Chapter 7 Finance!!!!
What if the company starts increasing dividends by 3% per year beginning with the next dividend? The required return remains at 15%.
constant growth 2(1.03)/(.15-.03)= 17.17
Efficient Market reaction
the price instantaneously adjusts to and fully reflects new information; there is no tendency for subsequent increases and decreases
Overreaction and correction
the price over adjusts to the new information; it overshoots the new price and subsequently corrects
Nonconstant dividend growth
Dividend growth is not consistent initially, but settles down to constant growth eventually
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? What is the dividend yield? What is the capital gains yield?
Required return: R= [1(1.05)/10.50] + .05= 15% Dividend Yield: 1(1.05)/10.50= 10% Capital gains yield: g=5%
Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?
P0=.50/(.1/4)=$20
Constant dividend growth
The firm will increase the dividend by a constant percent every period
Delayed Reaction
the price partially adjusts to the new information; eight days elapse before the price completely reflects the new information
If the firm's market value is $416.94 million and it has $40 million in debt and has 10 million shares of stock, what is the firm's intrinsic value per share?
MV of equity = MV of firm - MV of debt = $416.94 - $40 = $376.94 million Value per share = MV of equity / # of shares = $376.94 / 10 = $37.69
Antiques 'R' Us is a mature manufacturing firm. The company just paid a dividend of $10.80, but management expects to reduce the payout by 5.25 percent per year, indefinitely. If you require a return of 9 percent on this stock, what will you pay for a share today?
The constant growth model can be applied even if the dividends are declining by a constant percentage, just make sure to recognize the negative growth. So, the price of the stock today will be: P0 = D0(1 + g) / (R - g) P0 = $10.80(1 - .0525) / [(.09 - (-.0525)] P0 = $71.81
Zero Growth
The firm will pay a constant dividend forever This is like preferred stock The price is computed using the perpetuity formula
Suppose you know that a company's stock currently sells for $58 per share and the required return on the stock is 12 percent. You also know that the total return on the stock is evenly divided between capital gains yield and dividend yield. If it's the company's policy to always maintain a constant growth rate in its dividends, what is the current dividend per share?
We know the stock has a required return of 12 percent, and the dividend and capital gains yield are equal, so: Dividend yield = 1/2(.12) Dividend yield = .06 = Capital gains yield Now we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so: D1 = .06($58) D1 = $3.48 This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year: D1 = D0(1 + g) We can solve for the dividend that was just paid: $3.48 = D0(1 + .06) D0 = $3.48 / 1.06 D0 = $3.28
Analysts often use the following multiples to value stocks.
P / E P / CF P / Sales
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?
P0=.[50(1+.02)]/[.15-.02]=$3.92
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?
P0=2/(.2-.05)=$13.33
The next dividend payment by Wyatt, Inc., will be $2.30 per share. The dividends are anticipated to maintain a growth rate of 4.5 percent forever. If the stock currently sells for $39.85 per share, what is the required return?
R = (D1 / P0) + g R = ($2.30 / $39.85) + .045 R = .1027, or 10.27%
Nofal Corporation will pay a $3.65 per share dividend next year. The company pledges to increase its dividend by 5.1 percent per year, indefinitely. If you require a return of 12 percent on your investment, how much will you pay for the company's stock today?
Using the constant growth model, we find the price of the stock today is: P0 = D1 / (R - g) P0 = $3.65 / (.12 - .051) P0 = $52.90
Apocalyptica Corporation is expected to pay the following dividends over the next four years: $3, $10, $15, and $3.08. Afterwards, the company pledges to maintain a constant 5 percent growth rate in dividends, forever. Required: If the required return on the stock is 11 percent, what is the current share price?
With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth after the fourth dividend is paid, so we can find the price of the stock at Year 4, when the constant dividend growth begins, as: P4 = D4 (1 + g) / (R - g) P4 = $3.08(1.05) / (.11 - .05) P4 = $53.90 The price of the stock today is the present value of the first four dividends, plus the present value of the Year 4 stock price. So, the price of the stock today will be: P0 = ($3 / 1.11) + ($10 / 1.11)^2 + ($15 / 1.11)^3 + ($3.08 / 1.11)^4 + ($53.90 / 1.11)^4 P0 = $59.32
The price of stock is really just .....
the present value of ALL expected future dividends
What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%?
zero growth 2/.15=13.33
Dividend Characteristics
-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; therefore, they are not tax-deductible *Dividends received by individuals have historically been taxed as ordinary income *Dividends received by corporations have a minimum 70% exclusion from taxable income
Strong Form Efficiency
-Prices reflect all information, including public and private -If the market is strong form efficient, then investors could not earn abnormal returns regardless of the information they possessed -Empirical evidence indicates that markets are NOT strong form efficient and that insiders could earn abnormal returns
The next dividend payment by Wyatt, Inc., will be $2.30 per share. The dividends are anticipated to maintain a growth rate of 4.5 percent forever. Assume the stock currently sells for $39.85 per share. What is the dividend yield? What is the expected capital gains yield?
