Question

XanEx is a new firm that just paid an annual dividend of $1 a share. The firm plans to increase its dividend by 10 percent a year for the next 4 years and then decrease the growth rate to 2 percent annually. If the required rate of return is 18.25 percent, what is one share of this stock worth today?

Answer 1

The current value of the stock is computed as shown below:

= Dividend in year 1 / (1 + required rate of return)¹ + Dividend in year 2 / (1 + required rate of return)² + Dividend in year 3 / (1 + required rate of return)³ + Dividend in year 4/ (1 + required rate of return)⁴ + 1 / (1 + required rate of return)⁴[ ( Dividend in year 4 (1 + growth rate) / ( required rate of return - growth rate) ]

= ($ 1 x 1.10) / 1.1825 + ($ 1 x 1.10²) / 1.1825² + ($ 1 x 1.10³) / 1.1825³ + ($ 1 x 1.10⁴) / 1.1825⁴ + 1 / 1.1825⁴ x [ ($ 1 x 1.10⁴ x 1.02) / (0.1825 - 0.02) ]

= $ 1.10 / 1.825 + $ 1.21 / 1.1825² + $ 1.331 / 1.1825³ + $ 1.4641 / 1.1825⁴ + $ 9.190043077 / 1.1825⁴

= $ 1.10 / 1.825 + $ 1.21 / 1.1825² + $ 1.331 / 1.1825³ + $ 10.65414308 / 1.1825⁴

= $ 8.05

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