FIN 468: Intermediate Corporate Finance

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FIN 468: Intermediate Corporate Finance

Topic 4–Discounted Dividend Valuation

Larry Schrenk, Instructor

http://www.kogod.american.edu/


Topics

Review of Stock

Review of Dividends

Discounted Dividend Valuation


Stock Basics



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Common Equity

Dividend (d) Required Rate of Return Ownership Governance Issues Residual Status Absolute Priority Rule


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Preferred Shares (PS) Features

Dividend (d) Two Types of Dividends

Required Rate of Return History Uses Technical Features


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Comparison

A COMPARISON OF COMMON EQUITY, PREFERRED SHARES AND DEBT Asset Common Equity Preferred Shares Debt

Ownership Yes No No Priority Low Medium High

Cash Flow Required No Conditional Yes Maturity No Often Yes

Risk High Medium Low


Review of Dividends



Different Types of Dividends

Regular Cash Dividend Ad Hoc Cash Dividend Liquidating Dividend Stock Dividends Dividend in Kind


Procedure for Cash Dividend25 Oct. 1 Nov. 2 Nov. 5 Nov. 7 Dec.

Declaration Date

Cum-dividend

Date

Ex-dividend

Date

Record Date

Payment Date

…

Declaration Date: The Board of Directors declares a payment of dividends.Cum-Dividend Date: Buyer of stock still receives the dividend.Ex-Dividend Date: Seller of the stock retains the dividend.Record Date: The corporation prepares a list of all individuals believed to be stockholders as of 5 November.


Price Behavior

In a perfect world, the stock price will fall by the amount of the dividend on the ex-dividend date.

$P

$P - divEx-dividend

DateThe price drops by the amount of the cash dividend.

-t … -2 -1 0 +1 +2 …

Taxes complicate things a bit. Empirically, the price drop is less than the dividend and occurs within a few minutes of the ex-date.


The Irrelevance of Dividend Policy

A compelling case can be made that dividend policy is irrelevant.

Since investors do not need dividends to convert shares to cash; they will not pay higher prices for firms with higher dividends.

In other words, dividend policy will have no impact on the value of the firm because investors can create whatever income stream they prefer by using homemade dividends.


Dividends and Investment Policy

Firms should never forgo positive NPV projects to increase a dividend (or to pay a dividend for the first time).

Recall that one of the assumptions underlying the dividend-irrelevance argument is: “The investment policy of the firm is set ahead of time and is not altered by changes in dividend policy.”


Personal Taxes, Issuance Costs, and Dividends To get the result that dividend policy is irrelevant,

we needed three assumptions: No taxes No transactions costs No uncertainty

In the United States, both cash dividends and capital gains are taxed at a maximum rate of 15 percent.

Since capital gains can be deferred, the tax rate on dividends is greater than the effective rate on capital gains.


Taxes, Issuance Costs, and Dividends

In the presence of personal taxes:1. A firm should not issue stock to pay a dividend.2. Managers have an incentive to seek alternative

uses for funds to reduce dividends.3. Though personal taxes mitigate against the

payment of dividends, these taxes are not sufficient to lead firms to eliminate all dividends.


Empirical Facts

What are the empirical facts about dividends? Significant amount of dividends paid out of earnings. Individuals in high tax brackets receive large amounts

of dividend income and pay a significant amount of tax on it.

Corporations smooth dividends The market reacts positively (negatively) to

announcements of dividend increases (decreases).


Real-World Factors Favoring High Dividends

Desire for Current Income Behavioral Finance

It forces investors to be disciplined. Tax Arbitrage

Investors can create positions in high dividend yield securities that avoid tax liabilities.

Agency Costs High dividends reduce free cash flow.


