Answer to Question #114164 in Finance for rita

Question #114164
Storico Co. just paid a dividend of $2.10 per share. The company will increase its dividend by 20 percent next year and 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 required return on the company's stock is 11 percent, what will a share of stock sell for today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Expert's answer
  1. Present value of the stock is equial to its discounted cash flow.
  2. Cash flow of Storico Co. will be structured like this:

at "(T+1)" investor will get "2.1*1.2=2.52"

at "(T+2)" investor will get "2.52*1.15=2.898"

at "(T+3)" investor will get "2.898*1.10=3.1878"

at "(T+4)" investor will get "3.1878*1.05=3.34719"

at "(T+5)" investor will get "3.34719* 1.05"

at "(T+6)" investor will get "3.34719* 1.05^2"


at "(T+N)" investor will get "3.34719* 1.05^{N-4}"

3 Given that required return on the stock is 11%, we can calculate price using  two-stage dividend discount model :

"P = \\frac{2.52}{1.11}+\\frac{2.898}{1.11^2}+\\frac{3.1878}{1.11^3}+PV"

where "PV" - present value of all payments starting from "(T+4)".

4 At time "(T+4)", i.e. in the future, value of all payments will be equial to:

"PV(T+4) = 3.34719+\\frac{3.34719*1.05}{1.11} + \\frac{3.34719*1.05^2}{1.11^2} + ... =\\\\\\\\=3.34719*(1+\\frac{1.05}{1.11}+(\\frac{1.05}{1.11})^2+....)=3.34719*\\frac{1}{1-\\frac{1.05}{1.11}}=\\\\\\\\=3.34719*\\frac{1.11}{0.06}"

5 By plugging in result of step 4 into formula from step 3 we get:

"P = \\frac{2.52}{1.11}+\\frac{2.898}{1.11^2}+\\frac{3.1878}{1.11^3}+\\frac{3.34719*\\frac{1.11}{0.06}}{1.11^4}=\\\\\\\\= \\frac{2.52}{1.11}+\\frac{2.898}{1.11^2}+\\frac{3.1878}{1.11^3}+\\frac{3.34719*\\frac{1}{0.06}}{1.11^3}=47.74"

Today's price for the share of stock will be 47.74

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