1. 1 Finance School of Management Chapter 9. Valuation of Common Stocks Objective Explain equity evaluation Using discounting Dividend policy and wealth

2. 2 Finance School of Management Chapter 9 Contents  Common Stock  Reading Stock Listings  The Discounted Dividend Model  Earnings and Investment Opportunities  A Reconsideration of the Price/Earnings Multiple Approach  Does Dividend Policy Affect Shareholder Wealth?

3. 3 Finance School of Management Common Stock  Common stock is the best known security, but many people know comparatively little about it.  People who own stock have an equity interest in the organization.  If a business has shares of stock, it is organized as a corporation rather than a proprietorship or a partnership.  Shareholder Rights: –the right to receive declared dividends on a pro rata basis, –the right to vote, –the right to maintain ownership percentage.

4. 4 Finance School of Management Reading Stock Listings 52 Weeks Hi Lo Stock Sym Div Yld % PE Vol100s Hi Lo Close Net Chg 25.38 20.38 IBM IBM 1.54 7.2 12 371 21.25 20.88 21.25 +.13 Dividend Yield Price/Earnings Ratio

5. 5 Finance School of Management The Discounted Dividend Model  Chapter 8 shows how the Law of One Price can be used to deduce the value of known cash flows from the observed market prices of bonds.  In this chapter we consider the valuation of uncertain cash flows using a discounted cash flow (DCF) approach.  The DCF approach to determining the value of a stock discounts the expected cash flows-either dividends paid to shareholders or net cash flows from trading. Assume: buy and hold for ever

6. 6 Finance School of Management The Discounted Dividend Model  Discount-dividend model (DDM) is defined as any model that computes the value of a share of stock as the present value of its expected future cash dividends.  The risk-adjusted discount rate or market capitalization rate is the expected rate of return that investors require to be willing to invest in the stock.

7. 7 Finance School of Management The Discounted Dividend Model  The rate of return that investors expect, E(r 1 ), equals the market capitalization rate, k. The price is the present value of the expected end-of- year dividend plus the expected ex-dividend price discounted at the required rate return.

8. 8 Finance School of Management The Discounted Dividend Model  Using the same logic employed to derive P 0, the expected price of stock at the beginning of the second year is:   By substitution, we can express P 0 in terms of D 1, D 2, and P 2 :

9. 9 Finance School of Management The Discounted Dividend Model   By repeating this chain of substitutions, we get the general formula of the DDM: The price of a share of stock is the present value of all expected future dividends per share, discounted at the market capitalization rate.

10. 10 Finance School of Management Does the trading behavior affect the stock price ？

11. 11 Finance School of Management  T with the selling price P T  Suppose that an investor buys one stock from the beginning and sells it at time T with the selling price P T.   From the DDM, we have ： and Therefore   The trading behavior has no effect on stock price.

12. 12 Finance School of Management The Constant-Growth-Rate and the Discounted Dividend Model  The most basic assumption is that dividends will grow at a constant rate g.  Substituting the dividend growth forecast, D t =D 1 (1+g) t-1, into DDM formula, we find that the present value of a perpetual of dividends growing at a constant rate, g, is

13. 13 Finance School of Management   IBM stock is expected to pay a dividend of $3 per share a year from now.   Its dividends are expected to grow by 8% per year thereafter.   If its price is now $30 per share, what must be the market capitalization rate? An Illustration

14. 14 Finance School of Management  If g equals to zero (D 1 =D 2 =…), the formula reduces to the formula for the present value of a level perpetuity: The Constant-Growth-Rate and the Discounted Dividend Model

15. 15 Finance School of Management The Constant-Growth-Rate and the Discounted Dividend Model  Another implication of the constant growth rate DDM is that the stock price is expected to grow at the same rate as dividends.

16. 16 Finance School of Management Earning and Investment Opportunity  A second approach to DCF valuation focuses on future earnings and investment opportunities.  Focusing on earnings and investment opportunities rather than dividend helps to concentrate the analyst's attention on the core business determinants of value. –Consider an investor planning to take over a firm.  To simplify the analysis, suppose that no new shares are issues, and no taxes. Dividends = Earnings − Net New Investment

17. 17 Finance School of Management Earnings and Investment Opportunities   The formula for valuing stock is  The firm’s value equals the present value of its expected future earning less the present value of the earnings reinvested in the firm. –In a declining industry, net investment is negative and capacity would decline over time. –In a stable or stagnant industry, net investment is zero and capacity remains about constant over time. –In an expanding industry, net investment is positive and capacity increases over time.

