Chapter 12
IN THIS CHAPTER
Estimating the value of entire companies by using discounted free cash flow analysis
Determining how to forecast cash flows from companies
Finding out how to estimate a company’s cost of capital
Understanding the capital asset pricing model
Finding out how to value a share of stock
The real meat and potatoes of investment banking involves developing and applying financial models. And financial models aren’t plastic pieces you glue together with pungentsmelling glue. Financial models are built by running numbers to demonstrate the best ways to improve the efficiencies, net incomes, and valuations of businesses.
Investment bankers earn their big paychecks by showing CEOs, boards, and management teams that by issuing or buying back certain securities they’ve already sold, going public or going private, purchasing companies or spinning off divisions, and making other changes in the way the firm operates, the value of the firm can be increased. Sellside investment banking analysts earn their keep by identifying undervalued companies for clients to buy the stock of, or by identifying overvalued companies their clients should sell. Investment banking is a very bottomline oriented industry, and financial models are the foundation — the raw materials of the investment banking process.
Financial models are typically developed and manipulated by young 20something investment banking associates who join investment banking firms after studying these standard models in elite business schools. Junior analysts often command sixfigure salaries immediately upon graduation from business school, and they typically work long hours honing their skills by preparing financial models and presentations for more senior investment bankers to pitch to clients and potential clients.
The financial value and longevity of any firm rests upon its ability to generate positive cash flow. It’s just like a working household, where the cash coming in must exceed the cash going out in order for the family to be able to stay afloat financially in the long term. Financial models are built on the premise that the value of any firm is simply the present value of all future cash flows. (For more detail about present value, refer to Chapter 11.) Unlike other assets, such as sports cars, jewelry, boats, and homes, holders of financial assets don’t draw psychic income by owning a flashy physical asset that they can show off to friends and make their neighbors jealous. Financial assets like stocks and bonds are generally valued in a very unromantic and unemotional fashion. As Dragnet’s Joe Friday said, “Just the facts, ma’am.”
This chapter presents the primary financial model that investment bankers employ: the discounted free cash flow model. At its core, the discounted free cash flow model is pretty simple, and you can get a solid handle on this model and its variations in the pages that follow.
Chapter 20 details ten ways to improve these models. But first, the basics.
The basic discounted free cash flow model requires the analyst to complete two basic tasks: First, the analyst must estimate future cash flows to the firm. After creating the cash flow estimate, the analyst must forecast the appropriate discount rate (an interest rate that is used to put a future cash sum into today’s dollars; see Chapter 11) to apply to those cash flows.
where is cash flow at the time n and r is the appropriate discount rate.
Don’t let the scary appearance of the formula rattle you. It’s just the mathematical way to state that the value of any asset is simply the present value of all future cash flows that the owner of that asset is entitled to. So, as we show in Chapter 11, the value of a bond is simply the present value of all the interest payments and the return of principal value that the bondholder receives. Likewise, the value of a share of stock is equal to the present value of all the future dividend payments that the stockholder receives. (See the “Valuing a Share of Stock” section at the end of this chapter for more information.)
The value of an entire corporation is determined via a model that estimates free cash flows to the firm and discounts them back to the present via a discount rate called the weighted average cost of capital (WACC; see “Calculating the Weighted Average Cost of Capital,” later in this chapter).
FCF = CFO + Interest Expense (1 – Tax Rate) – Capital Expenditures
The discounted free cash flow model states that the value of the firm is equal to the value of all future free cash flows to the firm discounted at the WACC:
One thing that may trouble you when looking at the formula is that it has an infinite number of terms. Don’t despair. As you’ll see, by making a simple assumption or two, the formula breaks down into a finite and very manageable number of terms.
Virtually all investment bankers begin their analysis with the most recent period of performance of the company in question. Suppose we wanted to determine the free cash flow for IBM for the most recent year. We can go to the Securities and Exchange Commission’s online EDGAR system and get the latest 10K filing for IBM (Chapter 6 gives detailed instructions on using EDGAR).
For this example, the following values are provided for IBM for the year ended December 31, 2018 (amounts are in millions of dollars):
Income Statement Item 
Amount (In Millions of Dollars) 
Cash flow from operations 
$15,247 
Payments for property, plant, and equipment 
($3,395) 
Proceeds from disposition of property, plant, and equipment 
$248 
Investments and business acquisitions (net) 
($139) 
From supplemental disclosures on EDGAR, we find that IBM paid $1,482 million of interest to debt holders in 2018 and had an effective tax rate of 23 percent.
From this information, we compute free cash flow to the firm as follows:
Add the cash flow from operations to the aftertax interest.
