Chapter 6. Stock Valuation

Size: px

Start display at page:

Download "Chapter 6. Stock Valuation"

Susan Jody James
6 years ago
Views:

Chapter 6 Stock Valuation Comprehend that

growth opportunities affect stock values

1 Chapter 6 Stock Valuation Comprehend that stock prices depend on future dividends and dividend growth Compute stock prices using the dividend growth model Understand how growth opportunities affect stock values Appreciate the PE ratio Know how stock markets work 6-1 1

2 6.1 The Present Value of Common Stocks 6.2 Estimates of Parameters in the Dividend Discount Model 6.3 Growth Opportunities 6.4 Price-Earnings Ratio 6.5 Some Features of Common and Preferred Stock 6.6 The Stock Markets 6-2 The value of any asset is the present value of its expected future cash flows. Stock ownership produces cash flows from: Dividends Capital Gains Valuation of Different Types of Stocks Zero Growth Constant Growth Differential Growth 6-3 2

Assume that dividends will remain at the same level forever Since future cash flows are constant, the value of a zero growth stock is the present value of

pay an annual dividend of $2.00 per common share that will never increase or decrease. The market rate of return is 8.5%.

3 Assume that dividends will remain at the same level forever Since future cash flows are constant, the value of a zero growth stock is the present value of a perpetuity: or Div r Often simplified, because all dividends are the same but remember, the numerator is really Div Suppose Big Deal Company will pay an annual dividend of $2.00 per common share that will never increase or decrease. The market rate of return is 8.5%. What is the maximum amount you should be willing pay for a common share of Big Deal Corporation? Formula for Zero Growth Model: P = Div 1 / R Solution: P = $2.00 / P = $

present value of a growing perpetuity: 6-6 Suppose Big D, Inc., just paid a dividend of $0.50.

4 Assume that dividends will grow at a constant rate, g, forever, i.e.,. Since future cash flows grow at a constant rate forever, the value of a constant growth stock is the present value of a growing perpetuity: 6-6 Suppose Big D, Inc., just paid a dividend of $0.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk level, how much should the stock be selling for? P 0 = 0.50(1+0.02) / ( ) = $

5 It is critical to understand that in the constant growth model calculations are based on the next dividend, i.e., the dividend at t=1 If a situation only provides information on the last dividend it must be increased by the growth rate to arrive at the next dividend If a situation provides the value of the next dividend (i.e., of Div 1, then the data necessary for the calculation is known and need not be derived. An analyst must discriminate whether they have information about the next or last dividend and proceed with calculation accordingly 6-8 Assume that dividends will grow at different rates in the foreseeable future & then grow at a constant rate thereafter. To value a Differential Growth Stock, we need to: Estimate future dividends in the foreseeable future. Estimate the future stock price one period before the growing perpetuity starts (as in case 2). Compute the total present value of the estimated future dividends and future stock price at the appropriate discount rate

6 This graph demonstrates the dividend profile for a company with differential growth 6-10 Assume that dividends will grow at rate g 1 for N years and grow at rate g 2 thereafter.. Div N is the first dividend in the growing perpetuity

Dividends will grow at rate g 1 for N years and grow at rate g 2 thereafter 0 1 2

as the sum of: PV of an N-minus-1-year annuity growing at rate g 1 : annuity plus

7 Dividends will grow at rate g 1 for N years and grow at rate g 2 thereafter Div N is the first dividend in the growing perpetuity N N We can value this as the sum of: PV of an N-minus-1-year annuity growing at rate g 1 : annuity plus the discounted value of a perpetuity growing at rate g 2 that starts in year N

8 Consolidating gives: Or, we can cash flow it out A common stock just paid a dividend of $2. The dividend is expected to grow at 8% for 3 years, then it will grow at 4% in perpetuity. What is the stock worth? The discount rate is 12%

0 1 2 3 4 5 Div 1 = 2.00 x.1.08 Div 2 = 2.00 x.1.08 2 Growing Annuity, albeit a short one Div 3 Div 3 = 2.00 x.1.08 3 Div 4 = 2.00 x.1.08 3 x1.

9 Div 1 = 2.00 x.1.08 Div 2 = 2.00 x Growing Annuity, albeit a short one Div 3 Div 3 = 2.00 x Div 4 = 2.00 x x1.04 Div 5 = 2.00 x x Growing Perpetuity with First Dividend at t= Alternately, to value Div 1 & Div 2, you could simply do PV of two single sums: 2.16/ /

10 The value of a firm depends upon its growth rate, g, and its discount rate, R. Where does g come from? g = Retention ratio Return on retained earnings Example: Suppose a company has a retention ratio of 70% and earns an ROE of 12%. What is the Growth Rate, g? g = 0.70 X 0.12 g = = 8.4% 6-18 As we ll see in a much later chapter, the required return (R) should be a function of the risk the stock s expected cash flows In practice, there is a great deal of estimation error involved in selecting R If we have information about P 0, Div 1, and g for a stock, we can infer an expected return If P 0 is the right price for the stock, how should this expected return compare to the required return that was used in calculating price (P 0 ) in the first place? SAME

I prefer to say that we are inferring r, given other information that might be available for a particular stock Start with the DGM: Rearrange and solve

65 per share. Solar s dividends are growing at a rate of 4%/year and the current price per share is $11.25. What is the R implicit in Solar s price?

