The market price of a security is $50. Its expected rate of return is 13%. The risk-free rate is 4% and the market risk premium is 6%. What will be the market price of the security if its beta doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity.

New Market price =$29.55

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