Question #152194
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.
1
Expert's answer
2020-12-21T14:48:15-0500

r=Rf+β(RmRf)=3+1.2(133)=15r=Rf+\beta(Rm-Rf)=3+1.2(13-3)=15


V=D(1+r)t=(20+20)×0.75(1+0.1)5=14.92V=\frac{D}{(1+r)^t}=\frac{(20+20)\times0.75}{(1+0.1)^5}=14.92

V=D×1+gkg=20×0.751+8158=19.29V=D\times\frac{1+g}{k-g}=20\times0.75\frac{1+8}{15-8}=19.29

(i)V=D×1+gkg=1×0.751+8158=0.96V=D\times\frac{1+g}{k-g}=1\times0.75\frac{1+8}{15-8}=0.96


(ii)V=D×1+gkg=22×0.751+8158=28.29V=D\times\frac{1+g}{k-g}=22\times0.75\frac{1+8}{15-8}=28.29


20×0.1+20=2220\times0.1+20=22


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