You have the opportunity to buy a stock that just paid a dividend (D0) of $1.50.

Question

You have the opportunity to buy a stock that just paid a dividend (D0) of $1.50. After doing some research, you have made the following forecasted growth rates for the firm’s dividends:

g1 = 100%             g2 = 50%               g3 = 25%               g4 = 10%               g5 = 5%                 g6 through infinity= -2%

In addition, you estimate that the required return for this stock should be 11% (Note that the constant growth rate here is NEGATIVE 3%, not positive 2%).  Show your work.

A)     Calculate the forecasted dividends for years 1 through 6

B)      Calculate the forecasted stock price for year 5 (which represents the value of all dividends in years 6 through infinity as of five years from today)

C)      Calculate the value of the stock today

Explanation / Answer

A.

D1 = 1.5*2 = 3

D2 = 3*1.5 = 4.5

D3 = 4.5*1.25 = 5.625

D4 = 5.625*1.1 = 6.1875

D5 = 6.1875*1.05 = 6.5

D6 = 6.5*0.97 = 6.3

B. From year 6, there's a constant growth rate of -3%, we can calculate the stock price for year 5 with constant growth rate

P5 = D6/(r-g) = 6.3/(0.11-(-0.03)) = 6.3/0.14 = 45

Present value of the stock

41.249

Value of the stock today = 41.249

Interst rate 0.11 Year Cashflow (x) Discount rate = 1/(1+0.11)^n Present Value 1 3 0.9009009 2.702702703 2 4.5 0.81162243 3.65230095 3 5.625 0.73119138 4.11295152 4 6.1875 0.65873097 4.075897903 5 0.59345133 48.2179204 Present value

41.249

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