Chapter 9

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Chapter 9Valuing Shares

Copyright © 2011 Pearson Australia (a division of Pearson Australia Group Ltd) –9781442502000 / Berk/DeMarzo/Harford / Fundamentals of Corporate Finance / 1st edition

9.1 Share Basics Ordinary share: a share of ownership in the

corporation, which gives its owner rights to vote on the election of directors, mergers or other major events. As an ownership claim, ordinary shares carry the

right to share in the profits of the corporation through dividend payments.

Dividends: periodic payments, usually in the form of cash, that are made to shareholders as a partial return on their investment in the corporation. Shareholders are paid dividends in proportion to the

amount of shares they own.

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A one-year investor Two potential sources of cash flows from shares:

1. The firm might pay out cash to its shareholders in the form of a dividend.

2. The investor might generate cash by selling the shares at some future date.

Future dividend payments and share price are unknown.

Investors will be willing to pay a price up to that point that the investment has a zero NPV—at which the current share price equals the PV of the expected future dividend and sale price.

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9.2 The Dividend-Discount Model


A one-year investor (cont’d) As the expected cash flows are risky, we cannot

discount them with the risk-free interest rate, but need to use the cost of capital for the firm’s equity.

Equity cost of capital rE: the expected return of other investments available in the market with equivalent risk to the firm’s share.

P0: the price of the share at the beginning of the period

P1: the price of the share at the end of the period

Div1: the expected dividend during the period

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A one-year investor (cont’d) Share Price = PV(future cash flows)

Share Price = PV(Dividends + Capital Gains)

Po = (Dividends + P1 – Po )

(1+rE)



The expected total return of a share should equal its equity cost of capital—it should equal the expected return of other investments available in the market with equivalent risk.

(Eq. 9.2)

Total return:

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FORMULA!


Dividend yield: the expected annual dividend of the share divided by its current price.

Capital gain: the amount the investor will earn on the share - difference between the expected sale price and the original purchase price for an asset.

Total return: the sum of the dividend yield and the capital gain rate - the expected return the investor will earn for a one-year investment in the share.

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Example 9.1 Share Prices and Returns (pp.267-8)

Problem: Suppose you expect Coca Cola to pay an annual

dividend of $0.56 per share in the coming year and to trade $45.50 per share at the end of the year.

If investments with equivalent risk to Coca Cola shares have an expected return of 6.80%, what is the most you would pay today for Coca Cola shares?

What dividend yield and capital gain rate would you expect at this price?

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Solution:Plan: We can use Eq. 9.1 to solve for the beginning

price we would pay now (P0) given our expectations about dividends (Div1=0.56) and future price (P1=$45.50) and the return we need to expect to earn to be willing to invest (rE=6.8%).

We can then use Eq. 9.2 to calculate the dividend yield and capital gain.

(Eq. 9.1)

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FORMULA!



Execute:

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Evaluate: At a price of , Coca Cola expected total return is

which is equal to its equity cost of capital.

This amount is the most we would be willing to pay for the share. If we paid more, our expected return would be less than 6.8% and we would rather invest elsewhere.

If current share prices are less than this amount, it would be a positive NPV investment.

If current share price exceeds this amount, selling it would produce a positive NPV and the share price would quickly fall.

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A multi-year investor We now extend the intuition we developed for the

1-year investor’s return to a multi-year investor. Eq. 9.1 depends upon the expected share price

in one year, P1

But suppose we planned to hold the shares for two years. Then, we would receive dividends in both year 1 and year 2 before selling the shares, as shown in the following timeline:

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Setting the share price equal to the present value of the future cash flows:

As a two-year investor, we care about the dividend and share price in year 2.

(Eq. 9.3)

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FORMULA!


Dividend-discount model This equation applies to a N-year investor. The share price is equal to the present value of all

of the expected future dividends it will pay.

(Eq. 9.4)

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FORMULA!

Dividend–discount model:

(Eq. 9.5)


Constant dividend growth model A constantly used approximation is to assume that

dividends will grow at a constant rate, g, forever.

