In: Finance
Your firm just paid a dividend of $1.80 that you plan to raise by 50% per year for the next three years and then grow at a constant rate of 6%. If investors require a return of 11%, what should be the current price of your stock?
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 year 3 | ||||
g2 | 0.06 | |||
D4 | 6.075*(1+.06) | |||
D4 | 6.4395 | |||
According to the dividend growth model. | ||||
P3 = D4/(R-g2) | ||||
where R is the required return on the stock. | ||||
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 of present 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. |