Stock Valuation


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  • Refer to hand-written examples.
  • Refer to handout – Nortel Networks
  • Stock Valuation

    1. 1. Stock Valuation Stock Features and Valuation Components of Required Return
    2. 2. Common Stock Valuation <ul><li>Unlike bonds, valuing common stock is more difficult. Why? </li></ul><ul><li>The timing and amount of future cash flows is not known. </li></ul><ul><li>The life of the investment is essentially forever. </li></ul><ul><li>There is no way to observe the rate of return that the market requires. </li></ul>
    3. 3. Common Stock Valuation <ul><li>One method to determine the price of a share of stock is to calculate present value of all future dividends. </li></ul><ul><li>P 0 = Σ [D t /(1 + r) t ] where t = 1 to ∞ </li></ul><ul><li>How many future dividends are there? In principle, there can be an infinite number. </li></ul>
    4. 4. Common Stock Valuation <ul><li>To help us value a share of stock, we need to make some simplifying assumptions about the pattern of future dividends. </li></ul><ul><li>The three cases we consider are: </li></ul><ul><ul><li>The dividend has a zero growth rate. </li></ul></ul><ul><ul><li>The dividend grows at a constant rate. </li></ul></ul><ul><ul><li>The dividend grows at a constant rate after some length of time. </li></ul></ul>
    5. 5. 1. Zero Growth Stocks <ul><li>A share of common stock in a company with a constant dividend is much like a share of preferred stock – D 1 = D 2 = D 3 = … = D </li></ul><ul><li>Since the dividend is always the same, the stock can be viewed as an ordinary perpetuity with a cash flow equal to D every period. </li></ul><ul><li>Thus, P 0 = D/r </li></ul>
    6. 6. 2. Constant Growth <ul><li>Suppose we knew that the dividend for some company always grows at a steady rate (g). </li></ul><ul><li>As long as the growth rate is less than the discount rate (r), the present value of the series of cash flows can be written simply using the growing perpetuity formula: </li></ul><ul><li>P 0 = D 0 x (1 + g) = D 1 r – g r – g where D 0 = the most recent dividend paid D 1 = the next dividend to be paid </li></ul>
    7. 7. 2. Constant Growth <ul><li>We can actually use the dividend growth model to get the stock price at any point in time, not just today. In general, the price of the stock as of time t is: </li></ul><ul><li>P t = D t x (1 + g) = D t+1 r – g r – g </li></ul><ul><li>Note: The model only works when the discount rate is greater than the growth rate. </li></ul>
    8. 8. 2. Constant Growth <ul><li>Example: </li></ul><ul><li>ABC Corporation just paid a $2.50 per share dividend to its common shareholders. An investment in ABC is considered relatively risking and requires a discount rate of 20% per annum. It is forecasted that dividends in ABC are going grow at a rate of 6% per annum indefinitely into the future. How much will an ABC share be worth today? In 10 years? </li></ul>
    9. 9. 2. Constant Growth <ul><li>Step 1: Solve for D 0 and D 10 </li></ul><ul><li>D 0 = $2.50 D 10 = 2.50 x (1 + .06) 10 = $4.48 </li></ul><ul><li>Step 2: Solve for P 0 and P 10 </li></ul><ul><li>P 0 = (2.50 x 1.06)/(.20 - .06) = $18.93 P 10 = (4.48 x 1.06)/(.20 - .06) = $33.92 </li></ul>
    10. 10. 3. Non-Constant Growth <ul><li>At times, a new company may pay no dividends early in its life but start paying dividends that grow at a constant rate some time in the future. </li></ul><ul><li>At other times, a new company may pay small dividends initially and, at some point in the future, start paying dividends that grow at a constant rate. </li></ul><ul><li>However, as always, the value of the stock is the present value of all future dividends. </li></ul><ul><li>Many cash flow scenarios are possible in this situation. </li></ul>
    11. 11. 3. Non-Constant Growth <ul><li>Example: </li></ul><ul><li>ABC Company does not plan to pay a dividend until year 5. ABC’s expects the dividend in year five to be $1 and dividends in future years to grow at a constant rate of 5%. If the firm’s risk-adjusted required rate of return is 13%, what is the value of a share of stock in the company today? </li></ul><ul><ul><li>P 4 = 1/(.13 – .05) = $12.50 </li></ul></ul><ul><ul><li>P 0 = 12.50(1.13) -4 = $7.67 </li></ul></ul>
    12. 12. Common Stock Valuation <ul><li>When investment analysts use the dividend valuation model, they generally consider a range of growth scenarios. </li></ul><ul><li>The resulting range of stock prices will be used in establishing a “fair” price for a share of stock. </li></ul><ul><li>However, while the dividend growth model is a useful analytical tool, the model is not the last word on stock valuation; other techniques for valuing a share of stock in a company are available. </li></ul>
    13. 13. Components of Required Return <ul><li>Thus far, the discount rate or required rate of return has been given to us. </li></ul><ul><li>Later chapters have more to say about this, but for now, using the dividend growth model, lets analysis the required rate of return: </li></ul><ul><li>Rearranging: r = D 1 /P 0 + g where D 1 /P 0 = the dividend yield g = the capital gains yield </li></ul>
