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Financial Management ­ MGT201
VU
Lesson 17
COMMON STOCK PRICING AND DIVIDEND GROWTH MODELS
Learning Objectives:
After going through this lecture, you would be able to have an understanding of the following topics
·  Common Stock pricing
·  Dividend Growth Models
In this lecture, we continue our discussion on the topic of stock price valuation.
In previous lecture, we have discussed that there are two types of Shares (or Stocks or Equity
Securities)
1. Preferred Stock:
These stocks have regular Constant / Fixed Future Dividends Certain for the Preferred
Shareholders. Use old Perpetuity Cash Flow Pattern and formulas to estimate theoretical
Fair Stock Price.
2. Common Stock:
Theses stocks have variable future dividends expected by the common shareholders. Use Zero
& Constant Growth Models to simplify future Dividend forecasts in estimated Theoretical Stock Price
(or PV) equation. There dividend depend upon the income earned by the company and also upon the
management decision regarding the dividend declaration.
Both stocks represent ownership of Real Assets in Company.
Dividends are the Shareholder's portion of the Distributed Net Income. The value of direct
securities (piece of paper) derived from the cash flows generated from the underlying real assets.
There are two types of Investment Time Horizons
1. Finite Investment:
In this duration of our investment is limited. Cash inflow from Forecasted Selling
Price must be taken into account in price estimate.
2. Perpetual Investment:
It is very long term horizon for long term investment. It is Perpetual so Forecasted Selling Price not
significant and can be eliminated. If you are planning to buy and hold the share for 20 or 30 years then
you can consider it as a long term assets. Similarly, an investment in the share for the period of one or
two years
Value of a Share (which is a Direct Claim Security) can be estimated based on the Cash Flows that
is generates. A Share generates Cash Dividends just like a Real Asset Project generates Cash Income.
The Formulas for the theoretical price valuation vary depending upon the time horizon. As in
previous lectures the formula for preferred shares varies depending on whether your time horizon is
finite or perpetual.
Let us compare both common shares and preferred shares with the help of numerical example.
Example:
Company ABC has issued 2 Types of Shares (both of Par Value = Rs 10) and you are
considering Investing in both shares for 2 years because you think the price will rise to Rs 13 by then.
The Market Risk Free Return (Opportunity cost) is 10% pa.
ABC Preferred Shares:
Dividend Fixed by the Company at Rs 2 per share per year. Your required rate of return for the
risky preferred shares is 15%. This is the rate of return that you expect to get if you take risk of
investing the money in preferred shares. Preferred shares are considered to be more risky then the
deposit in the bank. So, our required rate of return in case of preferred stock should be higher then 10%.
ABC Common Shares:
Dividend varies. After analyzing the Company's Annual Report, Balance Sheet, Income & Cash
Flow Statements, you forecast the future Dividends to be Rs 2 in the first year and Rs 4 in the second
year. The required rate of return does not have to be identical to the required rate of return on preferred
shares. As, there is no guarantying you a fixed rate of return on common shares. Your required rate of
return for the more risky common shares is 20% pa. Finally, based upon the analysis of financial
statements of the company you expect that the price of share will rise to Rs. 13 after 2 years. You
planned to look at different investment cases you are interested in estimating what the theoretical market
price of this share should be if you invest perpetually and you are also interested in the price of the share
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Financial Management ­ MGT201
VU
if you invested for a short period time. So, for the case of preferred stock, we calculate the expected
market price for long term investment would be.
Solution:
Preferred Stock (Risky Investment: rPE= 15% > 10%=risk free)
Perpetual:
PV = DIV1/ rPE = 2 / 15% = 2/0.15 = Rs 13.33
Now in case of finite investment
2 Year (Finite): PV=2/1.15+ 2/ (1.15)2 +13/ (1.15)2 =Rs 13.08
Common Stock Valuation (More Risky Investment: rCE= 20%)
Perpetual Investment: PV =? We don't have enough Dividend forecast data in order to calculate
the value for 20 or 30 years from now. We discuss the solution of this problem later in the lecture .Here
1.2 = (1+20%). We use Rs 13 because we expect to sell these shares for Rs.13 after 2 Years.
2 Year (Finite): PV =2/1.2 + 4/ (1.2)2 +13/(1.2)2 = Rs 13.47
Interpretation:
In our example, Common Stock has higher Intrinsic Present Value or Fair Value (or Estimated
Market Price) than Preferred Stock because Common Stock offers higher expected Dividends which
more than compensates for the higher risk of the common stock. We discuss this in detail when we
study the topic of Risk and Return.
Share Values:
Fair Value VS Market Price
Fair Value:
It is estimated from PV Equation. We calculate this from NPV equation based on a required rate
of return as the discount rate or r in the equation. This is very important to understand because the ROR
is our personal ROR and its value varies depending on the investor who is doing the calculation. Every
person has a different Risk Profile. Therefore, Fair Value varies depending on the investor who is doing
the calculation and his/her Personal Required Return.
Market Price:
It is actual price at which it is bought or sold. It is determined by Share's Demand/Supply &
Investor Perceptions & Psychology about the company behind the share. Market Price is almost
identical for everyone.
