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.) (Do not round intermediate calculations and round your final answer to 1 decimal place. (e.g., 32.16)) Must Show Work.

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%