a 5.5% equity risk premium). I then adjust the risk premium up or down to capture any other risks highlighted in the fundamental factors above.

Using this system, the costs of capital that I come up will generally range between 8% and 14%. Companies at the low end of this range tend to be stable, large-cap firms such as Coca-Cola (KO) and Johnson & Johnson (JNJ). On the other hand, riskier companies where future cash flows are more difficult to predict, such as many biotech firms, usually end up with higher WACCs.

It's important to note that in general, debt usually costs less than equity. One reason for this is that the interest payments associated with debt are tax deductible, thus lowering the company's cost structure. As a result, a company with a large debt load will usually enjoy a lower WACC than a less leveraged firm. Of course, an increasing debt load can lead to bankruptcy risk if a company can't meet its interest and repayment obligations. When a company takes on so much debt that it becomes financially unsound, both its cost of debt and equity will rise exponentially, causing its cost of capital to rise as well.

To reiterate, a higher WACC, or discount rate, will lead to a lower estimated present value of future cash flows, and vice versa. The riskier a company is, the higher its discount rate should be, and the lower the value of its future cash flows, all else equal. Conversely, stable companies with predictable cash flows and strong competitive advantages will generally warrant a lower discount rate.

## The Perpetuity Value

The last piece of the puzzle is the perpetuity value. This figure is necessary because it's not feasible to project a company's future cash flows out to infinity, year by year. At some point, we have to stop, even if we believe the company will continue generating profits for a long time. We can solve this problem by estimating a company's future cash flows for a certain period--say five or 10 years -- and then estimating the value of all cash flows after that in one lump sum. This lump sum is the perpetuity value.

A company's cost of capital also plays an important part in calculating the perpetuity value. The most common way to do this is to take the last cash flow estimated, increase it by the rate at which you expect cash flows to grow over the long term, and divide the result by the cost of capital minus the estimated growth rate.

Perpetuity Value =
( CFn x (1+ g) ) / R - g
CFn = Cash Flow in the Last Individual Year Estimated
g = Long-Term Growth Rate
R = Discount Rate, or Cost of Capital

To better understand the perpetuity value, suppose we're using a five-year DCF model for a company with a 9% cost of capital. I estimate that the company's free cash flow in Year 5 will be \$100 million, and that its cash flow will grow at 5% after that. The perpetuity value will equal:

( 100 million x (1 + .05) ) / (.09 -.05) = \$2.625 billion

Remember, the perpetuity value is calculated as of five years from now. To find out what the value is today, we have to discount the calculated value using the formula we learned earlier:

Present Value of Perpetuity Value =
\$2.625 billion / (1 + .09)^5 = \$1.706 billion

Once we've found the present value of the perpetuity, we simply add this number to the present value of the cash flows we estimated in Years 1 through 5 to determine the fair value, or intrinsic value, of the company. In the next lesson, we'll walk through a sample DCF model that will help you put this into practice.

Prof's. Guidance: Too much work? Sometimes, Yes and I don't often put myself through these exercises. I still review these courses from time to time.

## The Bottom Line

While DCF is certainly a complicated way to value stocks, there are many benefits that come with the increased effort. This Course was merely an introduction to the concepts. In the next Course, we'll go over a detailed example of how to actually use a DCF model to value a stock.

Prof's. Guidance: You may decide to skip the next Course! Please do it anyway - it is worth your time.

Quiz 403
There is only one correct answer to each question.

