Common stock value long dash— Constant growth Personal Finance Problem Elk Count
ID: 2797723 • Letter: C
Question
Common stock
valuelong dash—Constant
growthPersonal Finance ProblemElk County Telephone has paid the dividends shown in the following table over the previous 6 years:
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(Click on the icon located on the top-right corner of the data table below in order to copy its contents into a spreadsheet.)
Year
Dividend per share
20152015
$2.212.21
20142014
$2.162.16
20132013
$2.122.12
20122012
$2.082.08
20112011
$2.042.04
20102010
$2.002.00
. The firm's dividend per share next year is expected to be
2.25.
a.If you can earn
15%
on similar-risk investments, what is the most you would be willing to pay per share?b.If you can earn only
12%
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?
a.If you can earn
15%
on similar-risk investments, the most you would be willing to pay per share is
$nothing.
(Round to the nearest cent.)
Year
Dividend per share
20152015
$2.212.21
20142014
$2.162.16
20132013
$2.122.12
20122012
$2.082.08
20112011
$2.042.04
20102010
$2.002.00
Explanation / Answer
Estimated Dividend growth rate g = (dividend at 2016/dividend at 2010)^(1/6) -1 = (2.25/2.00)^(1/6) -1 = 1.02 -1 = 2%
By gordon growth model:
Value of stock = D1/ (k - g)
where:
D1 = next year's expected annual dividend per share
k = the investor's discount rate or required rate of return, which he can earn on similar risk investments
g = the expected dividend growth rate (note that this is assumed to be constant)
a) When k = 15%
value of stock = 2.25/(.15-.02) = 2.25/.13 = $17.31 i.e. most I would be willing to pay per share
b) When k = 12%
value of stock = 2.25/(.12-.02) = 2.25/.1 = $22.5 i.e. most I would be willing to pay per share
c) The lower the risk of an instrument, lesser is the required return on than instrument. The lower the expected return lower is the discount rate of future cash flows and thus higher is the price of the share.
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