Your firm just paid a dividend
Your firm just paid a dividend of $1.80 that you plan to raiseby 50% per year for the next three years and then grow at aconstant rate of 6%. If investors require a return of 11%, whatshould be the current price of your stock?
Answer:
| D0 | 1.8 | |||
| For the first two years | ||||
| g1 | 0.5 | |||
| D1 | 1.8*(1+.5) | |||
| D1 | 2.7 | |||
| D2 | 2.7*(1+.5) | |||
| D2 | 4.05 | |||
| D3 | 4.05*(1+.5) | |||
| D3 | 6.075 | |||
| Find the price of the stock in year3 | ||||
| g2 | 0.06 | |||
| D4 | 6.075*(1+.06) | |||
| D4 | 6.4395 | |||
| According to the dividend growthmodel. | ||||
| P3 = D4/(R-g2) | ||||
| where R is the required return on thestock. | ||||
| R = .11. | ||||
| P3 | 6.4395/(.11 – .06) | |||
| P3 | 128.79 | |||
| Cash flow in year 3 | P3 +D3 | |||
| Cash flow in year 3 | 134.865 | |||
| The price of the stock today = sum ofpresent value of future cash flows. | ||||
| Using R = .11 | ||||
| Year | 1 | 2 | 3 | |
| Cash flow | 2.7 | 4.05 | 134.865 | |
| Present value | 2.43 | 3.29 | 98.61 | |
| sum of present values | 104.33 | |||
| The stocks current price is equal to$104.33. |
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