Question

5. The risk-free rate of return is 8%, the expected rate of return on the market portfolio is 15%, and the stock of Xyong Corporation has a beta of 1.2. Xyong pays out 40% of its earnings in dividends, and the latest earnings announced were $10 per share. Dividends were just paid and are expected to be paid annually. You expect that Xyong will earn an ROE of 20% per year on all reinvested earnings forever.

(a) What is the intrinsic value of a share of Xyong stock?

(b) If the market price of a share is currently $100 and you expect the market price to be equal to the intrinsic value one year from now, what is your expected one-year holding period return on Xyong stock?

Answer 1

Answer :

First, let us find out the growth rate .

Growth rate = retention ratio * roe.

here,

retention ratio = 1- dividend payout ratio............(dividend pay out ratio =40% =0.40)

=> 1 -0.4

=>0.6

ROE = 20% given.

=> growth rate = 20% *0.6

=>12%.

Now,

Intrinsic value of stock using dividend growth rate can be found as:

D( 1+ g) / k -g

here,

d is dividend just paid = $10*40% =$4.

g is growth rate = 12% =>0.12.

k is cost of capital = risk free rate + beta(market rate - risk free rate)

=> 8% + 1.2 (15 -8)

=> 8 % +1.2(7%)

=> 16.4%

=>0.164

now,

intrinsic value of stock = $4 (1+ 0.12) / 0.164-0.12

=> $4.48 / 0.0044

=>$101.81818181818.

=>101.82 (rounded to two decimals).(this is the current intrinsic value of stock)

b.To solve this part we need to know the expected intrinsic value of of share after 1 year.

Dividend after 1 year = current dividend ( 1+ growth rate)

=> $4 *(1.12)

=>$4.48.

now, intrinsic value after 1 year using growth model

d (1+g) / (k -g):

here,

dividend = $4.48

g =0.12

k =0.164

$4.48(1+0.12) / (0.164 -0.12)

=> $5.0176 / 0.044

=>$114.04.(rounded to on decimal place).

1 year holding period return = (expected intrisic value after 1 year - current market price ) / current market price ]*100

=> [($114.04 - $100) / $100] *100

=>14.04%