Question

1. Suppose you expect dividend in the first year is $6.00 and for the following four years, it’s $10.50 per year. After the fifth year, the dividend will grow at a constant rate of 10 percent per year. The required return is 15 percent. What is the value of the stock today? What is the value of the stock after one year?

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 + Dividend in year 5 / (1 + required rate of return)⁵ + 1 / (1 + required rate of return)⁵ [ ( Dividend in year 5 (1 + growth rate) / ( required rate of return - growth rate) ]

= $ 6 / 1.15 + $ 10.50 / 1.15² + $ 10.50 / 1.15³ + $ 10.50 / 1.15⁴ + $ 10.50 / 1.15⁵ + 1 / 1.15⁵ x [ ($ 10.50 x 1.10) / (0.15 - 0.10) ]

= $ 6 / 1.15 + $ 10.50 / 1.15² + $ 10.50 / 1.15³ + $ 10.50 / 1.15⁴ + $ 241.50 / 1.15⁵

= $ 146.13 Approximately

The value of the stock after one year is computed as follows:

= $ 146.1324109 x 1.10

= $ 160.75 Approximately

Feel free to ask in case of any query relating to this question