Question

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.

Answer 1

(a) = 57.14

(b) Shown below

Step-by-step 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%