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Bennie Waller [email protected] 434-395-2046 Longwood University 201 High Street Farmville, VA 23901. Shares of Stock Represent Pieces of a Business

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Bennie Waller

[email protected]

434-395-2046

Longwood University201 High StreetFarmville, VA 23901


Shares of Stock Represent Pieces of a Business

Owning stock in a company in essence indicates that you are part-owner in the company. Generally each share of stock entitles the stockholder to be have one vote toward the election of the Board of Director (typically charged with the oversight of management).

When organizations need to raise capital (money), they typically have two broad options. One they can borrow the money (either from a bank or issue debt (bonds) or they can give up ownership in the firm and sell stock.


Shares of Stock Represent Pieces of a Business

Imagine you start you own landscaping business. You decide that you need $1,000 to get the business started. You divide the company into 10 pieces, or "shares" of stock. You price each new share of stock at $100. If you sell all of the shares, you should have the $1,000 you need. If the business earns $500 after taxes during its first year, each share of stock would be entitled to 1/10th of the profit. You'd take $500 and divide it by 10, resulting in $50.00 earnings per share (EPS).

Source: http://beginnersinvest.about.com/od/stocksoptionswarrants/a/what-is-stock.htm


  • Stock investors expect to earn a return (no guarantee).

  • Capital Appreciation –

  • Income - dividends

  • Firm’s that pay dividends?

    • Why firms may not pay a dividend

    • Types of investors that invest in these firms

  • Firm’s that don’t pay dividends, and why?

    • Types of investors that invest in these firms and why

  • Many/most firms pay some dividends as well as enjoy price appreciation.


  • Stocks are liquid

  • Limited liability (unlimited potential)

  • Claim on income (declaration and ex-dividend dates)

  • Stock splits / reverse splits

  • Stock repurchases

  • Bear market – falling prices

  • Bull market – rising prices



  • Stock market indices – groups of stocks performance that represent the market or segment of market

    • DJIA

    • S&P 500

    • NASDAQ

  • Classification of stocks

    • Blue-chip – large well known firms

    • Growth – firms with growth above industry average (many times these are new firms)

    • Income –

    • Speculative -


  • Classification of stocks represent the market or segment of market

    • Blue-chip – large well known firms

    • Growth – firms with growth above industry average (many times these are new firms)

    • Income –

    • Speculative –

    • Defensive – stocks that tend not to be affected in economic swings

    • Large caps - >$5 billion

    • Small caps - <$1 billion



Dividend Per Share (DPS) - represents the dollar amount of dividends that is paid to stockholders.

Price Earnings (PE)- is an earnings multiple. The P/E is sometimes referred to as the "multiple", because it shows how much investors are willing to pay per dollar of earnings. If a company were currently trading at a multiple (P/E) of 10, the interpretation is that an investor is willing to pay $10 for $1 of current earnings.


Earnings Per Share (EPS) - measures the earnings of the firm on a per share basis.

Payout ratio (PO) - dictates what percent of earnings the firm will payout to stockholders in the form of dividend. Conversely 1-PO indicates what percent of net income the firm plans to retain. A payout ratio of 60% illustrates that the firm is planning on paying out 60% of the firm's net income and retaining 40 percent.


  • Dividend on a per share basis.Growth Model – used to value stocks that pay dividends

  • In essence, taking present value of future cash flows

  • As you go further out into the future, the impact of the cash flows decrease


Stock Valuation assuming constant growth - on a per share basis.Constant Growth (Gordon Dividend) Model – used to determine the intrinsic value of a stock, based on a future series of dividends that grow at a constant rate. Given a dividend per share that is payable in one year, and the assumption that the dividend grows at a constant rate in perpetuity, the model solves for the present value of the infinite series of future dividends.

Stock Value =

Because the model assumes a constant growth rate, it is generally only used for mature companies (or broad market indices) with low to moderate growth rates.


  • Stock Valuation assuming on a per share basis.abnormal growth – firms with high growth or emerging areas such as technology or pharmaceutical are likely to experience periods of abnormal or super-abnormal growth.

  • Assume that a biotech firm discovers a cure for a terminal disease. The firm is expected to have growth rates of 30%, 25% and 20% over the next three years at which time, growth is expected to level off and remain constant at 10% for the foreseeable future. The current required rate of return is 12% for investors (k=.12) and the last dividend paid was $2.00 (D0=2.00).

  • Since the growth will become constant in year 4, we can then apply the constant growth formula.