The value of the firm depends on the dividend level of next year, divided by the equity cost of capital adjusted by the growth rate.

(Eq. 9.6)

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9.3 Estimating Dividends in the Dividend-Discount Model

FORMULA!

Constant dividend growth model:


Example 9.2 Valuing a Firm with Constant Dividend Growth (p.270)

Problem: Greta’s Garbos is a waste collection company. Suppose Greta’s Garbos plans to pay $2.30 per

share in dividends in the coming year. If its equity cost of capital is 7% and dividends

are expected to grow by 2% per year in the future, estimate the value of Greta’s Garbos’ shares.

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Plan: Because the dividends are expected to grow

perpetually at a constant rate, we can use Eq. 9.6 to value Greta’s Garbos.

The next dividend (Div1) is expected to be $2.30, the growth rate (g) is 2% and the equity cost of capital (rE) is 7%.

Execute:

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Evaluate: You would be willing to pay 20 times this year’s

dividend of $2.30 to own Greta’s Garbos shares because you are buying a claim to this year’s dividend and to an infinite growing series of future dividends.

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Dividend versus investment and growth Often firms face a trade-off—increasing growth may

require investment, and money spent on investment cannot be used to pay dividends.

What determines the rate of growth of a firm’s dividend?

We can define a firm’s dividend payout rate as the fraction of earnings that the firm pays as dividends each year:

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Dividend payout rate The firm’s dividend each year is equal to the firm’s

earnings per share (EPS) multiplied by its dividend payout rate.

The firm can, increase its dividend in three ways:

1. It can increase its earnings (net income).

2. It can increase its dividend payout rate.

3. It can decrease its number of shares outstanding.

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FORMULA! (Eq. 9.8)


Retention rate New investment equals the firm’s earnings

multiplied by its retention rate, or the fraction of current earnings that the firm retains:

Retention Rate = 1 – Dividend Payout Rate

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FORMULA!


A simple model of growth A firm can do two things with its earnings—it can

pay them out to investors, or it can retain and invest them.

If all increases in future earnings result exclusively from new investment made with retained earnings, then:

(Eq. 9.9)

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Change in earnings =New

investment x Return on new

investment


The equation shows that a firm can increase its growth by retaining more of its earnings, but will have to reduce its dividends.

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FORMULA!

New investment = Earnings x Retention rate

Change in earnings =New

investment x Return on new

investment

Earnings growth rate = Change in earnings

(g) Earnings

g =Return on new

investment xRetention Rate


Example 9.3 Cutting Dividends for Profitable Growth (pp.272-3)

Problem: Crane Sporting Goods expects to have earnings

per share of $6 in the coming year. Rather than reinvest these earnings and grow,

the firm plans to pay out all of its earnings as a dividend.

With these expectations of no growth, Crane’s current share price is $60.

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Problem (cont'd): Suppose Crane could cut its dividend payout rate

to 75% for the foreseeable future and use the retained earnings to open new stores.

The return on investment in these stores is expected to be 12%.

If we assume that the risk of these new investments is the same as the risk of its existing investments, then the firm’s equity cost of capital is unchanged.

What effect would this new policy have on Crane’s share price?

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Solution:Plan: We need to calculate Crane’s equity cost of capital and

determine its dividend and growth rate under the new policy.

Because we know that Crane currently has a growth rate of 0 (g = 0), a dividend of $6 and a price of $60, we can use Eq. 9.6 to estimate rE.

Next, the new dividend will simply be 75% of the old dividend of $6.

Finally, given a retention rate of 25% and a return on new investment of 12%, we can calculate the new growth rate (g) and calculate the price of Crane’s shares if it institutes the new policy.

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Execute:

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Execute (cont’d):

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Evaluate: Crane’s share price should rise from $60 to

$64.29 if the company cuts its dividend in order to increase its investment and growth, implying that the investment has positive NPV.

By using its earnings to invest in projects that offer a rate of return (12%) greater than its equity cost of capital (10%), Crane has created value for its shareholders.

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Changing growth rates Successful young firms have very high initial growth

rates and often retain 100% of their earnings to exploit investment opportunities.

