ABC is expected to maintain a constant dividend payout ratio and constant growth

Question

ABC is expected to maintain a constant dividend payout ratio and constant growth rate of earning , earning were 4.50 per share last year. the dividend payout is 55% , ROE is 10% , and the required return is 11% . calculate the current valu of the stock . after an aggressive marketing program, it is appers that EPS and ROE will grow rapidly over the next two years. calulate the value of common stock assuming the divdend will grow at a 15% rate for the next two years , returning in the third year to the historical growth rate .

Explanation / Answer

(a)
Price of stock = Dividend per share/(discount rate - dividend growth rate)
= (Earnings per share * dividend payout)/(discount rate - dividend growth rate)

dividend growth rate = (1-payout)*ROE
= (1-55%)*10% = 4.5%
discount rate = irr = 11%

Price of stock = 4.5 * 55%/(11%-4.5%) = 4.5 * 0.55/0.065 = 38.0769231

(b)
After the marketing program dividend growth = 15% in first 2 years
Share price = discounted value of dividends
= present value of year1 dividend + present value of year2 dividend + present value of stock price in year 3

present value of stock price in year 3 = as stock will return to historical dividends, it will be 38.0769231 in year 3 (from question a)

Share price = 4.5*55%*(1+15%)/(1+11%) + 4.5*55%*(1+15%)^2/(1+11%)^2 + 38.0769231/(1+11%)^2
= 4.5*0.55*1.15/1.11 + 4.5*0.55*1.15*1.15/(1.11*1.11) + 38.0769231/(1.11*1.11)
= 2.56418919 + 2.65659241 + 30.9040849
= 36.1248664

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