Lecture 6

Equity Valuation

Introduction

Analysts gather and process information to make investment decisions, including buy and sell
recommendations. What information is gathered and how it is processed depend on the analyst and
the purpose of the analysis. Technical analysis uses such information as stock price and trading volume
as the basis for investment decisions. Fundamental analysis uses information about the economy,
industry, and company as the basis for investment decisions. Examples of fundamentals are
unemployment rates, gross domestic product (GDP) growth, industry growth, and quality of and
growth in company earnings. Whereas technical analysts use information to predict price movements
and base investment decisions on the direction of predicted change in prices, fundamental analysts
use information to estimate the value of a security and to compare the estimated value to the market
price and then base investment decisions on that comparison.

Equity valuation models used to estimate the intrinsic value (synonym: fundamental value) of a
security; intrinsic value is based on an analysis of investment fundamentals and characteristics. The
fundamentals to be considered depend on the analyst’s approach to valuation. In a top-down
approach, an analyst examines the economic environment, identifies sectors that are expected to
prosper in that environment, and analyzes securities of companies from previously identified
attractive sectors. In a bottom-up approach, an analyst typically follows an industry or industries and
forecasts fundamentals for the companies in those industries in order to determine valuation.
Whatever the approach, an analyst who estimates the intrinsic value of an equity security is implicitly
questioning the accuracy of the market price as an estimate of value. Valuation is particularly
important in active equity portfolio management, which aims to improve on the return–risk trade-off
of a portfolio’s benchmark by identifying mispriced securities.

Estimated value and Market Price

By comparing estimates of value and market price, an analyst can arrive at one of three conclusions:
The security is undervalued, overvalued, or fairly valued in the marketplace. For example, if the market
price of an asset is $10 and the analyst estimates intrinsic value at $10, a logical conclusion is that the
security is fairly valued. If the security is selling for $20, the security would be considered overvalued.
If the security is selling for $5, the security would be considered undervalued. Basically, by estimating
value, the analyst is assuming that the market price is not necessarily the best estimate of intrinsic
value. If the estimated value exceeds the market price, the analyst infers the security is undervalued.
If the estimated value equals the market price, the analyst infers the security is fairly valued. If the
estimated value is less than the market price, the analyst infers the security is overvalued.

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Background for the Dividend Discount Model

Present value models follow a fundamental tenet of economics which states that individuals defer
consumption—that is, they invest—for the future benefits expected. Individuals and companies make
an investment because they expect thereby to earn a rate of return over the investment period.
Logically, the value of an investment should be equal to the present value of the expected future
benefits. For common shares, an analyst can equate benefits to the cash flows to be generated by the
investment. The simplest present value model of equity valuation is the dividend discount model
(DDM), which specifies cash flows from a common stock investment to be dividends.

Generally, there are two sources of return from investing in equities: (1) cash dividends received by
an investor over his or her holding period and (2) the change in the market price of equities over that
holding period.

The payment of dividends is not a legal obligation: dividends must be declared (i.e., authorized) by a
company’s board of directors; in some jurisdictions, they must also be approved by shareholders.

Dividend discount models address discounting expected cash dividends. A stock dividend (also known
as a bonus issue of shares) is a type of dividend in which a company distributes additional shares of its
common stock (typically, 2%–10% of the shares then outstanding) to shareholders instead of cash. A
stock dividend divides the “pie” (the market value of shareholders’ equity) into smaller pieces without
affecting the value of the pie or any shareholder’s proportional ownership in the company. Thus, stock
dividends are not relevant for valuation.

Stock splits and reverse stock splits are similar to stock dividends in that they have no economic effect
on the company or shareholders. A stock split involves an increase in the number of shares
outstanding with a consequent decrease in share price. An example of a stock split is a two-for one
stock split in which each shareholder is issued an additional share for each share currently owned. A
reverse stock split involves a reduction in the number of shares outstanding with a corresponding
increase in share price. In a one-for-two reverse stock split, each shareholder would receive one new
share for every two old shares held, thereby reducing the number of shares outstanding by half.

In contrast to stock dividends and stock splits, share repurchases are an alternative to cash dividend
payments. A share repurchase (or buyback) is a transaction in which a company uses cash to buy back
its own shares. Shares that have been repurchased are not considered for dividends, voting, or
computing earnings per share. A share repurchase is viewed as equivalent to the payment of cash
dividends of equal value in terms of the effect on shareholders’ wealth, all other things being equal.

