Question

AEY Inc is a company based in the U.S. assuming growth for them is set at 5%, the current risk free rate in the U.S. is 3% and market premium is 8%. AEY Inc. paid a dividend yesterday of $1.20 and has a Beta of 1.3, What is current price per share? If the Beta was 0.8 (all else remains constant) what would be new price per share?

Answer 1

Step-by-step explanation:

A.)

Use CAPM to find rate of return ;

r = risk free + beta (Market risk premium)

risk free = 3% or 0.03 as a decimal

beta = 1.3

Market risk premium = 8% or 0.08

Next, plug in the numbers into the equation to find r ;

r = 0.03 + (1.3*0.08)

r = 0.134 or 13.4%

Use Dividend discount formula to price the stock;

Price (P₀) =
`(D0 (1+g))/(r-g)`

whereby, D0= current dividend = $1.20

g= growth rate = 5%

r= required return ( calculated above) = 13.4% or 0.134 as a decimal

P₀ =
`(1.20(1.05))/(0.134-0.05) \\ \\ =(1.26)/(0.084) \\ \\ = 15`

Therefore current price per share is $15

B.)

If beta is 0.8, you do the exact same thing above and change beta from 1.3 to 0.8;

Use CAPM to find rate of return ;

r = risk free + beta (Market risk premium)

risk free = 3% or 0.03 as a decimal

beta = 0.8

Market risk premium = 8% or 0.08

Next, plug in the numbers into the equation to find r ;

r = 0.03 + (0.8*0.08)

r = 0.094 or 9.4%

Use Dividend discount formula to price the stock;

Price (P₀) =
`(D0 (1+g))/(r-g)`

whereby, D0= current dividend = $1.20

g= growth rate = 5%

r= required return ( calculated above) = 9.4% or 0.094 as a decimal

P₀ =
`(1.20(1.05))/(0.094-0.05) \\ \\ =(1.26)/(0.044) \\ \\ = 28.636`

Therefore current price per share when beta is 0.8 is = $28.64