1. FIN 360: Corporate Finance
Topics 10: Stocks and their Valuation
Larry Schrenk, Instructor

2. Stock Valuation Stock Basics Valuing Common Stock
Valuing Preferred Stock
‘Implied’ Required Rate of Return

3. Stock Basics

4. Common Equity Dividends Required Rate of Return Ownership
Residual Status
Absolute Priority Rule

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

6. Common Stock: Owners, Directors, and Managers
Represents Ownership
Ownership Implies Control
Stockholders Elect Directors
Directors Hire Management
Since Managers are ‘Agents’ of Shareholders, their Goal Should Be: Maximize Stock Price

7. Ownership of Common Stock
Mostly owned (70%) by institutional investors
Institutional investors include:
Pension Plan Funds (CALPERS)
Insurance Companies
Mutual Funds
Hedge Funds

8. Pros of Equity Financing
No obligation to pay dividends.
Risk averse management doesn’t like debt
Reduces financial risk (e.g. total debt ratio)
This may be a more important advantage to firms that already are relatively risky due to the kind of business they do (e.g. high tech has high business risk)

9. Cons of Equity Financing
Dilution of ownership and power due to more shares of stock outstanding.
Lower earnings per share/stock price
More work than debt offering
Flotation costs (expensive)
Fees paid to investment bankers, lawyers, accountants, printers
Usually much higher than for debt issues.

10. Comparison

11. Valuing Common Stock

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

13. Stock Valuation Issues
Stock cash flows are less certain than that of bond cash flows because:
Bond cash flows are fixed and defined by contract
Whereas stock cash flows are:
Dividends: residual and determined by the Board of Director’s vote
Proceeds from sale of stock: Not guaranteed
Difficulties in Stock Valuation:
Dividend cash flows are not known in advance
Life of stock is essentially forever
No easy way to observe the rate of return required for a stock

14. Discounted Dividend Model (DDM)

15. Capital Gains vs. Dividends▪

16. 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.

17. Discounted Dividend Model (DDM)
Constant Model
Dividends remain constant
Growth Model
Dividends change at a constant rate
Mixed Model
Dividends change at different rates.

18. Constant Model
If dividend is constant, then stock is a perpetuity.

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

20. Growth Model
If dividend is changing at a constant rate, then stock is a growing perpetuity.

21. Growth Model
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

22. Growth Model
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

23. Mixed Model Both patterns possible,
but not likely to apply to very many firms.
Generally, 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.

24. Mixed Model Problem
Estimate year-by-year dividends 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?

25. Mixed Model Strategy Short Term Long Term
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

26. Mixed Model: Short Term
Period over which we can reasonably estimate the expected dividends:
As specific dollar amounts, or
E.g., $ $ $ $4.90
As subject to some growth forecast
E.g., $4.00 growing at 10% for 4 years
Dividend ‘Smoothing’

27. Mixed Model: Long Term Period over which we cannot predict dividends.
We cannot ignore the long term,
For many firms the long term provides much of the value of the firm.
NOTE: The more value is derived from the future, the harder to use the DDM as a method.

28. The Long Term Solution
Estimate the long term dividends as growing at a reasonable, constant growth rate.
Estimate as growing perpetuity.
Infinite growth rate cannot be very large.
One good estimate is the long term growth for the economy, perhaps 3 or 4%.

29. Calculations
Value of the short term dividends is PV of the individual dividends.
2) Value of the long term dividends is a delayed growing perpetuity.
NOTE: It is a delayed growing perpetuity because the long term dividends do not begin until after the short term dividends end.
3) Stock price = PVshort term + PVlong term

30. Mixed Model Example 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?

31. Mixed Model Example
Data:
d0 = 2
g1 = 30%
g2-3 = 20%
g4+ = 3%
r = 12%

32. Mixed Model Example Data Dividends Calculation
d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12%
Dividends Calculation
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.

33. Mixed Model Example The Timeline Short Term Long Term 1 2 3 4 d0 d1 d21 2 3 4 d0 d1 d2 d3 d4
2.00
2.60
3.12
3.74
3.85

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

35. Mixed Model Example EXAMPLE
Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12%
Long Term
d4 = 3.85

36. Mixed Model Example EXAMPLE or Short Term Long Term
Data: d0 = 2; g1 = 30%; g2-3 = 20%; g4+ = 3%; r = 12% or
Short Term Long Term

37. Mixed Model Formula

38. Valuing Preferred Stock

39. 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:

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

41. The ‘Implied’ Required Rate of Return

42. ‘Implied’ Required Rate of Return
The term ‘implied’ sometimes has a semi-technical meaning.
Recall implied future interest rates
Normally
We use a formula of the form:
Price = …
to determine the price of an asset.
Then compare the predicted price with the asset’s market value

43. ‘Implied’ Required Rate of Return
An alternative
Use the market price to estimate what the ‘market’ assumes to be one of the ‘implied’ input variables
We have already used this in the YTM of bonds.
Given the market price of a bond, what ‘implied’ discount rate, i.e., YTM
What discount rate must the market apply to arrive at the market price.
YTM is the implied required rate of return on a bond.

44. ‘Implied’ Required Rate of Return
If the stock (common or preferred) is modeled as a (growing) perpetuity,
Solve the equation for i) the ‘implied’ required rate of return or ii) the ‘implied’ growth rate:

45. ‘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

46. ‘Implied’ Required Rate of Return
If the stock dividends are not constant,
Then the implied rate of return is internal rate of return (IRR)
The IRR calculation (in a later topic) is analogous to finding the YTM of a bond.