Dividend Smoothing

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General Electric

$0.10$0.15$0.20$0.25$0.30$0.35$0.40$0.45$0.50

2Q 20

00

4Q 20

00

2Q 20

01

4Q 20

01

2Q 20

02

EPSDividend

General Electric

30%35%40%45%50%55%60%

2Q 20

00

4Q 20

00

2Q 20

01

4Q 20

01

2Q 20

02

Payout Ratio


The Clientele Effect

Clienteles for various dividend payout policies are likely to form in the following way:

Group Stock Type

High Tax Bracket Individuals

Low Tax Bracket Individuals

Tax-Free Institutions

Corporations

Zero-to-Low payout

Low-to-Medium payout

Medium payout

High payout

Once the clienteles have been satisfied, a corporation is unlikely to create value by changing its dividend policy.


What We Know and Do Not Know Corporations “smooth” dividends. Dividends provide information to the market. Firms should follow a sensible dividend policy:

Don’t forgo positive NPV projects just to pay a dividend.

Avoid issuing stock to pay dividends. Consider share repurchase when there are few better

uses for the cash.


Stock Dividends

Pay additional shares of stock instead of cash

Increases the number of outstanding shares Small stock dividend

Less than 20 to 25% If you own 100 shares and the company declared

a 10% stock dividend, you would receive an additional 10 shares.

Large stock dividend – more than 20 to 25%


Stock Splits

Stock splits – essentially the same as a stock dividend except it is expressed as a ratio For example, a 2 for 1 stock split is the same as a

100% stock dividend. Stock price is reduced when the stock splits. Common explanation for split is to return

price to a “more desirable trading range.”


Valuing Common Stock



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Valuing Common Stock

Methods Discounted Dividend Model (DDM) P/E Ratio Methodologies

Other Ratio Methodologies Capital Asset Pricing Model (CAPM) Relative Valuation


Discounted Dividend Model (DDM)



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Motivation Dividends are the cash flows derived from

common stock. The price is the present value of cash flows. Thus, the price of a common share should be the

present value of its dividends Problems

Dividends (especially far future ones) are not easily estimated.


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Three Possible Assumptions about Dividends:

They are constant (No-Growth Assumption). They are always changing at a constant rate

(Constant Growth Assumption). Neither of the above two conditions applies

(Non-Constant Assumption).


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No-Growth Assumption

If a stock is always expected to produce an unchanging dividend, then it is merely a perpetuity.

CECE

dVr


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If a stock is always expected to pay an annual dividend of $4.00 and r = 7%, then

4.00 $57.140.07CEV


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Constant Growth Assumption

If a stock is always expected to produce an dividend that is changing at a constant rate, then it is merely a growing perpetuity.

1CE

CE

dVr g


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If a stock has just paid an annual dividend of $4.00, and the dividend is expected to increase (infinitely) at 2% (r = 7%), then

4.00(1.02) $81.600.07 0.02CEV


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The same methodology applies if the dividend is expected to decline.

If a stock has just paid an annual dividend of $4.00, and the dividend is expected to decrease (infinitely) at 2% (r = 7%), then

4.00(0.98) $43.56

0.07 0.02CEV


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Non-Constant Assumption

While both of these assumptions are possible, they are not likely to apply to very many firms.

Instead, we would expect the firm’s dividend to change at different rates over time. A high growth firm might increase is cash flows at

30% for a few years, but this could not be sustained for any extended period.


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But if we were to try to estimate the dividends of a firm year-by-year for an extended period, e.g., ten years, this would become a pure, unfounded guess at values.

What will the dividend be for IBM 8 years from now?


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To alleviate this problem, we divide the forecast of dividends into two periods: Short Term Prediction/Horizon Long Term Prediction/Horizon

Short Term Long Term

0 1 2 3 t

d0 d1 d2 dtd3


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The Short Term This is the period over which we can rationally

estimate the expected dividends either: As specific dollar amounts, or

E.g., $4.00 $4.15 $4.25 $4.90 As subject to some growth prediction

E.g., $4.00 growing at 10% Dividend ‘Smoothing’


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The Long Term By definition the ‘Long Term’ is the period over

which we cannot predict dividends. We cannot ignore the long term, since for many

firms the long term provides much of the value of the firm. NOTE: The more a firm’s value is derived from the future

the harder it will be to use the DDM as a valuation method.


