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Chapter 6 Valuing Stocks
Primary Market Place where the sale of new stock first occurs. Initial Public Offering (IPO) First offering of stock to the general public. Seasoned Issue Sale of new shares by a firm that has already been through an IPO Google Secondary Offering Raises $4B+ It's not clear how the company plans to use the cash; one speculation is that Google might build a wireless network to extend the reach of its search engine
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Stocks & Stock Market
Stocks & Stock Market
Common Stock Ownership shares in a publicly held corporation. Secondary Market market in which already issued securities are traded by investors. Dividend Periodic cash distribution from the firm to the shareholders. P/E Ratio Price per share divided by earnings per share.
Stocks & Stock Market
Book Value Net worth of the firm according to the balance sheet. Liquidation Value Net proceeds that would be realized by selling the firm's assets and paying off its creditors. Market Value Balance Sheet Financial statement that uses market value of assets and liabilities.
Valuing Common Stocks
Expected Return The percentage yield that an investor forecasts from a specific investment over a set period of time. Sometimes called the holding period return (HPR).
Div1 + P - P0 1 Expected Return = r = P0
Valuing Common Stocks
The formula can be broken into two parts. Dividend Yield + Capital Appreciation
Expected Return = r = Div1/P0 + (P1P0)/P0
Valuing Common Stocks
Dividend Discount Model Computation of today's stock price which states that share value equals the present value of all expected future dividends.
P0 = Div1/(1+r)1 + Div2/(1+r)2 + ... + (DivH +PH)/(1+r)H
H Time horizon for your investment.
Valuing Common Stocks
Example Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?
Example Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?
3.00 3.24 350 + 94.48 . PV = + + 1 2 3 (1+.12) (1+.12) (1+.12) PV = $75.00
Valuing Common Stocks
If we forecast no growth, and plan to hold our stock indefinitely, we will then value the stock as a PERPETUITY
P = Div1/r or EPS1/r
Valuing Common Stocks
Constant Growth DDM A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model).
Div1 P0 = r-g
Given any combination of variables in the equation, you can solve for the unknown variable. Make sure you use Div1 and not Div0 this is a trick!
Valuing Common Stocks
Example What is the value of a stock that expects to pay a $3.00 dividend next year, and then increase the dividend at a rate of 8% per year, indefinitely? Assume a 12% expected return.
Div1 $3.00 P0 = = = $75.00 r - g .12 -.08
Example continued If the same stock is selling for $100 in the stock market, what might the market be assuming about the growth in dividends?
Valuing Common Stocks
$3.00 $100 = .12 - g g =.09
Answer The market is assuming the dividend will grow at 9% per year, indefinitely.
Valuing Common Stocks
If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher.
Payout Ratio Fraction of earnings paid out as dividends Plowback Ratio Fraction of earnings retained by the firm.
Growth in the Value of Common Stocks
Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations. Assuming that ROE stays constant
g = return on equity X plowback ratio
Valuing Common Stocks
Example Our company forecasts paying a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm's current return on equity of 20%. What is the value of the stock before and after the plowback decision?
Example Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm's current return on equity of 20%. What is the value of the stock before and after the plowback decision?
No Growth ($5 dividend)
With Growth ($3 dividend)
5 P0 = = $41.67 .12
g =.20.40 =.08 3 P0 = = $75.00 .12 -.08
Present Value of Growth Opportunities
Example continued If the company did not plow back some earnings, the stock price would remain at $41.67. With the plowback, the price rose to $75.00.
The difference between these two numbers (75.0041.67=33.33) is called the Present Value of Growth
Valuing Common Stocks
Present Value of Growth Opportunities (PVGO) = Net present value of a firm's future investments. Sustainable Growth Rate Steady rate at which a firm can grow: plowback ratio x return on equity.
PROBLEMS
Chapter 6: Question 2
Favored stock will pay a dividend this year of $2.40 per share. Its dividend yield is 8 percent. At what price is the stock selling?
Favored stock will pay a dividend this year of $2.40 per share. Its dividend yield is 8 percent. At what price is the stock selling?
Dividend yield = Dividend/Price =DIV1/P0 0.08 = 2.40/P0 P0 = $30
Chapter 6: Question 4
Waterworks has a dividend yield of 8 percent. If its dividend is expected to grow at a constant rate of 5 percent, what must the expected rate of return be on the company's stock?
Waterworks has a dividend yield of 8 percent. If its dividend is expected to grow at a constant rate of 5 percent, what must the expected rate of return be on the company's stock?
r = DIV1/P0 + g =
8% + 5% =
13%
Chapter 6: Question 7
BMM Industries pays a dividend of $2 per quarter. The dividend yield on its stock is reported at 4.8 percent. At what price is the stock selling?
