【文章內(nèi)容簡介】 less of it than under the passive strategy. It might even pay to go short on ABC stock, as we discussed in Chapter 3.In market equilibrium, the current market price will reflect the intrinsic value estimates of all market participants. This means the individual investor whose V0 estimate differs from the market price, P0, in effect must disagree with some or all of the market consensus estimates of E(D1), E(P1), or k. A mon term for the market consensus value of the required rate of return, k, is the market capitalization rate The marketconsensus estimate of the appropriate discount rate for a firm39。s cash flows., which we use often throughout this chapter.CONCEPTCHECK1You expect the price of IBX stock to be $ per share a year from now. Its current market price is $50, and you expect it to pay a dividend 1 year from now of $ per share.a.What is the stock39。s expected dividend yield, rate of price appreciation, and holdingperiod return?b.If the stock has a beta of , the riskfree rate is 6% per year, and the expected rate of return on the market portfolio is 14% per year, what is the required rate of return on IBX stock?c.What is the intrinsic value of IBX stock, and how does it pare to the current market price?Chapter18: Equity Valuation Models Dividend Discount ModelsConsider an investor who buys a share of Steady State Electronics stock, planning to hold it for 1 year. The intrinsic value of the share is the present value of the dividend to be received at the end of the first year, D1, and the expected sales price, P1. We will henceforth use the simpler notation P1 instead of E(P1) to avoid clutter. Keep in mind, though, that future prices and dividends are unknown, and we are dealing with expected values, not certain values. We39。ve already establishedAlthough this year39。s dividends are fairly predictable given a pany39。s history, you might ask how we can estimate P1, the yearend price. According to Equation , V1 (the yearend intrinsic value) will beIf we assume the stock will be selling for its intrinsic value next year, then V1 = P1, and we can substitute this value for P1 into Equation to findp. 588This equation may be interpreted as the present value of dividends plus sales price for a 2year holding period. Of course, now we need to e up with a forecast of P2. Continuing in the same way, we can replace P2 by (D3 + P3)/(1 + k), which relates P0 to the value of dividends plus the expected sales price for a 3year holding period.More generally, for a holding period of H years, we can write the stock value as the present value of dividends over the H years, plus the ultimate sale price, PH:Note the similarity between this formula and the bond valuation formula developed in Chapter 14. Each relates price to the present value of a stream of payments (coupons in the case of bonds, dividends in the case of stocks) and a final payment (the face value of the bond, or the sales price of the stock). The key differences in the case of stocks are the uncertainty of dividends, the lack of a fixed maturity date, and the unknown sales price at the horizon date. Indeed, one can continue to substitute for price indefinitely, to concludeEquation states that the stock price should equal the present value of all expected future dividends into perpetuity. This formula is called the dividend discount model (DDM) A formula stating that the intrinsic value of a firm is the present value of all expected future dividends. of stock prices.It is tempting, but incorrect, to conclude from Equation that the DDM focuses exclusively on dividends and ignores capital gains as a motive for investing in stock. Indeed, we assume explicitly in Equation that capital gains (as reflected in the expected sales price, P1) are part of the stock39。s value. Our point is that the price at which you can sell a stock in the future depends on dividend forecasts at that time.The reason only dividends appear in Equation is not that investors ignore capital gains. It is instead that those capital gains will be determined by dividend forecasts at the time the stock is sold. That is why in Equation we can write the stock price as the present value of dividends plus sales price for any horizon date. PH is the present value at time H of all dividends expected to be paid after the horizon date. That value is then discounted back to today, time 0. The DDM asserts that stock prices are determined ultimately by the cash flows accruing to stockholders, and those are The ConstantGrowth DDMEquation as it stands is still not very useful in valuing a stock because it requires dividend forecasts for every year into the indefinite future. To make the DDM practical, we need to introduce some simplifying assumptions. A useful and mon first pass at the problem is to assume that dividends are trending upward at a stable growth rate that we will call g. Then if g = .05, and the most recently paid dividend was D0 = , expected future dividends areand so on. Using these dividend forecasts in Equation , we solve for intrinsic value asp. 589This equation can be simplified to2Note in Equation that we divide D1 (not D0) by k ? g to calculate intrinsic value. If the market capitalization rate for Steady State is 12%, now we can use Equation to show that the intrinsic value of a share of Steady State stock isEquation is called the constantgrowth DDM A form of the dividend discount model that assumes dividends will grow at a constant rate., or the Gordon model, after Myron J. Gordon, who popularized the model. It should remind you of the formula for the present value of a perpetuity. If dividends were expected not to grow, then the dividend stream would be a simple perpetuity, and the valuation formula would be3V0 = D1/ is a generalization of the perpetuity formula to cover the case of a growing perpetuity. As g increas