The dividend yield is the dividend next year divided by the current price, so the dividend yield is: Dividend yield = D1 / P0 Dividend yield = $2.30 / $39.85 Dividend yield = .0577, or 5.77% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so: Capital gains yield = 4.5%
The stock price of Webber Co. is $68. Investors require an 11 percent rate of return on similar stocks. If the company plans to pay a dividend of $3.85 next year, what growth rate is expected for the company's stock price?
We need to find the growth rate of dividends. Using the constant growth model, we can solve the equation for g. Doing so, we find: g = R - (D1 / P0) g = .11 - ($3.85 / $68) g = .0534, or 5.34%
Weak Form Efficiency
-Prices reflect all past market information such as price and volume -If the market is weak form efficient, then investors cannot earn abnormal returns by trading on market information -Implies that technical analysis will not lead to abnormal returns -Empirical evidence indicates that markets are generally weak form efficient
Rabie, Inc., has an issue of preferred stock outstanding that pays a $3.80 dividend every year, in perpetuity. If this issue currently sells for $78.45 per share, what is the required return?
The price a share of preferred stock is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero percent. Remember, most preferred stock pays a fixed dividend, so the growth rate is zero. This is a special case of the dividend growth model where the growth rate is zero, or the level perpetuity equation. Using this equation, we find the price per share of the preferred stock is: R = D/P0 R = $3.80/$78.45 R = .0484, or 4.84%
Hot Wings, Inc., has an odd dividend policy. The company has just paid a dividend of $4 per share and has announced that it will increase the dividend by $5 per share for each of the next four years, and then never pay another dividend. If you require a return of 12 percent on the company's stock, how much will you pay for a share today?
The price of a stock is the PV of the future dividends. This stock is paying four dividends, so the price of the stock is the PV of these dividends discounted at the required return. So, the price of the stock is: P0 = ($9 / 1.12) + ($14 / 1.12)^2 + ($19 / 1.12)^3 + ($24 / 1.12)^4 P0 = $47.97
Bui Corp. pays a constant $12 dividend on its stock. The company will maintain this dividend for the next nine years and will then cease paying dividends forever. If the required return on this stock is 10 percent, what is the current share price?
The price of any financial instrument is the present value of the future cash flows. The future dividends of this stock are an annuity for 9 years, so the price of the stock is the present value of an annuity, which will be: P0 = $12.00(PVIFA10%,9) P0 = $69.11
Features of Preferred Stock
-Dividends *Stated dividend that 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 does not generally carry voting rights
Semistrong Form Efficiency
-Prices reflect all publicly available information including trading information, annual reports, press releases, etc. -If the market is semistrong form efficient, then investors cannot earn abnormal returns by trading on public information -Implies that fundamental analysis will not lead to abnormal returns
Efficient Capital Markets
-Stock prices are in equilibrium or are "fairly" priced. In equilibrium, a stock's price should equal its "true" or intrinsic value. -Efficient markets do not mean that you can't make money -They do mean that, on average, you will earn a return that is appropriate for the risk undertaken and there is not a bias in prices that can be exploited to earn excess returns
Features of Common Stock
-Voting Rights: Common stock represents ownership. Ownership implies control. Stockholders elect directors and then directors elect management -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
Three basic models in valuing a firm's common stock
-dividend growth model* -corporate value model -using multiples of comparable firms
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 current price? What is price expected to be in 4 years? What is the implied return given the change in price during the four year period?
1. P0=4/(.16-.06)=$40 2. P4= 4(1.06)^4/(.16-.06)= $50.50 3. 50.50 = 40(1+r)^4; r = 6%
Constant Growth Model Conditions
1. Dividend expected to grow at g forever 2. Stock price expected to grow at g forever 3. Expected dividend yield is constant 4. Expected capital gains yield is constant and equal to g 5. Expected total return, R, must be > g 6. Expected total return (R): = expected dividend yield (DY) + expected growth rate (g) = dividend yield + g
