Patience, Inc., just paid a dividend of $2.90 per share on its stock. The dividends are expected to grow at a constant rate of 4.75 percent per year, indefinitely. Assume investors require an 9 percent return on this stock. Requirement 1: What is the current price? (Do not include the dollar sign ($). Round your answer to 2 decimal places (e.g., 32.16).) Current price $ Requirement 2: What will the price be in six years and in thirteen years? (Do not include the dollar signs ($). Round your answers to 2 decimal places (e.g., 32.16).) Six years $ Thirteen years $ Explanation: 1: The constant dividend growth model is: P t = D t × (1 + g ) / ( R – g ) So, the price of the stock today is: P0 = D0 (1 + g ) / ( R – g ) P0 = $2.90 (1.0475) / (0.09 – 0.0475) P0 = $71.48 2: The dividend at year 7 is the dividend today times the FVIF for the growth rate in dividends and seven years, so: P 6 = D 6 (1 + g ) / ( R – g ) P 6 = D0 (1 + g) 7 / ( R – g ) P 6 = $2.90 (1.0475) 7 / (0.09 – 0.0475) P 6 = $94.43 We can do the same thing to find the dividend in Year 14, which gives us the price in Year 13, so: P 13 = D 13 (1 + g ) / ( R – g ) P 13 = D0 (1 + g) 14 / ( R – g ) P 13 = $2.90 (1.0475) 14 / (0.09 – 0.0475) P 13 = $130.67 There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in six years, and we have already calculated the stock price today. The stock price in six years will be: P 6 = P0 (1 + g ) 6 P 6 = $71.48(1 + 0.0475) 6 P 6 = $94.43
And the stock price in 13 years will be: P 13 = P0 (1 + g ) 13 P 13 = $71.48(1 + 0.0475) 13 P 13 = $130.67 2. The next dividend payment by Mosby, Inc., will be $2.65 per share. The dividends are anticipated to maintain a 6.50 percent growth rate, forever. Required: If the stock currently sells for $48.90 per share, what is the required return? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Required return % Explanation: We need to find the required return of the stock. Using the constant growth model, we can solve the equation for R . Doing so, we find: R = (D 1 / P0 ) + g R = ($2.65 / $48.90) + 0.0650 R = 0.1192 or 11.92% 3. The stock price of Jenkins Co. is $54.00. Investors require a 14 percent rate of return on similar stocks. Required: If the company plans to pay a dividend of $3.65 next year, what growth rate is expected for the company’s stock price? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).) Growth rate % Explanation:
We need to find the growth rate of dividends. Using the constant growth model, we can solve the equation for g . Doing so, we find:
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