Church Inc. is presently enjoying relatively high growth because of a surge in t
ID: 2705652 • Letter: C
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 40% 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 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 40% 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 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 40% 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 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 40% 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, D , 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? AnswerExplanation / Answer
Required Rate of Return r(m) = r(f) + b r(p), where r(f) is the risk free rate and the r(p) is the risk premium and b is beta and therefore:
r(m) = 3.00 + 1.20 * 5.5 = 9.6%.
Hence current price P(0),
= D1/(1+k) +D2/(1+k)^2 + D3/(1+k)^3 + D4/(1+k)^4 + P4/(1+k)^4
D1 = D0 * 1.4 = 1.25*1.4 = 1.75
D2 = 1.4D1 = 2.45
D3 = 1.4D2 = 3.43
D4 = 1.4D3 = 4.802
D5 = 1*D4 = 4.802
P4 = D5/k = 4.802/0.096
So, P(0)
= 1.75/1.096 +2.45/1.096^2 +3.43/1.096^3 +4.802/1.096^4 +4.802/(0.096*1.096^4)
=44.236 = 44.24