In Efficient Markets where investors have almost equal information, Fair Value will basically
match Market Price. But, temporarily they can differ. Then what happens? Usually, you think that
whether the price of the thing purchased by you have that much price or not. Similar question will be
asked in share trading
If Market Price < Fair Value: then Stock is under valued by the Market. It is a bargain and
investors will rush to buy it. Therefore, Share's Demand will rise and Market Price will rise to match the
Fair Value. Dynamic Equilibrium.
If Market Price > Fair Value then Stock is Over Valued
Share Price Valuation -Perpetual Investment in Common Stock:
Perpetual Investment in Common Stock
The PV Formula would require us to make Dividends Forecast for every year in future. Which
is not feasible for us? Therefore, we can not use the old version of PV formula. We use 2 approaches to
solve this problem.
Zero Growth Dividends Model:
In this we assume Perpetual Dividends at Zero Growth i.e. Constant Perpetual Dividends.
Similar to Preferred Stock Valuation Formula i.e. DIV1 = DIV 2 = DIV3 In this method the
simplification we made is this
In this there is a Fixed Regular Dividends Cash Flow Stream for every year in future.
This is very simple method as the dividend for first year and the last year remains identical. It is a
simple perpetuity model. Therefore we use Perpetuity Formula. Which is Similar to Preferred Stocks
(Perpetual Investment) except Preferred Dividends (which are declared by the Company) not same as
Common Stock Dividends (which are estimated).
The Formula for common stock
PV = Po*= DIV1 / (1+ rCE) + DIV1 / (1+ rCE) 2 + DIV1 / (1+ rCE) 3 + ... +...
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Financial Management ­ MGT201
VU
= DIV 1 / rCE.
Po* is the Expected (Theoretical) Present Price. The Price depends on DIV1 which is the
Expected Future Dividend for Year 1 (and all other years in future).There is difference in case of
common stock & preferred stock. In common stock we assume the constant growth but in preferred
stock the company has assured the preferred stockholder that he will get fixed rate of dividend.
Constant Growth Dividends Model:
In this, we need only to forecast the next year dividend and assume constant dividends Growth
at Inflationary Growth Rate "g" which equals 5 - 10% pa (depending on country).
DIVt+1 = DIVt x (1 + g) t. t = time in years i.e. If g = 10%
Dividends Cash Flow Stream grows according to the Discrete Compound Growth Formula
DIVt+1 = DIVt x (1 + g) t.
t = time in years.
So if you have estimated the present Dividend (DIVo) or the next year's Dividend (DIV1) then
you can estimate all future dividends using this formula. In this, the trick is how to pick the right growth
rate. Generally, we pick the rate of growth of inflation. As common stock holders we assume that the
dividends are continue to grow at constant rate which is equal to rate of growth of inflation. If inflation
rate is 10% then the dividend will grow at 10%.you have dividend of Rs 10 in first year then you will
have dividend of Rs 10 plus 10% of Rs 10 which is equal to Rs.11.
Estimate Growth Rate = "g" using:
1. Financial Statements (calculate Dividends' growth rate)
2. Inflationary Growth Rate of Economy (say 5 - 10% pa)
Formula:
PV = Po* =DIV1 (1+g) /(1+ rCE ) +DIV1 (1+g)2 / (1+ rCE )2 + DIV 1 (1+g)3 / (1+ rCE )3 + ...
= DIV 1 / (rCE - g)
DIVI= dividend for first year
In this we can derive the answer as sum of geometric series. Growing Perpetuity formula.
Example:
You are considering making a very long term investment in the common stock of Company ABC.
Your Required Return on the investment (based on risk) is 20% (rCE). The present Dividend
offered by Company ABC is Rs 4. Par Value is Rs 10.
