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**FIN 468: Intermediate Corporate Finance**

Topic 4–Discounted Dividend Valuation Larry Schrenk, Instructor

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**Topics Review of Stock Review of Dividends**

Discounted Dividend Valuation

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Stock Basics

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**Common Equity Dividend (d) Required Rate of Return Ownership**

Governance Issues Residual Status Absolute Priority Rule 4

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**Preferred Shares (PS) Features**

Dividend (d) Two Types of Dividends Required Rate of Return History Uses Technical Features 5

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Comparison 6

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Review of Dividends

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**Different Types of Dividends**

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

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**Procedure for Cash Dividend**

25 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.

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Price Behavior In a perfect world, the stock price will fall by the amount of the dividend on the ex-dividend date. -t … … $P $P - div The price drops by the amount of the cash dividend. Ex-dividend Date Taxes complicate things a bit. Empirically, the price drop is less than the dividend and occurs within a few minutes of the ex-date.

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**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.

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**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.”

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**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. The dividend and capital gains tax rates are subject to change at the discretion of Congress.

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**Taxes, Issuance Costs, and Dividends**

In the presence of personal taxes: A firm should not issue stock to pay a dividend. Managers have an incentive to seek alternative uses for funds to reduce dividends. Though personal taxes mitigate against the payment of dividends, these taxes are not sufficient to lead firms to eliminate all dividends.

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**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).

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**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.

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Dividend Smoothing

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The Clientele Effect Clienteles for various dividend payout policies are likely to form in the following way: Group Stock Type High Tax Bracket Individuals Zero-to-Low payout Low Tax Bracket Individuals Low-to-Medium payout Tax-Free Institutions Medium payout Corporations High payout Once the clienteles have been satisfied, a corporation is unlikely to create value by changing its dividend policy.

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**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.

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**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%

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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.” www: Click on the web surfer icon to find out about upcoming stock splits and dividends

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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 23

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**Discounted Dividend Model (DDM)**

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**Discounted Dividend Model (DDM)**

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. 25

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**Discounted Dividend Model (DDM)**

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). 26

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No-Growth Assumption If a stock is always expected to produce an unchanging dividend, then it is merely a perpetuity. 27

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No-Growth Assumption If a stock is always expected to pay an annual dividend of $4.00 and r = 7%, then 28

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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. 29

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No-Growth Assumption 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 30

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No-Growth Assumption 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 31

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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. 32

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**Non-Constant Assumption**

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? 33

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**Non-Constant Assumption**

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 1 2 3 t d0 d1 d2 d3 dt 34

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**Non-Constant Assumption**

The Short Term This is the period over which we can rationally estimate the expected dividends either: As specific dollar amounts, or E.g., $ $ $ $4.90 As subject to some growth prediction E.g., $4.00 growing at 10% Dividend ‘Smoothing’ 35

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**Non-Constant Assumption**

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. 36

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**Non-Constant Assumption**

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%. 37

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**Non-Constant Assumption**

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. 38

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**Non-Constant Assumption**

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? 39

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**Non-Constant Assumption**

EXAMPLE Data: d0 = 2 g1 = 30% g2-3 = 20% g4+ = 3% r = 12% 40

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**Non-Constant Assumption**

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 = 3.74 d4 = 2(1.30)(1.20)2 (1.03) = 3.85 etc. 41

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**Non-Constant Assumption**

The Timeline Short Term Long Term 1 2 3 4 d0 d1 d2 d3 d4 2.00 2.60 3.12 3.74 3.85 42

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**Non-Constant Assumption**

EXAMPLE Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12% Short Term d1 = d2 = d3 = 3.74 43

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**Non-Constant Assumption**

EXAMPLE Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12% Long Term d4 = 3.85 44

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**Non-Constant Assumption**

EXAMPLE Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12% or Short Term Long Term 45

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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. 46

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**Valuing Preferred Stock**

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**Valuing Preferred Stock**

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: 48

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**Valuing Preferred Stock**

EXAMPLE If a preferred share pays an annual dividend of $3.00 and r = 15%, then 49

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**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. 51

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**‘Implied’ Required Rate of Return**

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. 52

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**‘Implied’ Required Rate of Return**

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: or 53

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**‘Implied’ Required Rate of Return**

Example If a share is selling for $75 and it is paying a constant, annual dividend of $6.00, then 54

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**‘Implied’ Required Rate of Return**

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. 55

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