Answer: New Market price =$29.55
Step-by-step explanation:
Using the CAPM,Capital Asset Pricing Model CAPM formule , The expected return on stock is given as
Er = Rf +β( Mr)
which means
Expected return = Risk free rate + beta (market risk premium)
13%= 4% +beta (6%)
beta= 13%-4%/6%=0.13-0.04 /0.06
beta= 1.5
The dividend expected to be paid is given as
Expected dividend, D = Price of security X Expected return
= 50 X 13%
= $6.5
Now, if beta doubles, Expected return becomes
Er = Rf + 2β( Mr)
Er= 4% + 2 x 1.5( 6%)
=4%+ 3.0( 6%)
0.04 + 0.18
Er = 0.22 = 22%
New Market price
Expected dividend, D = Price of security X Expected return
Price = Expected dividend, D/Expected return
= $6.5/0.22
=$29.55