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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?

An unlevered firm cuts its dividends and re-invests in zero-NPV projects with the same risk as its existing projects. This decreases the dividend yield, but increases the firm's equity's dividend growth rate and duration, while its total required return on equity remains unchanged. The equity can be valued as a perpetuity and the duration of a perpetuity is given below:

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

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. The company's equity beta will: