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Question 999  duration, duration of a perpetuity with growth, CAPM, DDM

A stock has a beta of 0.5. Its next dividend is expected to be $3, paid one year from now. Dividends are expected to be paid annually and grow by 2% pa forever. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. All returns are effective annual rates.

What is the Macaulay duration of the stock now?

Question 1000  duration, duration of a perpetuity with growth

A stock's duration increases since its dividend growth rate increases while its total required return on equity remains unchanged.

###D_\text{Macaulay} = \dfrac{1+r}{r-g}###

What will be the effect on the stock's CAPM beta? Assume that there's no change in the risk free rate or market risk premium and that the dividend growth rate increases due to the company cutting dividends to re-invest in zero-NPV projects. The firm is unlevered. The company's equity beta will: