Question

Firm DCF, ROE = 35% , Dividend Payout Ratio=70%, next year’s earning per share (EPS) = $8.00, assuming that market expected return is 20% and the risk-free rate is 5%. If increasing DPR will decrease firm value and we can use the constant dividend growth model to value the stock price, the stock beta must be larger than [a] and less than [b]

what is [a] and [b]?

Answer 1

For constant growth model to be used,
required return>growth rate
risk free rate+beta*(market return-risk free rate)>RoE*(1-DPR)
=>5%+beta*(20%-5%)>35%*(1-70%)
=>beta>(35%*0.3-5%)/(20%-5%)
=>beta>0.36667

and
risk free rate+beta*(market return-risk free rate)<RoE
=>beta<(35%-5%)/(20%-5%)
=>beta<2

a=0.36667 and b=2.0000