The cash flow from operations is $15,247. The aftertax interest is $1,482 × (1 – 0.23) = $1,141.14, which we’ll round down to $1,141. So $15,247 + $1,141 = $16,388.
Subtract the payments for property, plant, and equipment.
Payments for property, tax, and equipment total $3,395. So $16,388 – $3,395 = $12,993.
Add the proceeds from disposition of property, plant, and equipment.
The proceeds from disposition of property, plant, and equipment total $248. So $12,993 + $248 = $13,241.
Subtract the investments and business acquisitions (net).
Investments and business acquisitions (net) total $139. So $13,241 – $139 = $13,102.
So the current free cash flow to the firm for IBM is $13,102 million, or more clearly stated, $13.1 billion. Wow, that’s a lot of zeros.
Determining free cash flow for any past year isn’t difficult and most analysts would, in fact, agree on its calculation. You simply take historical values and plug and chug into the formulas and — voilà! — you have a value for free cash flow. But valuation models aren’t based upon the past; they’re based upon expected future cash flows.
The basic models they’re applying are the same, and the historical data they’re reviewing is the same. The difference involves the assumptions about the future that they make. As Shakespeare wrote, “Therein lies the rub.” That’s why financial analysis is part science and part art.
To forecast free cash flow, analysts must forecast cash flow from operations. Cash flow from operations is simply:
Now, this is starting to sound complicated, but to get to earnings before interest and taxes, analysts must forecast sales and how much it cost to produce and sell those products. In essence, analysts must forecast the entire income statement of the firm for the foreseeable future.
The typical income statement of a manufacturing firm looks something like this:
The weighted average cost of capital (WACC) is a very important input into the discounted cash flow models. It’s defined as the average rate of return of a company’s suppliers of capital, and it’s the rate at which the future cash flows of the firm are discounted back to a present value for valuation purposes. All else equal, the higher the WACC, the lower the value of the firm. That’s because the cost of capital is higher for riskier firms.
IBM can access capital much more inexpensively than can an unproven, startup firm. And investing in IBM is much less risky than investing in an unproven startup firm. One thing that market participants agree on is that to induce investors to make riskier investments, they must expect higher returns.
The formula for WACC is simple: It’s a weighted average. The individual component costs of the different types of capital (stocks and bonds) are weighted by the percentage of stocks and bonds in the capital structure (how the firm is financed — the percentage of financing that has come from stock and the percentage that has come from bonds). So the WACC formula is simply
where D is the value of debt, E is the value of equity, is the required return on debt, and is the required return on equity.
So, if we have a company that is financed with onethird debt and twothirds equity, and the aftertax required return on debt is 5 percent, and the required return on equity is 10 percent, the WACC for the firm is:
When we apply the discounted cash flow models for this firm, we would discount all the future cash flows at an 8.34 percent annual rate.
Because WACC is an estimate of the cost of funding for a firm, the concept of WACC is critically important for the internal operations and planning of the firm. If the firm’s managers — often with the help of their investment bankers — can identify opportunities to invest in projects or ideas that return more than the cost of capital, the value of the firm will increase. This is how wealth is created.
Profitable projects or ideas could be a new product line, expansion of a current product line into a new market, the acquisition of a product line from a competitor, or even the acquisition of a competitor. If a firm can acquire funds at a cost of 8 percent and earn 12 percent on those funds, the value of the firm will increase, and the stockholders (and management and the investment bankers) will be very happy.
Adjusting WACC for a project’s risk works both ways. If a firm is manufacturing a product and can reduce its costs by acquiring a more efficient production machine that already exists, then that project isn’t very risky. Most analysts would agree that the cash flows from this project could be reasonably discounted at a much lower rate than the firm’s WACC because the risk implicit in this project is very low. Conversely, a firm may be considering selling an entirely new product line in a brandnew market. You could reasonably argue that the cash flows from this project should be discounted at a rate higher than the WACC because of the higher risk level.
To determine the WACC, an analyst must first estimate the individual component costs of capital — the cost of debt and the cost of equity. As you see in this section, the cost of debt capital is very straightforward — there is little controversy on how it’s estimated and there are few alternatives. The cost of equity, on the other hand, can be estimated using several different methods, which may produce widely different cost estimates. Again, this is where the art of investment banking deviates a bit from the science.
To estimate the cost of debt capital for a firm with publicly traded bonds, the investment banking analyst must look no further than the bond market to determine at what yield to maturity the firm’s bonds are selling for in the marketplace. (For more on yield to maturity, see Chapter 11.)
Companies usually have more than one outstanding bond issue, so analysts will calculate an average bond yield — using market value weights. This average yield to maturity of all the outstanding debt of the firm is that firm’s beforetax cost of debt.
