Suppose that a firm\'s recent earnings per share and dividend per share are $2.8

Question

Suppose that a firm's recent earnings per share and dividend per share are $2.83 and $2.00, respectively. Both are expected to grow at 10.0 percent. However, the firm's current P/E ratio of 25.5 seems high for this growth rate. The P/E ratio is expected to fall to 21.0 within five years.


Required:
Compute a value for this stock by first estimating the dividends over the next five years and the stock price in five years. Then discount these cash flows using an 16.5 percent required rate. (Do not round your intermediate calculations and round your final answer to 2 decimal places. Omit the "$" sign in your response.)

Stock value $

Explanation / Answer

According to the given problem, Dividend in the year-0 is $2.00 Earning per share is $2.83 Growth rate = 10% P/E ratio = 25.5 But we know that from P/E ratio,                                    P / E ratio = Market price per share / Earning per share But we know the value of Earning per share. Substituting the value of Earning per share in the above formula.                                  25.5 = Market price per share / $2.83      Market price per share = 25.5 * $2.83                                          = $72.165 Therefore, the price of the share (P0) in the year-0 is $72 But the P/E ratio falls to 21.0 in five years. So,computing the price of the share in five years using P/E ratio.                                        P/E ratio = Market price per share / Earning per share                                             21.0  = Market price per share / $2.83 (1.1)^5 Since earning per share is also expected to grow at 10% for the next five years.                                              21.0 = Market price per share / $4.56                 Market price per share = 21.0 * $4.56                                                      = $95.76 Therefore, the market price per share (P5) in the year-5 is $95.76 Computing the price of the stock using the required rate of return: To compute the value of the stock, first we have to calculate the dividends over the next five years. D1 = D0 (1 + g) where D0 is the dividend in year-0            g is the growth rate            Substituting the values in the above formula, we get                                                      D1 = $2.00 (1+0.10)                                                                                                                  = $2.2                                                      D2 = D1 (1+g)                                                            = $2.2 (1+0.10)                                                            = $2.42                                                      D3 = D2 (1+g)                                                            = $2.42 (1+0.10)                                                            = $2.66                                                       D4 = D3 (1+g)                                                             = $2.66 (1+0.1)                                                             = $2.93                                                        D5 = D4 (1+g)                                                              = $2.93 (1+0.1)                                                              = $3.22 Now, substituting the values in the above formula, P0 = D1 / (1 + R)^1 + D2 / (1+R)^2 + D3 / (1+R)^3 + D4 / (1+R)^4 + D5 / (1+R)^5 + P5 / (1+R)^5     = $2 / (1+0.165) + $2.42 / (1.165)^2 + $2.66 / (1.165)^3 + $2.93 / (1.165)^4 + $3.22 / (1.165)^5 + $95.76 / (1.165)^5     = $2 / (1+0.165) + $2.42 / 1.36 + $2.66 / 1.58 + $2.93 / 1.84 + $3.22 / 2.15 + $95.76 / 2.15     = $1.72 + $1.78 + $1.68 + $1.6 + $1.5 + $44.54     = $52.82 Therefore, the value of the stock is $52.82

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