Question

Storico Co. just paid a dividend of $2.10 per share. The company
will increase its dividend by 20 percent next year and will then
reduce its dividend growth rate by 5 percentage points per year
until it reaches the industry average of 5 percent dividend growth,
after which the company will keep a constant growth rate forever.
If the stock price is $33.99, what required return must investors
be demanding on Storico stock? (Hint: Set up the valuation formula
with all the relevant cash flows, and use trial and error to find
the unknown rate of return.) |

Answer #1

current dividend , d0 = $2.10

growth rate for year 1 , g1 = 20% = 0.20

dividend at the end of year 1, D1 = d0*(1+g1) = 2.10*(1.20) = $2.52

growth rate for year 2, g2 = 20-5 = 15%

dividend at the end of year 2, D2 = D1*(1+g2) = 2.52*(1.15) = $2.898

growth rate for year 3, g3 = 15-5 = 10%

dividend at the end of year 3, D3 = D2*(1+g3) = 2.898*(1.10) = $3.1878

growth rate for year 4, g4 = 10-5 = 5%

dividend at the end of year 4, D4 = D3*(1+g4) = 3.1878*(1.05) = $3.34719

p0 =[ D1/(1+R) ] + [ D2/(1+R)^{2} ] + [
D3/(1+R)^{3} ] + [ D4/((R-0.05)*(1+R)^{3}) ]

33.99 = [ 2.52/(1+R) ] + [ 2.898/(1+R)^{2} ] + [
3.1878/(1+R)^{3} ] + [ 3.34719/((R-0.05)*(1+R)^{3})
]

then we have to find R by trial and error

by trial and error , we find that R = 0.134 or 13.40%

required return = R = 13.4%

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