As they mature, growth slows, earnings exceed their investment needs and they begin to pay dividends.

We cannot use the constant dividend model to value such a firm for two reasons:1. These firms often pay no dividends when they are

young.2. Their growth rate continues to change over time until

they mature.30



Limitations of the DDM Uncertainty is associated with forecasting a firm’s future

dividends. Let’s consider an example, where a firm pays annual

dividends of $0.72. With an equity cost of capital of 11% and expected

dividend growth of 8%, the DDM implies a share price of:

With a 10% growth rate, however, this estimate would rise to $72 per share; with a 5% growth rate it would fall to $12 per share (Figure 9.2).

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Figure 9.2 Share Prices for Different Expected Growth Rates


Discounted free cash flow model The discounted free cash flow model determines the

total value of the firm to all investors - equity holders and debt holders.

The enterprise value is equivalent to owning the unlevered business. It can be interpreted as the net cost of acquiring the firm’s equity, taking its cash and paying off all debt.

Enterprise value(V0)= Market value of equity + Debt – Cash

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9.4 Total Payout and Free Cash Flow Valuation Models

(Eq. 9.16)

FORMULA!


P0 =V0 – Debt0+ Cash0

Shares outstanding0

Discounted free cash flow model (cont’d) Measures the cash generated by the firm before any

payments to debt and equity holders are consideredEnterprise Value (V0)= PV (Future free cash flow of firm)

Given the enterprise value, V0, we can estimate the share price by using Eq. 9.16 to solve for the value of equity and then divide by the total number of shares outstanding.

Market Value of Equity = V0 – Debt0 + Cash0

(Eq. 9.19)

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FORMULA!

(Eq. 9.18)


Implementing the model A key difference between the discounted free cash

flow model and the dividend discount model is the discount rate.

Previously, we used the firm’s equity cost of capital, rE, because we were discounting the cash flow to equity holders.

Here, we are discounting the free cash flow that will be paid to both debt and equity holders, thus, we use the firm’s weighted average cost of capital (WACC)—it is the cost of capital that reflects the overall risk of the business, rWACC, and is the expected return that a firm needs to pay to investors.

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Free cash flow (FCF) measures the cash generated by the firm before any payments to debt or equity holders are considered

We can forecast the firm’s free cash flow up to some horizon and add a terminal (continuation) value of the enterprise

Often we estimate the terminal value(Vn) by assuming a constant long-run growth rate g FCF for free cash flows beyond year n

(Eq. 9.20)

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(Eq. 9.17)

FCF= EBIT * (1 - tax rate) + Depreciation – Capital Expenditure – Increases in net working capital

(Eq. 9.21)

FORMULA!


Problem: JBH’s free cash flows over the next 5 years are estimated

as follows

After then, the free cash flows are expected to grow at the industry average of 4% per year.

The weighted average cost of capital of JBH is 10%, while JBH has $30 million in cash and $90 million in debt and 107.25 million shares outstanding

Estimate the value of JBH shares in 2009 using the free cash flow method.

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Example 9.8 Valuation Using free cash flow (pp.281)

Year 2010 2011 2012 2013 2014 2015

FCF ($ million) 128.5 155.2 173 181.7 189 196.6


Plan: In order to calculate the enterprise value of JBH we

need the terminal value for JBH at the end of the given projections.

Given an expected constant growth rate (4%) for JBH after 2015, we can use eq 9.21 to calculate a terminal enterprise value.

The present value of the free cash flows during years 2010-2015 and the terminal value will be the total enterprise value for JBH.

Using that value, we can subtract the debt, add the cash and divide by the number of shares outstanding to calculate the price per share.

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Execute:

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Evaluate: The valuation principal tells us that the present

value of all future cash flows generated by JBH plus the value of the cash held by the firm today must equal the total value today of all the claims, both debt and equity, on those cash flows and cash.

Using that principal we calculate the total value of all of JBH’s claims and then subtract the debt portion to value the equity.



9.5 Valuation Based on Comparable Firms

Method of comparables: estimates the value of the firm based on the value of other comparable firms or investments that we expect will generate very similar cash flows in the future.