But there’s one more step. Because the Internal Revenue Service allows companies to deduct interest costs before arriving at net income that is subject to taxation, the true aftertax cost of debt is considerably lower than the beforetax cost of debt. In fact, it’s adjusted for the firm’s corporate tax rate. Thus, the formula for aftertax cost of debt is as follows:
If the average yield to maturity on a company’s bonds is 6 percent and the company’s tax rate is 21 percent, the firm’s aftertax cost of debt is as follows:
One of the most difficult and controversial aspects of completing a discounted cash flow analysis is determining the appropriate required rate of return (or cost) on equity. The relationship between risk and required return is perhaps the most basic in investments.
Riskier assets should provide higher returns in the long run to compensate investors for assuming that risk. There is an old saying in investments: You can eat well or you can sleep well. This refers to the fact that if you take more risks, your returns are likely to be higher. However, in the short run, the volatility of those riskier investments may cause you to lose sleep at night.
In general, stocks are riskier than bonds, so stockholders should expect to earn higher returns than bondholders over the long run — and they do. Table 111 in Chapter 11 shows that over the long run, stocks return significantly higher returns than bonds and small stocks return significantly higher returns than large stocks. We refer to the expected return of one asset class over another as a risk premium. But how do we determine the theoretically correct required rate of return for a specific company’s equity?
Two of the more popular methods for determining the cost of equity capital are the buildup method and the capital asset pricing model (CAPM). The buildup method is generally used for smaller, privately held firms, while the CAPM is more appropriate for large, publicly traded firms. The CAPM occupies a prominent place in investment banking and is discussed in the following section. Here, we focus on the buildup method.
The buildup method simply starts with the current riskfree rate (usually estimated as the yield on longterm U.S. Treasury securities) and adds various premiums for different sources of risk inherent in equity securities. Both the number of premiums and the values for each of the categories will vary from analyst to analyst, but a typical buildup method will add premiums for the following categories:
Market risk premium: This is the additional return that is required for an investor to purchase an average stock rather than simply invest and earn the riskfree rate by buying government securities. The equity risk premium is generally considered for the market as a whole and often is thought of as the premium applying to large capitalization stocks (like the Standard & Poor’s 500).
The equity risk premium is most often determined by using historical data. For example, Table 111 shows that large stocks have returned a premium of 6.0 percent annually over the return for longterm government bonds for the time period from 1926 through 2018.
Some analysts choose not to use historical equity risk premiums and instead simply plug in a forwardlooking forecast that they believe is more applicable to the current investing environment. To that point, many investment professionals believe that the equity risk premium is smaller today than it has been historically. More on this in the following section.
So assuming that current yields on longterm government bonds (the riskfree rate) was 3.2 percent, for a hypothetical small company with an idiosyncratic premium of 2 percent, using historical values for the premiums, the buildup method would estimate the cost of equity capital at:
Unlike the cost of debt, the IRS does not provide a tax break for payments to equity holders. So the aftertax cost of equity is the same as the beforetax cost of equity.
The CAPM is a financial model that was developed in 1964 by Nobel Prize winner and Stanford finance professor William Sharpe. It transformed the way that financial professionals think about risk and return.
The intuition behind the CAPM is that you measure an asset’s risk relative to the average risk of the market. For simplicity’s sake, most analysts define the market as the most widely followed market indices — typically, a largecap index such as the S&P 500 Index.
The measure of risk for the CAPM is called beta (). An asset’s beta is calculated by determining, on average, if an asset is more or less volatile than the market as a whole.
The good news is that you don’t need to compute betas. Many financial websites compute betas for you, and you can simply look them up. For instance, Yahoo! Finance (http://finance.yahoo.com
), Morningstar (www.morningstar.com
), and MSN Money (http://money.msn.com
) report betas for securities. Betas are estimates calculated over different time periods and in relation to different indices, so you’ll find that the betas reported by different providers will vary. You’ll also find that the beta for a particular security will vary over time.
Table 121 provides a listing of betas for several S&P 500 companies as of October 25, 2019. You’ll see that according to the beta measure, Amazon is much riskier — when added to a portfolio — than the market, while Berkshire Hathaway is much less risky than the market. Facebook, on the other hand, has a risk nearly identical to the market.
TABLE 121 Betas for Stocks as of October 25, 2019
Stock 
Beta 
Amazon 
1.55 
Apple 
1.24 
Berkshire Hathaway 
0.84 

1.04 
IBM 
1.32 
Source: Morningstar.com
All you need to know to estimate the required rate of return on equity () according to the CAPM are the following three inputs:
www.bloomberg.com
). On October 25, 2019, the yield on 90day Treasury bills was 1.66 percent.
