Question

Cartwright Brothers’ stock is currently selling for $40 a share. The stock is expected to pay a $4 dividend at the end of the year. The stock’s dividend is expected to grow at a constant rate of 7 percent a year forever. The risk-free rate (kRF) is 7 percent and the market risk premium (kM – kRF) is 5 percent. What is the stock’s beta?

	a.	5.00
	b.	1.00
	c.	2.00
	d.	3.00
	e.	4.00

Answer 1

Using Gordon Growth model,

Stock Price = P0 = D1/(r - g)

where, P0 = current stock price = 40

g = growth rate = 0.07

D1 = dividend = 4

r = rate of return

=> 40 = 4/(r - 0.07) => r = 0.17 = 17%

Using the CAPM model,

r = k_RF + β(k_M - k_RF)

given k_RF = 0.07

(k_M - k_RF) = 0.05

=> 0.17 = 0.07 + β*0.05

=> β = 2

Hence, (c) is the correct ooption