Hello.
The theoretical current price, or present value, of the stock is the
combined value of:
(1) the present value of the dividends for the 4th and 5th years; and
(2) the present value of the stream of dividends beginning in the
sixth year.
Let's start with part (1):
The formula we use is Present Value = C4/(1+r)^4 + C5/(1+r)^5
where C4 is the dividend for the 4th year (i.e., $0.50), C5 is the
dividend for the 5th year (i.e., $0.75) and "r" is the required rate
of return (i.e., 18% or 0.18).
Present Value = C4/(1+r)^4 + C5/(1+r)^5
PV = 0.50/(1+.18)^4 + 0.75/(1+.18)^5
PV = 0.25789 + 0.3278
PV = 0.5857
Now we move on to (2) the present value of the stream of dividends
beginning in the sixth year.
In the 6th year, the dividend will grow 3%, so it will be:
$0.75 * 1.03 = $0.7725
From that point on, the dividend will continue to grow at 3%. Thus,
we treat this as a growing perpetuity that begins in the 6th year.
The formula for present value of this delayed growing perpetuity is
PV = [C6 / r - g ] * [(1 / 1 + r)^(t - 1)]
where C6 is the dividend in the sixth year (i.e., $0.7725), r is the discount
rate (0.18), g is the growth rate (i.e., 3% or .03), and t is the time
period (year 6 here).
PV = [C6 / r - g ] * [(1 / 1 + r)^(t - 1)]
PV = [0.7725 / 0.18 - .03] * [(1 / 1 + .18)^(6 - 1)]
PV = [0.7725 / 0.15] * [(1 /1.18)^5]
PV = 5.15 * 0.4371
PV = 2.251
Finally, we must combine the present value of the dividends for the
4th and 5th years (i.e., 0.5857) with the present value of the stream
of dividends beginning in the 6th year (i.e., 2.251).
0.5857 + 2.251 = 2.84
Thus, the theoretical current price, or present value, of the stock is $2.84.
See this powerpoint on Corporate Finance for more information:
http://waltoncollege.uark.edu/lab/CWann/Powerpoint/Chap004.ppt
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search strategy:
"delayed growing perpetuity"
Thanks. |