Valuation multiples: ratio of the value to some measure of the firm’s scale.

Trailing earnings: earnings over the prior 12 months. Forward earnings: expected earnings over the

coming 12 months. Trailing P/E: the resulting ratio from trailing earnings. Forward P/E: the resulting ratio from forward

earnings.

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Problem: Suppose electronics retailer Great Spark has

earnings per share of $1.38.

If the average P/E of comparable retail shares is 21.3, estimate a value for Great Spark’s shares using the P/E as a valuation multiple.

What are the assumptions underlying this estimate?

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Example 9.9 Valuation Using the Price–Earnings Ratio (pp.284-5)


Solution:

Plan: We estimate a share price for Great Spark by

multiplying its EPS by the P/E of comparable firms.

Execute:

P0 = $1.38 x 21.3 = $29.39 This estimate assumes that Great Spark will have

similar future risk, payout rates and growth rates to comparable firms in the industry.

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Evaluate: Although valuation multiples are simple to use,

they rely on some very strong assumptions about the similarity of the comparable firms to the firm you are valuing.

It is important to consider these assumptions are likely to be reasonable—and thus to hold—in each case.

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Limitations of multiples Firms are not identical, so usefulness of a valuation

multiple will depend on the nature of the differences. Furthermore, multiples only provide information

about value of the firm relative to other firms in the comparison set.

Table 9.1 lists several valuation multiples for selected firms in the retail industry as of October 2009.

Data shows that the retail industry has a lot of dispersion for all of the multiples, which most likely reflects differences in expected growth rates and risks (therefore, cost of capital).

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Table 9.1 Share Prices and Multiples for Selected Firms in the Retail Sector


Share valuation techniques—the final word

No single technique provides a final answer regarding a share’s true value.

Practitioners use a combination of these approaches.

Confidence comes from consistent results from a variety of these methods.

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Information in share prices Investors trade until they reach a consensus

regarding the value of the shares, which aggregate the information and views of many different investors.

A valuation model is best applied to tell us something about the firm’s future cash flows or cost of capital, based on its current share price.

Only if we have some superior information that other investors lack regarding the firm’s cash flows and cost of capital would it make sense to second-guess the stock price.

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9.6 Information, Competition and Share Prices


Figure 9.5 The Valuation Triad

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Example 9.10 Using the Information in Share Prices (p.289)

Problem: Suppose Tecnor Industries will pay a dividend this

year of $5 per share.

Its equity cost of capital is 10%, and you expect its dividend to grow at a rate of approximately 4% per year, though you are somewhat unsure of the precise growth rate.

If shares are currently trading at $76.92, how would you update your beliefs about its dividend growth rate?

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Solution:Plan: If we apply the constant dividend growth model

based on a 4% growth rate, we can estimate a share price.

If the market price is higher than our estimate, it implies that the market expects higher growth in dividends than 4%.

Conversely, if the market price is lower, it expects dividend growth to be less than 4%.

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Execute:

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Evaluate: Given the $76.92 market price for the share, we

would lower our expectations for the dividend growth rate from 4%, unless we have very strong reasons to trust our own estimate.

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Competition and efficient markets Efficient markets hypothesis: the idea that

competition among investors works to eliminate all positive NPV trading opportunities.

It implies that securities will be fairly priced, based on their future cash flows, given all information that is available to investors.

Underlying rational is the presence of competition.

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9.7 Information, Competition and Stock Prices


Competition and efficient markets Public, easily available information: information

available to all investors includes information in news reports, financial statements, corporate press releases or other public data sources.

If effects of this information on the firm’s future cash flows can be readily ascertained, then all investors determine how this information changes the firm’s value.

We expect share prices to react instantaneously to such news.

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Competition and efficient markets Private or difficult-to-interpret information: some

expert information is not publicly available or might be difficult to interpret.

While fundamental information may be public, the interpretation of that information will affect the firm’s future cash flows.

When private information is only in the hands of a relatively small number of investors, these investors may be able to profit by trading on their information.

As these traders begin to trade, their actions will tend to move prices, so over time prices will reflect their information as well.

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