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McGaha Enterprises expects earnings and dividends to grow at a rate of 25% for the next 4 years, after the growth rate in earnings and dividends will fall to zero, i.e., g = 0. The company's last dividend, D0, was $1.25, its beta is 1.20, the market risk premium is 5.50%, and the risk-free rate is 3.00%. What is the current price of the common stock? a. $27.89 b. $29.05 c. $26.77 d. $31.42 e. $30.21

Respuesta :

Answer:

The correct option is B,$29.05

Explanation:

The required rate of return is can be computed using  Miller and Modgiliani CAPM formula below:

Ke=Rf+Beta*Mrp

Ke is the cost of equity which is unknown

Rf is the risk free rate of 3.00%

Mrp is the market risk premium of 5.50%

Beta is 1.2

Ke=3.00%+(1.2*5.50%)

Ke =9.6%

The current price of the common stock is the present value of dividends payment and stock price(terminal value) as shown below discounted with Ke of 9.6%

Year 1 $1.25*(1+25%)=$1.56 *1/(1+9.6%)^1=$1.43

Year 2 $1.56*(1+25%)=$1.95 *1/(1+9.6%)^2=$1.63

Year 3 $1.95*(1+25%)=$2.44 *1/(1+9.6%)^3=$1.85

Year 4  $2.44*(1+25%)=$3.05 *1/(1+9.6%)^4=$2.11

Terminal value=year 4 dividend/ke=$3.05/9.6%=$31.79*1/(1+9.6%)^4=$22.03

Total present values=$1.43 +$1.63+$1.85 +$2.11 +$22.03=$29.05

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