Question

Church Inc. is presently enjoying relatively high growth because of a surge in the demand for its new product. Management expects earnings and dividends to grow at a rate of 37% for the next 4 years, after which competition will probably reduce the growth rate in earnings and dividends 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. $44.06

b. $44.47

c. $34.68

d. $36.31

e. $40.80

Answer 1

Required return=Risk free rate+Beta*Market risk premium

=3+(1.2*5.5)=9.6%

D1=(1.25*1.37)=$1.7125

D2=(1.7125*1.37)=$2.346125

D3=(2.346125*1.37)=$3.21419125

D4=(3.21419125*1.37)=$4.403442013

Value after year 4=(D4*Growth rate)/(Required return-Growth rate)

=4.403442013/0.096=$45.86918763

Hence current price=Future dividends*Present value of discounting factor(9.6%,time period)

=1.7125/1.096+2.346125/1.096^2+3.21419125/1.096^3+4.403442013/1.096^4+45.86918763/1.096^4

which is equal to

=$40.80(Approx).