    14. 14. Components of Required Return <ul><li>Going back to our constant growth example where: </li></ul><ul><li>D 1 = 2.50 x 1.06 = $2.65 P 0 = $18.93 g = 6% </li></ul><ul><li>we can solve for r, </li></ul><ul><li>r = D 1 /P 0 + g = 2.65/18.93 + .06 = .14 + .06 = .20 or 20%  the discount rate used in the problem. </li></ul>
    15. 15. Components of Required Return <ul><li>Also notice that given: </li></ul><ul><li>P 0 = $18.93 P 10 = $33.92 </li></ul><ul><li>we can solve for g, </li></ul><ul><li>33.92 = 18.93(1 + g) 10 g = .060 or 6%  the capital gains yield </li></ul>
    16. 16. Common Stock Features <ul><li>The term common stock usually implies the shareholder has no special preference either in dividends or in bankruptcy. </li></ul><ul><li>Shareholders, however, control the corporation through their right to elect the directors. The directors in turn hire management to carry out their directives. </li></ul><ul><li>Directors are elected at an annual shareholders’ meeting by a vote of the holding of a majority of shares present and entitled to vote. </li></ul>
    17. 17. Common Stock Features <ul><li>Shareholders usually have the following rights also: </li></ul><ul><ul><li>The right to share proportionally in dividends paid. </li></ul></ul><ul><ul><li>The right to share proportionally in assets remaining after liabilities and preferred shareholders have been paid in a liquidation. </li></ul></ul><ul><ul><li>The right to vote on stockholder matters of great importance, such as a merger or new share issuance. </li></ul></ul>
    18. 18. Common Stock Features <ul><li>Dividends </li></ul><ul><li>Dividend payments are at the discretion of the B of D. </li></ul><ul><li>Dividends are not a liability of the corporation until declared by the B of D. </li></ul><ul><li>Dividends are not tax deductible for the issuing corporation. </li></ul><ul><li>Dividends received by shareholders are partially tax-sheltered by a dividend tax credit. </li></ul>
    19. 19. Common Stock Features <ul><li>Classes of Stock </li></ul><ul><li>Some firms have more than one class of common stock; often, the classes are created with unequal voting rights. </li></ul><ul><li>Canadian Tire Corporation is an example of a company with non-voting common stock trading in the market. </li></ul><ul><li>Non-voting shares must receive dividends no lower than dividends on voting shares. </li></ul><ul><li>A primary reason for creating dual classes of stock has to do with control of the firm. </li></ul>
    20. 20. Preferred Stock Features <ul><li>Preferred stock differs from common stock because it has preference over common stock on payment of dividends and in the distribution of corporation assets in the event of liquidation. </li></ul><ul><li>Preferred stock is a form of equity from a legal, tax, and regulatory standpoint. </li></ul><ul><li>Holders of preferred stock generally have no voting privileges. </li></ul><ul><li>However, holders of preferred stock are often granted voting and other rights if preferred dividends have not been paid for some time. </li></ul>
    21. 21. Preferred Stock Features <ul><li>Preferred stock have a stated liquidating value. </li></ul><ul><li>The cash dividend is described in dollars per share. </li></ul><ul><li>A preferred dividend is not like bond interest – unless the B of D declares a dividend, no liability arises. </li></ul><ul><li>Dividends on preferred stock are either cumulative or non-cumulative. </li></ul><ul><li>Dividends not declared on cumulative preferred stock are carried forward and must be paid before common shareholders can receive anything. </li></ul>
    22. 22. Stock Market Reporting <ul><li>If you look through the pages of the National Post or another financial newspaper, you can find information on a large number of of stocks in several different markets. </li></ul><ul><li>As a outsider to the market, we need to generally assume that the listed market value of a share of stock is right. </li></ul><ul><ul><li>The benchmark for comparison in most valuations remains the market price. </li></ul></ul><ul><ul><li>If your numbers do not match with the market, take a second look at your numbers. </li></ul></ul>
    23. 23. The Price Earnings Ratio <ul><li>Even though our stock valuation formulas focused on dividends, not earnings, financial analysts often rely on price earnings ratios (P/E). </li></ul><ul><li>Why do some firms paying identical dividends have different P/E ratios? </li></ul><ul><li>Growth opportunities – the firm with more growth opportunities should sell at a higher price because investors are buying both current income and growth opportunities. </li></ul>
    24. 24. The Price Earning Ratio <ul><li>P/E ratios and the Boston Consulting Group Model: </li></ul>Dog Low MS – Low GM Very low or no P/E ratio Failure companies No Current Earnings + No Growth Opportunities Cash Cow High MS – Low GM Stable (lower) P/E ratio Mature companies Current Earnings Problem Child Low MS – High GM Volatile P/E ratio New companies Growth Opportunities Star High MS – High GM High P/E ratio Growth companies Current Earnings + Growth Opportunities