Question

A share of common stock pays dividends with a constant growth rate as D0=${div0}, D1= $2.08, D2= $2.1632, …. The trend of dividend payments continues indefinitely. Suppose the return on the stock market is 8.2%, the return on the risk free assets is 3%, and the company’s beta is 1. Compute the value of this stock. Note that you should round off your answer at two decimal points. For example, 23.4567 = 23.46

Answer 1

First we need to find out Perpetual Growth Rate
D2 = D1*(1 + Growth Rate)
$2.1632 = $2.08 * (1 + Growth Rate)
(1 + Growth Rate) = $2.1632 / $2.08
(1 + Growth Rate) = 1.04
Growth Rate = 1.04 - 1
Growth Rate = 0.04
i.e. Growth Rate = 4%
Now,
Cost of Equity
= Risk Free Rate + Beta * (Market Return-Risk Free Rate)
= 3% + 1 * (8.2% - 3%)
= 3% + 1 * 5.2%
= 3% + 5.2%
= 8.2%
Value of Stock
= D1 / (Cost of Equity - Growth Rate)
= $2.08 / (8.20% - 4%)
= $2.08 / 4.20%
= $49.52