Question

Consider a security of which we expect to pay a constant dividend of $18.49 in perpetuity. Furthermore, its expected rate of return is 20.1%. Using the equation for present value of a perpetuity, we know that the price of the security ought to be , where D is the constant dividend and k is the expected rate of return.
Assume that the risk-free rate is 3%, and the market risk premium is 6.4%. 

What will happen to the market price of the security if its correlation with the market portfolio doubles, while all other variables, including the dividend, remain unchanged?

Answer 1

Please find below solution.. let me know if you need any clarification..

Answer 1)

Using the equation for present value of a perpetuity, we know that the price of the security ought to be ,

Price = Annual dividend/required rate

=18.49/20.1%

91.99

Answer 2)

we have to use CAPM to compute required rate

As per CAPM required rate = risk free rate + Market risk premium *beta

Risk free rate

3%

Market risk premium

6.40%

Beta

2

therefore required rate = 3%+6.4%*2

15.80%

therefore price today = 18.49/15.8%

117.03