The first two inputs — the riskfree rate of return and the market risk premium — are the same for all stocks. So, according to the CAPM, the only variable that changes when we examine different stocks is beta.
where is the riskfree rate and is, well, beta.
To compute the required rate of return on Amazon equity, we simply plug the values into the equation:
So the appropriate required return on equity capital for Amazon stock, according to the CAPM, is 14.8 percent.
The same calculation for Berkshire Hathaway results in a much lower required rate of return on equity capital of 8.8 percent. Because Berkshire Hathaway is considered much less risky than Amazon, investors will require a lower expected rate of return to invest in it.
One of the great debates in academic financial circles involves how well CAPM works — that is, how well it explains the longterm relationship between risk and return for stocks over time. More databased studies — academics refer to them as empirical studies — have been done critiquing the CAPM than on virtually any other topic in finance over the past halfcentury. At best, the evidence on the veracity of CAPM is mixed. Suffice it to say that the relationship between risk and return isn’t as simple or as reliable as the CAPM hypothesizes. The evidence is not consistent with a simple straightline (or linear) relationship between risk (beta) and return over either longterm or shortterm time periods. In fact, over some time periods, lowerbeta stocks have outperformed higherbeta stocks — and, stocks in general have underperformed government bonds.
So, what does the analyst take from this? CAPM is a terrific starting point to determine the cost of equity capital, but most analysts understand that it isn’t a perfect depiction of reality and adjust their estimates of the cost of equity accordingly.
Up to this point, we’ve presented the basic valuation model and have discussed how to estimate the different components of the model — the free cash flows and the weighted average cost of capital. In this section, we put it all together and show you how investment bankers arrive at the value of a company.
As we show earlier in this chapter, the discounted free cash flow model states that the value of the firm is equal to the value of all future free cash flows to the firm discounted at the WACC:
It may seem like an impossibility to apply a valuation model that has an infinite number of terms. But, depending upon the simplifying assumptions the analyst makes about the growth of free cash flows, the model is actually quite workable. In this section, we look at three variations: the nogrowth case, the constant growth case, and the twostage growth case.
The simplest application of the formula for firm value is that case in which the free cash flows are assumed to be constant through the foreseeable future. This may be the case for very mature firms that aren’t expected to change or evolve much in the future. In this case, the formula for firm value reduces to the following:
That’s it! A formula with a seemingly infinite number of terms reduces to dividing two numbers. You simply take the estimate of FCF and divide by your estimate of WACC. For example, if a firm with a WACC of 10 percent had free cash flow of $400 million annually, and that was expected to remain the same for the foreseeable future, the estimate of firm value would be:
Thus, a fair value for this entire firm — including both the debt and the equity — would be $4 billion. If all the debt and equity could be acquired for less than $4 billion, it would be a good investment if the assumptions embedded in the analysis prove to be sound.
It is a rare case that free cash flows to the firm would remain constant for the foreseeable future. Cash flows are expected to grow over time for most firms. Does that mean that our valuation model gets a lot more complicated? The answer, thankfully, is no. In fact, the model is quite simple if we can assume a constant growth rate in free cash flow for the foreseeable future. This is likely for firms that have been established for quite some time, but are still very much in the growth stage and won’t be in the mature, nogrowth stage for quite some time.
In the case of constant growth of free cash flow, an estimate of firm value is the following:
where is free cash flow for the current year, g is the growth rate expected in free cash flow, and WACC is the estimate of the weighted average cost of capital.
So, for our hypothetical firm with current free cash flow of $400 million and a WACC of 10 percent, if we assume that free cash flows are going to grow at 5 percent for the foreseeable future, firm value is estimated to be:
Note, that in this case, the value of the firm is more than double the value in the nogrowth situation. This shows that compound growth is a wonderful concept. That is why none other than Albert Einstein is rumored to have said that “Compound interest is the eighth wonder of the world.” The same concept applies with compound growth of free cash flows.
What if we want to value a firm that has free cash flows that are expected to grow in the future but are not expected to grow at that same rate forever? For instance, suppose that our firm with current free cash flow of $400 million is expected to grow at a robust 20 percent for the next two years and then grow at a more pedestrian 5 percent rate thereafter. How do we value the firm?