BMM Industries pays a dividend of $2 per quarter. The dividend yield on its stock is reported at 4.8 percent. At what price is the stock selling? The annual dividend is: $2 4 = $8 DIV1/P0 = 0.048 $8/P0 = 0.048 P0 = $8/0.048 = $166.67
Chapter 6: Question 12
A stock sells for $40. The next dividend will be $4 per share. If the rate of return earned on reinvested funds is 15 percent and the company reinvests 40 percent of earnings in the firm, what must be the discount rate?
40 =
A stock sells for $40. The next dividend will be $4 per share. If the rate of return earned on reinvested funds is 15 percent and the company reinvests 40 percent of earnings in the firm, what must be the discount rate?
4 4 r= + 0.06 = 0.16 = 16.0% r - 0.06 40
P = Div1/(rg) First, solve for g g = return on equity plowback ratio = 0.15 0.40 = g =0.06 = 6.0%
P = Div1/(rg) 40 = 4/(r.06) 40 (r.06) = 4 40r.06(40)=4 40r2.40 = 4 40r = 6.40 r = .16 = 16%
A stock sells for $40. The next dividend will be $4 per share. If the rate of return earned on reinvested funds is 15 percent and the company reinvests 40 percent of earnings in the firm, what must be the discount rate?
Chapter 6: Question 16
You believe that the Nonstick Gum Factory will pay a dividend of $2 on its common stock next year. Thereafter, you expect the dividends to grow at a rate of 6 percent a year in perpetuity. If you require a return of 12 percent on your investment, how much should you be prepared to pay for the stock?
You believe that the Nonstick Gum Factory will pay a dividend of $2 on its common stock next year. Thereafter, you expect the dividends to grow at a rate of 6 percent a year in perpetuity. If you require a return of 12 percent on your investment, how much should you be prepared to pay for the stock?
P0 = DIV1/(r - g) = $2/(0.12 0.06) = $33.33
Chapter 6 Question 26
Castles in the Sand generates a rate of return of 20 percent on its investments and maintains a plowback ratio of .30. Its earnings this year will be $4 per share. Investors expect a 12% rate of return on the stock. a. Find the price and P/E ratio of the firm. P0 = DIV1/rg g = 20% 0.30 = 6% P0 = $4(1 0.30)/(0.12 - 0.06) = $46.67 P/E = $46.67/$4 = 11.667
26. Castles in the Sand generates a rate of return of 20 percent on its investments and maintains a plowback ratio of .30. Its earnings this year will be $4 per share. Investors expect a 12% rate of return on the stock.
b. What happens to the P/E ratio if the plowback ratio is reduced to .20? Why? If the plowback ratio is reduced to 0.20 g = 20% 0.20 = 4% P0 = $4(1 0.20)/(0.12 0.04) = $40 P/E = $40/$4 = 10 P/E falls because the firm's value of growth opportunities is now lower: It takes less advantage of its attractive investment opportunities
26. Castles in the Sand generates a rate of return of 20 percent on its investments and maintains a plowback ratio of .30. Its earnings this year will be $4 per share. Investors expect a 12% rate of return on the stock.
c. Show that if plowback equals zero, the earningsprice ratio, E/P, falls to the expected rate of return on the stock. If the plowback ratio = 0 g = 0 and DIV1 = $4 P0 = $4/0.12 = $33.33 and E/P = $4/$33.33 = 0.12 = 12.0%
Chapter 6: Question 27
Grandiose Growth has a dividend growth rate of 20 percent. The discount rate is 10 percent. The endofyear dividend will be $2 per share.
What is the present value of the dividend to be paid in Year 1? Year 2? Year 3? Could anyone rationally expect this growth rate to continue indefinitely?
Grandiose Growth has a dividend growth rate of 20 percent. The discount rate is 10 percent. The end ofyear dividend will be $2 per share. What is the present value of the dividend to be paid in Year 1? Year 2? Year 3?
Yr 1 DIV1 = $2.00 PV =$2/1.10 = $1.818 Yr 2 DIV2= $2(1.20)= $2.40 PV = $2.40/1.102 = $1.983 Yr 3 DIV3= $2(1.20)2= $2.88 PV = $2.88/1.103
Grandiose Growth has a dividend growth rate of 20 percent. The discount rate is 10 percent. The endof year dividend will be $2 per share. Could anyone rationally expect this growth rate to continue indefinitely?
Year 1 $1.818 Year 2 $1.983 Year 3 $2.164.......... This could not continue indefinitely. If it did, the stock would be worth an infinite amount (which is a lot of money, more even than Bill Gates has).
Chapter 6 Valuing Stocks
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