【正文】 = $Present value of dividends paid in 2010 – 2012:YearPV of Dividend2010$$2011$$2012$$Total = $Price at yearend 2012PV in 2009 of this stock priceIntrinsic value of stock = $ + $ = $c. The data in the problem indicate that Quick Brush is selling at a price substantially below its intrinsic value, while the calculations above demonstrate that SmileWhite is selling at a price somewhat above the estimate of its intrinsic value. Based on this analysis, Quick Brush offers the potential for considerable abnormal returns, while SmileWhite offers slightly belowmarket riskadjusted returns.d. Strengths of twostage versus constant growth DDM: Retention rate = 180。Current value per share=Sum of discounted projected 2012 and 2013 total FCFEc. i. The DDM uses a strict definition of cash flows to equity, . the expected dividends on the mon stock. In fact, taken to its extreme, the DDM cannot be used to estimate the value of a stock that pays no dividends. The FCFE model expands the definition of cash flows to include the balance of residual cash flows after all financial obligations and investment needs have been met. Thus the FCFE model explicitly recognizes the firm’s investment and financing policies as well as its dividend policy. In instances of a change of corporate control, and therefore the possibility of changing dividend policy, the FCFE model provides a better estimate of value. The DDM is biased toward finding low P/E ratio stocks with high dividend yields to be undervalued and conversely, high P/E ratio stocks with low dividend yields to be overvalued. It is considered a conservative model in that it tends to identify fewer undervalued firms as market prices rise relative to fundamentals. The DDM does not allow for the potential tax disadvantage of high dividends relative to the capital gains achievable from retention of earnings.ii. Both twostage valuation models allow for two distinct phases of growth, an initial finite period where the growth rate is abnormal, followed by a stable growth period that is expected to last indefinitely. These twostage models share the same limitations with respect to the growth assumptions. First, there is the difficulty of defining the duration of the extraordinary growth period. For example, a longer period of high growth will lead to a higher valuation, and there is the temptation to assume an unrealistically long period of extraordinary growth. Second, the assumption of a sudden shift from high growth to lower, stable growth is unrealistic. The transformation is more likely to occur gradually, over a period of time. Given that the assumed total horizon does not shift (., is infinite), the timing of the shift from high to stable growth is a critical determinant of the valuation estimate. Third, because the value is quite sensitive to the steadystate growth assumption, over or underestimating this rate can lead to large errors in value. The two models share other limitations as well, notably difficulties in accurately forecasting required rates of return, in dealing with the distortions that result from substantial and/or volatile debt ratios, and in accurately valuing assets that do not generate any cash flows.4. a. The formula for calculating a price earnings ratio (P/E) for a stable growth firm is the dividend payout ratio divided by the difference between the required rate of return and the growth rate of dividends. If the P/E is calculated based on trailing earnings (year 0), the payout ratio is increased by the growth rate. If the P/E is calculated based on next year’s earnings (year 1), the numerator is the payout ratio.P/E on trailing earnings:P/E = [payout ratio 180。 = $ 180。 plowback) will fall as plowback ratio falls.(ii) The increased dividend payout rate will reduce the growth rate of book value for the same reason less funds are reinvested in the firm.2. Using a twostage dividend discount model, the current value of a share of Sundanci is calculated as follows.where:E0 = $D0 = $E1 = E0 ()1 = $ 180。 = Therefore: k = ($1/$10) + = , or 20%b. Since k = ROE, the NPV of future investment opportunities is zero:c. Since k = ROE, the stock price would be unaffected by cutting the dividend and investing the additional earnings.13. a. k = rf + β [E(rM ) – rf ] = 8% + (15% – 8%) = %g = b 180。 (1 + g) 180。 in this scenario, we would be valuing expected dividends in the relatively more distant future. However, as a practical matter, such estimates of payments to be made in the more distant future are notoriously inaccurate, rendering dividend discount models problematic for valuation of such panies。 (1 – b) = $2 180。 ROE = 15%c. Assuming ROE = k,