18. 18 Finance School of Management Earnings and Investment Opportunities  A useful way to estimate a firm’s value based on earnings and investment opportunities is to partition the firm’s value into two parts: –The present value of the current level of earnings projected into the future as a perpetuity, and –The net present value of any future investment opportunities. + Net Present Value of Future Investment Opportunities

19. 19 Finance School of Management An Example  consider a firm called Nogrowth Corporation, whose earnings per share are $15.  It pays all of its earnings out as dividends, and there is no growth.  Assuming that the capitalization rate is 15% per year, Nogrowth's stock price would be: P 0 =$15/0.15=$100

20. 20 Finance School of Management  Growthstock initially has the same earnings as Nogrowth, but it reinvests 60% of its earnings each year into new investments that yield a rate of return of 20% per year.  Growthstock will pay out only 40% of $15 as dividends, or $6 per share.  Although Growth stock’s dividend per share is initially lower than Nogrowth’s, Growth stock’s dividends will grow over time. g = Earnings Retention Rate × Rate of Return on New Investments g = 0.6 ×0.2 = 0.12 Another Example

21. 21 Finance School of Management   The net present value of Growthstock’s future investments is the difference in price between its shares and Nogrowth’s shares: NPV of Future Investments = $200 − $100 = $100 Continued

22. 22 Finance School of Management Continued   It is important to realize that the reason that Growthstock has a higher share price than Nogrowth is not growth per se, but rather the fact that its reinvested earnings yield a rate of return in excess of the market capitalization rate.   Normalprofit's rate of return on future investments is 15% per year and it reinvests 60% of its earnings each year g = 0.6 × 0.15=0.09

23. 23 Finance School of Management

24. 24 Finance School of Management $166.67-$66.67 = $100 Further Illustration   An analyst uses the constant growth DDM to evaluate IBM stock.   She assumes expected earnings of $10 per share, an earnings retention rate of 75%, an expected rate of return on future investments of 18% per year, and a market capitalization rate of 15% per year.   What is the implied net present value of future investments?

25. 25 Finance School of Management   Growth per se does not add value. What adds value is the opportunity to invest in projects that can earn rates of return in excess of the required rate, k.   When a firm’s future investment opportunities yield a rate of return equals to k, the stock’s value can be estimated using the formula:P 0 =E 1 /k Earnings and Investment Opportunities

26. 26 Finance School of Management A Reconsideration of the Price/Earnings Multiple Approach   A widely used approach for quickly estimating the value of a share of a firm's stock is to take its projected earnings per share and to multiply it by an appropriate price/earnings (P/E) multiple derived from other comparable firms.

27. 27 Finance School of Management A Reconsideration of the Price/Earnings Multiple Approach   The expected earnings of Digital Biomed Corporation per share are $2 per year.   If you apply the industry average P/E, which is 15, the resultant value for Digital Biomed stock is $30.   However, the actual price at which Digital Biomed stock is trading in the stock market is $100 per share.   How can you account for the difference?

28. 28 Finance School of Management A Reconsideration of the Price/Earnings Multiple Approach + Net Present Value of Future Investment Opportunities   It is not growth per se that produces a high P/E ratio, but rather the presence of future investment opportunities that are expected to yield a rate of return greater than the market’s required risk- adjusted rate

29. 29 Finance School of Management Effects of Dividend Policy means a corporation’s regarding to its shareholders.  Dividend policy means a corporation’s regarding paying out cash to its shareholders holding constant its investment and borrowing decisions.  Does dividend policy affect shareholder wealth?

30. 30 Finance School of Management Cash Dividends & Share Repurchases  Cash dividends –All shareholders receive cash in amounts proportional to the number of shares they own. –All else the same, the share price declines immediately after payment by the amount of the dividend.

31. 31 Finance School of Management Cash Dividends & Share Repurchases  Share repurchases –The company pays cash to buy shares of its stock in the stock market, reducing the number of shares outstanding. –All else the same, the share price remains unchanged.

32. 32 Finance School of Management Cash Dividends & Share Repurchases  Stock dividends –Corporations sometimes declare stock splits and distribute stock dividend. These activities do not distribute cash to shareholders; they increase the number of shares of stock outstanding. –Payment of a stock dividend can be seen as distributing a cash dividend to existing shareholders, and then requiring them to immediately use the cash to buy additional shares of the company's stock. –All else the same, the share price declines immediately after payment of the dividend.

