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(2) Example: For years 1 through 4, g = 25 percent; for years 5 on, g = 5 percent; D1 = $1, and k = 10 percent Solve for the stock s value (a) Step 1 Project dividends into the future: D1 = $1, D2 = $125, D3 = 156, D4 = 195, D5 = $204 (b) Step 2 Find the value of the stock at the end of year 4, using D5: V4 = D5/(k g) = $204/(010 005) = $4080 (c) Find the present value using the supernormal growth model: 100 11 010 2 125 11 010 2 2 156 11 010 2 3 195 11 010 2 4 4080 11 010 2 4 $3231

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Note: The present value of $4080 is found by discounting four periods, not ve periods, because the stock price was found at the end of year 4 3 Ratio analysis A Price/earnings (1) The price/earnings (P/E) ratio (earnings multiplier) is used to determine the value of a stock The earnings multiplier tells an investor the price being paid for each $1 of earnings For example, a stock earning $5 per share with a 15 P/E means an investor is willing to pay $75 a share for the stock (2) The expected earnings multiplier is used to value a stock by estimating earnings for the next 12 months The equation becomes: E1 P0 P0 Current market price E1 (3) The P/E ratio is really just a reinstatement of the dividend discount model The rm s dividend is related to earnings and the proportion distributed In dividing both sides of the formula by expected earnings for the next 12 months, E1, the result is P0 E1 D1 E1 k g

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(b) The previous formula shows that a P/E ratio depends on the same factors to value a stock as those achieved through the use of the dividend discount model The factors

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152 - Investment Planning include (1) the dividend payout ratio (dividend divided by earnings, D/E), (2) the required rate of return (k), and (3) the expected growth rate of dividends (g) Advantage: P/E ratio can be applied to stocks that are not paying cash dividends The dividend discount model assumes the rm is paying or is going to pay a cash dividend Disadvantage: P/E ratio does not tell whether a stock is overvalued or undervalued to its market price Investors are required to draw inferences to historical P/E ratios in determining if the P/E ratio is high or low The dividend discount model allows for comparison to determine whether a stock is overvalued or undervalued to its actual price The estimated value of a stock can be determined by using the P/E ratio and applying it to estimated earnings for the next year (E1) Example: A rm has an expected payout ratio of 50 percent, a required rate of return of 11 percent, and an expected dividend growth rate of 6 percent Earnings for the current year (E0) are $200 The future earnings multiplier is computed as (a) P/Efuture ratio

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050 10 011 006 (b) Current earnings are $200 and g is 6 percent, so earnings per shareestimate = 200(106) = $212 (c) The future value of the stock is estimated as V1 = (EPSestimate) (P/Efuture) = $212 10 = $2120 (8) Compare this estimated value (end of year 1) of the stock to its market price to determine whether the stock should be bought or sold the price and ending dividend must be discounted by the required rate of return of 11 percent If the present value of the future stock price and dividend payment are greater than the current market price, the stock is undervalued and should be bought If the present value of the future stock value and dividend payments are less than the current market price, the stock is overpriced and should be avoided (9) There is a relationship between the P/E ratio and all components of the dividend discount model First, the higher the payout ratio, the higher the P/E Second, the higher the expected growth rate, g, the higher the P/E Finally, the higher the required rate of return, k, the lower the P/E The spread between k and g is the main determinant of the P/E ratio, but the dividend payout ratio does have an impact The expected (P0/E1) earnings multiplier is what should be used when valuing stocks, not the historical (P0/E0) ratio B Price/free cash ows (1) The price to cash ow ratio is de ned as the market value divided by per-share cash ow (2) This ratio is often used in conjunction with the P/E ratio, because emphasis is placed on growth in cash ows versus earnings; earnings are often subject to accounting manipulation, whereas cash ows are often more stable Cash ows are often used to predict nancial strength and potential problems C Price/sales (1) This ratio is de ned as the rm s stock price divided by its per-share sales (2) Advantages: The ratio is meaningful for distressed rms; sales gures are not as easily manipulated as earnings; less volatile than P/E multiples Disadvantage: It can distort valuation when earnings drop

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Topic 46: Portfolio Management and Measurement Concepts - 153 (3) A low P/S ratio indicates low valuation, whereas a high P/S ratio indicates high valuation D Price/earnings/growth (PEG) (1) PEG is calculated by dividing the P/E ratio by the estimated earnings growth rate If dividends are signi cant, add the dividend yield to the growth rate when calculating the PEG ratio (2) It indicates the price the market placed on earning expectations 4 Intrinsic value A Intrinsic value is the underlying value that a careful evaluation would produce B An ef cient market would always price stocks at their intrinsic value; an inef cient market would not necessarily do so C Under the dividend discount model, the intrinsic value of stock is the present value of the stock s expected future dividends, discounted at the stock s required rate of return D If a stock trades above its intrinsic value, the stock should be sold If a stock trades below its intrinsic value, the stock should be bought 5 Book value A Book value is stockholder s equity divided by outstanding shares Stockholder s equity includes the sum of stock, additional paid-in capital, and retained earnings on a rm s balance sheet B Value investors pick stocks that trade below book value C The price/book value is de ned as the rm s stock price divided by its per-share book value (1) A low ratio suggests that a stock is undervalued; a high ratio suggests that it is overvalued (2) What is considered high or low is up to the discretion of the analyst, but should be used in comparison with other stocks It has become an important measure of relative value among stocks

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