Dr Nalan Gulpinar

1. Stocks and Their Valuation Dr Nalan Gulpinar 381 Computational Finance 6-7 February 2006 Imperial College London

2. Topics Covered Stocks and their valuation zero dividend growth constant dividend growth non-constant dividend growth earning and sales based valuation methods

3. Stocks Shares, securities or equities – an ownership in part of a company You are entitled to a portion of company’s profits and any voting rights attached to stock A company issues the stocks –shares the profits with stock holders sells some ownership in company (in form of stocks) to raise money (equity financing)to use for upgrading equipment, marketing, expansion… Profits are paid out in dividends – the more shares you own, the larger profits you own Common Stock yields higher return than other forms of investment securities ownership in a company & a portion of profits (variable dividends) voting rights in case of bankrupt, shareholders receive no money until rest of stockholders is paid Preferred Stock some degree of ownership in a company no voting rights guaranteed a fixed dividend forever may be callable – company has an option to purchase shares from shareholders at anytime for a premium paid off before common shareholders

4. Stock Prices The price of a stock shows what investors feel the company is worth. Stock prices change everyday by the market – risky + many factors Buyers and sellers cause prices to change because of supply and demand If more people want to buy a stock than sell it, then price moves up sell a stock, there would be more supply than demand, price would start to fall Many factors drive stock prices – earnings (profit) of a company For securities issued by the company, there is uncertainty and also no maturity date, no dividend rate, need to estimate expected selling price to calculate current price Discounted Dividend Model Stock price is PV (future cash flows to be received by investor)

5. Valuation of Stocks If investor buys a stock, he is entitled to receive all future dividends and can sell the stock in the future The cash flow of common stock consists of dividends plus a future sale price The stock discount rate reis the rate of return that investors expect to earn on securities with similar risk Time 0 1 2 … T … Cash-Flow D1 D2 … DT … They buy stock for P0and sell for P1 after one year and receive dividend D1, The next buyer also sells after one year At time period T,

6. Valuation of Stocks Using recursive substitution, the current price of the stock is Expression for expected price can be neglected for a large time horizon The current value of the stock is the present value of all future cash flows: dividends and expected selling price the value of T is determined by the investor dividends are uncertain need to estimate the expected selling price

7. Required Returns The return on equity is sum of dividend yield and expected capital gain D1is not known since it is an expected value about future dividend dividend yield –percentage return for the dividend –annual dividend per share is divided by price per share historic or trailing dividend yield prospective dividend yield

8. Stock’s Value Estimation The Zero Dividend Growth Model If the dividend is expected to stay constant over time, shares are valued like perpetual bonds expected return on equity is equal to dividend yield. Do not reflect reality because of constancy of dividends

9. Constant Dividend Growth Model an amount grows at a constant rate forever is called a growing perpetuity stock with a constant dividend growth is a growing perpetuity let g be a constant dividend growth rate current stock price

10. Constant Dividend Growth Model If , then The growth rate is If the company in steady state where dividends are expected to grow at a constant rate g, the stock price grows at the same constant rate. Example: Next year dividends per share for Company X is expected to be £0.95. The dividends are expected to grow at 14% per year in the future. What should be the current price if the required rate of return is 16% per year? growing perpetuity

11. Non-constant Dividend Growth Model If the company is not a steady state, not possible to use the previous model Define sub periods with different growth rates Estimate the value of stock by considering each sub period with their discounting PV of non-constant growth dividends at each period PV of constant growth dividends PV(Pt) Value of the stock is

12. Example The next three years dividends for Company Y are expected to be £0.50, £1.00, £1.50. Then the dividends are expected to grow at a constant 5% forever. If the required return is 10%, then what is the value of the stock? • Constant dividend growth based on 3rd dividend • Non-constant dividend growth • The current price of the stock

13. Dividend Forecast stock valuation formula is a function of all future dividends forecasting method for dividends is needed Forecast dividends for a finite time horizon T Apply the constant growth formula for the horizon value by substituting for the dividends after period T

14. Forecast Dividends 1 Period into Future special version T=1 is obtained If we do not have a forecast for this year’s dividend, then the historic dividend value can be used

15. Example Consider a company pays a dividend of £0.75 per share. Demand for this company’s product is growing at 2% per year and inflation averages 2.5% per year. The company expects its profits and dividends to grow at about 4.55% per year (1.02X1.025= 1.0455). Stockholders require a 10% rate of return. What is the market price of this company’s stock? The dividend next period is

16. Price-Earnings (P/E) Ratio used to price equities: a fair value of stock can be determined with the P/E multiple the earning yield = E1 / P0 where E1 is the earnings per share. dividends and earnings are related via the company’s pay out policy; explained by the pay out ratiop required return on equity is related to earnings yield If companies have the same pay out ratio, discount rate, growth rate, they have the same P/E ratio

17. Price-Earnings (P/E) Ratio Analysts often report historical price earning ratio P0 /E0 When dividends and earnings grow at the same constant rate g from now on, The required return and P / E ratio are