Exam Question. XYZ common just paid a dividend of $1 per share. What is the highest price that you are willing to pay, if you require a 13% rate of return, and if you expect that dividends will grow at an annual rate of 20% for the next five years, and at 8% thereafter.
| D(t+1) = D(t)*(1+g1) | |||||
| D0 | 1 | ||||
| For the first two years | |||||
| g1 | 0.2 | ||||
| D1 | 1.2 | ||||
| D2 | 1.44 | ||||
| D3 | 1.728 | ||||
| D4 | 2.0736 | ||||
| D5 | 2.48832 | ||||
| Find the price of the stock in year 5 | |||||
| g2 | 0.08 | ||||
| D6 = D5*(1+g2) | |||||
| D6 | 2.687386 | ||||
| According to the dividend growth model. | |||||
| P5 = D6/(R-g2) | |||||
| where R is .13 | |||||
| P5 | 53.74771 | ||||
| Cash flow in year 5 = D5+P5 | |||||
| The value of the stock today = sum of present value of future cash flows. | |||||
| Using R = .13 | |||||
| Year | 1 | 2 | 3 | 4 | 5 |
| Cash flow | 1.2 | 1.44 | 1.728 | 2.0736 | 56.23603 |
| Present value | 1.06 | 1.13 | 1.20 | 1.27 | 30.52 |
| sum of present values | 35.18 | ||||
| The highest price you are willing to pay is $35.18. | |||||
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