A company will pay a $2 per share dividend in 1 year. The dividend in 2 years will be $4 per share, and it is expected that dividends will grow at %5 per year thereafter. The expected rate of return on the stock is 12%.

a) What is the expected price of the stock in a year?

b) Show that the expected return, 12%, equals dividend yield plus capital appreciation.

(a) = 57.14

(b) Shown below

Explanation:

According to the scenario, computation of the given data are as follow:-

Expected Rate of Return (R) = 12%

Growth Rate (g) = 5%

P2 = Div. Per Share * (1+g) : (R-g)

P2 = 4 * 1.05 : (0.12 - 0.05) = 60

One Year Stock's Expected Price = Div. Per Share : (1+R) t + P2 / (1+R) t

a). Expected price (P1) = 4 : (1+0.12) 1 + 60 : (1+0.12) 1

= 3.57 + 53.57

= 57.14

b).

One Year Dividend (P0) = 2 : (0+0.12) + 4 : (1+0.12) 2 + 60: (1+0.12) 2

= 1.79 + 3.19 + 47.83

= 52.81

Dividend Yield Plus Capital Appreciation = Share Dividend in One Year : Current Price Per Share

= 2 : 52.81 = 0.0379 or 3.79%

Capital Gain = (P1 - P0) : P0

= (57.14 - 52.81) : 52.81

= 0.0820 or 8.20%

Total = Dividend Yield Plus Capital Appreciation + Capital Gain

= 3.79% + 8.20%

= 11.99% or 12%