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Chapter Eight Stock Valuation © 2003 The McGraw-Hill Companies, Inc. All rights reserved. 8.1 Chapter Outline Common Stock Valuation Common Stock Features Preferred Stock Features Stock Market Reporting 8.2 Cash Flows for Shareholders 8.1 If you buy a share of stock, you can receive cash in two ways Dividends Selling your shares As with any asset, the market price of common stock is equal to the present value of the expected future cash flows the stock will generate 8.3 One Period Example Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay? Compute the PV of the expected cash flows Div 1 Sale Price 1 r 2 14 1.20 $13.33 PVStock Calculator Approach 16 FV 0 PMT 1 N 20 I PV $13.33 8.4 Two Period Example Now what if you decide to hold the stock for two years? In addition to the $2 dividend in one year, you expect a dividend of $2.10 in two years and a stock price of $14.70 at the end of year 2. Now how much would you be willing to pay now? PVStock Div 1 Div 2 Sale Price 1 r 1 r 2 2 2.10 14.70 1.20 1.20 2 $13.33 Calculator Approach 0 CFj 2 CFj 16.80 CFj 20 I 2nd NPV $13.33 8.5 Three Period Example Finally, what if you decide to hold the stock for three periods? In addition to the dividends at the end of years 1 and 2, you expect to receive a dividend of $2.205 at the end of year 3 and a stock price of $15.435. Now how much would you be willing to pay? PVStock Div 3 Sale Pr ice Div 1 Div 2 1 r 1 r 2 1 r 3 2 2.10 2.205 15.435 1.20 1.20 2 1.203 $13.33 Calculator Approach 0 CFj 2 CFj 2.10 CFj 17.64 CFj 20 I 2nd NPV $13.33 8.6 Developing The Model We could continue this process for many time periods In fact, the price of the stock is just the present value of all expected future dividends So, how can we estimate all future dividend payments? 8.7 Estimating Dividends: Special Cases Constant dividend The firm will pay a constant dividend forever Market instrument – preferred stock Price is computed using the level perpetuity formula [PV = C/r] Constant dividend growth The firm will increase the dividend by a constant percent every period Market instrument – common stock Price is computed using a growing perpetuity formula [PV = C/(r-g)] Supernormal growth Dividend growth is high initially, but later settles down to a long-run constant growth rate 8.8 Zero Growth Rate The dividends on most preferred stocks are expressed as a constant percentage of the share’s face value Suppose a preferred share is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price? Div 1 r 0.50 0.10 4 $20.00 PVPreferred Stock 8.9 Constant Growth Rate To value a common stock, we usually assume the dividend stream will grow at some constant growth rate over time P0 Div 3 Div 1 Div 2 Div . . . 1 r 1 r 2 1 r 3 1 r Div 0 1 g Div 0 1 g Div 0 1 g Div 0 1 g . . . 1 r 1 r 2 1 r 3 1 r 2 With a little algebra, this reduces to: Div 0 (1 g) Div 1 P0 r -g r -g 3 8.10 Constant Growth: Example 1 Suppose Big D, Inc. just paid a dividend of $.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, how much should the stock be selling for? Div 0 (1 g) r -g 0.50(1.02) 0.15 - 0.02 $3.92 P0 8.11 Constant Growth: Example 2 Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price? Div 1 r -g 2.00 0.20 - 0.05 $13.33 P0 Stock Price Sensitivity to Dividend Growth, g 250 Div1 = $2; r = 20% 200 Stock Price 8.12 150 100 50 0 0 0.05 0.1 Growth Rate 0.15 0.2 Stock Price Sensitivity to Required Return, r 250 Div1 = $2; g = 5% 200 Stock Price 8.13 150 100 50 0 0 0.05 0.1 0.15 Required Return 0.2 0.25 0.3 8.14 Gordon Growth Company – Example 1 Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%. What is the current price? Div 1 r -g 4.00 0.16 - 0.06 $40.00 P0 8.15 Gordon Growth Company – Example 2 What is the price expected to be in year 4? P4 Div 5 r -g Div 1 1 g r -g 4 4.001.06 0.16 - 0.06 $50.50 4 8.16 Gordon Growth Company - Continued What is the holding period return (capital gains yield) due to the capital gain over the four year period? HPR P1 P0 P0 50.50 40.00 40.00 26.25% 8.17 Non-constant Dividend Growth Suppose a firm is expected to increase dividends by 20% in one year and by 15% in year 2. After that, dividends will increase at a rate of 5% per year indefinitely. If the last dividend that was just paid was $1 and the required return is 20%, what is the price of the stock? Remember that we have to find the PV of all expected future dividends. 