HB 307 1st Edition Lecture 5Valuation of Stock Pt. 2Growth Models of Common Stock Valuation • Realistically most people tend to forecast growth rates rather than cash flows– Because forecasting exact future prices and dividends is very difficult• Growth rates work like interest rates– If growth is expected to be 6% next year then $100 experiencing a 6% growth willincrease by $6, or $100 x 6%• The ending value after 6% growth will be $106, or $100 + $6, or $100 x (1.06)The Constant Growth Model • If dividends are assumed to be growing at a constant rate forever and we know the last dividend paid, D0, then the model simplifies to:• If k>g the fractions get smaller (approach zero) as the exponents get larger– If k>g growth is normal– If k<g growth is supernormal• Can occur but lasts for limited time periodThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.Constant Normal Growth-The Gordon Model • Constant growth model can be simplified to • The Gordon model is a simple expression for forecasting the price of a stock that’s expected to grow at a constant, normal rateThe Zero Growth Rate Case - A constant Dividend • If a stock is expected to pay a constant, non-growing dividend, each dollar dividend is the same• Gordon model simplifies to:• A zero growth stock is a perpetuity to the investorThe Expected Return • Can recast Gordon model to focus on the return (k) implied by the constant growth assumption• The expected return reflects investors’ knowledge of a company– If we know D0 (most recent dividend paid) and P0 (current actual stock price), investors’ expectations are input via the growth rate assumptionTwo Stage Growth• At times a firm’s future growth may not be expected to be constant– For example, a new product may lead to temporary high growth• The two-stage growth model allows us to value a stock that is expected to grow at an unusual rate for a limited time– Use the Gordon model to value the constant portion– Find the present value of the non-constant growth periodsPractical Limitations of Pricing Models • Stock valuation models give approximate results because the inputs are approximations of reality– Bond valuation is precise because inputs are exact• With bonds future cash flows are contractually guaranteed in amount andtime• Actual growth rate can be VERY different from predicted growth rates– Even if growth rates differ only slightly, it can make a big difference in our decision• So, it’s best to allow a margin for error in your estimations• Stocks That Don’t Pay Dividends– Some firms don’t pay dividends even if they are profitable– Many companies claim they never intend to pay dividends• These firms can still have a substantial stock price– Firms of this type typically are growing and are using their profits to finance their growth• However rapid growth won’t last forever• When growth slows, the firm will begin paying dividends• It’s these distant dividends that impart