  • g on a per share basis.1=.30 – expected growth in year 1

  • g2 =.25 – expected growth in year 2

  • g3 =.20 – expected growth in year 3

  • G4+=.10 – expected growth in year 4 and thereafter

  • D0=2.00 – last dividend paid

  • k=.12 –required rate of return (rate firm must pay to encourage investment in firm)

  • Since the growth will become constant in year 4, we can then apply the constant growth formula using the formula below.

We need to calculate the dividends for each of the next 4 years

D1=D0(1+g1) = 2(1.30) =2.60

D2=D1(1+g2) = 2.60(1.25) =3.25

D3=D2(1+g3) = 3.25(1.20) = 3.90

D4=D3(1+g4) = 3.90(1.10) = 4.29


We need to calculate the dividends for each of the next 4 years

D1=D0(1+g1) = 2(1.30) =2.60

D2=D1(1+g2) = 2.60(1.25) =3.25

D3=D2(1+g3) = 3.25(1.20) = 3.90

D4=D3(1+g4) = 3.90(1.10) = 4.29


We need to calculate the dividends for each of the next 4 years

D1=D0(1+g1) = 2(1.30) =2.60

D2=D1(1+g2) = 2.60(1.25) =3.25

D3=D2(1+g3) = 3.25(1.20) = 3.90

D4=D3(1+g4) = 3.90(1.10) = 4.29

2.32 + 2.59 + 2.78 +

So how do we interpret this estimated price?


The last dividend paid by Klein Company was $1.00.  Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever.  Klein’s required rate of return on equity (ks) is 12 percent. 

How much should a prudent investor be willing to pay for this stock based on the above assumptions?


  • g Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever.  Klein’s required rate of return on equity (1=.05 – expected growth in year 1

  • g2 =.05 – expected growth in year 2

  • g3+ =.10 – expected growth in year 3 and thereafter

  • D0=1.00 – last dividend paid

  • k=.12 –required rate of return (rate firm must pay to encourage investment in firm)

This problem has been set up, calculate the expected stock price


Another example Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever.  Klein’s required rate of return on equity (

Assume that you plan to buy a share of XYZ stock today and to hold it for 2 years.  Your expectations are that you will not receive a dividend at the end of Year 1, but you will receive a dividend of $9.25 at the end of Year 2.  In addition, you expect to sell the stock for $150 at the end of Year 2.  If your expected rate of return is 16 percent, how much should you be willing to pay for this stock today?


Another example Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever.  Klein’s required rate of return on equity (

Womack Toy Company’s stock is currently trading at $25 per share.  The stock’s dividend is projected to increase at a constant rate of 7 percent per year.  The required rate of return on the stock, ks, is 10 percent.  What is the expected price of the stock 4 years from today?


Capital Klein’s growth rate is expected to be a constant 5 percent for 2 years, after which dividends are expected to grow at a rate of 10 percent forever.  Klein’s required rate of return on equity (Asset Pricing Model or CAPM –describes the relationship between risk and expected return and is commonly used in the pricing of risky securities.

The idea behind CAPM is that investors need to be compensated in two ways: time value of money and risk. The time value of money is represented by the risk-free () rate in the formula and compensates the investors for placing money in any investment over a period of time. The other half of the formula represents risk and calculates the amount of compensation the investor needs for taking on additional risk. This risk measure (β) that compares the returns of the asset to the market over a period of time and to the market premium (). Beta measure the systematic or business risk.

Source: investopdia.com



The CAPM says that the expected return of a security or a portfolio equals the rate on a risk-free security plus a risk premium. If this expected return does not meet or beat the required return, then the investment should not be undertaken.

Using the CAPM model and the following assumptions, we can compute the expected return of a stock in this CAPM example: if the risk-free rate is 3%, the beta (risk measure) of the stock is 2 and the expected market return over the period is 10%, the stock is expected to return 17% (3%+2(10%-3%)).

The security market line plots the results of the CAPM for all different risks (betas).

SML illustrated

Source: investopdia.com


Security Market Line (SML) portfolio equals the rate on a risk-free security plus a risk premium. If

Return

Rm

Rf

β=0

β=1

β


EXAMPLE portfolio equals the rate on a risk-free security plus a risk premium. If

The common stock of Anthony Steel has a beta of 1.20. The risk-free rate is 5 percent and the market risk premium (kM - kRF) is 6 percent. Assume the firm will be able to use retained earnings to fund the equity portion of its capital budget. What is the company’s cost of retained earnings, ks?

122

= .122


Security Market Line (SML) portfolio equals the rate on a risk-free security plus a risk premium. If

Return

.122

Overpriced stocks will fall below the SML In the previous example, if the stock was currently trading at $9.00/share, the expected return would only be 11%, which is well below the required return of 12.2%

Rm

Rf

β=0

β=1

β=1.2

β


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