9-12 Investors require a 15% rate of return on Levine Company’s stock (that is,

Question

9-12 Investors require a 15% rate of return on Levine Company’s stock (that is, rs =15%) .

a)What is its value if the previous dividend was D0 =$2 and investors expect dividend to grow at a constant annual rate of (1) -5%, (2) 0%, (3) 5%, or (4) 10%.

b)Using data from part a, what would the Gordon (constant growth) model value be if the required rate of return were 15% and the expected growth rate were (1) 15% or (2) 20%? Are these reasonable results? Explain

c)Is it reasonable to think that a constant growth stock could have g > rs? Explain

Explanation / Answer

a.

P0= Div0(1+g)/r-g
Growth rate=-5%
P0= 2(1+(-.05))/(.15-(-.05)
P0=$9.5

g=0%
P0=2(1+0)/.15-0
P0=$13.33

g=5%
P0=2(1+.05)/.15-.05
P0=$21

g=10%
P0=2(1+.10)/.15-.10
P0=$44


b.Gordon model
P0= Div1/r-g

g= 15%
P0=2(1+.15)/.15-.15
P0=infinity

g=20%
P0=2(1+.20)/.15 -.20
P0=-$48 These results are not reasonable because of the assumption that internal rate of return(rs) and cost of capital(k) are constant ,which underlie the model.Thus, to get meaniful value of the share the value of growth rate (g)should be less than K or rs. d. It's possible. Short run variations could cause it. It's possible. Short run variations could cause it.

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