Respuesta :
Answer: The market price of this stock is $22.57.
In this question, we ignore last year's dividend of $1.80 as it is irrelevant.
We compute the Present Value (PV) of the dividends of each of the following four years as follows:
[tex]PV_{dividends} = \frac{2}{1.13} + \frac{2.5}{1.13^2} +\frac{2.75}{1.13^3} + \frac{3}{1.13^4}[/tex]
[tex]PV_{dividends} = 7.473622342[/tex]
Next, we calculate the PV of dividends from the 5 year onwards. Here dividend is constant at $3.20 and is expected to be paid for ever. The PV of a perpetuity at the end of year 4 is:
[tex]V_{perpetual dividend} = \frac{Perpetuity Amount}{Discount Rate}[/tex]
[tex]V_{perpetual dividend} = \frac{3.2}{0.13}[/tex]
The value of a perpetual dividend of $3.20 at the end of year 4 is $24.61538462
Next we find the PV of the value of perpetual dividend as follows:
[tex]PV_{perpetual dividend} = \frac{24.61538462}{1.13^4}[/tex]
[tex]PV_{perpetual dividend} = 15.09707637 [/tex]
[tex]Market Price of the stock = PV_{dividends} + PV_{perpetual dividend}[/tex]
[tex]Market Price of the stock = 7.473622342 + 15.09707637[/tex]
Market price of the stock = $22.57069872
