Chapter 8 Stocks and Their Valuation

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1 Chapter 8 Stocks and Their Valuation Stock Valuation k s the required rate of return the minimum rate of return on the stock, given the stock s riskiness and the returns available on other similar assets P the price at which a stock sells for in the market today, at Time P T the price at which a stock sells for in the market at Time T D T dividend the stockholder expects to receive at the end of time T D the most recent dividend, has already been paid D the next expected dividend, to be paid at the end of this year 2 P? D D 2 D Generally, the value of an asset is the present value of the benefits expected from the asset; what are the benefits expected from stock ownership? 2 3 P D( + k s ) + D 2 ( + k s ) + D 3 ( + k s ) + K Preferred Stock Hybrid security. Similar to bonds with fixed dividend amounts. Similar to common stock as dividends are not required and have no fixed maturity date. Preference over common stock in distribution of dividends and assets Preferred stock options: cumulative dividends conversion into common stock voting rights dividend participation sinking funds, call provisions, and even maturity

2 Which to use, bonds or preferred stock? Bonds fixed interest payments does not represent ownership interest expense is deductible may have restrictive covenants Pros/Cons Preferred Stock fixed payment - but not obligated no voting rights higher after-tax cost since dividends are not tax deductible expenses Generally, 7% of corporate dividends received by corporations are exempt from taxation Preferred Stock Valuation Generally, the value of an asset is the present value of the benefits expected from that asset..the benefits expected from stock ownership are constant dividend payments. Preferred stock is a special case where the growth rate is zero. Preferred stock can be valued as a perpetuity. The formula: D P p k p p Preferred Stock Example: What is the market value of a preferred stock that pays an annual $5 dividend when the required rate of return on preferred stock is %? Common stock: Common stock dividends are not constant, so D D 2 D Assume dividends grow forever at a constant annual rate, g 2 P? D D (+g) D (+g) 2 D (+g )

3 If g is constant, today's value of common stock, P, can be found be summing the present value of all dividends to be received beginning with the next one, D. D D ( + g) k s g k s g Common Stock Example: What is the value of a common stock that just paid a dividend of $2, expects a growth rate of 6% and has a required rate of return of 3%? A more general statement is that Time T's value of common stock, P T, can be found be summing the time T value of all dividends to be received beginning with the next one, D T+. DT+ PT k g s Continuation of Common Stock Example: What is the Time value of a common that just paid a dividend of $2, expects a growth rate of 4% and has a required rate of return of 4%? D will have been paid, so expected dividends are D 2, D 3, D 4 and so on. When calculating P, then D T+ is D 2 Investors buy common stock for:. dividends 2. price appreciation (capital gains)

4 D Dividend yield Pˆ Capital gains yield Continuation of common stock example: Find the expected dividend yield and capital gains yield during the first year for the common stock in the previous example. D Dividend yield P $2.2 $3.29 Capital gains Pˆ yield P P $32. $3.29 $3.29 The total return for a common stockholder consists of the dividend yield and the capital gains yield. The total return expected for the first year for the above example is: Total return Dividend yield + Capital gains yield 7% + 6% 3%. Total return 3% k s. For the constant growth stock: Capital gains yield 6% g. Rearranging the common stock formula to solve for k: D D rearrangel k s + g k s g What if growth is negative? If g -6%, would anyone buy the stock? If so, at what price? Assume the last dividend was $2. and the required rate of return is 3%. The firm still has earnings and still pays dividends, so P >.

5 Nonconstant Growth A firm may experience a part of its life cycle where its growth is either much faster or much slower than its normal growth rate of g To value nonconstant growth stock, follow the following three steps:. Compute the nonconstant growth dividends 2. Find the price of the stock at the end of the nonconstant growth period, at which time it has become a constant growth stock 3. Sum the present value of steps. and 2. Nonconstant growth valuation example: What is the value of a stock that just paid a dividend of $2, expects 3% growth for the next three years then expects the growth to settle to a normal growth of 6% per year forever? Assume a required rate of return of 3%?

Gatton College of Business and Economics Department of Finance & Quantitative Methods. Chapter 8. Finance 300 David Moore

Gatton College of Business and Economics Department of Finance & Quantitative Methods Chapter 8 Finance 300 David Moore Cash Flows for Stockholders If you own a share of stock, you can receive cash in