Valuation

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```					          Valuation

An Application of Present
Value Arithmetic
Basic Principle of
Valuation

Financial assets (stocks and bonds, etc.)
are valued for the cash flow that they
will provide.

Value = PV of all future cash flows from
the asset
Applying the Basic
Principle to Bond
Valuation:
What are Corporate
Bonds?

Securities that document a loan to the
corporation
The standard denomination of a bond is
\$1,000. This is called the face value or
par value of the bond.
The corporation has agreed to pay back
this amount at the maturity date of the
bond.
Bonds have a coupon
interest rate.

The coupon rate is the contracted rate of
interest which the corporation has
promised to pay the bond holder.
The coupon rate is expressed as a percent
of the face value and doesn’t change.
The coupon rate multiplied by the face
value gives the amount of cash paid to
the bond holder each year.
Most bonds pay the
coupon interest in two
semi-annual payments.

Thus, in summary, the total cash flow that
a bond investor expects to receive from a
bond are:
The semi-annual coupon payments (an
annuity) from now until the maturity date,
AND the \$1,000 face value at the maturity
date.
An example:

What cash flows will a bond pay if it is a
7% coupon bond maturing 18 years from
today?
Answer: \$35 every six months for 18
years (36 payments), and \$1,000 one
time only after 36 periods.
The Yield-to-maturity on a
bond

The rate of return a bond investor actually earns
depends on the bond price paid.
Note that bonds usually sell at market prices
quite different from their face value, so
investors can earn actual rates of return quite
different from the bond’s coupon rate.
The rate of return that will actually be earned
by buying a bond at a given price is called the
yield-to-maturity, or simply the yield.
To find the value of a bond,
calculate the present
value of all the future cash
flows, using the yield-to-
maturity as the time value
of money
For the example bond:

Assume the bond is priced to yield 8%
per year. (YTM = 8%)
Since the bond pays semi-annual
coupons, the time value discount rate is
8%/2= 4% per semi-annual period.
The present value of the \$35 annuity is
\$661.79, and the present value of \$1,000
is \$243.67.
Thus, the bond has a total
value of \$905.46.

We can say that the bond has a value of
\$905.46 when it is yielding 8%,

OR, we can say that the bond yields 8%
when it sells at a price of \$905.46.
Bond prices change as
interest rates in the
economy change

Higher interest rates mean that investors
will require higher yields on bond
investments.
Present value calculation methods imply
higher yields mean lower bond prices.
Bond prices and interest rates always
move in opposite directions.
If you read that the central
bank is raising interest
rates, what will happen to
bond prices?
Bond investors will require a higher yield
to invest in bonds.
Bond prices will fall to increase the yield
provided by a bond. (Price = PV of cash
flows)
Note: The face value and coupon rate do
not change! Only the price (value) and
the yield changes.
Applying the Basic
Principle of valuation to
Stock Valuation:
Common stocks pay only
one kind of cash flow to
investors:

DIVIDENDS!
The value of a common
stock is the present value
of all future dividends the
stock is expected to pay.
An example:

Assume a stock is expected to pay a
dividend of \$10 per share next year, and
to increase the dividend payout by 3%
per year every year thereafter.
Assume investors require a 15% rate of
return on this stock.
The stock’s value is the present value of a
growing perpetuity.
Using the formula: Value = \$10/(.15-.03)
= \$83.33.
Preferred stocks are
stocks that pay a fixed
dividend.

Preferred stock dividends must be paid
before paying any dividends on common
stock. Thus the name “preferred” stock.

Since the dividends don’t grow, the value
of a preferred stock is simply the present
value of an ordinary perpetuity.
A preferred stock valuation
example:

What is the value of a preferred stock that
pays a dividend of \$20 per share every
year, assuming investors require a 15%
rate of return?

Answer:    Value = \$20/.15 = \$133.33
per share.
Since stock prices are
present values, they also
(like bonds) tend to move
in the opposite direction
as interest rates.
However, the biggest
factor affecting stock
prices is the forecasted
dividends
(and the dividend growth
rate).
Since investors differ in their expectations
about the future dividends that a stock
will pay, they also differ in their valuations
of stocks. (This is why investors trade
stocks in the market.)

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