Question

The market expected return is 14% with a standard deviation of 18%. The risk-free rate is 6%. Security XYZ has just paid a dividend of $1 and has a current price of $13.95. What is the beta of Security XYZ if its dividend is expected to grow at 6% per year indefinitely?

1.05

0.85

0.90

0.95

Answer 1

Answer:

Calculation of the beta of security:

Step1 : Calculation of the required rate of return (ke)

Formula,

Current price = Dividend in year 1 / (Required rate of return - growth rate)

Dividend in year 1 = Dividend just paid x (1+growth rate)

= $1 x (1+0.06)

= $1.06

Solve for required rate of return (ke):

ke = (Dividend in year 1 / Current price) + growth rate

= ($1.06 / $13.95) + 6%

= 0.0760 + 6%

= 7.60% + 6%

= 13.60%

Step 2: Calculation of the beta of the stock:

Ke = Risk free rate + Beta x (Market rate of return - risk free rate)

Solve of Beta:

Beta = (Ke - Risk free rate) / (Market rate of return - risk free rate)

= (13.60% - 6%) / (14% -6%)

= 7.60% / 8%

= 0.95 (Answer)