Managerial Finance
Stock Valuation: Key Concepts and Skills
- Understand how stock prices depend on future dividends and dividend growth
- Be able to compute stock prices using the dividend growth model
- Understand how corporate directors are elected
- Understand how stock markets work
- Understand how stock prices are quoted
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Outline
- Common Stock Valuation
- Some Features of Common and Preferred Stocks
- The Stock Markets
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Cash Flows for Stockholders
- If you buy a share of stock, you can receive cash in two ways
- The company pays dividends
- You sell your shares, either to another investor in the market or back to the company
- As with bonds, the price of the stock is the present value of these expected cash flows
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One-Period Example
- Suppose you are thinking of purchasing the stock of Moore Oil, Inc. 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
- Price = (14 + 2) / (1.2) = $13.33
- Or FV = 16; I/Y = 20; N = 1; CPT PV = -13.33
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Two-Period Example
- Now, what if you decide to hold the stock for two years? In addition to the 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?
- PV = 2 / (1.2) + (2.10 + 14.70) / (1.2)2 = 13.33
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Three-Period Example
- Finally, what if you decide to hold the stock for three years? 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 the stock price is expected to be $15.435. Now how much would you be willing to pay?
- PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 = 13.33
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Developing The Model
- You could continue to push back the year in which you will sell the stock
- You would find that the price of the stock is really just the present value of all expected future dividends
- So, how can we estimate all future dividend payments?
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Estimating Dividends:
Special Cases
- Constant dividend
- The firm will pay a constant dividend forever
- This is like preferred stock
- The price is computed using the perpetuity formula
- Constant dividend growth
- The firm will increase the dividend by a constant percent every period
- The price is computed using the growing perpetuity model
- Supernormal growth
- Dividend growth is not consistent initially, but settles down to constant growth eventually
- The price is computed using a multistage model
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Zero Growth
- If dividends are expected at regular intervals forever, then this is a perpetuity and the present value of expected future dividends can be found using the perpetuity formula
- P0 = D / R
- 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
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Dividend Growth Model
- Dividends are expected to grow at a constant percent per period.
- P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + …
- P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + …
- With a little algebra and some series work, this reduces to:
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DGM – Example 1
- Suppose Big D, Inc., just paid a dividend of $0.50 per share. 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
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DGM – 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?
- P0 = 2 / (.2 – .05) = $13.33
- Why isn’t the $2 in the numerator multiplied by (1.05) in this example?
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Stock Price Sensitivity to Dividend Growth, g
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Stock Price Sensitivity to Required Return, R
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Example 8.3 Gordon Growth
Company – I
- 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?
- P0 = 4 / (.16 – .06) = $40
- Remember that we already have the dividend expected next year, so we don’t multiply the dividend by 1+g
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Example 8.3 – Gordon Growth
Company – II
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- What is the price expected to be in year 4?
- P4 = D4(1 + g) / (R – g) = D5 / (R – g)
- P4 = 4(1+.06)4 / (.16 – .06) = 50.50
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- What is the implied return given the change in price during the four year period?
- 50.50 = 40(1+return)4; return = 6%
- PV = -40; FV = 50.50; N = 4; CPT I/Y = 6%
- The price is assumed to grow at the same rate as the dividends
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Nonconstant Growth
Problem Statement
- Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that, dividends will increase at a rate of 5% per year indefinitely. If the last dividend 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.
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Nonconstant Growth
Example Solution
- Compute the dividends until growth levels off
- D1 = 1(1.2) = $1.20
- D2 = 1.20(1.15) = $1.38
- D3 = 1.38(1.05) = $1.449
- Find the expected future price
- P2 = D3 / (R – g) = 1.449 / (.2 – .05) = 9.66
- Find the present value of the expected future cash flows
- P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67
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Using the DGM to Find R
- Start with the DGM:
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Finding the Required Return – Example
- Suppose a firm’s stock is selling for $10.50. It just paid a $1 dividend, and dividends are expected to grow at 5% per year. What is the required return?
- R = [1(1.05)/10.50] + .05 = 15%
- What is the dividend yield?
- 1(1.05) / 10.50 = 10%
- What is the capital gains yield?
- g =5%
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Table 8.1 – Stock Valuation Summary
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Features of Common Stock
- Voting Rights
- 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
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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
- The taxation of dividends received by individuals depends on the holding period
- Dividends received by corporations have a minimum 70% exclusion from taxable income
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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 generally does not carry voting rights
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Stock Market
- Dealers vs. Brokers
- New York Stock Exchange (NYSE)
- Largest stock market in the world
- License holders (1,366)
- Commission brokers
- Specialists
- Floor brokers
- Floor traders
- Operations
- Floor activity
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NASDAQ
- 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
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Work the Web Example
- Electronic Communications Networks provide trading in NASDAQ securities
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- Sample Quote
What information is provided in the stock quote?
Click on the web surfer to go to Bloomberg for current stock quotes.
Reading Stock Quotes
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