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Homework answers / question archive / You are now considering buying shares of common stock for a firm that is expected to have extraordinary divided growth of 25% per year for 3 years, after which it will face more competition and slip into a constant growth rate of 5% per year for many, many years to come
You are now considering buying shares of common stock for a firm that is expected to have extraordinary divided growth of 25% per year for 3 years, after which it will face more competition and slip into a constant growth rate of 5% per year for many, many years to come. The next year's dividend is expected to be $4 per share. Would you buy this stock at the current market price of $70? Assume that the discount rate is 13%.
Given Information
Next Year’s Dividend (D1) = $4
Growth in dividend for 3 years (2 to 4 years) = 25%
Growth in dividend 4th year onwards (g)=5%
Discount Rate (r) = 13%
Dividend over next 5 years are –
|
Year |
1 |
2 |
3 |
4 |
5 |
|
Dividend Growth Rate |
25% |
25% |
25% |
5% |
|
|
Dividend |
D1= 4.00 |
D2= 5.00 |
D3= 6.25 |
D4= 7.81 |
D5= 8.20 |
At the end of/ after year 4, dividends grow at constant growth rate of 5%
So, price at end of 4th year (P4) = D5/(r-g) = 8.20/(0.13-0.05) = $102.54
Now, price today (P0) = D1/(1+r) + D2/(1+r)2 + D3/(1+r)3 + D4/(1+r)4 + P4/(1+r)4
P0 = 4/(1+0.13) + 5/(1+0.13)2 + 6.25/(1+0.13)3 + 7.81/(1+0.13)4 + 102.54/(1+0.13)4 = $79.47
As present value of dividends (79.47) is greater than current stock price of $70. So, one will buy the stock.
