【導(dǎo)讀】ChapterOpener. PART  V. p.583. p.584.    Forexample,ananalyst

　　

【正文】 sumption is that the discrepancy will never disappear and that the market price will trend upward at rate g forever. This implies that the discrepancy between intrinsic value and market price also will grow at the same rate. In our example:Under this assumption the expected HPR will exceed the required rate, because the dividend yield is higher than it would be if P0 were equal to V0. In our example the dividend yield would be % instead of 8%, so that the expected HPR would be % rather than 12%:An investor who identifies this undervalued stock can get an expected dividend that exceeds the required yield by 33 basis points. This excess return is earned each year, and the market price never catches up to intrinsic value.An alternative assumption is that the gap between market price and intrinsic value will disappear by the end of the year. In that case we would have P1 = V1 = $52, andThe assumption of plete catchup to intrinsic value produces a much larger 1year HPR. In future years, however, the stock is expected to generate only fair rates of return.Many stock analysts assume that a stock39。s price will approach its intrinsic value gradually over time—for example, over a 5year period. This puts their expected 1year HPR somewhere between the bounds of % and %.Stock Prices and Investment OpportunitiesConsider two panies, Cash Cow, Inc., and Growth Prospects, each with expected earnings in the ing year of $5 per share. Both panies could in principle pay out all of these earnings as dividends, maintaining a perpetual dividend flow of $5 per share. If the market capitalization rate were k = %, both panies would then be valued at D1/k = $5/.125 = $40 per share. Neither firm would grow in value, because with all earnings paid out as dividends, and no earnings reinvested in the firm, both panies39。 capital stock and earnings capacity would remain unchanged over time。 earnings4 and dividends would not grow.p. 593Now suppose one of the firms, Growth Prospects, engages in projects that generate a return on investment of 15%, which is greater than the required rate of return, k = %. It would be foolish for such a pany to pay out all of its earnings as dividends. If Growth Prospects retains or plows back some of its earnings into its profitable projects, it can earn a 15% rate of return for its shareholders, whereas if it pays out all earnings as dividends, it forgoes the projects, leaving shareholders to invest the dividends in other opportunities at a fair market rate of only %. Suppose, therefore, that Growth Prospects chooses a lower dividend payout ratio Percentage of earnings paid out as dividends. (the fraction of earnings paid out as dividends), reducing payout from 100% to 40%, maintaining a plowback ratio The proportion of the firm39。s earnings that is reinvested in the business (and not paid out as dividends). The plowback ratio equals 1 minus the dividend payout ratio. (the fraction of earnings reinvested in the firm) at 60%. The plowback ratio is also referred to as the earnings retention ratio Plowback ratio..Figure Dividend growth for two earnings reinvestment policiesThe dividend of the pany, therefore, will be $2 (40% of $5 earnings) instead of $5. Will share price fall? No—it will rise! Although dividends initially fall under the earnings reinvestment policy, subsequent growth in the assets of the firm because of reinvested profits will generate growth in future dividends, which will be reflected in today39。s share price.Figure illustrates the dividend streams generated by Growth Prospects under two dividend policies. A lowreinvestmentrate plan allows the firm to pay higher initial dividends, but results in a lower dividend growth rate. Eventually, a highreinvestmentrate plan will provide higher dividends. If the dividend growth generated by the reinvested earnings is high enough, the stock will be worth more under the highreinvestment strategy.How much growth will be generated? Suppose Growth Prospects starts with plant and equipment of $100 million and is all equity financed. With a return on investment or equity (ROE) of 15%, total earnings are ROE $100 million = .15 $100 million = $15 million. There are 3 million shares of stock outstanding, so earnings per share are $5, as posited above. If 60% of the $15 million in this year39。s earnings is reinvested, then the value of the firm39。s assets will increase by .60 $15 million = $9 million, or by 9%. The percentage increase in assets is the rate at which ine was generated (ROE) times the plowback ratio (the fraction of earnings reinvested in the firm), which we will denote as b.Now endowed with 9% more assets, the pany earns 9% more ine, and pays out 9% higher dividends. The growth rate of the dividends, therefore, is5If the stock price equals its intrinsic value, it should sell atp. 594When Growth Prospects pursued a nogrowth policy and paid out all earnings as dividends, the stock price was only $40. Therefore, you can think of $40 as the value per share of the assets the pany already has in place.When Growth Prospects decided to reduce current dividends and reinvest some of its earnings in new investments, its stock price increased. The increase in the stock price reflects the fact that the planned investments provide an expected rate of return greater than the required rate. In other words, the investment opportunities have positive net present value. The value of the firm rises by the NPV of these investment opportunities. This net present value is also called the present value of growth opportunities Net present value of a firm39。s future investments., or PVGO Net present value of a firm39。s future investments..Therefore, we can think of the value of the firm as the sum of the value of assets already in place, or the nogrowth value of the firm, plus the net present value of the future investments the firm will make, which