Suppose that a firm\'s recent earnings per share and dividend per share are $3.3

Question

Suppose that a firm's recent earnings per share and dividend per share are $3.35 and $3.00, respectively Both are expected to grow at 7 percent. However, the firm's current P/E ratio of 31 seems high for this growth rate. The P/E ratio is expected to fall to 27 within five years. Compute the dividends over the next five years. (Do not round intermediate calculations. Round your final answer to 3 decimal places.) Dividends Years First year Second year Third year Fourth year Fifth year Compute the value of this stock price in five years. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Stock price Calculate the present value of these cash flows using a 9 percent discount rate. (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Present value

Explanation / Answer

Solution: 1. First year $3.210 Second year $3.435 Third year $3.675 Fourth year $3.932 Fifth year $4.208 Working Notes : Since, dividend per share constantly growing @ 7% per year nth year = recent Dividend per share x (1+.07)^n First year = $3 x ( 1.07)^1 = $3.210 Second year = $3 x ( 1.07)^2 = $3.435 Third year = $3 x ( 1.07)^3 = $3.675 Fourth year = $3 x ( 1.07)^4 = $3.932 Fifth year = $3 x ( 1.07)^5 = $4.208 2. The stock price in year 5 = $126.86 Working Notes: stock price in year 5 = P/E ratio of 5th year x recent Earning per share x (1+growth rate )^5 = 27 x $3.35 x (1.07)^5 =$126.860804 =$126.86 3. Present value                                            $ 96.65 Working Notes: Cash flow is Dividend & stock price in year 5 Year PVF @9% Present value 1 $3.210 0.917431193 2.94 2 $3.435 0.841679993 2.89 3 $3.675 0.77218348 2.84 4 $3.932 0.708425211 2.79 5 $4.208 0.649931386 2.73 5 $126.861 0.649931386 82.45 Total present value 96.65 PVF @ 9% for nth period is calculated by = 1/(1+0.09)^n Notes: Cash flow is taken from above calculation done in 1. & 2. Please feel free to ask if anything about above solution in comment section of the question.

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