33. 33 Finance School of Management Illustration: Cashrich Corporation   Total assets with a market value of $12 million: $2 million in cash, and $10 million in other assets.   The market value of its debts is $2 million, and the market value of its equity is $10 million.   500,000 shares of common stock outstanding, each with a market price of $20.

34. 34 Finance School of Management Original Balance Sheet

35. 35 Finance School of Management Dividend Payment (A cash dividend of $2 per share, Price=$18) Was 2 Was 10 Were 12

36. 36 Finance School of Management Dividend Payment (Repurchases shares worth $1 million, Price=$20) Was 2 Was 10 Were 12

37. 37 Finance School of Management Dividend Payment (10% stock dividend, 550,000 shares outstanding, Price=$18.18) Was 2 Was 10 Were 12

38. 38 Finance School of Management Dividend Policy in Frictionless Financial Environment — M&M Theory  Does dividend policy affect stockholders’ wealth?  Modigliani and Miller (1961) proves that In a frictionless financial environment, corporations cannot increase stockholders’ wealth through dividend policy. no taxes and no transaction costs

39. 39 Finance School of Management M&M Theory: Cashrich Corporation   Instead of paying $1 million cash dividends, the management of Cashrich decides to invest it in a project.   A stockholder, who holds 100 shares and wants to receive a cash dividend of $2 per share, can – –sell 10 shares for $200 cash. – –His total wealth is 90 shares of stocks with a market value of $1,800+$200 cash.

40. 40 Finance School of Management M&M Theory: Cashrich Corporation   Cashrich does distributes a cash dividend of $2 per share.   A stockholder, who holds 100 shares and does not wand to hold cash, can – –use the cash dividends to buy shares with a value of $200. – –His total wealth is original 100 shares with a market value of $1,800+news shares with a market value of $200.

41. 41 Finance School of Management Illustration: Cashpoor Corporation   Total assets: $0.5 million in cash, and $1 million in plant and equipment.   The market value of its debts is $1 million.   A project with NPV of $1.5 million needs an initial investment of $0.5 million for plant and equipment.   1,000,000 shares of common stock outstanding, each with a market price of $2.

42. 42 Finance School of Management Balance Sheet of Cashpoor   The stock price fully reflects all the available information, including NPV of the new investment.

43. 43 Finance School of Management M&M Theory: Cashpoor Corporation   If Cashpoor uses its $0.5 million to finance the investment, – –a $0.5 million reduction in the firm’s cash account, – –an increase of $0.5 million in plant and equipment, – –the stock price is still $2 per share.

44. 44 Finance School of Management M&M Theory: Cashpoor Corporation   If Cashpoor pays a cash dividend of $0.5 per share (total $0.5 million) to its shareholders, and issues new stocks to finance the purchase of plant and equipment, – –the stock price will decline from $2 to $1.5, – –the wealth of old shareholders is still $2 million, – –333,333 new shares should be issued to raise the $0.5 million needed for the new plant and equipment.

45. 45 Finance School of Management Dividend Policy in the Real World   In the real world, there are a number of frictions: taxes, regulations, the costs of external finance, and the information content of dividends.

46. 46 Finance School of Management Dividend Policy in the Real World   Personal taxes: paying cash dividends or repurchasing shares.   Regulations: laws that prevent corporations – –from using shares repurchases as an alternative to dividends as a regular mechanism for paying cash to shareholders, – –from retaining cash in the business that is not needed to run the business.

47. 47 Finance School of Management Dividend Policy in the Real World   Cost of raising funds externally – –the fees the investment bankers charge – –a bargain price to induce outsiders to buy new shares   Informational content of dividends – –a dividend increase: good sign and price increase – –a dividend decrease: bad sign and price decline

48. 48 Finance School of Management Review   The discounted dividend model (DDM) shows that the current price of a share is the present value of all expected future dividends.   In the constant growth rate DDM, the growth rate of dividends is also the expected rate of price appreciation.   Growth per se does not add value to a share's current price.   What adds value is the opportunity to invest in projects that yield a rate of return in excess of the market capitalization rate.

49. 49 Finance School of Management Review   In a frictionless financial environment, the wealth of shareholders is the same no matter what dividend policy the firm adopts.   In the real world there are a number of frictions that can cause dividend policy to have an effect on the wealth of shareholders.   These frictions include taxes, regulations, the costs of external finance, and the informational content of dividends.