Question

The market price of a security is $60. Its expected rate of return is 10%. The risk-free rate is 6%, and the market risk premium is 8%. What will the market price of the security be if its beta doubles (and all other variables remain unchanged)? Assume the stock is expected to pay a constant dividend in perpetuity. (Round your answer to 2 decimal places.)

Answer 1

Answer:

The market price of the security will be $42.86 when the Beta doubles and all other variables remains constant.

Explanation:

Given information -       Current market price    = $60

                                      Risk free rate                 = 6%

                                      Expected rate of return = 10%

                                      Market risk premium      = 8%

In this question we have to find the market price of the security when beta doubles it self, the formula which we can use to take out the market price is,

 \frac{DIVIDEND}{NEW\:EXPECTED\:RATE\: OF\: RETURN}

But here we have to first find out both the dividend and new expected rate of return and it is also told here that beta doubles itself but we don't know what the initial beta is, so lets take out what beta is , using formula for expected rate of return

Expected rate of return = Risk free rate + Beta x Market risk premium

                 10%               = 6% + Beta x 8%

                 4%                 = Beta x 8%

           Beta                  = 4% / 8%

           Beta                  = 1% / 2%    = .01 / .02 = .5

Now doubling the beta = .5 x 2 = 1

Putting this value of beta in the expected rate of return formula to calculate the new expected rate of return,

New expected rate of return = 6% + 1 x 8%

                                                = 14%

Now we just have to find the dividend , which we can by using formula of

Market price =  \frac{DIVIDEND}{\:EXPECTED\:RATE\: OF\: RETURN}

$60               = Dividend / 10%              (10% = .1)

$60 x .1          = Dividend

$6                  = Dividend

Now we have both dividend and new market rate of return and we just have to put these values in the formula

 \frac{DIVIDEND}{NEW\:EXPECTED\:RATE\: OF\: RETURN}

New market price = $6 / 14%            (14% = .14)

                              = $6 / .14

                              = $42.86

Answer 2

Answer: $42.85 per share

Explanation:

Given that,

The market price of a security(P) = $60 per share

expected rate of return(ERR) = 10%

the market risk premium(MRP) = 8%

risk-free rate(RFR) = 6%

ERR = RFR + Beta × (MRP)

10 = 6 + Beta(8)

Beta = $\frac{4}{8}$

= 0.5

In this question, it is given that constant dividend paid in perpetuity

current market price per share, P = $\frac{DPS}{ERR}$

Where, DPS - dividend per share

60 × 0.1 = DPS

$6 per share = DPS

If beta doubles then,

Beta = 0.5 × 2

= 1

∴ Required rate of return = 6 + 1 × 8

= 14%

So, market price of security = $\frac{DPS}{Required rate of return}$

= $\frac{6}{0.14}$

= $42.85 per share