1. Illini Widgets will earn \$350 million in cash flow four years from now. Assuming an 8.5% weighted average cost of capital, what is that cash flow worth today?
1. \$253 million.
2. \$323 million.
3. \$380 million.
1. Chicago Flames Fire Retardant, Inc. is expected to generate \$1 billion in cash flow one year from now. If that company has a 10% cost of capital, what is that future cash flow worth today?
1. \$1 billion.
2. \$909 million.
3. \$900 million.
1. Suppose a company has a capital structure with 40% debt and 60% equity. If its aftertax cost of debt is 6% and the cost of equity is 10.5%, what is the company's weighted average cost of capital?
1. 7.8%
2. 8.7%
3. 9.3%
1. Suppose Company A has a long history of profitability, and its outlook is stable, and Company B has yet to make a profit in its short history, and its outlook is much more uncertain. Company A's cost of equity should be:
1. Equal to that of Company
2. Greater than that of Company
3. Less than that of Company
1. Suppose we're using a DCF model with 10 years worth of projections for a company with a 9.5% cost of capital. We estimate that the company's free cash flow in Year 10 will be \$350 million, and that its cash flow will grow at 4% in perpetuity after that. The present value of the perpetuity value will equal:
1. \$6.6 billion.
2. \$2.7 billion.
3. \$4.8 billion.

Thanks for attending class this week - and - don't put off doing some extra homework (using Google - for information and answers to your questions) and perhaps sharing with the Prof. your questions and concerns.

Investment Basics (a 38 Week - Comprehensive Course)
By: Professor Steven Bauer

Each week you will receive your Course Materials. There will be two kinds of highlights: a) Prof's Guidance, and b) Italic within the text material. You should consider printing the Course Materials and making notes of those areas of questions and perhaps the highlights and go to Google to see what is available to supplement those highlights. I'm here to help.

Freshman Year

Course 101 - Stock Versus Other Investments
Course 102 - The Magic of Compounding
Course 103 - Investing for the Long Run
Course 104 - What Matters & What Doesn't
Course 105 - The Purpose of a Company
Course 106 - Gathering Information
Course 107 - Introduction to Financial Statements
Course 108 - Learn the Lingo & Some Basic Ratios

Sophomore Year

Course 201 - Stocks & Taxes
Course 202 - Using Financial Services Wisely
Course 203 - Understanding the News
Course 204 - Start Thinking Like an Analyst
Course 205 - Economic Moats
Course 206 - More on Competitive Positioning
Course 207 - Weighting Management Quality

Junor Year

Course 301 - The Income Statement
Course 302 - The Balance Sheet
Course 303 - The Statement of Cash Flows
Course 304 - Interpreting the Numbers
Course 305 - Quantifying Competitive Advantages

Senor Year

Course 401 - Understanding Value
Course 402 - Using Ratios and Multiples
Course 403 - Introduction to Discounted Cash Flow
Course 404 - Putting OCF into Action
Course 405 - The Fat-Pitch Strategy
Course 406 - Using Morningstar as a Reference
Course 407 - Psychology and Investing
Course 408 - The Case for Dividends
Course 409 - The Dividend Drill

Course 501 - Constructing a Portfolio
Course 502 - Introduction to Options
Course 503 - Unconventional Equities
Course 504 - Wise Analysts: Benjamin Graham
Course 505 - Wise Analysts: Philip Fisher
Course 506 - Wise Analysts: Warren Buffett
Course 507 - Wise Analysts: Peter Lynch
Course 508 - Wise Analysts: Others
Course 509 - 20 Stock & Investing Tips

This Completes the List of Courses.

Wishing you a wonderful learning experience and the continued desire to grow your knowledge. Education is an essential part of living wisely and the experiences of life, I hope you make it fun.

Learning how to consistently profit in the Stock Market, in good times and in not so good times requires time and unfortunately mistakes which are called losses. Why not be profitable while you are learning? Let me know if I can help.

## Author: Steve Bauer

Steven H. Bauer, Ph.D.

Steve has several degrees, i.e. post graduate degrees and doctorate and a great deal of (too much) continued education. For seven years, he did a stent as a University Professor of Finance and Economics.

He owned a privately held asset management firm and managed individual investor and corporate accounts as a Registered Investment Advisor - for over 40 years.

Professionally he is a financial analyst and private asset manager / consultant / mentor.

Steve can be reach at senorstevedrmx@yahoo.com