The payout of regular cash dividends to common shareholders follows a fairly standard chronology
that is set in motion once the company’s board of directors votes to pay the dividend. First is the
declaration date, the day that the company issues a statement declaring a specific dividend. Next
comes the ex-dividend date (or exdate), the first date that a share trades without (i.e., “ex”) the
dividend. This is followed closely (one or two business days later) by the holder-of-record date (also
called the owner-of-record date, shareholder-of-record date, record date, date of record, or date of
book closure), the date that a shareholder listed on the company’s books will be deemed to have
ownership of the shares for purposes of receiving the upcoming dividend. The final milestone is the

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payment date (or payable date), which is the day that the company actually mails out (or electronically
transfers) a dividend payment to shareholders.

Dividend Discount Model (DDM) and Free Cash Flow to Equity Model (FCFE)

At the shareholder level, cash received from a common stock investment includes any dividends
received and the proceeds when shares are sold.

The expected value of a share at the end of the investment horizon—in effect, the expected selling
price— is often referred to as the terminal stock value (or terminal value).

In practice, many analysts prefer to use a free-cash-flow-to-equity (FCFE) valuation model. To use a
DDM, the analyst needs to predict the timing and amount of the first dividend and all the dividends
or dividend growth thereafter. Making these predictions for non-dividend-paying stock accurately is
typically difficult, so in such cases, analysts often resort to FCFE models.

FCFE is a measure of cash flow generated in a period that is available for distribution to common
shareholders. What does “available for distribution” mean? The entire CFO (Cash Flow from
Operations) is not available for distribution; the portion of the CFO needed for fixed capital investment
(FCInv) during the period to maintain the value of the company as a going concern is not viewed as
available for distribution to common shareholders. Net amounts borrowed (borrowings minus

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repayments) are considered to be available for distribution to common shareholders. Thus, FCFE can
be expressed as

FCFE = CFO – FCInv + Net borrowing

Valuation obtained by using FCFE involves discounting expected future FCFE by the required rate of
return on equity;

Common methods for estimating the required rate of return for the stock of a company include adding
a risk premium that is based on economic judgments to an appropriate risk-free rate (usually a
government bond) and adding a risk premium to the yield on the company’s bonds. Good business
and economic judgment is paramount in estimating the required rate of return. In many investment
firms, required rates of return are determined by firm policy.

Preferred Stock Valuation

A preferred stock is a form of equity (generally, non-voting) that has priority over common stock in
the receipt of dividends and on the issuer’s assets in the event of a company’s liquidation. It may have
a stated maturity date at which time payment of the stock’s par (face) value is made or it may be
perpetual with no maturity date; additionally, it may be callable or convertible.

For a non-callable, non-convertible perpetual preferred share paying a level dividend D and assuming
a constant required rate of return over time:

For example, a $100 par value non-callable perpetual preferred stock offers an annual dividend of
$5.50. If its required rate of return is 6 percent, the value estimate would be $5.50/0.06 = $91.67.

For a non-callable, non-convertible preferred stock with maturity at time n, the estimated intrinsic
value can be estimated by using the following formula:

F = Face Value

For example, a non-convertible preferred stock with a par value of £20.00, maturity in six years, a
nominal required rate of return of 8.20 percent, and semi-annual dividends of £2.00 would be valued
by using an n of 12, an r of 4.10 percent, a D of £2.00, and an F of £20.00. The result would be an

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estimated value of £31.01. Assuming payments are annual rather than semi-annual (i.e., assuming
that n = 6, r = 8.20 percent, and D = £4.00) would result in an estimated value of £30.84.

The Gordon Growth Model

A rather obvious problem when one is trying to implement DDM for common equity is that it requires
the analyst to estimate an infinite series of expected dividends. To simplify this process, analysts
frequently make assumptions about how dividends will grow or change over time.

The Gordon (constant) growth model is a simple and well-recognized DDM. The model assumes
dividends grow indefinitely at a constant rate. Because of its assumption of a constant growth rate,
the Gordon growth model is particularly appropriate for valuing the equity of dividend-paying
companies that are relatively insensitive to the business cycle and in a mature growth phase. Examples
might include an electric utility serving a slowly growing area or a producer of a staple food product
(e.g., bread).

