summary of last lecture introduction to stocks stock valuation

Summary of Last Lecture

• Introduction to Stocks• Stock Valuation

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

Learning Objectives:

• 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).

Share Price Valuation - Common Stock

• Perpetual Investment in Common Stock:• It is an idealized Case. The Final Cash Flow

term (containing Pn) in the equation takes place at Year n = infinity The last term (containing Pn) has a Present Value almost equal to Zero because the Discount Factor (1+rE) ^ n in the denominator becomes very large when n=infinity. So, you can ignore the Last Cash Flow terms taking place at Year n.

Share Price Valuation - Common Stock

• Simplified Formula (Pn term removed from the equation for large investment durations i.e. n = infinity):

• PV = DIV1/ (1+rE) + DIV2/ (1+rE) 2 + … DIVn/(1+rE)n

• = DIVt / (1+ rE) t. t = year. Sum from t =1 to n• This Equation is still impractical because need

to forecast Dividends for every year forever!!

Example:

• The Common Stock of Company ABC is being traded in the Islamabad Stock Market. Its Market Price is Rs.13. You study Company ABC’s Annual Report, Balance Sheet, Income Statement, and Cash Flow Statement and you forecast the future Dividends to be Rs 2 in the first year and Rs 4 in the second year.

Example:

• You forecast the Market Price to be Rs 13 after 2 years. The Par Value of each share is Rs 10. The Risk Free Return is 10% pa. Your expected Minimum Required Return from the high-risk Common Stock of ABC is 20%. Calculate the Fair (or Expected) Price of the Common Stock Common Stock Valuation (Risky Investment: rCE= 20%)

Example:

• 1st year will be Rs.2 and dividend in 2nd year will be Rs.4 assume risk free rate of return is 10% and high rate of return to be required is 20%. Again this 20% is higher than 10% in a country and this 20% minimum required rate of return is higher than the preferred stock required by that company is 15 %.

Example:

• This is because common stock is considered more risky than preferred stock and bank deposit in a country . Let’s calculate the value of common stock for company ABC we will use our old present value formula for finite investment :

• PV=2/12+4/(1.2)^2+1.3/(1.2)^2

Example:

• Finite Investment for 2 Years: • PV = 2/1.2 + 4 / (1.2)2 + 13 / (1.2)2 = Rs 13.47• This is estimated price for 2nd year investment

based on forecasted dividend let’s see the long term investment use present value formula about which we talked earlier on Perpetual Investment: PV =??

Example:

• We can not determine it because we don’t have Dividend forecast data for every year forever!! We need to use Models for approximating future Dividends Cash Flow Stream:

• Zero Growth Model• Constant Growth Model

We will discuss about these in the next lecture.

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.

2. Common Stock:

• 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.

2. Common Stock:

• 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.

Investment Time Horizons

• 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.


• 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.


• 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.


• 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.

ABC 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.

ABC Common 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.

ABC Common Shares:

• 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 if you invested for a short period time.

ABC Common Shares:

• So, for the case of preferred stock, we calculate the expected market price for long term investment would be.

Preferred Stock

• 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

• 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.

Share Values:

• 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.

Fair Value VS Market Price

• 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.

• Vice Versa.

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 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).


• PV = Po*= DIV1 / (1+ rCE) + DIV1 / (1+ rCE) 2 + DIV1 / (1+ rCE) 3 + ... +...

• = 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.

Example:

• 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

Example:

• Interpretation of Result:• Constant Growth Pricing gives a higher

Estimate of Present Price because it assumes perpetual 10% compounded growth in dividends forever.

Summary

• Common Stock pricing• Dividend Growth Models

summary of last lecture introduction to stocks stock valuation

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