We may approach these problems is 2 ways:
–
Given the current price and the expected future price
and dividend, we can solve for the return (discount
rate) – for the 1-year case, this is akin to solving for
the “i” in a lump-sum TVM problem
–
Or, we may be given an expected future price and
dividend and a required rate of return (or, discount
rate) and then use the rate of return to discount the
future expected cash flows to get our price (PV) today
FIN 300 - Stocks Pt. 1
16

What About Non-Dividend Payers?
•
Actually, many firms pay no dividends
–
In particular, young, high-growth (tech, especially) firms
–
Generally dividend-payers are larger, more-established, mature
firms
•
How do we price non-dividend-paying stocks?
–
Well, if we have an expectation of a future selling price for the
stock and a discount rate, we can solve for the PV of the future
sale price
–
In practice, many investors apply a couple of methods:
•
Look at similar firms and calculate the stock price (per share) and
divide by the earnings-per-share (EPS) – then multiply the comparable
firms P/E by your firm’s
EPS – to get a price estimate
•
Or, more sophisticated “discounted cash flow (DCF) methods” –
where, an analyst projects the future cash flows (based on the
projected future accounting numbers of a firm and then applies a
discount rate to estimate the value of the company
FIN 300 - Stocks Pt. 1
17
Just an
FYI:
Not on
the
exam!

Dividend-Paying Stocks
•
In this class, we will focus on dividend-paying
stocks
•
When we focus on stock pricing, we are generally
talking about common shares
•
However, what we are doing (in terms of the
math) is pretty generic
•
As we have discussed before, preferred shares
are generally seen to pay a level dividend that
never changes
–
In the last part of this chapter’s coverage we will do
some examples that speak specifically to “perpetual”
preferred shares of stock
FIN 300 - Stocks Pt. 1
18

Extending Stock Pricing to 2 Years
•
For example, let’s assume that we can look 2 years
(or, 2 periods) ahead:
FIN 300 - Stocks Pt. 1
19
DIV
2
+ P
2
P
0
0
2y
1y
DIV
1
Dividends Paid at the ends
of the 1
st
and 2
nd
years
(t=1 & t=2)
Expected Sale
Price (of the share)
in 2 yrs. (t=2)
𝑃𝑃
0
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
(1 +
𝑅𝑅
)
+
(
𝐷𝐷𝐷𝐷𝐷𝐷
2
+
𝑃𝑃
2
)
(1 +
𝑅𝑅
)
2
R = expected total return
(or, discount rate) per
period for the stock

Stock Pricing Out 3 or More Years
FIN 300 - Stocks Pt. 1
20
DIV
3
+ P
3
P
0
0
3y
1y
DIV
1
DIV
2
2y
𝑃𝑃
0
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
(1 +
𝑅𝑅
)
+
𝐷𝐷𝐷𝐷𝐷𝐷
2
(1 +
𝑅𝑅
)
2
+
𝐷𝐷𝐷𝐷𝐷𝐷
3
+
𝑃𝑃
3
(1 +
𝑅𝑅
)
3
𝑃𝑃
0
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
(1 +
𝑅𝑅
)
+
𝐷𝐷𝐷𝐷𝐷𝐷
2
(1 +
𝑅𝑅
)
2
+
𝐷𝐷𝐷𝐷𝐷𝐷
3
(1 +
𝑅𝑅
)
3
+
𝐷𝐷𝐷𝐷𝐷𝐷
4
+
𝑃𝑃
4
(1 +
𝑅𝑅
)
4
Or, 4 years
𝑃𝑃
0
=
𝐷𝐷𝐷𝐷𝐷𝐷
1
(1 +
𝑅𝑅
)
+
𝐷𝐷𝐷𝐷𝐷𝐷
2
(1 +
𝑅𝑅
)
2
+
𝐷𝐷𝐷𝐷𝐷𝐷
3
(1 +
𝑅𝑅
)
3
+
𝐷𝐷𝐷𝐷𝐷𝐷
4
(1 +
𝑅𝑅
)
4
+
⋯
to
∞
Or, forever!

Price (PV) of an Infinite Stream of Dividends
•

#### You've reached the end of your free preview.

Want to read all 41 pages?

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