For an illustration of the expression, suppose the current (most recent) annual dividend on a share is
€5.00 and dividends are expected to grow at 4 percent per year. The required rate of return on equity
is 8 percent. The Gordon growth model estimate of intrinsic value is, therefore, €5.00(1.04)/(0.08 –
0.04) = €5.20/0.04 = €130 per share.

In estimating a long-term growth rate, analysts use a variety of methods, including assessing the
growth in dividends or earnings over time, using the industry median growth rate, and using the
relationship shown below:

g = b × ROE

where g = dividend growth rate

b = earnings retention rate = (1 – Dividend payout ratio)
ROE = return on equity

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Example

Siemens AG operates in the capital goods and technology space. It is involved in the engineering,
manufacturing, automation, power and transportation sectors. It operates globally and is one of the
largest companies in the sectors in which it operates. It is a substantial employer in both its original,
domestic German market, as well as dozens of countries around the world. Selected financial
information for Siemens appears in the exhibit below.

Year 2017 2016 2015 2014 2013

EPS € 7.45 € 6.74 € 8.85 € 6.37 € 5.08
DPS € 3.70 € 3.60 € 3.50 € 3.30 € 3.00
Payout ratio 50% 53% 40% 52% 59%
ROE 15.6% 15.9% 22.3% 18.2% 14.6%
Share price € 119.2 € 104.2 € 79.94 € 94.37 € 89.06

The analyst estimates the growth rate to be approximately 5.4 percent based on the dividend growth
rate over the period 2013 to 2017 [3(1 + g) 4 = 3.7, so g = 5.4%]. To verify that the estimated growth
rate of 5.4 percent is feasible in the future, the analyst also uses the average of Siemens’s retention
rate and ROE for the previous five years (g ≈ 0.49 × 17.3% ≈ 8.5%) to estimate the sustainable growth
rate.

The analyst estimates a required return of 7.5 percent. The most recent dividend of €3.70 is used for
D0.

1. Use the Gordon growth model to estimate Siemens’s intrinsic value.

2. Based on the estimated intrinsic value, is a share of Siemens undervalued, overvalued, or fairly
valued?
3. What is the intrinsic value if the growth rate estimate is lowered to 4.4 percent?
4. What is the intrinsic value if the growth rate estimate is lowered to 4.4 percent and the required
rate of return estimate is increased to 8.5 percent?

Solution to 1

Solution to 2

A share of Siemens appears to be undervalued.

Solution to 3

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Solution to 4

Example continued (Sensitivity Analysis)

The Gordon growth model estimate of intrinsic value is extremely sensitive to the choice of required
rate of return r and growth rate g. It is possible that the growth rate assumption and the required
return assumption used initially were too high. Worldwide economic growth is typically in the low
single digits, which may mean that a large company such as Siemens may struggle to grow dividends
at 5.4 percent into perpetuity. The exhibit below presents a further sensitivity analysis of Siemens’s
intrinsic value to the required return and growth estimates.

The assumptions of the Gordon model are as follows:

■ Dividends are the correct metric to use for valuation purposes.
■ The dividend growth rate is forever: It is perpetual and never changes.
■ The required rate of return is also constant over time.
■ The dividend growth rate is strictly less than the required rate of return.

Applying a DDM is difficult if the company being analyzed is not currently paying a dividend. A
company may not be paying a dividend if 1) the investment opportunities the company has are all so
attractive that the retention and reinvestment of funds is preferable, from a return perspective, to
the distribution of a dividend to shareholders or 2) the company is in such shaky financial condition
that it cannot afford to pay a dividend. An analyst might still use a DDM to value such companies by
assuming that dividends will begin at some future point in time. The analyst might further assume that
constant growth occurs after that date and use the Gordon growth model for valuation.

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Multistage Dividend Discount Models

Multistage growth models are often used to model rapidly growing companies. The two-stage DDM
assumes that at some point the company will begin to pay dividends that grow at a constant rate, but
prior to that time the company will pay dividends that are growing at a higher rate than can be
sustained in the long run. That is, the company is assumed to experience an initial, finite period of high
growth, perhaps prior to the entry of competitors, followed by an infinite period of sustainable
growth. The two-stage DDM thus makes use of two growth rates: a high growth rate for an initial,
finite period followed by a lower, sustainable growth rate into perpetuity. The Gordon growth model
is used to estimate a terminal value at time n that reflects the present value at time n of the dividends
received during the sustainable growth period.