Question

Prove that for a stock with dividends that grow at a constant rate, the capital gains yield equals the growth rate. (Hint: to prove the result, remember that the required rate of return is equal to the capital gains yield plus the dividend yield).

Answer 1

when dividends that grow at a constant rate we know

required rate of return=(dividend next year/current price)+growth rate

here we know that (dividend next year/current price)=dividend yield

so

required rate of return=dividend yield+growth rate

now we know required rate of return=capital gains yield+dividend yield

replace it in earlier equation we get

capital gains yield+dividend yield=dividend yield+growth rate

capital gains yield+dividend yield-dividend yield=growth rate

capital gains yield=growth rate (proved)

the above is answer..