1. CDA COLLEGE BUS235: PRINCIPLES OF FINANCIAL ANALYSIS Lecture 6 Lecture 6 Lecturer: Kleanthis Zisimos

2. Characteristics of stocks Characteristics of stocks Common stock valuation Common stock valuation Preferred stock valuation Preferred stock valuation Stock Market equilibrium Stock Market equilibrium Lecture Topic List

3. Definition of stocks Common stock represents an ownership interest in a corporation. Common stock represents an ownership interest in a corporation. Common stockholders have the right to elect the directors of the company. In small companies usually the director is the main stockholder Common stockholders have the right to elect the directors of the company. In small companies usually the director is the main stockholder Common stockholders have the right to receive dividends, but only if the company has earnings out of which dividends can be paid and only if management chooses to pay dividends rather than to retain and reinvest all the earnings. Common stockholders have the right to receive dividends, but only if the company has earnings out of which dividends can be paid and only if management chooses to pay dividends rather than to retain and reinvest all the earnings. Stock can be sold at some future date, hopefully at a price greater than the purchase price. If the stock is actually sold at price above its purchase price, the investor will receive a capital gain. Stock can be sold at some future date, hopefully at a price greater than the purchase price. If the stock is actually sold at price above its purchase price, the investor will receive a capital gain.

4. Definitions used in the stock valuation P 0 =actual market price of stock today P 0 =actual market price of stock today D t = Expected Dividend in year t. D t = Expected Dividend in year t. P e =expected price of stock. This is a theoretical value because it depends on the expectation of each investor of the future dividend yield and riskiness of the stock. Hense, where P0 is identical for all investors, Pe differs among investors P e =expected price of stock. This is a theoretical value because it depends on the expectation of each investor of the future dividend yield and riskiness of the stock. Hense, where P0 is identical for all investors, Pe differs among investors Ks=require rate of return Ks=require rate of return

5. Stock Valuation The value of the stock is the present value of the expected future dividends The value of the stock is the present value of the expected future dividends ∞ Pe= Σ D t t t=1 (1+k s ) t=1 (1+k s ) This is the basic formula for stock valuation. This is the basic formula for stock valuation. To find the value of the stock though we need more data and these data are depended according To find the value of the stock though we need more data and these data are depended according 1. g=Expected growth rates of dividends

6. Stock Value with zero growth rate A stock that is expected to pay the same dividend each year forever is the same as a perpetuity so the formula for a zero growth stock is: A stock that is expected to pay the same dividend each year forever is the same as a perpetuity so the formula for a zero growth stock is: P 0 = D Ks Ks Example. What is the value of a stock with dividend 1.5 euro per year and Ks= 14% Example. What is the value of a stock with dividend 1.5 euro per year and Ks= 14%

7. The value of a stock that is expected to pay a dividend which increases by the same growth rate, g, each year each year forever is found by the following formula The value of a stock that is expected to pay a dividend which increases by the same growth rate, g, each year each year forever is found by the following formula P 0 = D(1+g) Ks-g Ks-g Example. What is the value of a stock with dividend 1.5 euro per year, growth rate 10% and Ks= 14% Example. What is the value of a stock with dividend 1.5 euro per year, growth rate 10% and Ks= 14% Stock Value with constant growth rate

8. Preferred Stock Preferred stock valuation is similar to bond valuation in some respects and to common stock in other respects. Preferred stock valuation is similar to bond valuation in some respects and to common stock in other respects. Preferred dividends are similar to interest payments on bonds because they are fixed in amount and generally must be paid before common stock dividends can be paid. Preferred dividends are similar to interest payments on bonds because they are fixed in amount and generally must be paid before common stock dividends can be paid. However like common dividends they can be omitted without bankrupting the firm. However like common dividends they can be omitted without bankrupting the firm. 8

9. Preferred Stock Valuation Vps = Dps Kps Kps Vps = is the value of the preferred stock. Vps = is the value of the preferred stock. Dps = is the preferred dividend. Dps = is the preferred dividend. Kps = is the required rate of return. Kps = is the required rate of return. The formula is based on the assumption that preferred dividends last forever The formula is based on the assumption that preferred dividends last forever

10. Expected rate of return on a constant growth stock From the stock valuation equation we can solve for ks and we come to the conclusion From the stock valuation equation we can solve for ks and we come to the conclusion Ks= D 0 (1+g) + g P 0 P 0

11. Stock market Equilibrium All this calculations help us choose whether we want to buy or sell a stock. All this calculations help us choose whether we want to buy or sell a stock. If you remember from the CAPM the expected rate of return of a stock is Ki = KRF + (KM – KRF)bi If you remember from the CAPM the expected rate of return of a stock is Ki = KRF + (KM – KRF)bi If ks>Ki an investor will want to buy the stock If ks>Ki an investor will want to buy the stock If Ks<Ki an investor will want to sell the stock If Ks<Ki an investor will want to sell the stock If Ks=Ki an investor will be indifferent. If Ks=Ki an investor will be indifferent. In the efficient market hypothesis the stocks are always consider to be in equilibrium that means Ks=Ki and the price of the stock is equal to the expected price of the stock In the efficient market hypothesis the stocks are always consider to be in equilibrium that means Ks=Ki and the price of the stock is equal to the expected price of the stock