Question

ART has come out with a new and improved product. As a result, the firm projects an ROE of 21%, and it will maintain a plowback ratio of 0.40. Its earnings this year will be $2.0 per share. Investors expect a 13% rate of return on the stock. What price do you expect ART shares to sell for in 4 years?

Answer 1

g = ROE x b

g = Constant growth rate

ROE = Return on equity = 21 %

b = Plow back ratio = 0.40

g = 0.21 x 0.40 = 0.084

Expected dividend, D1 = E1 x (1-b)

E1 = Expected earnings per share = $ 2

D1 = $ 2 x (1-0.4)

    = $ 2 x 0.6 = $ 1.2

Current share price, P0 = D1/k -g

k = Rate of return on the stock = 13 %

P0 = $ 1.2/ (0.13 - 0.084)

   = $ 1.2/0.046

= $ 26.08695652

Share price in 4 years = P0 x (1+k)4

                                      = $ 26.08695652 x (1+0.13)4

                                      = $ 26.08695652 x (1.13)4

                                      = $ 26.08695652 x 1.63047361

                                      = $ 42.53409417 or $ 42.53

ART is expected to sell the shares for $ 42.53 in year 4.