Castles in the Sand generates a rate of return of 18% on its investments and mai

Question

Castles in the Sand generates a rate of return of 18% on its investments and maintains a plowback ratio of .50. Its earnings this year will be $2 per share. Investors expect a 15% rate of return on the stock.

Find the price and P/E ratio of the firm. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Find the price and P/E ratio of the firm, if the plowback ratio is reduced to .40? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Castles in the Sand generates a rate of return of 18% on its investments and maintains a plowback ratio of .50. Its earnings this year will be $2 per share. Investors expect a 15% rate of return on the stock.

Explanation / Answer

a Company's return on investment= 18% plowback ratio=retention ratio of the company= 0.5=50% Dividend Growth Rate= companys return on investment* Plowback ratio 18% * 0.5 = 9% Currents Earnings per share(EPS)=$ 2 Current dividend per share = $ 2(1-50%)= $ 1 Expected dividend per share = current Dividend (1+ growth rate) = $ 1(1+9%)= $ 1.09 By using Gordons growth model or perpetual growth model price = Expected dividend/ Investors required rate of return - Growth rate 1.09/15%-9%=$ 18.17 P/E Ratio= MPS/EPS= $ 18.17/$ 2 = 9.09 Alternatively, price can also be found using Walters model by using below formula Market price= Dividend   + (Earnings per share- Dividend per share)(Internal rate of return/Cost of capital)/cost of capital $ 1 +($2-$1)(18%/15%)   / 15% = 14.67 P/E ratio = market price per share/ Earnings per share 14.67/2 = 7.3 b Plough back ratio = 40% Growth rate = 18% *0.4 = 7.2% Currents Earnings per share(EPS)=$ 2 Current dividend per share = $ 2(1-40%)= $ 1.2 Expected dividend per share = current Dividend (1+ growth rate) = $ 1.2(1+7.2%)= $ 1.2864 By using Gordons growth model or perpetual growth model price = Expected dividend/ Investors required rate of return - Growth rate $ 1.2864/15%-7.2% = $ 16.49 P/ E Ratio= MPS/EPS = $ 16.49/2= 8.25 Alternatively, price can also be found using Walters model by using below formula Market price= Dividend   + (Earnings per share- Dividend per share)(Internal rate of return/Cost of capital)/cost of capital 1.2 + (2-1.2)(18%/15%)   / 15% = $14.4 P/ E Ratio= MPS/EPS = $ 14.4/$ 2= $ 7.2

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