Question

Suppose that the rate of return on the market portfolio is 13% and the risk-free rate is 3%. Consider a
stock with  = 1.2. The firm is expected to have no earnings for three years (E1 = E2 = E3 = 0), and
then 20 earnings-per-share for two years (E4 = E5 = 20). After that, earnings are expected to grow at a
constant annual rate of 8%. If the retention ratio (i.e. the fraction of earnings which is retained and not
paid out as dividends) is 75% in all periods, find the fundamental value of the stock. Determine what
would happen to the fundamental value in each of the following cases: (i) the asset  falls to 1, (ii) the
earnings growth rate rises to 10%. Treat each case separately, and briefly discuss your findings.

Answer 1

$r=Rf+\beta(Rm-Rf)=3+1.2(13-3)=15$

$V=\frac{D}{(1+r)^t}=\frac{(20+20)\times0.75}{(1+0.1)^5}=14.92$

$V=D\times\frac{1+g}{k-g}=20\times0.75\frac{1+8}{15-8}=19.29$

(i)$V=D\times\frac{1+g}{k-g}=1\times0.75\frac{1+8}{15-8}=0.96$

(ii)$V=D\times\frac{1+g}{k-g}=22\times0.75\frac{1+8}{15-8}=28.29$

$20\times0.1+20=22$