Question

You find a stock with a beta of 1.3 that just paid a dividend of $1.45 that is expected to grow at 5%. If the risk-free rate is 3% and the market risk premium is 8%, what should be the price of the stock in four years? A. $22.03 B. $41.12 C. $20.98 D. $18.13

Answer 1

ANSWER

Working note 1

Calculation of dividend of 4^th year

Year	Calculation	Dividend
1	=$1.45*(1.05)	$1.52
2	=$1.52*(1.05)	$1.60
3	=$1.60(1.05)	$1.68
4	=$1.68(1.05)	$1.76

Working note 2

Calculation of cost of equity using CAPM approch

Ke= Rf+Beta*Market Premium

Ke= 3+1.3*8

ke=3+10.4

Ke= 13.40%

Where,

Ke= Cost of equity

Calculation of price of the stock at the end of 4^th year

P₄=D₅ /(Ke-g)

Where,

P₄= Price of stock at end of 4^th year

D₅= Dividend for 5^th year

g= Growth rate

P₄= 1.76(1.05) / (13.40% - 5%)

= $1.848 / 8.4%

Price at end of 4 year = $22.03

Hence option A is correct