1. FIN 468: Intermediate Corporate Finance
Topic 4–Discounted Dividend Valuation
Larry Schrenk, Instructor

2. Topics Review of Stock Review of Dividends
Discounted Dividend Valuation

3. Stock Basics

4. Common Equity Dividend (d) Required Rate of Return Ownership
Governance Issues
Residual Status
Absolute Priority Rule 4

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

6. Comparison 6

7. Review of Dividends

8. Different Types of Dividends
Regular Cash Dividend
Ad Hoc Cash Dividend
Liquidating Dividend
Stock Dividends
Dividend in Kind

9. 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.

10. 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.

11. 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.

12. 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.”

13. 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.

14. 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.

15. 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).

16. 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.

17. Dividend Smoothing

18. 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.

19. 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.

20. 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%

21. 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

22. Valuing Common Stock

23. Valuing Common Stock Methods Discounted Dividend Model (DDM)
P/E Ratio Methodologies
Other Ratio Methodologies
Capital Asset Pricing Model (CAPM)
Relative Valuation 23

24. Discounted Dividend Model (DDM)

25. 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

26. 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

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

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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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

38. 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

39. 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

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

41. 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

42. 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

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

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

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

46. 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

47. Valuing Preferred Stock

48. 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

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

50. The ‘Implied’ Required Rate of Return

51. ‘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

52. ‘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

53. ‘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

54. ‘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

55. ‘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