Firm Value = PV of FCF during NonConstant Growth + PV of FCF during Normal Growth
In our case, the free cash flows during the nonconstant growth period will be:
So the PV of the free cash flows during the nonconstant growth period is:
Now, we need to find the present value of the free cash flows during the constant growth period. Two years from now, the firm is expected to have free cash flows of $576 million, and those free cash flows are expected to grow at a constant rate of 5 percent. Because we can apply the constant growth formula, in two years, the firm will have an expected value of:
But remember, this is a value in two years, so to put it in terms of a present value, we must discount that amount back to the present:
So to complete the analysis, the firm value is:
Firm Value = $912 million + $9.997 billion = $10.909 billion
This example assumes one nonconstant growth period, but it can certainly be modified to encompass as many different nonconstant growth periods as the analyst can imagine.
Firm values are very sensitive to the major inputs to the valuation process — the estimates for growth in free cash flow and the estimate of the WACC. Even small modifications in these estimates can have a significant impact on firm value.
Investment bankers should stresstest their results to examine the impact of their major assumptions on firm value. Stress testing or using a combination of hypothetical values interpreted with human judgment, gives investment bankers an idea of how confident they should be in their valuations. To illustrate, we’ll assume the constant growth model, with a current free cash flow estimate of $400 million. Table 122 shows how much the firm value changes by changing either the WACC or the growth rate of free cash flow, or both.
TABLE 122 Firm Value (in Billions) for Various WACCs and Growth Rates

WACC  
Growth Rates 
8% 
9% 
10% 
11% 
12%  
7% 
$42.8 
$21.4 
$14.3 
$10.7 
$8.6  
6% 
$21.2 
$14.1 
$10.6 
$8.5 
$7.1  
5% 
$14.0 
$10.5 
$8.4 
$7.0 
$6.0  
4% 
$10.4 
$8.3 
$6.9 
$5.9 
$5.2  
3% 
$8.2 
$6.9 
$5.9 
$5.2 
$4.6 
As you can see, a relatively tight range of both WACC and growth estimates provides widely diverging firm values. For example, when you assume a constant WACC of 10 percent, firm value ranges from a low of $5.9 billion to a high of $14.3 billion when you change the constant growth estimate from 3 percent to 7 percent. Likewise, if you assume a constant growth rate of 5 percent, firm value ranges from a low of $6 billion to a high of $14 billion when you change the WACC estimate from a high of 12 percent to a low of 8 percent.
As you’ve seen throughout this chapter, investment banking analysts use variations of the free cash flow model to value entire firms. These models are the basis for suggesting potential actions — like mergers and acquisitions and stock repurchases — to increase the value of the firm. However, another very common variation of these discounted cash flow models involves valuing the common stock of a firm and forms the basis for making buy and sell recommendations to clients.
The discount rate used to discount those cash flows to a present value is the required return on equity discussed earlier and is most often computed by using the CAPM. The equation for the value of a share of stock is:
where is the dividend at year n and is the required return on equity.
Once again, it appears that we have a daunting task, because we must solve an equation with an infinite number of terms. But, as before, if we make the simplifying assumption that dividends are going to grow at a constant rate forever, the formula reduces to a very simple form:
So to value a share of stock assuming a constant growth rate in dividends, all we need to do is look up the current annual dividend and come up with estimates of that growth rate and an estimated required return on equity.
We can use publicly available data to apply this formula and value a share of stock of Genuine Parts Corporation (ticker symbol: GPC). As of October 25, 2019, according to Yahoo! Finance, the consensus estimate longterm earnings growth rate for Genuine Parts Corporation of the analysts who cover the stock is 4.7 percent. We can use this earnings growth rate as a proxy for dividend growth because, in the long run, the two growth rates tend to be very similar for established firms — particularly for dividend kings like Genuine Parts. Genuine Part’s beta as computed by Yahoo! Finance is 0.87. So to value a share of GPC stock, we simply need to compute the required return on equity for GPC. Using the CAPM, as shown earlier in this chapter, GPC’s required return on equity is:
Therefore, the value of a share of GPC stock is estimated to be:
According to this simple analysis, a share of GPC stock would be worth $72.28. At the time of the writing of this book, a share was selling for over $102 per share, so our analysis would imply that the shares are overvalued by a substantial amount — approximately $30 per share. Does this mean we should all run out and sell our shares of GPC and perhaps even short sell the shares? The answer is no. We would need to more carefully evaluate our assumptions and determine how realistic these inputs are.
Typically, the consensus longterm earnings growth estimates provided by financial websites have a very small sample size, and the estimates can vary widely. For instance, instead of a 4.7 percent earnings growth rate, assume that an optimistic analyst projects a 7 percent rate. With a 7 percent growth rate and a required return of 9.06 percent, the shares would be estimated to be worth over $156 each. This simple analysis illustrates why some investors are buying GPC at the market clearing price and other investors are selling the stock at that same price. They have different expectations for future cash flows from the firm.