Dividend Yield Pricing for Common Stock under Perpetual Investment
Zero Growth Model Pricing
PV = Po* = DIV1 / rCE = 4 / 0.20 = Rs 20
Constant Growth Model Pricing (assume g=10%)
PV = Po* = DIV1 / (rCE -g) = 4 / (0.2-0.1) = Rs 40
Interpretation of Result:
Constant Growth Pricing gives a higher Estimate of Present Price because it assumes perpetual
10% compounded growth in dividends forever
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Table of Contents:
  1. INTRODUCTION TO FINANCIAL MANAGEMENT:Corporate Financing & Capital Structure,
  2. OBJECTIVES OF FINANCIAL MANAGEMENT, FINANCIAL ASSETS AND FINANCIAL MARKETS:Real Assets, Bond
  3. ANALYSIS OF FINANCIAL STATEMENTS:Basic Financial Statements, Profit & Loss account or Income Statement
  4. TIME VALUE OF MONEY:Discounting & Net Present Value (NPV), Interest Theory
  5. FINANCIAL FORECASTING AND FINANCIAL PLANNING:Planning Documents, Drawback of Percent of Sales Method
  6. PRESENT VALUE AND DISCOUNTING:Interest Rates for Discounting Calculations
  7. DISCOUNTING CASH FLOW ANALYSIS, ANNUITIES AND PERPETUITIES:Multiple Compounding
  8. CAPITAL BUDGETING AND CAPITAL BUDGETING TECHNIQUES:Techniques of capital budgeting, Pay back period
  9. NET PRESENT VALUE (NPV) AND INTERNAL RATE OF RETURN (IRR):RANKING TWO DIFFERENT INVESTMENTS
  10. PROJECT CASH FLOWS, PROJECT TIMING, COMPARING PROJECTS, AND MODIFIED INTERNAL RATE OF RETURN (MIRR)
  11. SOME SPECIAL AREAS OF CAPITAL BUDGETING:SOME SPECIAL AREAS OF CAPITAL BUDGETING, SOME SPECIAL AREAS OF CAPITAL BUDGETING
  12. CAPITAL RATIONING AND INTERPRETATION OF IRR AND NPV WITH LIMITED CAPITAL.:Types of Problems in Capital Rationing
  13. BONDS AND CLASSIFICATION OF BONDS:Textile Weaving Factory Case Study, Characteristics of bonds, Convertible Bonds
  14. BONDS’ VALUATION:Long Bond - Risk Theory, Bond Portfolio Theory, Interest Rate Tradeoff
  15. BONDS VALUATION AND YIELD ON BONDS:Present Value formula for the bond
  16. INTRODUCTION TO STOCKS AND STOCK VALUATION:Share Concept, Finite Investment
  17. COMMON STOCK PRICING AND DIVIDEND GROWTH MODELS:Preferred Stock, Perpetual Investment
  18. COMMON STOCKS – RATE OF RETURN AND EPS PRICING MODEL:Earnings per Share (EPS) Pricing Model
  19. INTRODUCTION TO RISK, RISK AND RETURN FOR A SINGLE STOCK INVESTMENT:Diversifiable Risk, Diversification
  20. RISK FOR A SINGLE STOCK INVESTMENT, PROBABILITY GRAPHS AND COEFFICIENT OF VARIATION
  21. 2- STOCK PORTFOLIO THEORY, RISK AND EXPECTED RETURN:Diversification, Definition of Terms
  22. PORTFOLIO RISK ANALYSIS AND EFFICIENT PORTFOLIO MAPS
  23. EFFICIENT PORTFOLIOS, MARKET RISK AND CAPITAL MARKET LINE (CML):Market Risk & Portfolio Theory
  24. STOCK BETA, PORTFOLIO BETA AND INTRODUCTION TO SECURITY MARKET LINE:MARKET, Calculating Portfolio Beta
  25. STOCK BETAS &RISK, SML& RETURN AND STOCK PRICES IN EFFICIENT MARKS:Interpretation of Result
  26. SML GRAPH AND CAPITAL ASSET PRICING MODEL:NPV Calculations & Capital Budgeting
  27. RISK AND PORTFOLIO THEORY, CAPM, CRITICISM OF CAPM AND APPLICATION OF RISK THEORY:Think Out of the Box
  28. INTRODUCTION TO DEBT, EFFICIENT MARKETS AND COST OF CAPITAL:Real Assets Markets, Debt vs. Equity
  29. WEIGHTED AVERAGE COST OF CAPITAL (WACC):Summary of Formulas
  30. BUSINESS RISK FACED BY FIRM, OPERATING LEVERAGE, BREAK EVEN POINT& RETURN ON EQUITY
  31. OPERATING LEVERAGE, FINANCIAL LEVERAGE, ROE, BREAK EVEN POINT AND BUSINESS RISK
  32. FINANCIAL LEVERAGE AND CAPITAL STRUCTURE:Capital Structure Theory
  33. MODIFICATIONS IN MILLAR MODIGLIANI CAPITAL STRUCTURE THEORY:Modified MM - With Bankruptcy Cost
  34. APPLICATION OF MILLER MODIGLIANI AND OTHER CAPITAL STRUCTURE THEORIES:Problem of the theory
  35. NET INCOME AND TAX SHIELD APPROACHES TO WACC:Traditionalists -Real Markets Example
  36. MANAGEMENT OF CAPITAL STRUCTURE:Practical Capital Structure Management
  37. DIVIDEND PAYOUT:Other Factors Affecting Dividend Policy, Residual Dividend Model
  38. APPLICATION OF RESIDUAL DIVIDEND MODEL:Dividend Payout Procedure, Dividend Schemes for Optimizing Share Price
  39. WORKING CAPITAL MANAGEMENT:Impact of working capital on Firm Value, Monthly Cash Budget
  40. CASH MANAGEMENT AND WORKING CAPITAL FINANCING:Inventory Management, Accounts Receivables Management:
  41. SHORT TERM FINANCING, LONG TERM FINANCING AND LEASE FINANCING:
  42. LEASE FINANCING AND TYPES OF LEASE FINANCING:Sale & Lease-Back, Lease Analyses & Calculations
  43. MERGERS AND ACQUISITIONS:Leveraged Buy-Outs (LBO’s), Mergers - Good or Bad?
  44. INTERNATIONAL FINANCE (MULTINATIONAL FINANCE):Major Issues Faced by Multinationals
  45. FINAL REVIEW OF ENTIRE COURSE ON FINANCIAL MANAGEMENT:Financial Statements and Ratios