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The Long Term Solution We estimate the long term dividends as growing

at a reasonable, constant growth rate. That is we estimate long term dividends as a growing

perpetuity. Since the growth is assumed to continue infinitely, it

cannot be very large. One good estimate for the long term growth rate is the

estimated long term growth for the economy as a whole, perhaps 3 or 4%.


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Calculations:1) The present value of the short term dividends is the

discounted value of the individual dividends.2) The present value of the long term dividends is a

delayed growing perpetuity. It is a delayed growing perpetuity because the long term

dividends do not begin until after the short term dividends end.

3) The price of the stock is the sum of the present values of the short and long term dividends.


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EXAMPLE A firm has just paid an annual dividend of $2.00.

That dividend is expected to grow at a rate of 30% for one year, 20% for the next two years, then level off to a long term growth rate of 3%. If the discount rate is 12%, what should be the price of the stock?


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EXAMPLE Data:

d0 = 2 g1 = 30% g2-3 = 20% g4+ = 3% r = 12%


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EXAMPLE Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r =

12% The Dividends

d1 = 2(1.30) = 2.60 d2 = 2(1.30)(1.20) = 3.12 d3 = 2(1.30)(1.20)2 = 3.74d4 = 2(1.30)(1.20)2 (1.03) = 3.85etc.


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The Timeline


0 1 2 3 4

d0 d1 d2 d4d3

2.00 2.60 3.12 3.853.74


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EXAMPLE Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12% Short Term

d1 = 2.60 d2 = 3.12 d3 = 3.74

2 3

2.60 3.12 3.74 7.47(1.12) (1.12) (1.12)STCEV


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EXAMPLE Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r =

12% Long Term

d4 = 3.85

3

3.85 1 30.450.12 0.03 1.12LTCEV


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EXAMPLE Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12%

or


7.47 30.45 $37.92ST LTCE CE CEV V V

32 3

2.60 3.12 3.74 3.85 1 37.92(1.12) (1.12) (1.12) 0.12 0.03 1.12

CEV


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Capital Asset Pricing Model (CAPM)

In a later lecture we shall discuss the Capital Asset Pricing Model (CAPM). This model does not directly estimate the price for

common equity. Instead, it is a model for estimating the return on

equity, but should be mentioned here given its affinity to issues in stock valuation.


Valuing Preferred Stock



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Unlike common stock, the cash flows on preferred stock are typically of the form of a perpetuity, so we can use that formula for pricing:

PSPS

dVr


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EXAMPLE If a preferred share pays an annual dividend

of $3.00 and r = 15%, then

3.00 $20.000.15PSV


The ‘Implied’ Required Rate of Return



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‘Implied’ Required Rate of Return

The term ‘implied’ sometimes has a semi-technical meaning in finance. As we have seen, we more often than not use a

formula of the form: Price = …

The goal is to find appropriate input variable to determine the price of an asset.

We can then compare the price predicted by the model with the market value of the asset.


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An alternative use of these formulae would be to use the market price to estimate what the ‘market’ assumes to be one of the input variable, i.e., what is the ‘implied’ variable.

We have already used this approach in our yield to maturity calculations for bonds. In that calculation, we ask, given the market price of a

bond, what ‘implied’ discount rate, i.e., YTM, must the market be using to discount the cash flows of the bond to arrive at the market price.

YTM is the implied required rate of return on a bond.


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We can use the formulae in this lecture to find the analogous ‘implied’ required rate of return on a stock.

If the stock (common or preferred) is modeled as a perpetuity, we can solve the equation for the required rate of return:

ordrV

1dr gV


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Example If a share is selling for $75 and it is paying a

constant, annual dividend of $6.00, then

6.00 8%75.00

r


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If the stock dividends are not constant, then estimating the implied required rate of return requires us to find the internal rate of return (IRR) of the stock. The IRR calculation will be covered in the next

lecture, but is essentially identical to finding the YTM of a bond.


Documents

FIN 468: Intermediate Corporate Finance