Question

Common stock value—Constant growth  Over the past 6​ years, Elk County Telephone has paid the dividends shown in the following​ table:

Year	Dividend per share
2019	​$6.96
2018	​$6.75
2017	​$6.56
2016	​$6.37
2015	​$6.18
2014	​$6.00

The​ firm's dividend per share in 2020 is expected to be ​$7.16.

a.  If you can earn 13​% on​ similar-risk investments, what is the most you would be willing to pay per share in 2019​, just after the ​$6.96 ​dividend?

b.  If you can earn only 10​% on​ similar-risk investments, what is the most you would be willing to pay per​ share?

c.  Compare your findings in parts a and ​b, what is the impact of changing risk on share​ value?

Answer 1

Growth Rate = (Dividend in 2019 / Dividend in 2014)^(1/5) - 1
Growth Rate = ($6.96 / $6.00)^(1/5) - 1
Growth Rate = 1.16^(1/5) - 1
Growth Rate = 1.0301 - 1
Growth Rate = 0.0301 or 3.01%

Answer a.

Dividend in 2020 = $7.16
Growth Rate = 3.01%
Required Return = 13.00%

Stock Price, 2019 = Dividend in 2020 / (Required Return - Growth Rate)
Stock Price, 2019 = $7.16 / (0.1300 - 0.0301)
Stock Price, 2019 = $7.16 / 0.0999
Stock Price, 2019 = $71.67

Answer b.

Dividend in 2020 = $7.16
Growth Rate = 3.01%
Required Return = 10.00%

Stock Price, 2019 = Dividend in 2020 / (Required Return - Growth Rate)
Stock Price, 2019 = $7.16 / (0.1000 - 0.0301)
Stock Price, 2019 = $7.16 / 0.0699
Stock Price, 2019 = $102.43

Answer c.

According to the findings in part a and b, as risk decreases, the required rate of return decreases, causing the share price to rise.