The document discusses various methods for valuing common stock, including calculating the present value of future dividends using the dividend discount model. It outlines three cases for the pattern of future dividends: zero growth, constant growth, and non-constant growth. Key valuation formulas and an example are provided. Additional stock features and components of the required return such as the dividend yield and capital gains yield are also examined.

1. Stock Valuation Stock Features and Valuation Components of Required Return

2. Common Stock Valuation Unlike bonds, valuing common stock is more difficult. Why? The timing and amount of future cash flows is not known. The life of the investment is essentially forever. There is no way to observe the rate of return that the market requires.

3. Common Stock Valuation One method to determine the price of a share of stock is to calculate present value of all future dividends. P 0 = Σ [D t /(1 + r) t ] where t = 1 to ∞ How many future dividends are there? In principle, there can be an infinite number.

4. Common Stock Valuation To help us value a share of stock, we need to make some simplifying assumptions about the pattern of future dividends. The three cases we consider are: The dividend has a zero growth rate. The dividend grows at a constant rate. The dividend grows at a constant rate after some length of time.

5. 1. Zero Growth Stocks 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 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. Thus, P 0 = D/r

6. 2. Constant Growth Suppose we knew that the dividend for some company always grows at a steady rate (g). 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: 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

7. 2. Constant Growth 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: P t = D t x (1 + g) = D t+1 r – g r – g Note: The model only works when the discount rate is greater than the growth rate.

8. 2. Constant Growth Example: 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?

9. 2. Constant Growth Step 1: Solve for D 0 and D 10 D 0 = $2.50 D 10 = 2.50 x (1 + .06) 10 = $4.48 Step 2: Solve for P 0 and P 10 P 0 = (2.50 x 1.06)/(.20 - .06) = $18.93 P 10 = (4.48 x 1.06)/(.20 - .06) = $33.92

10. 3. Non-Constant Growth 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. 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. However, as always, the value of the stock is the present value of all future dividends. Many cash flow scenarios are possible in this situation.

11. 3. Non-Constant Growth Example: 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? P 4 = 1/(.13 – .05) = $12.50 P 0 = 12.50(1.13) -4 = $7.67

12. Common Stock Valuation When investment analysts use the dividend valuation model, they generally consider a range of growth scenarios. The resulting range of stock prices will be used in establishing a “fair” price for a share of stock. 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.

13. Components of Required Return Thus far, the discount rate or required rate of return has been given to us. Later chapters have more to say about this, but for now, using the dividend growth model, lets analysis the required rate of return: Rearranging: r = D 1 /P 0 + g where D 1 /P 0 = the dividend yield g = the capital gains yield

14. Components of Required Return Going back to our constant growth example where: D 1 = 2.50 x 1.06 = $2.65 P 0 = $18.93 g = 6% we can solve for r, r = D 1 /P 0 + g = 2.65/18.93 + .06 = .14 + .06 = .20 or 20%  the discount rate used in the problem.

15. Components of Required Return Also notice that given: P 0 = $18.93 P 10 = $33.92 we can solve for g, 33.92 = 18.93(1 + g) 10 g = .060 or 6%  the capital gains yield

16. Common Stock Features The term common stock usually implies the shareholder has no special preference either in dividends or in bankruptcy. Shareholders, however, control the corporation through their right to elect the directors. The directors in turn hire management to carry out their directives. Directors are elected at an annual shareholders’ meeting by a vote of the holding of a majority of shares present and entitled to vote.

17. Common Stock Features Shareholders usually have the following rights also: The right to share proportionally in dividends paid. The right to share proportionally in assets remaining after liabilities and preferred shareholders have been paid in a liquidation. The right to vote on stockholder matters of great importance, such as a merger or new share issuance.

18. Common Stock Features Dividends Dividend payments are at the discretion of the B of D. Dividends are not a liability of the corporation until declared by the B of D. Dividends are not tax deductible for the issuing corporation. Dividends received by shareholders are partially tax-sheltered by a dividend tax credit.

19. Common Stock Features Classes of Stock Some firms have more than one class of common stock; often, the classes are created with unequal voting rights. Canadian Tire Corporation is an example of a company with non-voting common stock trading in the market. Non-voting shares must receive dividends no lower than dividends on voting shares. A primary reason for creating dual classes of stock has to do with control of the firm.

20. Preferred Stock Features 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. Preferred stock is a form of equity from a legal, tax, and regulatory standpoint. Holders of preferred stock generally have no voting privileges. However, holders of preferred stock are often granted voting and other rights if preferred dividends have not been paid for some time.

21. Preferred Stock Features Preferred stock have a stated liquidating value. The cash dividend is described in dollars per share. A preferred dividend is not like bond interest – unless the B of D declares a dividend, no liability arises. Dividends on preferred stock are either cumulative or non-cumulative. Dividends not declared on cumulative preferred stock are carried forward and must be paid before common shareholders can receive anything.

22. Stock Market Reporting 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. As a outsider to the market, we need to generally assume that the listed market value of a share of stock is right. The benchmark for comparison in most valuations remains the market price. If your numbers do not match with the market, take a second look at your numbers.

23. The Price Earnings Ratio Even though our stock valuation formulas focused on dividends, not earnings, financial analysts often rely on price earnings ratios (P/E). Why do some firms paying identical dividends have different P/E ratios? Growth opportunities – the firm with more growth opportunities should sell at a higher price because investors are buying both current income and growth opportunities.

24. The Price Earning Ratio P/E ratios and the Boston Consulting Group Model: 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