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Valuation of Stocks with Time Value and Dividend Growth Models - Prof. Steven Beach, Study notes of Finance

The use of time value equations for the valuation of preferred and common stock. It covers the concept of a share of preferred stock as a perpetuity, the dividend growth model for common stock, and the components of required return. Examples are provided for calculating the market price of preferred and common stock using given dividends, growth rates, and discount rates.

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Pre 2010

Uploaded on 02/12/2009

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FINC 331 – Business Finance
CHAPTER 7 – Equity Markets and Stock Valuation
How the time value equations can be used for the valuation of securities
Preferred stock (Zero Growth)
A share of preferred stock is a perpetuity. They pay a stated dividend every year,
forever. They fall in priority between bonds and common stock for bankruptcy
purposes. No dividends can be paid to common stockholders until all preferred
dividends have been paid.
Example:
Assume a preferred stock with yearly dividend of $10. Assume a real rate of 3% and
an inflation expectation of 3% and the risk premium is 2.5%, what is the market price for
a share of this stock?
Common Stock: A Growing Perpetuity
Common Stock dividends are equally spaced through time and continue indefinitely,
thus it acts like a perpetuity. On the other hand, the dividend may be changed, unlike a
perpetuity. In general, dividends grow over time, thus it can be referred to as a
growing perpetuity.
One of the most significant constructs in finance is the idea that the value of a share of
common stock is the expected future dividends discounted back to the present at the
appropriate required rate of return. An efficient market will price all stocks in this way.
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FINC 331 – Business Finance CHAPTER 7 – Equity Markets and Stock Valuation How the time value equations can be used for the valuation of securities Preferred stock (Zero Growth) A share of preferred stock is a perpetuity. They pay a stated dividend every year, forever. They fall in priority between bonds and common stock for bankruptcy purposes. No dividends can be paid to common stockholders until all preferred dividends have been paid. Example: Assume a preferred stock with yearly dividend of $10. Assume a real rate of 3% and an inflation expectation of 3% and the risk premium is 2.5%, what is the market price for a share of this stock? Common Stock: A Growing Perpetuity Common Stock dividends are equally spaced through time and continue indefinitely, thus it acts like a perpetuity. On the other hand, the dividend may be changed, unlike a perpetuity. In general, dividends grow over time, thus it can be referred to as a growing perpetuity. One of the most significant constructs in finance is the idea that the value of a share of common stock is the expected future dividends discounted back to the present at the appropriate required rate of return. An efficient market will price all stocks in this way.

Dividend Growth Model (The Gordon Growth Model ): This model assumes constant growth of the dividend (g does not change). R>g is assumed. Example: A stock just paid $2.00 annual dividend, dividends are expected to grow at 2% per year indefinitely, the required rate of return is 8% on this stock, what is the current price? Components in Required Return Rearranging the Dividend Growth Model gives us a useful look at the items that make up the return investors receive: P 0 = D 1 / (R - g) => R = D 1 /P 0 + g Total Return = Dividend yield + capital gains yield The total return is a combination of the return investors get from the dividend cash flows and the rate at which the value of the investment grows (capital gains yield).

Financial Markets – where securities are bought and sold A. Money Market – Very liquid market for short-term funds (securities with maturities < /= 1 yr.) Examples: US T-Bills (1 month, 3 month, 6 month, 1 year) Commercial Paper At maturity - the security dies THE market for investing “idle” funds B. Capital Market – Market for long-term funds (securities with maturities > 1 yr.) Examples: Stocks, bonds (Corporate or Treasury) Financial Markets include: a. Primary market – initial sale => issuing company gets the funds b. Secondary market – subsequent trading => prices observed, allows investors to buy, more important: allows investors to sell! Includes: Securities Exchanges (like Stock Markets) Provide: 1) Liquidity – the ability to sell quickly without loss in value

  1. Information – price of stock tells us about the performance of a company
  2. Organized Exchanges (NYSE, AMEX)- Secondary market with a specified location for trading NYSE and AMEX use “open outcry auctions” to establish one price
  3. Over-the-counter (OTC) Exchanges (NASDAQ) Secondary market with trading conducted by dealers on a computerized network Dealer – holds inventory of stocks: buys and sells, this is where the stocks exchange Bid – price at which dealer will buy asset from you Ask – price at which dealer will sell asset to you Broker – brings buyers and sellers together