Answer to Question #114164 in Finance for rita

Question

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.)

Answer 1

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