𝑃𝑃
2
=
𝐷𝐷𝐷𝐷𝐷𝐷
3
𝑅𝑅 − 𝐸𝐸
=
𝐷𝐷𝐷𝐷𝐷𝐷
2
1 +
𝐸𝐸
𝑅𝑅 − 𝐸𝐸
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
1 +
𝐸𝐸
2
𝑅𝑅 − 𝐸𝐸
•
Etc., etc., etc.
FIN 300 - Stocks Pt. 1
32
𝑃𝑃
1
=
𝐷𝐷𝐷𝐷𝐷𝐷
2
𝑅𝑅 − 𝐸𝐸
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
1 +
𝐸𝐸
𝑅𝑅 − 𝐸𝐸

Constant Price & Dividend Growth
•
Go back to this:
•
Note that:
•
Therefore:
FIN 300 - Stocks Pt. 1
33
𝑃𝑃
1
=
𝐷𝐷𝐷𝐷𝐷𝐷
2
𝑅𝑅 − 𝐸𝐸
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
1 +
𝐸𝐸
𝑅𝑅 − 𝐸𝐸
𝑃𝑃
0
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
𝑅𝑅 − 𝐸𝐸
𝑃𝑃
1
=
𝑃𝑃
0
1 +
𝐸𝐸
Important! – This means
that the price grows at the
same constant rate g

Constant Growth
•
When the dividend grows at a constant,
perpetual rate “g”
–
The price of the stock also grows from year to year at
the same growth rate
–
As seen before, the year-over-year growth rate of the
stock is the capital gains yield (or, return)
–
So, (in the constant growth model) the “g” also just
happens to be the capital gains yield (or, return)
–
The dividend grows at rate g forever; therefore, the
price grows at the same constant, perpetual rate
FIN 300 - Stocks Pt. 1
34

Total Return and Constant Growth
•
We know from earlier that
Total Return (R) = Dividend Yield + Capital Gains Yield
•
We now know that in the constant growth
model
Capital Gains Yield (or, return) = g
•
So,
R – g = R – capital gains yd. = dividend yd.
FIN 300 - Stocks Pt. 1
35
BTW, since R & g stay the same, the
div. yd. is constant, as well!

Constant Growth & Returns/Yields
Just to summarize – Important to know!
•
If the
dividend grows at a constant rate “g” forever
–
The
price grows at the same constant rate “g”
forever
–
The rate of price growth is also known as the
capital gains yield (or, return)
–
So, the same
“g” is also the capital gains yield (or,
return)
–
(Total)
Return (“R”) is the sum of the capital gains
yield “g” and the dividend yield
FIN 300 - Stocks Pt. 1
36

Re-Write Constant Growth Formula
FIN 300 - Stocks Pt. 1
37
𝑃𝑃
0
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
𝑅𝑅 − 𝐸𝐸
𝑅𝑅 − 𝐸𝐸
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
𝑃𝑃
0
𝑅𝑅
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
𝑃𝑃
0
+
𝐸𝐸
Multiply both sides by
(R-g) and divide both
sides by P
0
R = Total Return (or,
discount rate for
the stock investor)
Dividend Yield = End Div./Begin Price
g = capital gains yield
(also, dividend growth)

More Examples w/Constant Growth
•
Example 1 - Given:
–
A share of stock sells for $100 today
–
Shareholders require a 20% return on the stock
–
The share pays a $2 dividend at the end of the
year
–
Also, the dividends are expected to grow at a
constant perpetual rate forever
–
What should the stock sell for in 1 year?

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- Fall '08
- Olander
- Corporate Finance, Net Present Value, Dividend, Internal rate of return