In: Finance
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?
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: