Question

# a. ABC Company has just paid a dividend of \$1.00 per share. Dividends are paid annually....

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?

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%

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