11 I prefer to say that we are inferring r, given other information that might be available for a particular stock Start with the DGM: Rearrange and solve for R: Note that D 1 /P 0 is called the dividend yield and g is called the capital gains yield Imagine that Solar Corp. s last dividend was $0.65 per share. Solar s dividends are growing at a rate of 4%/year and the current price per share is $ What is the R implicit in Solar s price? Remember, the equation uses Div 1, not Div 0, and this problem statement tells Div 0 R= Div 1 /P 0 +g = ( 0.65 x 1.04 ) / = 0.10 or 10%

12 Two conditions must exist if a company is to grow: (1) It must not pay out all of its earnings as dividends, and (2) It must invest in projects with a positive NPV (2) Stated differently, it must have expected return on reinvested (i.e., retained) earnings (which are the property of the shareholders that exceeds the shareholders required rate of return 6-22 Why don t firms with no dividends have stock price of $0? Such firms believe their earnings are better used to pursue growth opportunities Investors pay a stock price that conforms to their own calculus of the NPVGO of the no-payout firm The dividend growth model does not work in valuing this firm The differential growth model can, but evaluating the timing of changes in growth is tricky

13 With that said, be careful. What would you pay for a stock that was never going to pay a dividend literally never? The only right answer is $0. A fair price for a perpetual series of zeroes is zero! Imagine Durham Inc. stock being originally issued to Alberto. Alberto in turn looks to sell the stock in a couple of years to Brianne. Brianne thinks that she can sell the stock to Charles about 3 years later. But imagine that Charles will find himself as the last interested investor Many analysts frequently relate earnings per share to price. The price-earnings ratio is calculated as the current stock price divided by annual earnings per share (EPS). P-E Ratio = Price per share / Earnings per share To get EPS for a firm, The Wall Street Journal, for example, uses the firm s last four quarters earnings Obviously, Current Price is easily observable

14 Generally, firms with growth opportunities command greater P/E than those with no such prospects A firm s R also impacts the P/E ratio. The P/E ratio and R are inversely related. A firm with conservative accounting principles will generally have a higher P/E ratio than one with aggressive policies I will provide a separate handout that offers deeper insight into the ratio 6-26 Voting rights (Cumulative vs. Straight) Proxy voting Classes of stock Other rights Share proportionally in declared dividends Share proportionally in remaining assets during liquidation Preemptive right first shot at new stock issue to maintain proportional ownership if desired

15 Dividends Stated dividend must be paid before dividends can be paid to common stockholders. Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely. Most preferred dividends are cumulative any missed preferred dividends have to be paid before common dividends can be paid. Preferred stock generally does not carry voting rights Dealers vs. Brokers New York Stock Exchange (NYSE) Largest stock market in the world License Holders (formerly Members ) Entitled to buy or sell on the exchange floor Specialists / also called Market makers Floor brokers Floor traders Operations Floor activity

Not a physical exchange computer-based quotation system Multiple market makers Electronic communications networks Three levels of information Level 1 median quotes,

as $25.72 in the last year. Gap pays a dividend of 18 cents/share. Given the current price, the dividend yield is.8%. Gap ended trading at $21.

16 Not a physical exchange computer-based quotation system Multiple market makers Electronic communications networks Three levels of information Level 1 median quotes, registered representatives Level 2 view quotes, brokers & dealers Level 3 view and update quotes, dealers only Large portion of technology stocks 6-30 Gap has been as high as $25.72 in the last year. Gap pays a dividend of 18 cents/share. Given the current price, the dividend yield is.8%. Gap ended trading at $21.35, which is unchanged from yesterday. Gap has been as low as $18.12 in the last year. Given the current price, the PE ratio is 18 times earnings. 3,996,100 shares traded hands in the last day s trading

17 What determines the price of a share of stock? What determines g and R in the DGM? Discuss the importance of the PE ratio. What are some of the major characteristics of common and preferred stock? Discuss the nature of the various markets for stocks

Chapter 6. Stock Valuation

Chapter 6. Stock Valuation Chapter 6 Stock Valuation Comprehend that stock prices depend on future dividends and dividend growth Compute stock prices using the dividend growth model Understand how growth opportunities affect stock