0 $1.00 20% 1 15% 2 5% 3 5% 4 5% ∞ 8.18 Non-constant Dividend Growth - Continued Compute the dividends until growth levels off 0 $1.00 20% 1 $1.20 15% 2 5% $1.38 3 5% $1.45 Find the present value of the expected future cash flows P0 Div 1 Div 2 Div 3 1 2 2 1 r 1 r r g 1 r 1.20 1.38 1.45 1 1.20 1.20 2 0.20 0.05 1.20 2 $8.67 4 5% ∞ 8.19 Calculating the Required Rate of Return Start with the constant dividend growth formula: Div 0(1 g) r-g Div 1 r-g rearrange and solve for r Div 0(1 g) r g P0 P0 Div 1 g P0 The required rate of return on a common stock can always be decomposed into: Dividend yield Capital gain or loss 8.20 Example – Finding the Required Return Suppose a firm’s stock is selling for $10.50. They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return? r Div 0(1 g) g P0 1.00(1.05) 0.05 10.50 15% What is the dividend yield? Dividend Yield Div 0(1 g) P0 1.00(1.05) 10.50 10% What is the capital gains yield? Capital Gain g 0.05 5% 8.21 Table 8.1 - Summary of Stock Valuation 8.22 Common Stock – Features Voting Rights 1- Cumulative voting- total number of votes each shareholder may cast = (# of shares owned) x (# of directors to be elected) All directors are elected at the same time. Cumulative voting favors minority stockholders. 2- Straight voting- directors are elected one at a time (i.e., each directors is voted on one at a time). Straight voting favors majority shareholders. Staggered elections- only a portion of the board is elected in any one year. This makes it difficult for minority shareholder to elect a specific director. 8.23 Example- Voting Rights A company has two shareholders: “A” (owns 50 shares); “B” (owns 249 shares). There are 5 directors to be elected and 7 candidates running (T, U, V, W, X, Y, Z). “A” wants candidate Z to be on the board. B wants candidates T, U, V, W, and Y. Using Straight voting- “A” has 50 votes and “B” has 249 votes. Since each director is voted on one at a time “B” will be able to vote in all his candidates and “A” will not be able to vote in his candidate. Using Cumulative voting“A” has 50 x 5 = 250 votes (all for Z) “B” has 249 x 5 = 1,245 votes (÷ 5 = 249 for T, U, V, W, and Y) Therefore, Z wins the most votes. “B” cannot arrange votes to block Z. 8.24 Common Stock – Features (cont.) Other Rights Share proportionally in declared dividends Share proportionally in remaining assets during liquidation Right to vote on major issues – e.g. mergers Preemptive right – the right to purchase new stock to maintain proportional ownership, if desired (i.e., the right to buy new shares proportionately) Example If an investor has 1% of ownership and 1 million new shares are issued. The investor will have first rights to buy 10,000 of the new shares. 8.25 Common Stock – Features (cont.) Classes of stock- one has voting power, one has high dividends Dual class shares Voting & not-voting (restricted) Allows founders to retain control while raising new equity e.g. Class A: 1 vote per share, 100% of dividends Class B: 10 votes per share, zero dividends (usually not publicly traded) Coattail provision Protects non-voting shareholders in the event of a take-over bid (it allows the non-voting shareholders either the right to vote or to convert their shares into voting shares that can be tendered to the takeover bid) 8.26 Dividends Dividend size is determined by the board of directors Dividends are not a liability of the firm until a dividend has been declared by the board Consequently, a firm cannot go bankrupt for not declaring dividends Dividends and Taxes Dividend payments are not considered a business expense and are not tax deductible Dividends received by individual shareholders are partially sheltered by the dividend tax credit (13⅓ %) Dividends received by corporate shareholders are not taxed, thus preventing the double taxation of dividends 8.27 Preferred Stock Valuation Preferred stock is a hybrid security with features of bonds and common stock. Its bond features is that preferred stockholders have preference over common stockholders and have no voting rights. Its common stock features is that dividends on preferred stock do not have to be paid (i.e., dividends go into arrears and don’t have to be paid on time). 8.28 Preferred Stock - Characteristics Preferred stock has priority over common stock upon liquidation Dividends Most preferred stock has a stated dividend that must be paid before common dividends can be paid Dividends are not a liability of the firm and preferred dividends can be deferred indefinitely Most preferred dividends are cumulative – any missed dividends on preferred stock have to be paid before a dividend can be paid on common stock Preferred stock generally does not carry voting rights 8.29 Preferred Stock & Taxes Companies with a low tax rate cannot make use of the tax shield available from interest Therefore, they have an incentive to issue preferred shares, which typically pay a dividend lower than a comparable interest rate. The dividend is non-taxable in the hands of the recipient corporation. The loophole was partially closed in 1987 by forcing issuers of preferreds to pay a tax of 40% of the preferred dividend. However, it may still be cheaper to use preferreds than debt for the firm with a zero marginal tax rate 8.30 Stock Market Reporting 8.4 Stock market quotations are published in the newspapers and are also available on-line (usually with 15-minute delays) In Canada, large cap stocks trade on the TSX Quotes and corporate information on stocks that trade on the TSX can be found at the exchange’s website 8.31 Figure 8.1 – Sample Stock Market Quotation