Question

a. ABC Company has just paid a dividend of $1.00 per share. Dividends are paid annually. Analysts estimate that dividends per share will grow at a rate of 20% for the next 2 years, at 15% for the subsequent 3 years, and at 3% thereafter. If the shareholders’ required rate of return is 12% per year, then what is the price of the stock today? What will be the ex-dividend price at the end of the first year? What will be the capital gains yield in the first year?    

Answer 1

Price of stock is equal to the present value of all future dividends

= 1(1+20%)/(1+12%) + 1(1.2)(1.2)/(1.12)^2 + 1(1.2)^2(1.15)/(1.12)^3 + 1(1.2)^2(1.15)^2/(1.12)^4 + 1(1.2)^2(1.15)^3/(1.12)^5 + 1(1.2)^2(1.15)^3(1.03)/(1.12)^5(12%-3%)

= $20.07 per share

Ex-dividend price after one year =

1(1.2)(1.2)/(1.12)^1 + 1(1.2)^2(1.15)/(1.12)^2 + 1(1.2)^2(1.15)^2/(1.12)^3 + 1(1.2)^2(1.15)^3/(1.12)^4 + 1(1.2)^2(1.15)^3(1.03)/(1.12)^4(12%-3%)

= $21.28 per share

Capital gains yield = (21.28-20.07)/20.07

= 6.03%