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Five years ago a XYZ stock paid a $1.15 dividend. Since then it has split two...

Five years ago a XYZ stock paid a $1.15 dividend. Since then it has split two for one once and three for two twice. XYZ current earnings per share are $1.15, and the plowback ratio is 50%. The dividends are expected to grow with their historical rate for the next three years. Beginning year four, XYZ return on equity is expected to be 9%. If the firm’s appropriate discount rate is 13.5% what the stock price should be?

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Expert Solution

Answer:

Stock Price = $9.28

Working:

Dividend paid five years ago adjusted for stock splits (till today) = 1.15*(1/2)*(2/3)*(2/3) = $0.25556

Current year dividend = EPS * (1 - plowback ratio) = 1.15 * (1 - 50%) = $0.575

Dividend growth rate = (0.575 / 0.25556) 1/5 - 1

= 17.61%

Hence:

Dividends are expected to grow for the next three years =17.61%

Beginning Year 4:

Return on equity is expected to be = 9%

Given: Plow-back ratio = 50%

Sustainable growth rate = ROE * Plow-back ratio = 9% * 50% = 4.5%

Hence:

Dividends for year 1, year 2, year 3 and year 4 will be:

Value of share at the end year 3 = Year 4 dividend / (Discount rate - Growth rate) = $0.977500 / (13.5% - 4.5%) = $10.86111

Calculation of stock price:

jeff jeffy answered 1 year ago
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